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Textbook of physical chemistry

Lincoln, Azariah Thomas, 1868-

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chemistry physicalandtheoretical

chemistry, physical and theoretical

TEXTBOOK OF

PHYSICAL CHEMISTRY

AZARIAH T. LINCOLN, PH.D.

PROFESSOR OF PHYSICAL CHEMISTRY RENSSELAER POLYTECHNIC INSTITUTE

D. C. HEATH £ CO., PUBLISHERS

BOSTON NEW YORK CHICAGO

PREFACE

THIS textbook is intended primarily for the use of classes beginning the subject of Physical Chemistry. In the preparation of the text I have endeavored to keep in mind that the presentation is to students who meet the subject matter for the first time, and that they are to acquire a broad foundation for their subsequent work. As some time intervenes between the elementary courses in which the fundamental ideas of chemistry are presented and the time at which the work in Physical Chemistry is given, it is found that a short review of these fundamental concepts is neces- sary in order to have the student properly oriented as to the relationship of his elementary work and that which is usually incorporated in a course in Physical Chemistry. That this is absolutely necessary is the experience of most teachers, and the result can be attained more quickly by briefly restating this fundamental matter in a form in which it can subsequently be utilized. Hence, there is given a resume* of some of the information which the student is assumed to have in order to place him in a position to correlate the new material with that which he already pos- sesses.

The order of topics usually follows the logical develop- ment of the subject matter in that the experimental data are first presented with the statement of the laws, then the explanation of the facts by the formulation of the theory. The limitations are then emphasized by presentation of experimental data which appear to be abnormal, with the subsequent modification of the theory to explain these, and in some cases to show that the facts are not in accord with

iii

IV PREFACE

the present theories. The historical setting is illustrated by recording after the names of the men who have been influential in developing the science of chemistry, the date at which each man was actively engaged in the work with which his name is associated. This chronological sequence of the main advances in chemistry is of vital importance in aiding the student to acquire a true perspective of the subject.

The subject matter has been presented by employing only the more elementary mathematics, — arithmetic and alge- bra, — and in but few cases has use been made of higher mathematics. Where the calculus has been employed, practically all of this matter has been incorporated in such a way that, if desired, it can be omitted without disturbing the order of the presentation of the subject. In the pres- entation it is recognized that only by many numerical examples can the principles be properly illustrated and emphasized. Therefore, there is incorporated in the Ap- pendix a large number of problems, the data for which are tabulated in such a way that the answers appear as one of the parts of the tabulation. By not expressing the con- ditions of the problem in words, much space is saved and the instructor may clothe the data in whatever form he desires.

The selection of the subject matter for a textbook of this character resolves itself into the process of exclusion, and the guiding factors in making the selections have been the general information for the student, the fundamental char- acter of the material, and the technical importance of the facts as well as of the theoretical considerations. Special emphasis has been placed upon the equilibrium reactions in gases with technical uses as illustrated by means of prob- lems. The conception of phases has been introduced early in the discussion, and their relation and utilization in ex- planation of many operations has been emphasized, particu-

PREFACE V

larly in the formulation of the Phase Rule, with illustrations of its industrial importance and applications. The theories of solutions have been presented so that the student may become familiar with their experimental basis, the assump- tions involved, and their limitations. It is necessary that students beginning the study of theoretical chemistry should acquire a working knowledge of the prevailing theories in order to make the voluminous literature more accessible to them. In order to accomplish this result the discussion has been extended to a consideration of concentrated solu- tions and nonaqueous solutions. The colloid state of matter is receiving such marked attention from the industrial as well as from the theoretical point of view, that it is be- coming of great importance. Hence, colloid chemistry has been presented in considerable detail.

There have been presented a large number of tables of ex- perimental data, most of which have been taken from Lan- dolt, Bornstein, and Roth's Tabellen, edition of 1912. With this material directly before the student, the discussion of the principles and facts presented may be more fully carried on, and in this way the subject can be much better presented to the student and he will be in a better position to see the significance of the conclusions. Then these data may be utilized as a valuable source of material from which prob- lems may be formulated.

Free use has been made of the available literature in ob- taining the material for this text, and the author desires to express his indebtedness for the same, and particularly to the following, to which the student is referred for further details :

Text Books of Physical Chemistry, edited by Sir William Ramsay, which include A System of Physical Chemistry by W. C. McC. Lewis, The Phase Rule and its Applications by Alexander Findlay, Stoichiometry by Sidney Young, Stereochemistry by Alfred W. Stewart, Metallography by Cecil H. Desch. Monographs on Inorganic and Physical Chemistry,

VI PREFACE

edited by Alexander Findlay ; particularly The Chemistry of the Radio- Elements by Frederick Soddy, and Osmotic Pressure by Alexander Findlay.

Text Book of Inorganic Chemistry, edited by J. Newton Friend ; Vol. I, An Introduction to Modern Inorganic Chemistry by J. Newton Friend, H. F. V. Little and W. E. S. Turner; Vol. IV, Aluminium and its Con- geners, Including the Rare Earth Metals by H. F. V. Little.

Organic Chemistry for Advanced Students by Julius B. Cohen ; Vol. II, Handbook of Colloid Chemistry by Wolfgang Ostwald, translated by Martin H. Fischer.

On the Physical Aspect of Colloidal Solutions by E. F. Burton, Uni- versity of Toronto Studies No. 36.

An Introduction to the Physics and Chemistry of Colloids by Emil Hatschek.

The Chemistry of Colloids by W. W. Taylor. Outlines of Chemistry by H. J. H. Fenton.

For valuable suggestions and assistance, the author wishes to express his appreciation to Dr. M. A. Hunter for reading the manuscript; to Dr. A. M. Greene for his kindly criti- cism on the chapter on Thermodynamic Considerations; to Mr. T. H. Learning for his most valuable assistance, particularly in collecting and verifying the data. But especially to Mr. G. B. Banks the author wishes to express his sincere gratitude and deep obligation for his untiring and painstaking criticisms and for his efforts to prevent errors which would otherwise have appeared. Corrections and suggestions from others will be appreciated.

A. T. LINCOLN. TROY, N.Y. May, 1918.

CONTENTS

CHAPTER

I. INTRODUCTION . . . ..'.",,

II. LAWS OF COMBINATION AND CHEMICAL UNITS. = .

III. THE GAS LAW . . . ^.. ^ \, . . . ; .

IV. DETERMINATION OF MOLECULAR AND SYMBOL

WEIGHTS . . . • ..- ;t »r. ..* .

V. ATOMIC AND MOLECULAR THEORIES . . . ,

VI. DEVIATIONS FROM THE GAS LAW AND DISSOCIATION

OF GASES . . . . . . . .

VII. THE PERIODIC SYSTEM . . . . . .

VIII. THE KINETIC THEORY OF GASES . . . .

IX. SPECIFIC HEAT OF GASES . . ,

X. VAN DER WAALS' EQUATION . . , . %

XI. THE PHYSICAL PROPERTIES OF LIQUIDS . . .

XII. REFRACTION OF LIGHT

XIII. OPTICAL ROTATION

XIV. SOLUTIONS

XV. SOLUTION OF LIQUIDS IN LIQUIDS — I . . • .

XVI. SOLUTION OF LIQUIDS IN LIQUIDS — II .

XVII. PHASE RULE

XVIII. SOLUTION OF SOLIDS IN LIQUIDS — I

XIX. SOLUTION OF SOLIDS IN LIQUIDS — II

XX. SOLUTION OF SOLIDS IN LIQUIDS — 'III .

XXI. SOLUTION OF SOLIDS IN LIQUIDS — IV

XXII. APPLICATION OF THE PHASE RULE ....

XXIII. OSMOTIC PRESSURE

XXIV. LOWERING OF VAPOR PRESSURE .... XXV. FREEZING POINTS AND BOILING POINTS OF SOLUTIONS

XXVI, THERMODYNAMIC CONSIDERATIONS

vii

PAGE I

29 36

46 64 82 90

97 in

122

133 I46

157

1 68 183 195 204 216 229 248

255 265 273 282

Vlll

CONTENTS

CHAPTER PAGE

XXVII. ELECTRICAL CONDUCTANCE 301

XXVIII. ELECTROLYTIC DISSOCIATION 321

XXIX. EQUILIBRIUM BETWEEN THE DISSOCIATED AND UN- DISSOCIATED PARTS OF AN ELECTROLYTE IN

SOLUTION . ,-.,. . ; . . . . 336

XXX. CONCENTRATED SOLUTIONS 358

XXXI. HYDRATION 368

XXXII. HYDROLYSIS 386

XXXIII. NONAQUEOUS SOLUTIONS 395

XXXIV. THERMOCHEMISTRY 410

XXXV. COLLOID CHEMISTRY 433

XXXVI. RATE OF CHEMICAL REACTIONS .... 475

APPENDIX 507

INDEX 541

PHYSICAL CHEMISTRY

CHAPTER I INTRODUCTION

Units of Measure. — The work in chemistry and physics consists chiefly in making measurements in order to ascer- tain the quantity of the materials present or the forces acting between these substances. Shortly after the intro- duction of the balance into the chemical laboratory there began a yigorous campaign to determine the weights of sub- stances as well as of the relative quantities of the constitu- ents of which these were composed and in what ratio various substances combined. It was not only necessary to have a unit of weight but also a unit to represent these combin- ing relations, just as it was necessary to have a unit of length to obtain the dimensions of substances or their distances apart. When an effort was made to measure the various forces, some convenient standard of reference had to be employed in terms of which these forces could be repre- sented. A unit for measurement is some convenient quan- tity of that particular thing which is to be applied as a di- visor in order to ascertain how many times this arbitrarily selected quantity is contained in the quantity of the thing to be measured. Or in other words, a unit is any quantity to which another quantity of the same kind can be compared for the purposes of measurement and for expressing the magnitude of the same. The measure of this unit quantity is represented by the number i. The fundamental units

CHEMISTRY

are selected arbitrarily, and the derived units are defined in terms of the fundamental units.

The method of measurement is the comparison of the quantity to be measured with our unit. This may be ac- complished (i) by applying the unit directly to the quantity to be measured, as that of a foot rule to a floor to find its dimensions, a graduated vessel to the liquid to be measured ; or (2) by the effect the particular quantity to be measured has as compared to the effect that unit quantity has, as in determining the strength of an alkali by titrating it against a standard acid which has been expressed in terms of our unit alkali, or any of our quantitative methods for deter- mining the quantity of a particular substance present, as by determining the refractivity of a liquid, the electrical conductance, etc.

The knowledge of the phenomena occurring about us has been obtained by accurate measurements, and the funda- mental units in which these have been expressed are the units of time, space, and mass. The scientific unit of time, the second, is the 86,4ooth part of a mean solar day, which is the average interval (or period) that elapses between suc- cessive transits of the sun across the meridian at any place during the whole year.

Owing to the fact that the speed of the rotation of the earth is decreasing, resulting in the corresponding increase in the length of the second, it has been suggested that the time of vibration of the atom of some element be selected as our unit of time, as this seems to be invariable and unal- terable.

Our conception of position is that of relative positions only, and the location of one object is expressed in relation to some other object. The change of the position of a body with respect to another is termed motion, i.e. motion is the change of position. The change of position in unit time is the speed, while the rate of change of position in a specified

INTRODUCTION 3

direction is the velocity. If this velocity is not constant during successive intervals of time, the amount of change in the velocity during the interval of unit time is designated

the acceleration, i.e. V2~Vl = a, where the change of velocity

has been from vi to v2 in the time /, giving an acceleration represented by a.

Matter. — Being familiar with handling various sub- stances, such as iron, sodium chloride, water, etc., we are able to distinguish them by certain individual characteris- tics that we call properties. These properties are always constant and persistent and are not detachable from the body. The embodiment of these properties is that some- thing which is familiarly known as matter. Closely asso- ciated with these properties are manifestations of what we designate energy, and in our experiences we have not been able to separate energy from matter. Yet it is through these manifestations that we know of the existence of that which we designate matter.

The quantity of matter is measured by means of the bal- ance, and its measure is expressed in terms of weight. This measure is the attraction of the earth for the particular quantity of the material substance or matter. Since the attraction of the earth varies with the distance from the center of the earth, a body would not have the same weight on all parts of the earth's surface. The quantity of matter does not change, and the mass, as it is termed, remains con- stant. Hence in stating the quantity of a substance, it is not sufficient to speak of its having a certain weight, but the term mass is used to definitely express the quantity of the substance. Masses are compared by comparing their weights.

Units of Mass. — The units of mass are founded on the kilogram, which is the metric standard of mass and is defined as the mass of a piece of platinum-iridium deposited at the

4 PHYSICAL CHEMISTRY

International Bureau of Weights and Measures near Paris. This standard of mass, known as the International Proto- type Kilogram, is equal to the " kilogramme des Archives " made by Borda, which was intended to have the same mass as a cubic decimeter of distilled water at the temperature of 4° C. and 760 mm. Hg pressure, which weighs i kilogram and equals actually 1.000027 cu. dm.

The English standard of mass is the pound and is the weight of a piece of platinum weighed in vacuo at the temperature of o° C., and which is deposited with the Board of Trade.

Force. — Force is that which changes or tends to change the velocity of a body. It may be measured by the gravi- tation method, the ordinary spring balance method, or the dynamic method; the first of which is the one generally used by chemists. The unit of force is that force which produces in unit mass unit acceleration. In the C.G.S. system the unit of force is the dyne and is defined as that force which acting on a body of unit mass produces an acceleration of one centimeter per second per second. The unit force is called a poundal when mass is expressed in pounds, length in feet, and time in seconds. Force may be defined by F — Ma, where M is mass and a is the accel- eration.

Weight. — The units of force, the dyne and poundal, are designated the absolute units, but the so-called gravitational units are more commonly employed, wherein use is made of the force of the attraction of the earth for the body. The unit of force then becomes the attraction of the earth for the unit of mass — one gram or one pound.

The attraction of the earth1 on one gram causes an acceleration of 98 1 cm./sec.2. The force of one dyne produces

an acceleration of one — ^when it acts on one gram. Hence sec.2

the weight of one gram is equivalent to 981 dynes. 1 This has different values at different places.

INTRODUCTION 5

Pressure. — Pressure is a distributed force. The inten- sity of pressure, i.e. the pressure per unit area, is used ex- tensively in science ; and in chemistry, particularly, when the term pressure is used the intensity of pressure is meant. -

Density and Specific Gravity. — The mass of a substance in unit volume is termed the density of that substance. Density

is represented by p. Then by definition p = . The

specific gravity of a substance is the ratio of the mass of a given volume of a substance to the mass of an equal volume of another substance taken as a standard. The specific

gravity is represented by s. Then s = — , where g is the mass

of the substance, and g, is the mass of an equal volume of the standard substance. It is not always customary to com- pare the substance at the same temperature. Hence if water at its greatest density (4° C.) is selected as the standard and the other substance compared with it at this tempera-

ture, this is usually expressed -^ , while if the substance is at

4 some other temperature, as 20°, the comparison with water

at 4° would be indicated as follows : ^-, and the expression

^ signifies that both the substance and the standard are to

be compared at 15°. We should also have s = — , in which

P»

p is the density of any substance, and p, is the density of the standard.

CHAPTER II LAWS OF COMBINATION AND CHEMICAL UNITS

THE uniform occurrence of natural phenomena is observed to take place and the conditions best suited for their repro- duction are ascertained by experimentation. The facts gathered by observation and experimentation are classified, and certain particular groups of related facts are then ex- pressed in a generalization which is the so-called law. Or, as Mellor expresses it, " The laws of chemical and physical phenomena are collocations of those circumstances which have been found by experiment and observation to accom- pany all chemical and physical changes included in the statement of the law." We have as some of the funda- mental generalizations of science the following : The Law of the Conservation of Energy ; the Law of the Conservation of Matter; Newton's Law of Gravitation; Boyle's Law; etc. We thus see that a Law of Science is a general statement of what has been found to be true by experiment and observation and of what will probably be true in the future.

THE LAW OF DEFINITE PROPORTIONS

When magnesium is burned, it is changed to the white oxide, and we have on the one hand metallic magnesium and on the other hand the white oxide, there being no gradation. The amount of the magnesium oxide that can be formed depends upon the quantities of magnesium and oxygen available, and there is a constant relation between the amounts of substances taken and the amount of sub-

LAWS OF COMBINATION AND CHEMICAL UNITS 7

stance formed. In general this may be stated that when substance A changes to substance B the ratio of the masses is constant. It was not possible to formulate any such law until the balance was introduced by Lavoisier. It was then demonstrated that 100 parts of zinc always yield 124.5 parts of zinc oxide. By using different amounts of potassium chloride, varying from 44 to 80 grams, the result of seven experiments showed that 100 parts of potassium chloride yield 135.645 parts of potassium nitrate.

If two chemically homogeneous substances, A and B, react upon each other and yield a third substance, C, then the following relations hold :

Mass A T. , AX Mass A T, Mass B „

TT7 ~ = K (constant) : ^ -^ = Ki ; ^ -^ — Kz.

Mass B ' Mass C Mass C

This may be demonstrated by adding, drop by drop, a solution of potassium bromide to a solution of silver nitrate. It has also been shown that these relations hold under what- ever conditions the substances react/ For example, the amount of silver chloride formed from a constant given weight of silver is always the same, whatever the method be by means of which it is prepared, as is shown by the following :

1. Burning Ag in Cl gas 100 g. Ag yielded 132.842 g. AgCl.

2. Dissolving Ag in KC1 100 g. Ag yielded 132.847 g. AgCl.

3. Precipitating AgNO3 with HC1 aq 100 g. Ag yielded 132.848 g. AgCl.

4. Precipitating AgNO3 with NaCl aq 100 g. Ag yielded 132.842 g. AgCl.

A large number of experiments were made to determine whether the mass formed was equal to the sum of the masses taking part in the reaction. In seven experiments with the formation of silver iodide from silver and iodine, in which quantities of silver varying from 27 to 136 grams were used, the weights of the silver iodide formed did not differ from the sum of the weights of the silver and the iodine taken by more than one part in 20,000 in any^ase. From this it is seen that there is a definite relation between the substances

8 PHYSICAL CHEMISTRY

used and the products formed. This may be expressed in the following form : The ratio of the mass formed to the con- stituents is constant and also the ratio of the constituents to the mass formed is constant. This is termed the Law of Definite or Constant Proportions.

While this has been fully demonstrated to the satisfaction of most investigators, there are some who still question whether the mass of a substance always remains constant during its passage through chemical changes. Very recently Landolt 1 published the result of his investigation on the ques- tion as to whether chemical changes alter the mass of a particular substance. Of 14 reactions of various types only two gave systematically a change in weight larger than the errors of observation. Each of the experiments, in which 250 to 310 grams were used, has corresponding differences in weights, varying from 0.068 mg. to o.n mg. Out of 70 ex- periments 6 1 showed losses in weight. Babcock, from his work upon the effect of molecular changes upon weight, states 2 that his experiments indicate that the weight of a body is an inverse function of its energy. While the difference between the weight of the ice and the water resulting from it is always small, the ice was always found to be heavier than the water.

THE LAW OF MULTIPLE PROPORTIONS

The mass of a system is not altered by chemical changes that occur in the system, or, as expressed above, the mass of a composite substance is equal to the sum of the masses of its component elements. By the term element we under- stand those particular substances which have so far resisted all efforts of the analyst to decompose them into simpler or more elementary constituents.3 We have already seen that

1 Landolt, Jour, de chem. phys. 6, 625-27 (1908).

2 In a private communication to the author.

3 The rare earth elements constitute a group of closely related ele- ments that require peculiar and special methods in order to separate

LAWS OF COMBINATION AND CHEMICAL UNITS 9

these elements combine in constant ratios to form chemically homogeneous substances. Such chemically homogeneous substances, whose percentage composition by mass is in- variable, are termed chemical compounds.

By burning portions of 10 grams of lead in oxygen the following quantities of lead oxide were formed: 10.77, 10.775, 10.78, and 10.75 grams, and Berzelius found as an average of his determinations 10.78 grams of the oxide of lead produced from 10 grams of lead. Taking 10.78 as the value, and expressing the amount of lead oxide produced from 100 grams of lead, we would obtain 107.8 grams of the yellow oxide of lead. It has also been found that 100 grams of lead unite with 11.7 grams of oxygen to form minium (red oxide of lead) and that 100 grams of lead unite with 15.6 grams of oxygen to form brown oxide (peroxide) of lead. These different quantities of oxygen combining with the same

and distinguish them. Certain elements, which include uranium, radium, polonium, actinium, etc., are designated radioactive elements and are characterized by giving rise to emanations. The theory of the disinte- gration of these radioactive elements assumes that the emanations give rise, in some cases, to active deposits which are transformed into another element, and this in turn is transformed into a non- radioactive and stable element. In some radioactive changes, the ex. particles emitted are charged atoms of helium, as is illustrated in the growth of helium from actinium. Resulting from these emanations there is a group of elements of different atomic weights but which are chemically identical. Such a group of elements is termed isotopes and the elements are called isotopic. The following members of the actinium series are given by Soddy : *

1. Radioactinium, thorium, radiothorium, ionium, uranium-X.

2. Actinium and mesothorium-2.

3. Actinium-X, radium, mesothorium-i, thorium-X.

4. Actinium emanation and emanations of radium and thorium.

5. Actinium-B, lead, radium-B, thorium-B, radium-D.

6. Actinium-C, bismuth, radium-C, thorium-C, radium-E.

7. Actinium-D, thallium, and thorium-D.

* Soddy, The Chemistry of the Radio-Elements (1914), and the Text-book of Inorganic Chemistry, Edited by J. Newton Friend, Vol. IV by H. F. V. Little, are sources of additional information and extensive references to the literature.

10 PHYSICAL CHEMISTRY

amount of lead (100 grams) are in the ratio of 7.8 : 11.7 : 15.6, which is the more simple ratio of 2 : 3 : 4 ; hence a con- stant quantity of lead combines with different quantities of oxygen in the simple integral ratio 2:3:4. Similarly it has been found that 100 grams of nitrogen unite with the fol- lowing quantities of oxygen to form distinct chemical indi- viduals: 57.1; 114.3; I7I-4> 228.6; 285.7 grams, which reduces to the following simple ratio : 1:2:3:4:5. In the case of hydrogen and oxygen the quantities of oxygen found in combination with the same quantity of hydrogen are in the ratio of 1:2. Hence from the above the following general statement may be made :

When an element combines with another element or group of elements to form different compounds, the masses of the first element that combine with a given mass of the other element or group of elements are in some simple ratio to one another.

THE LAW OF RECIPROCAL PROPORTIONS

In the above examples of ratios between the elements lead and oxygen, we expressed the amount of oxygen that com- bined with 100 parts by weight of lead. We could have expressed the ratio by stating the amount of lead that com- bined with i, or 10, or 100 parts of oxygen. The same is true in the case of oxygen and nitrogen; either element might have been selected as the unit of comparison, in any convenient quantity. Further, if the ratio of the two ele- ments, nitrogen and oxygen, is established, and also the ratio of hydrogen and oxygen, the ratio of hydrogen and nitro- gen can readily be ascertained by calculation. Again, if the ratio of hydrogen and chlorine be determined and the other two ratios, nitrogen to oxygen and oxygen to hydro- gen, then the cross-relation between chlorine and nitrogen can be calculated. This relation can be illustrated in the case of chlorine, iodine, and silver. Let us compare the ratios of the amounts of these elements that combine with

LAWS OF COMBINATION AND CHEMICAL UNITS II

equal amounts of silver, say 75.26 parts. In silver chloride we have 24.74 per cent chlorine and 75.26 per cent silver; in silver iodide we have 54.04 per cent iodine and 45.96 per cent silver ; in chlorine iodide we have 2 1.84 per cent chlorine and 78.16 per cent iodine. Then from the proportion

Iodine : Silver : : Iodine : Silver

we have 54-04 : 45.96 :: x: 75.26.

From which

x = 54"°4 X I5'26 = 88.49 45.96

the amount of iodine that would combine with 75.26 parts of silver. Since 24.74 parts of chlorine combine with this same amount of silver, 88.49 parts of iodine would be equivalent to 24.74 parts of chlorine. One part of iodine will be equiva- lent to 0Q = 0.279 part of chlorine. In the direct com- 88.49

bination of chlorine and iodine we have the ratio of 21.84

parts of chlorine : 78.16 parts of iodine, or ' . = 0.279

70.10

part of chlorine, uniting with one part of iodine, which is the same ratio as above. By a similar method these cross- relations can be calculated between all of the elements, and it is this relation that is known as the Law of Reciprocal Proportions, or the Law of Equivalents. It may be expressed as follows :

When different elements are combined successively with any other, or with a group of others, the masses of the former that are combined with a given mass of the latter are to one another in the same ratio in which these different elements combine with any other element or group of elements.

From our consideration of the previous laws, and our information concerning chemical compounds, it is evident that we have to distinguish between equal quantities of the

12 PHYSICAL CHEMISTRY

constituents of a compound and equal chemical quantities of the constituents. In the compounds cited above, silver chloride, for instance, contains 75.26 per cent of silver and 24.74 per cent of chlorine, i.e. these quantities of silver and chlorine are equal chemically. In the chemical sense, then, the equal quantities of matter are the weights or masses which unite with each other chemically. The amounts of the different substances that unite chemically are chemically equivalent and depend entirely upon the specific nature of the substances.

UNITS OF CHEMISTRY

We employ symbols to represent the elements and a com- bination of symbols in the form of a formula to represent the composition of a compound. For example, water is com- posed of hydrogen and oxygen, and hydrogen peroxide is composed of hydrogen and oxygen. We use H to represent the element hydrogen and O to represent the element oxygen ; then the combination HO represents both water and hydro- gen peroxide, but not their composition. By analysis we know that water contains 88.85 per cent of oxygen and 11.15 per cent of hydrogen, and hydrogen peroxide 5.91 per cent of hydrogen and 94.09 per cent of oxygen. In water the ratio is 11.15:88.85. Then the amount which combines with 94.09 parts of oxygen in the hydrogen peroxide would be 11.15:88.85: :#:94.09. Solving for x we have 11.82 parts. The quantities of hydrogen combining with the same quantity of oxygen, 94.09 parts, are 11.82 parts and 5.91 parts, which are in the ratio of 2 : i. That is, there are two different quantities of hydrogen combining with the same quantity of oxygen to form these two different chem- ical substances, water and hydrogen peroxide. The hydro- gen has two combining weights or equivalents. We could use this weight of oxygen as our unit quantity and represent it by the symbol for oxygen, O, or we could select any

LAWS OF COMBINATION AND CHEMICAL UNITS 13

other quantity arbitrarily. The quantity that has been selected arbitrarily is 16, and so we shall arbitrarily select as our symbol weight of oxygen, 16 grams. Then the equiva- lent weights of hydrogen would be 2 in the compound water and i in the compound hydrogen peroxide. Then the formulae for these substances could be written respectively H2O and HO, if we let the symbol H represent the smaller amount of hydrogen combining with the 16 grams of oxy- gen, thus avoiding a fractional part of the symbol weight were we to select the larger value H = 2.

From 34 grams of hydrogen peroxide we can obtain 16 grams of oxygen and 18 grams of water at the same time. This 1 8 grams of water on decomposition will yield 16 grams of oxygen and 2 grams of hydrogen ; that is, the oxygen of hydrogen peroxide can be separated into two equal quantities, but the oxygen in the water cannot be thus separated, for we obtain free hydrogen and free oxygen. From this we assume that the oxygen in water is in the simplest amount possible and is the quantity represented by our symbol weight of oxygen, O, while in the peroxide there is twice this quantity, or O2.

In the decomposition of hydrogen peroxide we find that all of the hydrogen present remains with one part of the oxygen and is the same as that in the water. Now if we treat water with sodium, we obtain free hydrogen and a compound, sodium hydroxide, which upon analysis gives sodium, oxygen, and hydrogen, — all of the oxygen of the water appearing in this compound and the hydrogen of the water separating into two equal parts, one part appearing free and the other in combination with the oxygen and sodium. The formula for water must show that the hydro- gen can be divided ; therefore, the formula becomes H2O. vSimilarly, the formula for hydrogen peroxide must show that it contains the same amount of hydrogen as in water and also that the oxygen contained can be divided ; hence

14 PHYSICAL CHEMISTRY

the formula for hydrogen peroxide becomes H2O2, instead of HO, which we saw represents the chemical composition as well.

A chemical formula is a combination of symbols wherein each symbol represents that equivalent quantity of the ele- ment which we cannot further divide by chemical trans- formations. These chemical formulae are the result of ex- periment and are designated the empirical formulae. If our method is good, only integral multiples of the chemical units represented by symbols enter into and go out of combina- tion. The symbol weight of oxygen is defined as 16 grams of oxygen, and the symbol weight of hydrogen is then i. The sum of the symbol weights is designated the formula weight. This is usually called the molecular weight. For example, the formula we derived for the water is H20 ; two symbol weights of H = 2 and one of O = 16 and the sum 18 is the formula weight for water.

The symbol weight of other elements may be determined in a similar manner. Carbon when burned in air forms two oxides which are compounds of oxygen and carbon; by analysis one contains 12 grams of carbon and the other 6 grams of carbon in combination with 16 grams of oxygen. So the formulae would be C2O and CO or CO and CO2 re- spectively, depending upon whether we select 12 or 6 as the equivalent weight of C. Since carbon has two combining weights, it is necessary for us to have more data in order to decide which we shall select as the symbol weight. Either of the formulae would represent the chemical composition and would be designated an empirical formula.

In the case of nitrogen, we have five different compounds of nitrogen and oxygen. Expressed in terms of the quantities of nitrogen in combination with 16 grams of oxygen, we have 28, 14, 9^, 7, 5! grams of nitrogen respectively, i.e. we have five different combining weights of nitrogen, and the ques- tion arises, which of these equivalent weights shall be selected as the symbol weight of nitrogen ?

LAWS OF COMBINATION AND CHEMICAL UNITS 15

The answer to this question is obtained by a consideration of the volume relations of gaseous compounds and of the elements entering into the reactions. These volume rela- tions are summed up by Gay Lussac's Law of Combination by Volume, which is stated as follows : When reacting gaseous elements combine, the volumes of the different gases under the same conditions of pressure and temperature are in simple ratio to one another and to the resulting products.

Taking the volume of 16 grams of oxygen as the unit volume under specified conditions of temperature and pressure, we find experimentally under these same condi- tions of temperature and pressure the following volume re- lations between the reacting substances and the resulting product :

Hydrogen + Oxygen = Water

2 grams 16 grams 18 grams

+ n -;".

+ i vol. =

+ Hydrogen = Hyc i gram

+ D - ; :

-f- I vol. =

+ Oxygen = Niti 1 6 grams

* D -

•+• i vol. =

+ Nitrous oxide = Water 44 grams 18 grams

1 1

2 VOls.

Chlorine 35.5 grams

2 VOls.

Irochloric acid 36.5 grams

1 1

i vol.

Citric oxide 30 grams

2 VOls.

•ogen peroxide 46 grams

2 VOls.

Hydrogen 2 grams

2 VOls.

V Nitrogen 28 grams

2 VOls.

+ 2 VOls. = 2 VOls. + 2 VOls.

16 PHYSICAL CHEMISTRY

Nitrogen -j- Hydrogen = Ammonia

14 grams 3 grams 17 grams

i vol. + 3 vols. = 2 vols.

In No. i we observe that since 16 grams of oxygen is the arbitrarily selected symbol weight and the quantity of hydro- gen represents 2 symbol weights of hydrogen the prod- uct, 1 8 grams of water, is represented by the formula H2O. We notice that the formula weight of water occupies twice the volume of the one symbol weight of oxygen, while two symbol weights of hydrogen occupy the same volume as the formula weight of water or twice the volume of one symbol weight of oxygen. From an examination of the weights of these various compounds used and produced in these five examples, it will be noticed that the volume occupied by the formula weight of water (2 vols.) is the same as that occupied by the formula weights of the other compounds : hydro- chloric acid, nitric oxide, nitrogen peroxide, nitrous oxide, and ammonia. That is, the formula weight of every gaseous compound considered above occupies the same volume. We can generalize and state that the formula weight of all gaseous compounds occupies the same volume under the same conditions of temperature and pressure. This may be the same as the empirical formula, which is taken as the simplest formula, or it may be some integral multiple of the empirical formula.

Experimentally, it has been found that 16 grams of oxygen at o° C. and under 760 mm. mercury pressure occupies 11.2 liters. Under these conditions of temperature and pressure 22.4 liters is therefore the volume occupied by the formula weight of the gaseous compounds. This volume is termed the formula volume.

The formula of a compound is, then, a combination of symbols that represents the percentage composition of the

LAWS OF COMBINATION AND CHEMICAL UNITS 17

compound and such that the formula weight in grams of the compound in the gaseous state occupies 22.4 liters of space under standard conditions. A formula is, therefore, purely an arbitrary affair, subject to definition. It follows then that we can have a formula of an element ; thus O2 is a com- bination of two symbol weights of oxygen representing 32 grams of oxygen and occupying 22.4 liters under standard conditions of temperature and pressure. Similarly the for- mula of hydrogen is H2, of chlorine C^, of nitrogen N2.

Rewriting the above reactions, employing formulae for the reacting substances and products, we have :

1. 2 H2 + O2 =2H2O

2 vols. + I Vol. = 2 vols.

2. C12 + H2 =2HC1

I vol. + I vol. = 2 VOls.

3. 2 NO + O2 =2 NO2

2 VOls. + I VOl. = 2 VOls.

4. . H2 + N2O = H2O + N2

i vol. + I vol. = I vol. + i vol.

These chemical equations represent the chemical reaction and the quantities by weight of the reacting substances. The coefficients of the formulas appearing in the equation are the same as the number of volumes of the compounds in the gaseous state.

Experimentally, we have developed that equal volumes of substances in the gaseous state contain the same number of formula weights of the compounds. (This is Avogadro's Law.)

We have also established the following rule for checking the symbol weight of an element : Determine the weights in grams of the designated element in 2 2 .4 liters, under standard conditions, of the gaseous compounds of that element. The greatest common divisor of all these numbers is the symbol weight of the element.

CHAPTER III THE GAS LAW

THROUGH whatever chemical change a substance passes, the mass of it remains the same. The same may be said concerning physical transformations as well. If a definite mass of a gas is selected under a specific temperature and pressure, it will occupy a definite volume. If, however, this definite mass be subjected to different pressures and tem- peratures, the volume which it occupies may vary greatly, and hence the volume which this constant mass occupies depends upon the pressure and temperature ; that is, the values for the pressure, p, the temperature, /, and the volume, V, are so related to one another that simultaneous values of any two determine the functional relation. This may be expressed mathematically, V = f (p,t). This equation is known as the Equation of State. In the functional relation the volume which a given mass occupies depends upon the temperature and pressure. The pressure, p, and the tem- perature, /, are spoken of as the independent variables, and the volume, V, as the dependent variable, because its value depends upon the values arbitrarily selected for p and /. By keeping one of these independent variables constant it is possible to determine what relation exists between the de- pendent variable and the other independent variable.

i. Assume a constant mass of gas.

The volume which it occupies depends upon p and /. Then F is a dependent variable.

If we assume t and the mass constant, V depends on p,

THE GAS LAW 19

Let volume at pressure p be V and the volume at pressure pi beVi.

Now by experiment we find that if 1000 cc. of gas is at 500' mm. pressure, then the volume will be 500 cc. if the pres- sure is increased to 1000 mm. That is,

1000 cc. : 500 cc. : : 1000 mm. : 500 mm.

or V:Vn :pnp.

If the temperature is constant, the volumes are inversely proportional to the pressures. This is Boyle's Law.

2. Now assume pressure and mass constant and vary the temperature. Gay Lussac found experimentally that if 100 cc. of gas at o° C. were heated, the volume was 136.65 cc. at 100° C. or an increase of 36.65 cc. for a change of 100° C., or 0.3665 cc. for i°. The change for i cc. is y^ of this, or 0.003665 cc. That is, for every increase of one degree cen- tigrade the volume is increased this proportional amount, or i cc. increases 0.003665 cc. per degree C. But 0.003665 = 1/273. Any volume of gas at o° C. will increase for any

number of degrees of change of temperature times the

273 original volume.

Let Fo = volume of mass of gas at /0, at pressure po.

V = volume of mass of gas at t, and at the same

pressure.

Then V — Vo = increase in volume and t — to = change in temperature.

But a gas increases 1/273 of the original volume per de- gree; then 1/273 times Vo = increase in volume per degree.

t — toX — - = increase for change of temperature t — to on

273 the centigrade scale.

But the increase in volume is V — Vo,

hence V - V, = ^— ^ X F0 which becomes V ~ Vo = ^-°- 273 ^o 273

20 , PHYSICAL CHEMISTRY

We are expressing our temperature as temperature differ- ences on the arbitrarily selected centigrade scale.

The equation - - = - - could be simplified mathe- ^o 273

matically if we were to take /0 = 273 and substitute in the above equation. The zero of the centigrade scale then would become 273 centigrade divisions above the zero point on our new temperature scale. This new point is known as the Absolute Zero and is found to be practically the same as the Absolute Zero on the thermodynamic scale. The readings on the centigrade scale equal 273 -f- t on the Absolute scale, or T = TQ + t. Now having assigned these values,

the equation becomes — -- -, from which we ob-

Vo -To

tain — = — or V : Vo : : T : To which states that the volumes

Vo TQ

of a given mass of gas under constant pressure are directly proportional to the Absolute temperatures. This is Charles' or Gay Lussac's Law.

These two laws can be combined into one expression by assuming a constant mass of the gas : and then (i) with the temperature constant, change the pressure ; and then (2) with the pressure constant, change the temperature.

Assuming the mass constant and the temperature constant, then let V0 = the volume of the gas at pressure po and tem- perature TQ.

Vi = the volume of the gas at pressure pi and tem- perature TV

Then according to Boyle's Law

Vo : Vi : : pi : po. Solving for Vi, we have

THE GAS LAW 21

Now change the temperature on this new volume keep- ing the pressure constant, pi = p%; we have according to Charles' or Gay Lussac 's Law :

Vi : V2 : : Ti : T2 or ViT2 = V2Ti.

Substituting the value of Vi = -° we have ** = y2Ti.

pi pi

Now eliminate intermediate values and remember To =

~\7 >> T*

i and pi = p2. We have °^° 2 = V2T0. Rearranging, we

have

-To -/2

which is an expression for the combined laws of Gay Lussac and Boyle.

Now it is possible to change these last values to new ones

and obtain similarly the same relation. — ^ = — ^, or in

Tz 13

general the initial volume multiplied by its corresponding pressure divided by its corresponding temperature, is equal to any other volume times its corresponding pressure divided

by its corresponding temperature. -4p = — *, which is con-

To /

stant,

or X = constant : Vp = KT. (A)

ANOTHER DEVELOPMENT OF THE GAS LAW EQUATION

It has been shown experimentally that if we take a definite mass of gas, the volume it occupies will be dependent on its temperature and pressure. That is, keeping the mass constant,

V = f(p, t] or it may be stated that p = f(V, t) and also, / = f(V, p).

Gay Lussac showed by experiment that when the volume is constant, the change in pressure is directly proportional to the change in tern-

22 PHYSICAL CHEMISTRY

perature. Assuming this to be true for the entire range of temperature and pressure the functional relation p = f(V, t) is expressed by the equation

p - po = k(t - t0) (i)

where k may be a function of the volume. It will be recalled that

y = ax + b

is the ordinary equation of a straight line, in which a represents the tangent of the angle which the line makes with the x axie and b repre- sents the intercept on the y axis. Any given point (xf, y') on this line must satisfy the equation which gives y' = ax' + b. Eliminating b we get

y - y' = a(x - x'). (2)

This is the equation of a straight line through the point (#', y') making an angle, whose tangent is a, with the x axis.

Equation (i) is the same form as equation (2). Therefore the equa- tion

p-po = k(t -to)

represents a straight line through a given point (to, po) making an angle with the temperature axis whose tangent is k.

Since we may arbitrarily select (/0, po), let us assume it to be the melting point of ice under atmospheric pressure. This is the zero on the ordinary centigrade scale. That is, t = o and p = the pressure of one atmosphere. Substituting to = o in equation (i) we get

P - po = kt. (3)

In Fig. i let the melting point of ice (to, po), on the pressure axis and some distance above the temperature axis, be represented by A.

Now we know by experiment that, when ;>t the temperature is raised, the pressure is increased. Therefore, any other point representing a greater pressure will be to the right and above the point A, as point B (pi,ti). Then the straight line — — AB through these two points will be the FIG. i. locus of equation (3).

The value of po is taken as one atmos- phere above absolute zero pressure, as we selected the melting point at the pressure of one atmosphere, but the value of to was assumed

THE GAS LAW 23

without reference to any absolute zero of temperature. Therefore, where the locus cuts the temperature axis is represented the absolute zero of pressure, and it is of some advantage to us, to take the origin of the coordinants at this point 0. If we do this, all values of pres- sures remain the same, but the value of each temperature will be increased by the distance between this point O and the point A', the origin of our old system of axes, i.e. the distance OA ', which we will designate TV So if we refer the temperatures to our new coordinate axis by T, then

T = To + t or / = T - T0.

Substituting this value in equation (3) we get

p-pQ = k(T- To). (4)

Equation (4) may be written

p - kT = Po - kT0. (4')

Since the locus of this equation passes through the origin, the coordinates (0, O) of the origin must satisfy it. Substituting, we have

o — ko = po — kTQ or po — kT0 = o.

Substituting this value back in equation (4') it then becomes p — kT = o or

P = kT. (5)

This is a simple form of the equation (4) representing the same locus.

Now, equation (4) was developed directly from Gay Lussac's gener- alization, which, as he showed experimentally, is true for any gas assum- ing the mass and volume constant. Therefore, equation (5) is true for any gas.

Solving this equation for k, we have

*-f (50

Now Boyle's generalization is, that keeping the mass and tempera- ture constant, the pressures are inversely proportional to the volume ; or as we saw, V: V\\:p\:p which becomes Vp = V\pit or keeping the

mass and temperature constant the product of the volume and pressure

is a constant, i.e. pV = K\, or p = —±, the pressure is inversely pro- portional to the volume.

' ' . *'

24 PHYSICAL CHEMISTRY

y Applying this generalization to (5') we have k =-y» and remembering

T£

that T is constant we then have k = — -. This means that k is con- stant only when the mass and volume are constant ; but that when the

volume is increased, k is decreased.

jp Substituting this value of k in equation (5), we have p = — T or

pV = KiT. (6)

DISCUSSION OF THE CONSTANT OF THE GAS LAW

Equation (A) is developed from Boyle's and Gay Lussac's generalization, assuming a constant mass. This is true, however, only in the case of a true gas, which is a hypo- thetically perfect gas, wherein the internal energy is de- pendent on the temperature only. Oxygen, hydrogen, air, and nitrogen so nearly conform to perfect gases that for practical purposes they may be considered as ideally perfect and obeying the laws of perfect gases.

The equation K = ^ (i)

means that if the volume of a given mass of gas is changed, the pressure or the temperature, or both temperature and pressure, must change so that the pressure multiplied by the volume divided by the absolute temperature shall always be the same.

By experiment we find that keeping the pressure and temperature constant, the volumes of different masses of the same gas are directly proportional to the masses, i.e. V: Vi: :M: Mi, where V is the volume of mass M, and V\ is the volume of mass Mi. So, different masses of the same gas have different values of K. Also, by experiment, we know that equal masses of different gases have different volumes under the same conditions of temperature and

THE GAS LAW 25

pressure. In general, then, we must use different values of K for equal masses of the different gases.

The value of K for unit mass of a given gas is denoted by r. Let us denote the volume of unit mass of a gas by v, then equation (i) becomes

pv = rT. (2)

Since r has different values for different gases, the gas must be specified when using equation (2), and r is called the specific gas constant.

It follows, then, that K for any mass M is equal to Mr or K = Mr. (3)

If we choose the masses of the different gases so as to give the same volumes at the same temperature and pressure, K has the same value for every gas, according to equation (i). By experiment we find that the molecular weight of every chemical compound in the gaseous state occupies the same volume at a definite pressure and temperature.

If the molecular weight of a gas is chosen, the value of K is denoted by R. If m is the molecular weight, then from equation (3)

R = mr (4)

and equation (i) becomes

PV = RT. (5)

Since the value of R is the same for all gases, R is called the Universal Gas Constant.

The molecular weight of a compound in grams is called the gram-molecular weight, or mole. If any number of moles, n, are used, the more general form of the equation is pV = nRT. (6)

Since n = •£-,' where g is the weight in grams, we may sub- stitute in equation (6) and obtain

(7)

26 PHYSICAL CHEMISTRY

Solving equation (5) pV = RT for R, we have R — £-?-• But we saw that for the same mass of gas under different

conditions of pressure and temperature we have Ki =

/ T To

therefore,

And by definition we have p0 = the pressure of one atmos- phere, which is equivalent to 760 mm. of mercury, i.e. to the pressure of a column of mercury of one sq. cm. cross- section and 76 cm. high, or to the weight of 76 cubic centi- meters of mercury. Now, since one cubic centimeter of mercury weighs 13.6 grams, 76 cc. will weigh 76 X 13.6, or 1033-6 grams. The pressure of one atmosphere is therefore equivalent to 1033.6 grams per unit area of one square cen- timeter. The temperature To = 273° absolute on the cen- tigrade scale, while Vo is denned as the volume of one gram-molecule of oxygen, O2, i.e. 32 grams of oxygen. Since the weight of one liter of oxygen is 1.429 grams, this

volume of oxygen will be 32 , or 22.4 liters. Therefore,

1.429

Vo = 22.4 liters, which is designated the gram-molecular volume.

Substituting these values in our equation R = ^-=-* , we

have R = * 22'4 = 0.08204 liter-atmosphere per degree,

273 of R=s 1033-6 X 22400 = 84?78o gram.centimeters per

2 73 degree.

It is customary in Thermodynamics to express the terms in the Gas Law Equation in the English system and the Fahrenheit temperature scale.

If we have a mass of gas at the temperature of melting ice, 32° F., and at atmospheric pressure, then

THE GAS LAW 27

PQ = i atmosphere = 14.6967 Ib. per square inch = 2116.32 Ib. per square foot. To = 491.6° absolute on the Fahrenheit scale. v = volume of unit weight of the gas (i pound). B = characteristic gas constant and is the symbol used in place of r when the English system of units is employed.

Then equation (2) becomes

pv = BT. (B)

From equation (4) we obtain R = mB. If p is the mass

of unit volume of the gas, we have v = — •

Substituting for v and B their values in equation (B), we obtain

£ = RT

P m Solving for R, we get

R = *%• (C)

If m and p are known for any gas, R can be calculated.

For oxygen p = 0.089222 Ib. per cubic foot at atmos- pheric pressure and 32° F. and m = 32.

Substituting in above equation, we have

R = »'v '« = I544 ft--lb- per degree-

0.089222 X 491.6

The universal gas constant R is then equal to 1544 ft.-lb. per degree.

From this value of R, the characteristic or specific con- stant B of any gas may be determined if its molecular weight is known.

For carbon dioxide we have B = I^44 = 35.09.

It is often convenient to express the density and the volume of unit weight of a gas in terms of the molecular

28 PHYSICAL CHEMISTRY

weight m when referred to standard conditions of tempera- ture and pressure.

From R = ~, we have p = , hence substituting the pi Rl

numerical values

p = 2116.3 lb. Per sq.ft., R = i544ft.-lb. per degree, and T = 491.6° F., we have

= 2116.3 Xm =0-002788 m rb. per cubic foot per

1544 X 491-6 degree.

And for the normal specific volume we have

X 4T-6 = ^^5 cubic feet per pound.

p pm 2116.3 m m

CHAPTER IV DETERMINATION OF MOLECULAR AND SYMBOL WEIGHTS

THE method employed for the determination of symbol weights at present is virtually that of Cannizzaro, wherein the weight of the gram-molecular volume is obtained for a large number of gaseous compounds containing that element, and the greatest common divisor of these quantities of the - element occurring in the gram-molecular volume is selected as the symbol weight of the element and is also termed the atomic weight.

We selected arbitrarily as the unit volume of combina- tion the volume occupied by one gram-molecule of oxygen, i.e. 32 grams of oxygen under the standard conditions of temperature and pressure. For the standard conditions we have defined the standard pressure as the pressure of one atmosphere at sea-level and latitude 45°, or 760 mm. of mercury, and the temperature as the zero on the Centigrade scale or 273° absolute. The unit for volume measurements is the cubic centimeter, one thousand of which are designated a liter. The weight of one cubic centimeter of oxygen under standard conditions of temperature and pressure has been determined very accurately and is found to be 0.001429 gram. One liter weighs 1.429 grams. The volume oc- cupied by one gram molecule of oxygen, i.e. 32 grams, is 32 -r- 1.429 = 22.4 liters under the standard conditions of temperature and pressure. Hence, we designate 22.4 liters as the gram-molecular volume, as it is the volume of one gram molecule, i.e. the volume which the molecular weight of a

30 PHYSICAL CHEMISTRY

gas expressed in grams would occupy under standard con- ditions.

Density Relations. — We have seen that pV = nR T holds generally for gases. Let us assume that it does for those with which we are dealing, and let g, — grams of a gaseous body we select as our standard, g = grams of some other gas measured at the same pressure and temperature, and occupying the same volume as the standard, ma the weight of a gram-molecular volume, 22.4 liters of the standard, m the weight of a gram-molecular volume, 22.4 liters of the other gas. From the definition of the number of formula

weights of any gas we have na = — for the standard, and

nig

n = -&- f or the other gas. Substituting, the Gas Law Equa- tion becomes

and pV = RT. (2)

Solving,

. RT ma RT m ma m

g t g

Solving this for m, we have m = — m,. But since 5 = — >

6* &«

we have m = smt.

Since air obeys the Generalized Gas Law very closely, it is considered for this reason a very good standard. The weight of air has been determined very accurately, and it has been found that one liter of air at o° C. and 760 mm. pressure at sea-level in the latitude of 45° weighs 1.293 grams. If one liter under standard conditions weighs 1.293 grams, then 22.4 liters, the gram-molecular volume, weighs 28.96 grams. If we now substitute this value for m, in the equation above, we have m = s X 28.96. That is, the molecular weight of a gas is equal to its specific gravity

DETERMINATION OF MOLECULAR WEIGHT 31

expressed in terms of air multiplied by 28.96, which is the weight of 22.4 liters of our standard (air). So, to determine the molecular weight of a gaseous substance we need only determine its specific gravity with respect to air, and mul- tiply this by 28.96. This is nothing more than finding the weight of the gas that would occupy one gram-molecular volume under standard conditions.

It is not even necessary to determine the specific gravity with respect to air, but any other gas may be used as a standard. In that case, however, we have to multiply the specific gravity with reference to that particular gas as a standard, by an entirely different factor. For instance, if we use hydrogen as our standard, the weight of the gram- molecular volume, 22.4 liters of hydrogen, is 2.016 grams, and the equation would then become m = SH X 2.016. If we use oxygen as the standard, we have m = s0 X 32, i.e. the specific gravity of the gas with reference to oxygen multi- plied by 32 is equal to the molecular weight of the gas.

From what has preceded, in order to determine the molecu- lar weight of a gaseous body, all we need to do is to deter- mine the specific gravity, and from this to calculate the amount by weight that will occupy the gram-molecular volume, 22.4 liters, under the standard conditions of tem- perature and pressure. This number we call the formula weight, or molecular weight.

The two chief methods for the determination of vapor densities are the Dumas method and the Victor Meyer method. Only a brief description of the principles of these methods will be given. The technique of the operations may be found in the laboratory manuals on physico-chemical methods.

Dumas' Method. — A weighed glass bulb of about 200 cc. capacity, into which some of the substance has been in- troduced, is immersed in a water-bath, the temperature of which is kept about 30° above the boiling-point of the sub-

32 PHYSICAL CHEMISTRY

stance. When the substance is all in the form of vapor, the end of the bulb is sealed, at which time the temperature of the bath is recorded, and also the barometric pressure. The bulb is then removed, cooled, and weighed, and the weight of substance found. By filling with water at known temperature and weighing, the weight of the water is found by difference. The volume which this weight occupies is found from tables of densities of water at different temperatures. Then, knowing the volume, temperature, and weight of the substance, and the barometric reading, the density and specific gravity can readily be calculated. This method is but little used at present.

The Victor Meyer Method. — The Victor Meyer method consists in measuring the increase in volume of a quantity of air, caused by introducing into it a weighed quantity of the substance whose density is to be determined, and vaporiz- ing it. The vaporized substance displaces an equal volume of air, and this displaced volume of air is collected and measured, and at the same time its temperature and the barometric pressure are observed and recorded. This then gives the weight of the substance taken, and the volume, temperature, and pressure, from which the density, specific gravity, and the molecular weight can readily be calculated.

Molecular Formulae and Formula Weight. — Having just seen how the molecular weight of a gaseous substance can be obtained, we can ascertain the formula which expresses not only the relative quantities of the component elements, but also the weight of the substance which occupies a gram- molecular volume. Such formulae we designate as molecu- lar formulae, and they are now employed to represent the quantity of the substance designated by the molecular weight, whether it exists in the gaseous, liquid, or solid condition. Suppose benzene is found by analysis to con- tain 92.25 per cent of carbon and 7.75 per cent of hydrogen.

DETERMINATION OF MOLECULAR WEIGHT 33

Then in every 100 g. of the substance we should have as

Q 2 2 C

many symbol weights of carbon as - — , or 7.69, and of

hydrogen as -^~r, or 7.69. That is, for every symbol

weight of carbon there is one of hydrogen ; there are the same number of symbol weights of the two elements. As- suming the simplest number present, the empirical formula is CH. The specific gravity of benzene with respect to oxygen is 2.47 at 100° C. The molecular weight is, there- fore, 2.47 X 32 = 79.04, which is nearly six times the sum of the symbol weights of carbon and hydrogen as repre- sented by the empirical formula. The molecular formula is therefore CeHe, and the molecular weight is 78.06.

Symbol Weight. — The symbol (or atomic) weight of an element may be deduced from the molecular weights of its gaseous elements in the following manner : In order to ascer- tain the symbol weight of hydrogen a large number of gaseous compounds are selected which contain hydrogen, and the molecular weight of these substances is ascertained from density and specific gravity determinations. In Table I are given the names of the substances, in the second column the molecular weights, i.e. the grams of the substance that occupy 22.4 liters under standard conditions of temperature and pressure, while in the third column is given the number of grams of hydrogen found by analysis in the amount of the substance represented by the molecular weight given in the second column. In the last column is the greatest common divisor of the weights of hydrogen in column three, times the factor by which it is multiplied to give the amount of hydrogen in these various gram-molecules of the gases. Now in the case of hydrogen, the greatest common divisor of the quantities of this element appearing in the gram- molecules of these various substances is i g. ; hence we take the symbol weight of hydrogen to be i. Proceeding in a

PHYSICAL CHEMISTRY

similar manner, we can compile tables for other elements such as given for nitrogen.

TABLE I

HYDROGEN

NITROGEN

Compound

Hydrochloric acid . . .

S6.S

Ammonia . .

Xi4

Hydrobromic acid . .

Nitric oxide . .

Xi4

Hydriodic acid

128

Nitrogen peroxide

Xi4

Water

Methyl nitrate

Xi4

Hydrogen sulphide . .

Cyanogen chloride

61.5

Xi4

Hydrogen

Nitrogen . . .

Xi4

Ammonia

3 X

Nitrous oxide . .

Xi4

Hydrogen phosphide . .

Cyanogen . . .

Xi4

Methane

4 X

_, _ __

Ethane

(j. C. D. — 14

G. C. D. = i

In general, if an element has a large number of volatile compounds whose molecular weights can be obtained from their vapor densities, the symbol weight may be obtained in the manner just illustrated. As the weights of the ele- ment that are contained in the molecular weights of its com- pounds must be equal to its symbol weight (atomic weight) 1 or must be multiples of it, if we take the greatest common divisor of these weights, it must be a simple multiple of the symbol weight, or the symbol weight itself. It is hardly probable, however, that where there are a large number of volatile compounds of the element, the common divisor is a multiple of the symbol weight, but it is possible that another substance may be discovered, the molecular weight of which contains a weight of the given element which is not a mul- tiple of our greatest common divisor. Thus the symbol weight as determined in the manner indicated above would

1 The term symbol weight has been used in this book for what is usually termed atomic weight. Atomic weight is discussed in the fol- lowing chapter.

DETERMINATION OF MOLECULAR WEIGHT 35

not be the true one ; however, those so obtained have a high degree of probability.

If, however, there are but very few volatile compounds containing the element, which are available for vapor den- sity determinations, the method may fail. There are a number of other methods, however, for obtaining the molecular weight of substances, and these values may be used in our tabulations just as well as those obtained through the vapor density relations.

Some of the more recently discovered elements, the gases argon, helium, xenon, etc., are supposed to be elementary, and to contain only one symbol weight in their gram-molec- ular weight. As they form no compounds, we cannot use the method just suggested for determining the symbol weights. If, however, we remember that the molecular weight is the weight of the substance that occupies 22.4 1. under standard conditions of temperature and pressure, we can find the molecular weight by ascertaining the number of grams of the gas that are contained in a gram-molecular volume.

We have just seen that by our volumetric method we may determine which of several quantities is the correct one for the symbol weight of an element ; but in order to determine these values with a high degree of accuracy, it is necessary to employ quantitative gravimetric methods. By the above methods it is possible to determine which of a number of values is the correct one for both the symbol weight of elements and also the molecular weight of the compounds.

The International Committee on Atomic Weights publishes periodically a table of values, which it designates the Atomic Weights, based upon the unit of oxygen taken as 16 and representing relative weights.

CHAPTER V ATOMIC AND MOLECULAR THEORIES

FROM observed experimental scientific facts, conjectures are made as to how other substances react and these are employed as the starting point for additional experimentation and investigation. This is regarded as a working hypothesis. While a hypothesis is a tentative speculative conjecture of the causes for the observed facts, it is an assumption which goes beyond these observed facts and is to be used as a basis for their arrangement and classification as well as that of all other facts of the same class.

When a hypothesis explains all of the known facts, then it ranks as a theory. A theory is defined as " a systematic generalization seriously entertained as exclusively or emi- nently accounting for a series or group of phenomena." As soon as a number of facts are collected which the theory does not accord with or explain, the theory becomes unten- able, and a new one has to be formulated which will har- monize with the known facts. We have hypotheses and some theories undergoing frequent changes, as they always contain unproved assumptions.

How our path of progress is blazed out and marked is indicated by the following quotations from two noted pioneer investigators.

Tyndall states : " We are gifted with the power of im- agination, and by this power we can enlighten the darkness which surrounds the world of the senses. Bounded and con- ditioned by cooperant reason, imagination becomes the

ATOMIC AND MOLECULAR THEORIES 37

mightiest instrument of the physical discoverer. ... By his observations and reflections in the domain of fact the scientific philosopher is led irresistibly into the domain of theory, his final repose depending on the establishment of absolute harmony between both domains."

Faraday wrote : " The world little knows how many of the thoughts and theories which have passed through the mind of an investigator have been crushed in silence and secrecy by his own severe criticism and adverse examina- tion ; that is, in the most successful instances not a tenth of the suggestions, the hopes, the wishes, and the preliminary conclusions are realized."

THE ATOMIC THEORY

That matter is not continuous, but composed of minute, indivisible particles or atoms is a very ancient idea. This idea was purely speculative and not founded on observation or experiment. Democritus (460 B.C.) attributed the dif- ference in substances to the atoms of which they are con- stituted, and these atoms he considered to be different in size, shape, position, and motion. Lucretius (50 A.D.) for- mulated the ideas of the atomic constitution of matter in practically the form in which it is familiarly expressed to-day. The following are his conclusions :

1 . In a solid the atoms are squeezed closely together ; in a liquid the atoms are similar and less closely packed ; while in a gas there are but few atoms and they have considerable freedom of motion.

2. Atoms are imperishable, of a finite number of different shapes, each shape being infinite in number.

3. The atoms are always in motion and move through space at a greater speed than sunlight.

4. The properties of substances depend upon the manner in which the atoms combine.

During the seventeenth century the atomic conception of

38 PHYSICAL CHEMISTRY

the composition of matter was very popular and was em- ployed by Bacon, Boyle, Hooke, and others. Newton showed that Boyle's law of gases must necessarily follow from this assumption.

The two Irish chemists, Bryan Higgins (1737-1820) and his nephew and pupil, William Higgins (1765-1825), were among the first to seek quantitative relation between the atoms and to attempt to determine the number of atoms which combined to produce a new compound. They con- cluded that combinations took place most readily between the single ultimate particles of two substances, and William Higgins emphasized the law of multiple proportions, and also the greater stability of the products formed by the union of these single particles (atoms).

These views are substantially the same as those formu- lated later by Dalton, as early as 1803. The Daltonian Atomic Theory was based on facts obtained by experiment and was Dal ton's method of explaining these weight relations that he had obtained.

Dal ton's Atomic Theory is stated as follows :

1. Atoms are the smallest ultimate particles attainable and therefore cannot be subdivided by any known chemical means.

2. An elementary substance is composed of an enormous number of these particles, called atoms, which are of the same kind and equal in weight.

3. Atoms of different elements have different properties, such as weight, affinity, etc.

4. Chemical compounds are formed by the union of the atoms of different elements in the simplest numerical pro- portions.

In 1808, Dalton in his statement of the atomic theory emphasized how important it is to be able to arrive at a knowledge of the relative weights of these ultimate particles which combine to form compounds, and that these relative

ATOMIC AND MOLECULAR THEORIES 39

weights serve as a guide in obtaining the composition of other substances. These relative weights he collected in 1803 in what was termed a Table of Atomic Weights.

Dal ton considered atoms, the ultimate particles of com- pounds, as the ultimate particles of elementary substances. He assumed for example that one atom of hydrogen unites with one atom of oxygen to produce one atom of water. In the development of these atomic weight relations many discrepancies arose which were difficult to reconcile. Gay Lussac presented his Law of Combining Proportions by Volume (about 1 801-08), which is, that the weights of equal volumes of gaseous substances are proportional to their combining weights or, as Dal ton called them, atomic weights.

It has been shown that definite quantities by weight of certain substances called elements unite to form new sub- stances termed compounds ; it has further been demon- strated that when one element combines with another in two or more different ratios forming different substances, the quantities of the first element combining with a unit quantity of the second are in simple, integral ratios. It has further been shown by Gay Lussac, and has subsequently been confirmed, that when reacting gaseous elements com- bine, the volumes of the different gases under the same con- ditions of pressure and temperature are in simple ratios to one another and to the resulting gaseous product. The following facts will serve as examples :

I. i. The combination of one volume of chlorine, bromine, or iodine with one volume of hydrogen to form two volumes of the re- sulting compound.

2. The combination of one volume of chlorine with one volume of iodine to form two volumes of the resulting compound.

3. The substitution of chlorine, bromine, iodine, fluorine, and cyanogen in many organic compounds are reactions of equal volumes.

40 PHYSICAL CHEMISTRY

II. i. The combination of one volume of oxygen, or one volume of the vapor of sulphur or selenium, with two volumes of hydrogen to produce two volumes of the resulting product.

2. The combination of one volume of oxygen with two volumes of chlorine.

3. The combination of one volume of oxygen with two volumes of nitrogen.

III. i. The combination of one volume of nitrogen with three volumes

of hydrogen to form two volumes of the resulting product. 2. The combination of one volume of nitrogen with three volumes of chlorine.

As illustrated above, if a definite volume of hydrogen combines with chlorine, it has been shown experimentally that this volume of chlorine is the same, under the same conditions of temperature and pressure, as that occupied by the hydrogen with which it combined. We have seen that the law of combination by weight holds true and that it is abso- lutely exact. There must, therefore, be some weight rela- tion existing between these volume relations, since they combine with one another in such simple integral ratios. If we take the quantity of oxygen that is equivalent to the arbitrarily selected amount of our arbitrarily selected Unit of Reference, and the same volume of hydrogen under the same conditions of temperature and pressure, we shall find that the oxygen weighs 15.88 times as much as the hydrogen. If we take 16 g. of oxygen, the same volume of hydrogen will weigh i .008 g. This same volume of chlorine weighs 35.45 g. and the same volume of nitrogen weighs 14.0 g., it being understood that the volumes are under the standard condi- tions of temperature and pressure. It will be recalled that these numbers are the same as those representing the symbol weights of the elements hydrogen, chlorine, and nitrogen.

If we take the quantities of gaseous elements equivalent to these weights, called by Dalton atomic weights, the volumes which these occupy under the same conditions of temperature and pressure will be the same. Dalton con-

ATOMIC AND MOLECULAR THEORIES 41

eluded that in equal volumes of different gases at the same temperature and pressure there were not the same number of ultimate particles. Gay Lussac showed that the combining weights (or some multiple) of different substances were pro- portional to their densities. In 1811 Avogadro accepted this law of Gay Lussac and concluded that the number of " integral molecules " in equal volumes of all gases is the same for the same temperature and pressure. Avogadro insisted that if we were to assume the molecules of elementary gases identical with the atoms, the volumetric relations could not be explained, as it would'necessitate the subdivision of some of the atoms. It was this particular feature which met with such marked opposition from Dalton and his contem- poraries and at that time prevented the acceptance of Avo- gadro's hypothesis. Hence the existence of small particles of two different orders, the molecules and the atoms, as advo- cated by Avogadro, received little notice and the revival of the idea by Ampere in 1814 did not succeed in having it accepted.

For the next forty or fifty years a rather chaotic condition prevailed, and very little progress was made in the develop- ment of a system of atomic weights. In 1860 a conference of chemists met at Karlsruhe for the purpose of discussing the subject and eliminating the confusion arising from the use of the four systems of atomic weights then in use. These methods were that of : (i) Dalton, based on weight relations and chemical analysis ; (2) Berzelius, based partly on chemi- cal analysis, partly on physical principle (the Law of Iso- morphism) and partly on the Law of Combining Propor- tions by Volume, all of which did not differentiate between atom and molecule ; (3) Gmelin's weight method ; and (4) Gerhardt and Laurent's method, in which a realization of Avogadro's hypothesis was manifest, and had a far- reaching effect. The work of Cannizzaro, in 1858, revolu- tionized the atomic weight methods by making Avogadro's

42 PHYSICAL CHEMISTRY

hypothesis the basis of his system ,and thus established our modern system of atomic weights. This work was brought to the attention of those chemists while in session at Karlsruhe.

It was by affirming the universal applicability of Avo- gadro's supposition that Cannizzaro stated that results are obtained which are in keeping with certain formulated laws of chemistry and physics. Avogadro's method of deter- mination of molecular weights, which had been practically abandoned, was revived by Cannizzaro, who changed the unit to which vapor densities were referred and restated it as follows : " Instead of taking for your unit the weight of an entire molecule of hydrogen, take rather the half of this weight, that is to say, the quantity of hydrogen contained in a molecule of hydrochloric acid."

By using the hypothesis of Avogadro, Cannizzaro ex- amined the relative weights of compounds, the composition of which he determined, and described his method in the fol- lowing exact terms : "If the body is a compound, it is analyzed and the constant weight-relations of its constituents are determined ; the molecular weight is then divided into parts proportional to the relative weights of the compounds, and the result is the quantities of the elements contained in the molecule of the compound, referred to the same unit (namely, the semi-molecule of hydrogen) as is used for the expression of all molecular weights."

Cannizzaro 's law of atoms has made it possible to express the composition of molecules in terms of their constituent atoms, for all gaseous and gasifiable compounds, and was stated by him as follows :

By comparing the different quantities of one and the same element which are contained, either in the molecules of the free elements, or in the molecules of its compounds, the fol- lowing law stands out in relief : " The different weights of one and the same element contained in the various molecules are

ATOMIC AND MOLECULAR THEORIES 43

always whole multiples of one quantity, which is justly called the atom, because it invariably enters the compounds without division."

The atom of an element, Cannizzaro said, " is expressed by that quantity of it which invariably enters as a whole into equal volumes of the simpler substance and its com- pounds ; this quantity may be either the whole quantity con- tained in a volume of the free element or a fraction thereof." However, " In order to determine the atomic weights of any element it is essential to know the molecular weights, and the compositions, of all or most of its compounds."

We then have described by Cannizzaro a clear picture of the interrelations of all the fundamental conceptions of Dalton and Avogadro, which were at their time practically discarded ; in this way there was developed a complete theory which " placed the atomic weights of the metallic elements on their present consistent bases." Cannizzaro thus advanced the theory of atomic equivalency, which em- phasized " the unchangeability of the proportions between the atomic weights of the bodies which usually replace one another, whatever be the nature and number of the other constituents of the compounds." This is a law which limits the number of possible compounds and more especially applies to all cases of double exchange.

THE MOLECULAR THEORY

This is the method for the determination of the combin- ing or atomic weights which is employed at the present time, and which is illustrated in the following consideration :

For chemical reasons, chemists have accepted Avogadro's hypothesis, which leads to the molecular structure of matter. This hypothesis, known as the Molecular Theory of Matter, conceives matter as discontinuous and made up of minute particles called molecules. The molecules of the same sub- Stance are assumed to be alike in all respects. The mole-

44 PHYSICAL CHEMISTRY

cules are considered to be practically independent, with space between them, and may be defined as " that minute portion of a substance which moves about as a whole so that its parts, if it has any, do not part company during the excursions the molecule makes ; and the molecular weight is the weight of this ultimate particle referred to the weight of the molecule of a standard substance."

As a working hypothesis this assumption of Avogadro has been very fruitful, as the following illustration indicates.

i. Hydrogen and chlorine unite to produce hydrochloric acid.

Facts. We have determined experimentally :

i . Equal volumes of hydrogen and chlorine react to pro- duce two volumes of hydrochloric acid.

Hydrogen + Chlorine = Hydrochloric acid

i vol. + i vol. = 2 vols.

2. By analysis it has been shown that hydrochloric acid consists of hydrogen and chlorine in the ratio of one symbol weight of hydrogen to one symbol weight of chlorine.

Assumptions.

1. In unit volume let us assume that there are n molecules.

2. According to Avogadro's assumption equal volumes contain an equal number of molecules.

Since there are two volumes of hydrochloric acid, accord- ing to Avogadro's hypothesis this volume must contain twice as many molecules of hydrochloric acid as there are molecules of hydrogen in the one volume of hydrogen. That is, one volume of hydrogen contains n molecules of hydrogen, and two volumes of hydrochloric acid contain 2 n molecules of hydrochloric acid.

ATOMIC AND MOLECULAR THEORIES 45

It follows that the number of atomic weights of hydrogen in 2 n molecules of hydrochloric acid must be the same as in the n molecules of hydrogen.

If we assume, for simplicity, that each molecule of hydro- chloric acid contains one atom of hydrogen, then 2 n mole- cules of hydrochloric acid will contain 2 n atoms of hydrogen ; but these 2 n atoms of hydrogen must have been furnished by the n molecules of hydrogen. Therefore, one molecule of hydrogen must contain at least two atoms of hydrogen, and the formula is written H2, which represents the molecule of hydrogen. Similarly the molecule of chlorine may be shown to contain two atoms, and its formula is C12.

By pursuing a course of reasoning analogous to the above, it may be shown that the molecules of some other gaseous elements consist of at least two atoms. By grouping the symbols of the elements we obtain the formula of the ele- ment which represents the molecular weight and indicates the number of atoms of each element present in the molecule.

CHAPTER VI

DEVIATIONS FROM THE GAS LAW AND DISSOCIATION OF GASES

IT has already been stated that only for ideally perfect gases does the Gas Law Equation hold, but in the case of O2, N2, H2, and air the deviations are so small for moderate ranges of pressure and temperature that they conform to the laws very closely and therefore may be considered for all practical purposes as perfect gases. Although these de- viations are small, they are real, and there must be certain causes which produce these deviations from the theoretical laws.

Deviation from Boyle's Law. — If gases are subjected to very high pressures, the change in volume does not conform

too

FIG. 2.

to Boyle's Law : Vo : V : : p : po, or Vo X po = Vp, or Vp = constant. Or, expressed graphically, we would have the curve as represented in Fig. 2.

But the experimental results of Amagat on the effects of high pressure show that the value of p V is not a con-. stant for different pressures, and this is illustrated by the data given in Table II.

DEVIATIONS FROM THE GAS LAW TABLE II — Value of pV at o° C.

HYDROGEN

ATP

CARBON

IjTH YL EN E

IN ATM.

t\lR

DIOXIDE

100

.069

0.9265

0.9910

0-973

0.2O2O

0.310

2OO

.138

0.9140

1.039

I.OIO

0.385

0.565

300

.209

0.9624

1.136

1.097

0-559

0.806

500

.3565

1.1560

1.390

1.340

0.891

1.256

700

•504

1.385

1.662

1.602

1. 206

1.684

IOOO

.7200

1.7350

2.068

1.992

1.656

2.289

15-4° C.

15.6° C.

1 6° C.

15-7° C.

1000

1.893

1.800

2.134

2.062

1500

2.240

2.357

2.8995

2.661

2000

2.562

2.888

3.398

3.286

2500

2.870

3-375

3-990

3.855

3000

3.162

3.888

4.569

4.398

These data are represented graphically in Fig. 3.

Atmos.

FIG. 3.

PHYSICAL CHEMISTRY

From Fig. 3 it is apparent that with increase of pressure the value of pV first decreases, reaches a minimum, and then increases, except in the case of hydrogen, where we have only the portion of the curve representing an increase in the value of pV, which led Regnault to call hydrogen a " more than perfect gas," because the volume was not decreased as much as it should be according to Boyle's Law. That por- tion of the curve of all gases which represents the high pres- sure shows that the gases are not compressed as much as they should be according to Boyle's Law.

Confirmation of these results is found in the work of Wit- kowski, Kamerlingh Onnes and Brook, Ramsay and Young,

Barus, and others. The change of the value of p V with the change in p at various temperatures has been obtained by these workers, and this is illustrated in Fig. 4.

It appears, then, that there must be a particular temperature for each gas at which the depression in the isothermal just disappears, so that it is horizontal through a considerable range of pressures. At this temperature a gas follows Boyle's Law exactly, up to a fairly high pressure, and behaves to this extent like an ideal or perfect gas. This is also true for a short dis- tance at and near the minimum value for pV, while at the high pressures the isotherms approxi- mate nearly parallel straight lines. Low Pressures. — In the case of very low pressures, there is not so marked a variation, and the conformity to Boyle's Law is more marked. Experimentation along this line has

100 ZOO

Pressure In- Atmosphere

FlG. 4.

DEVIATIONS FROM THE GAS LAW 49

been carried out by Mendeleeff, Amagat, Ramsay and

Barly, Battelli, Rayleigh, Regnault, Leduc, and others. The

conclusion from their work is that in the equation ^ = b,

where V is the larger volume and p is the smaller pressure, the value of b approaches and finally reaches unity as the pressure falls. In the case of hydrogen the value rises, and for other gases it falls. For the range of pressures, of 75 to 150 mm. the differences from unity are quite negligible in the cases of hydrogen, air, and probably nitrogen. There is a slight difference in the case of oxygen, but this difference disappears at still lower pressures. For N2O the value of b is fairly high between 75 and 150 mm. The following are the values of b obtained by Rayleigh :

b Air ....... ..... 0.99997

H2 ............ 0.99997

O2 ............ 1.00024

Argon ........... 1.00021

N2O . ........... 1.00066

While the deviations from Boyle's Law are apparent, they are so small at low pressures that they are difficult to detect, even by very accurate experiments, yet they prove that these gases do not follow Boyle's Law absolutely.

Deviation from Charles' or Gay Lussac's Law. — The co- efficient of expansion of gases varies with a change of tem- perature and pressure. This is emphasized in the case of ethylene in Table III, taken from Amagat's data.

The pressure remaining constant, the horizontal lines in Table III show a variation of the coefficient of expansion with the change of temperature. There is no regularity in the change, but, in general, at higher temperatures the variation is less than at lower temperatures. The vertical columns show a marked decrease in the coefficient of expansion with increased pressure. The minimum value of the coefficient

PHYSICAL CHEMISTRY

of expansion corresponds closely with the minimum values for pV.

TABLE III — COEFFICIENTS OF EXPANSION OF ETHYLENE

PRESSURE METERS OF MERCURY

3o0-4o°

40°-SO°

6o°-8o°

8o°-ioo°

.0084

.0064

.0646

.0040

.0166

.0178

.0097

.0067

.OI2I

.0195

.0132

.0088

IOO

.0079

.0108

.0121

.OIOO

I2O

.OO62

.0075

.0095

.0082

I4O

.0048

.0062

.0076

0068

1 6O

.0041

.0057

.0061

.0058

2OO

.0034

.0043

.0044

240

.0030

•0035

.0036

•0034

280

.0027

.0031

.0030

.0029

320

.0025

.0027

.0024

This is in confirmation of the results of Regnault, who showed that no gas is really perfect, but he concluded that the coefficients for different gases become more and more nearly equal as the pressure falls, and that the statement that the coefficients are equal may be taken as correct only for very low pressures.

The relations of the coefficient of expansion and the co- efficient of increase of pressure are given in Table IV, com- piled by Young. At constant pressure, Vt = VQ(I + a/), where a is the coefficient of expansion ; at constant vol- ume, pt = po(i + (3t), where ft is the coefficient of increase of pressure and p is the constant pressure at which a was determined, and p0 the initial pressure in the determina- tions of /3.

Gay Lussac believed that all gases had the same coefficient of expansion at constant pressure and that this was 1/273 or 0.0036675 of the original volume at o° C. and under a pressure of one atmosphere, and since they obeyed Boyle's

DEVIATIONS FROM THE GAS LAW

Law they therefore all had the same coefficient of increase of pressure (|3) at constant volume, i.e. a = (3.

TABLE IV

GAS

OBSERVER

(o°-"oo°)

ft (o°-ioo°)

Hydrogen . .

Regnault

0.003661

i atmos.

0.003668

Hydrogen . .

Chappuis

0.00366004

i meter

0.00366254

Hydrogen . .

K. Onnes and Bondin

i meter

0.0036627

Hydrogen . .

Richards and Marks

0.0036609

Hydrogen . .

Travers and Jaquerod

700 mm.

0.00366255

Hydrogen . .

Travers and Jaquerod

500 mm.

0.0036628

Helium . . .

Travers and Jaquerod

700 mm.

0.00366255

Helium . . .

Travers and Jaquerod

500 mm.

0.0036628

Nitrogen . . .

Regnault

i atmos.

0.003668

Nitrogen . . .

Chappuis

0.00367313

i meter

0.0036744

Nitrogen . . .

Chappuis

530.8 mm.

0.0036638

Air

Regnault

0.003671

i atmos.

0.003665

Oxygen

Makower and Noble

mean values

663.38 mm.

0.0036738

Oxygen . . .

Makower and Noble

353.99 mm.

0.0036698

Carbon monoxide

Regnault

0.003669

i atmos.

0.003667

Carbon dioxide

Regnault

0.003710

i atmos.

0.003688

Carbon dioxide

Richards and Marks

0.0037282

Sulphur dioxide

Regnault

0.003903

i atmos.

0.003845

Nitrous oxide

Regnault

0.003719

i atmos.

0.003676

ft (o°-io67°)

Nitrogen . . .

Jaquerod and Perrot

240

0.0036643

Air

Jaquerod and Perrot

230

0.0036643

Oxygen . . .

Jaquerod and Perrot

180-230

0.0036652

Carbon monoxide

Jaquerod and Perrot

230

0.0036648

Carbon dioxide

Jaquerod and Perrot

240

0.0036756

Carbon dioxide

Jaquerod and Perrot

170

0.0036713

Chappuis found as the average of the values for the co- efficient of expansion of nitrogen 0.00366182, and Berthelot found for the values of hydrogen: 0.00366248, 0.00366206, and 0.00366169. The mean of the values of nitrogen and

hydrogen gives 0.00366193, or

273.080'

i.e. a =

273.1

o° C. = 273.1° absolute.

These variations from the laws of Boyle and of Gay Lussac are but slight in the case of those gases which are

52 PHYSICAL CHEMISTRY

difficult to liquefy, such as hydrogen, nitrogen, air, oxygen, etc., but the variations are very pronounced in the case of those which are readily liquefiable, such as sulphur dioxide, carbon dioxide, ethylene, etc. Various efforts have been made to explain these variations from The Gas Law, which we have seen show that at low pressures some gases are too compressible, while under high pressure they are not com- pressible enough. Among the most fruitful of the expla- nations offered is the one of van der Waals. There is an- other type of variation from The Gas Law in the case of certain other gases which give abnormal values for the den- sity with increased temperature. This variation is explained upon the supposition that the gas molecules are dissociated with the formation of new chemical individuals.

VARIATIONS FROM THE GAS LAW AS EXPLAINED UPON THE BASIS OF DISSOCIATION OF THE GAS

Attention has been called to the fact that a number of substances do not conform to the Gas Law Equation and that the vapor density determinations give abnormal values for the molecular weights. It was recognized by the ear- lier workers that the results must be due to abnormal molecular conditions and that Avogadro's hypothesis did not hold for these cases, such as ammonium chloride, phos- phorus pentachloride, nitrogen dioxide, etc. Almost simul- taneously Cannizzaro (1857), Kopp (1858), and Kekule* (1858) advanced the idea that these abnormal values were due to the decomposition of the substance. This decom- position was termed dissociation by St. Claire Deville (1857). This assumption of the dissociation of the gaseous mole- cules to account for the low density was not readily accepted, and it devolved upon the champions of the idea to prove that dissociation did take place.

The following four typical examples were employed to prove the dissociation of these substances :

DEVIATIONS FROM THE GAS LAW 53

1 . Deville found on raising the temperature of PC15 that at high temperatures the colorless gas became decidedly green. This may be explained by the following equation : PC15 = PCla -f C12 ; the green color being due to the chlorine gas present.

2. On heating N2O4, which is colorless, it becomes dark brown, and on cooling it decolorizes again. Salet showed (1868) that the color varied with the vapor density. Under high pressures approximately normal densities for N2O4 are obtained, while at high temperatures and low pressures, values approximating that of NO2 are obtained, and hence we conclude that the brown color is due to NO2.

3. Pebael heated ammonium chloride which had been incorporated in an asbestos plug. During the heating a current of air was passed through the tube. By means of litmus paper he proved that an excess of hydrochloric acid was present in one end of the tube, while at the other end ammonia was in excess. Thau used nitrogen instead of air, and by a slight modification of the method confirmed the dissociation of ammonium chloride.

4. In the case of chloral hydrate, Toost proved that the low density was due to dissociation by distilling chloral hydrate (melting point 57° C.), and collecting its vapor in chloroform. Chloral dissolves but the water does not ; hence he concluded that the chloral hydrate was dissociated according to the equation

CC13 • CH(OH)2 = CC13 • CHO + H2O.

The presentation of these data soon resulted in the general acceptance that dissociation was the cause of the abnormal values of the densities.

One of the common applications of dissociation is made use of in cleaning the soldering iron by rubbing it against solid ammonium chloride, the liberated hydrochloric acid acting as the cleaning agent. Commercial hydrochloric acid is now used extensively for that purpose.

54 PHYSICAL CHEMISTRY

Degree of Dissociation. —

Let a. = degree of dissociation or per cent dissociation

n = number of molecules / = number of parts into which each molecule is disso-

ciated

then an = number of molecules dissociated n — an = number of molecules undissociated

anf = number of parts resulting from dissociated molecules n — an + anf = total number of parts or molecules after dissociation. Let i denote the ratio of the number of molecules after dissociation to the number of molecules before dissociation,

Then i = n-cin+anf OT l _ a + a l

That is i = I + (/ - i)a or a = -*-=-^ (2)

Let p = density before dissociation

Pi = density after dissociation V = volume before dissociation Vi = volume after dissociation n = number of molecules before dissociation n — an + anf = number of molecules after dissociation.

Since , =

mass and*-

From Avogadro's Hypothesis = n ~ an + anf

Substituting we have £ = n ~ an + anf = !-«+«/

pi n

and solving for a we have a = P~Pl- (3)

Pi(f- 0

If 5 is the specific gravity before dissociation and 5i the specific gravity after dissociation, then from page 5, p = sps and pi = Sips. Substituting in formula (3) we have

Sps — Sips S — Si

r' ^ or « -

slPs(f-i)

DEVIATIONS FROM THE GAS LAW 55

If * = ^,we have « = — £ - ^^ = k.

rj /

That is, the degree of dissociation is complete, or 100 per cent.

If a substance dissociates into 2 parts, its vapor density

Pi = -, that is, £ of original density. If into 3 parts, pi = - 2 3

that is, \ of its original density. But if pi = p, then a = o and no dissociation takes place.

EXAMPLE. — At 90° C. the specific gravity of nitrogen peroxide (N2O4) is 24.8 (H = i). Calculate degree of dissociation.

''• a = J/"-*) = 2^8 7/- i) = °'8547 '' •'• 8547 per cent dissociated.

EXAMPLE. — When 5 g. of ammonium carbamate NH4CO2NH2 are completely vaporized at 200° C., it occupies a volume of 7.66 liters under a pressure of 740 mm. mercury. Calculate the degree of dissocia- tion.

2 NH3 + CO2

m = 78, molecular weight of ammonium carbamate

-£- — gram-molecules = -5- m 78

(i + 2 a)— = total number of molecules m

pV = nRT: pV = -£-(1 .+ 2 a)tfr; /> = 74? atmosphere w 760

24°. x 7-66 = -^ (i + 2 a) X 0.082 X 473. 700 78

Solving, find a = 0.999 °r 99-9 per cent dissociation.

56 PHYSICAL CHEMISTRY

On complete dissociation, we have in the case of nitrogen peroxide a simple gas, while in the case of ammonium car- bamate we have a gaseous mixture consisting of ammonia and carbon dioxide. Depending upon the temperature and pressure we have, in all intermediate states, partial dissocia- tion. We see that certain gaseous substances which give abnormal values for their densities, upon the basis that they are dissociated, confirm Avogadro's hypothesis, and that the state of an ideal gas is realized when there is complete dissociation, as in the case of the undissociated gases we have previously considered.

The Law of Mass Action. — In the type of reactions we have been discussing, at ordinary temperatures and pressures the substances nitrogen dioxide and ammonium carbamate are distinct chemical individuals, the one a gas and the other a solid. If they are heated, they dissociate, with the forma- tion of new chemical individuals as illustrated in the equa- tions above. As the temperature is increased more and more, the original substance is dissociated, while at any specified temperature the products of dissociation are in equilibrium with the undissociated substance. The state of equilibrium we represent by equations, such as N2O4 ^± 2 NO2, which means that the reaction may proceed in either direction and is designated a reversible reaction ; but for any specified conditions it does proceed in both directions at the same rate, and consequently an equilibrium is thus maintained. The law governing the state of equilibrium or this statical condition of the reaction is known as the Law of Mass Action and can be developed thermodynamically ; but this particular theoretical consideration of the subject will have to be deferred, and we will illustrate the meaning of the law by applying it to a few specific cases.

Suppose we have two substances, A and B, reacting to form their resulting product, AB. Then A -f B = AB,

DEVIATIONS FROM THE GAS LAW 57

or we may have the reverse, AB = A + B, or writing as one equation we have AB ^± A + B. A more general statement would be where more substances react, forming a homogeneous system. The reaction is represented thus,

A1 + Az + A3 - ^± AS + AJ + A3' ...

which indicates that only one molecule of each substance takes part in the reaction. That this reaction takes place depends, according to the kinetic theory of gases, upon the collision of the molecules, and it is obvious that the nearer they are together the more numerous such collisions and the greater the relative number of molecules per unit space. Hence the reaction (i.e. collisions) is proportional to the concentration. Then the velocity of the reaction is propor- tional to the products of the concentrations.

Let V = velocity from left to right, and ci, c2 ••• represent the concentrations of the substances A\, A2 —, i.e. the number of gram-molecules per liter. Then the reaction equation is V = KciC2 •••, where K is a constant for the given temperature.

If the reaction proceeds in the direction from right to left, we shall have V = Kfc\c2 — , in which the terms have analogous meaning to those in the first cases.

As the values of V and V cannot be measured alone, the course of the reaction can only be given by the difference of the two values. The total reaction velocity is made up of the difference between the two partial reacting velocities ; for the change actually observed for any amount of time is equal to the reaction in one direction minus the change in the opposite direction during this same time. When the condition of equilibrium has been reached, we are not to conclude that no further change takes place ; but should assume that the change, in the sense of the reaction equation from left to right, is compensated by a change from right to

58 PHYSICAL CHEMISTRY

left, and therefore that the total change to be observed = zero, i.e. the system stands in equilibrium. Then we have for equilibrium

V - V = o, or V = V .'.Kcic2'" = K'CI'CZ '».

A more general statement would be to remove the restric- tion that only one molecule takes place in the reaction and that there is only one molecule of each molecular species produced. In that case the formula takes the following form for the Generalized Mass Law Equation :

gl*.g.*. ,.«.... =IC k a Qon

ci'n*' • c2'n3' • c3'n3' - K

which is termed the equilibrium constant; but where applied to dissociation phenomena it is termed the dissociation constant.

Now applying this Mass Law Equation to the simplest case of dissociation, when a compound AB dissociated into the two parts A and B, we have AB ^± A + B,

(1) Kci = cz • cz. If the reacting substance is made up of like parts, then we have

A i ^± 2 A 2, which becomes

(2) Kci = C22, which is obtained from the above when c2 = cz. That is, where the substance dissociates into two like constituents.

Let c, the concentration = g/no' of L™1™\ Substitut-

FV vol. /

ing this value for the concentration in equations (i) and (2) we have

VJ V V

DEVIATIONS FROM THE GAS LAW 59

Now since n% = n$, we have

which becomes

That is, increasing the volume produces a relative increase of dissociation.

Many times it is difficult to determine the concentration of the components. We can avoid the necessity of doing so by introducing the pressure factor and measuring that instead of determining tjie concentration. The final form of the Gas Law Equation was

pV = nRT (3)

which becomes

n p ' V RT

But since — = c, we have c = -*• — V RT

The concentrations are directly proportional to the pres- sures. The equation then becomes

c = Idp. (4)

Now, since concentration is proportional to the pressure, for c\ we may substitute K\p in the equations above, and we have for equation (2) Kc\ = (c22) the following

K(KlPl) = (Kzp,Y or

Now since K—± represents a new constant, we may ex- press this by some single letter, as k, hence we have k = &->

60 PHYSICAL CHEMISTRY

This gives us the pressures due to the individual constituents of the gas mixture, and these are designated the partial pressures. The total pressure P is the sum of the partial pressures, i.e. P = pi + pz. This is Dalton's Law. From a consideration of The Gas Law we have, for several molecu- lar species occupying the same volume at the same tempera- ture, the relation ^ = — '• p2 nz

Mixtures of Gases. — We should expect that the most simple relations would be found to exist in the case of mix- tures of different gases. Such is the case where there is no chemical action between the gaseous particles. Each gas remains unchanged and conducts itself as though the other one was not present. The pressure exerted upon the walls of the containing vessel, the capacity of absorbing and re- flecting light, the specific heat, etc., in fact all of the proper- ties of the gases experience no change when the gases are mixed. These particular relations should hold only in the case of ideal gases ; and as all the gases only approximately follow The Gas Law, we should expect to find some slight deviations when the gases are mixed.

Dissociation of Gases. — Let us consider the following cases :

(i) PC15 ^± PC13 + C12 and (2) 2 HI ^± H2 + I2. Applying the mass law, we have

Kci = c2 • c3. Kci2 = c2 - c3.

Expressing concentrations in terms of number of mole- cules in unit volume, we have

7^wi_=tt2 nj x^ = ^ ^

V .V. V V2 V ' V*

Multiplying through by V, and by V2,

Kn, = 25- Km2 = n, • n3.

DEVIATIONS FROM THE GAS LAW 6l

In the case of PC15 the dissociation is proportional to the volume, while in HI as there is no value of V in the equa- tion, the dissociation is independent of the volume.

Introducing the pressures instead of the concentrations we have

Kipi = p2 - pi. KipS = p2 • p».

We can decrease the volume by increasing the pressure m-fold, when we shall have

which become

Kipi = p2 • mpz. Kipi2 = p2 - p3.

In the first case we have the dissociation forced back, while in the other case it is not affected by the increase of pressure, as the factor m disappears. Hence, in all cases where the number of reacting substances, i.e. the number of molecules on both sides of the equation, are equal, the change in the volume has no effect on the degree of dissociation.

Dissociation of Ammonium Carbamate. — Carbamic acid

may be considered as carbonic acid, C^OH, in which one

X)H of the hydroxyl groups (OH) has been replaced by the amido

group (NH2), C^-OH . The ammonium salt is formed by

\NH2

the direct addition of NH3, as in the reaction NH8 -f- HC1 = NH4C1, when we have (NH3)2CO2. On heating ammonium carbamate, we have

(NH3)2C02 ^± 2 NH3 + C02.

Now applying the mass law, we have

62 PHYSICAL CHEMISTRY

Since the carbamate is a solid, its concentration will re- main practically constant, and the vapor pressure is so small in comparison to the pressures of the dissociated products that it can be neglected, when we will have

Ki = C22 • ct. Substituting pressures for the concentrations, we have

K2 = p2z • pz.

But the total pressure is the sum of the partial pressures, i.e. P = p2 + ps, and since there are twice as many mole- cules of NH3 as of CO2, £2 = 2 p3. Substituting this value for pz we have

P = 2 p3 + p3 or /> = 3 p3 or p3 = £ P. Now substituting these values of p% and p3 we have ^2= (f P)2-iP or K2 = ^P^

It is evident that the addition of ammonia should force back the dissociation more than the addition of carbon dioxide.

In the case of ammonium chloride, NH4C1 ^± NH3 -f HC1, Neuberg found the density of NH4C1 in the vapor form to be 1.13, while the calculated value is 1.85. In an excess of 34.6 cc. of HC1 the density was 1.5, while in an excess of 60 cc. of NH3 it was 1.68. The dissociation was forced back by the addition of either of the components of dissociation.

Ammonium hydrogen sulphide dissociates according to the following equation :

NH4HS ^± NH3 + H2S. (solid)

Applying the mass law and using pressures, we have Kpi = p2 - p3.

But since NH4HS is solid, the concentration of NH4HS is practically constant, and its vapor pressure is so small

DEVIATIONS FROM THE GAS LAW 63

that it can be left out of consideration without introducing any appreciable error. We then have K2 = p2 • ps, and since P = p2 + ps and the number of dissociated products, NH3 and H2S, are equal, p2 = p3. Substituting p2 for p3, we have P = 2 p2 or p2 = -J P. Introducing these values in the original equation we have K2 = (^ P)2.

= |P*.

Isambert presents the following experimental data in confirmation of the dissociation constant :

VALUE OF _L_

TEMPERATURE

4-P2

Observed

Calculated

4.10° C.

37,900

37,000

7.00

60,000

58,OOO

25.1

62,500

62,750

At 25.1°, P = 501 mm., hence £P2 =-^- =62,750,

when the products of dissociation are in equal molecular quantities.

By experiment he found the following results, when the different quantities of the gases were present :

61,152 63,204 60,882 64,779 62,504

208 138 417 452

294 450 146 146

Mean

This is a close agreement with the theoretical value of approximately 62,750.

CHAPTER VII THE PERIODIC SYSTEM

DALTON presented a number of tables illustrating the " relative weight of the ultimate particles of gaseous and other bodies," but it was not until 1803 that he published his first table of atomic weights, and this was not printed until 1805. This table was on the basis of hydrogen equal to one. The other table of atomic weights that was used during the early part of the last century was that of Berze- lius, which was on the basis of oxygen equal to 100. With these relative weights of the elements available, numerous efforts were made to find relations existing between the ele- ments themselves as well as between their atomic weights and the various properties of the elements.

Prout's Hypothesis. — Among the first attempts to ex- press some relationship was that of W. Prout, in 1815, who aimed to show that the atomic weights of the elements were exact multiples of that of hydrogen, that is, that the ele- ments were aggregates of the fundamental element hydrogen. So, if the atomic weight of hydrogen be taken as unity, which was done in the atomic weight table of Dalton, the atomic weights of the other elements should be expressed by whole numbers. This hypothesis of Prout had many sup- porters, among whom was Thomas Thomson, who accepted the idea, but among those who opposed it was Berzelius, who renounced it. In the efforts to substantiate their respective positions a vigorous campaign was inaugurated, which re-

THE PERIODIC SYSTEM

suited in the early establishment of accurate values for the atomic weights.

It was found that the value given by Berzelius for carbon was wrong, and Dumas and his pupil Stas redetermined it and found the value for carbon to be exactly 12. This fact aided in making Dumas a strong advocate of Prout 's hy- pothesis and also led to the extensive accurate atomic weight determinations of Stas. It was found that about 24 out of the 70 elements had atomic weights that did not vary from a whole number by more than one unit in the first decimal place. (Of the elements listed in the Periodic Table, page 72, about half have values within one tenth of an integer.)

In Table V are given the comparative values of the atomic weights that Prout used, and the values for 191 5, one hun- dred years later.

TABLE V— (After Harkins)

ATOMIC

WEIGHTS

ELEMENTS

Prout 1815

International i9i5(H=i)

Hydrogen ...

I OO

Carbon

1 1 01

Nitrogen

IT. qo

Phosphorus

14.

?o 78

Oxygen

IS 88

Sulphur Calcium • Sodium

16 20

2J.

31.82 3976

22 82

Iron

e c JT

Zinc

•12

64 86

Chlorine

•7C 46

Potassium

A.O

18 80

Barium

1^6 ii

Iodine

I2d

12^ Qd.

The values used by Prout were the best available at that time, but the result of the accurate work of Stas and others

66 PHYSICAL CHEMISTRY

gave values, such as that of chlorine (35.5), which were hard to reconcile, and Marignac, who favored Prout's hypothesis, suggested that a unit one half that of hydrogen be selected. Then others suggested further subdivisions to account for the other irregularities, with the result that this brought Prout's hypothesis into disfavor for a time at least. In 1901 Strut t concluded from the theory of probabilities that the instances of the atomic weight approximating to or being a whole number were more numerous than chance would allow and hence were not accidental, but indicated some fundamental fact of nature. Prout's assumption, that all elements are simply condensations of hydrogen, contains the fundamental idea of the primal element or " mother substance " of which all the elements are composed and has been variously termed " earth," " fire," " protyle," hydrogen, and now the modern scientists embody this idea in the electron theory. That this idea is one of the live questions, as it was one hundred years ago, is evidenced by the extensive investigations at present along this line.1

Doebereiner's Triads. — Doebereiner (1817) arranged chemically similar elements in groups of three in the order of their symbol weights and showed that the symbol weight of the middle one was the mean of the other two. There is a constant difference in the symbol weights of succeeding members of the triads similar to the difference between homologous series in organic chemistry. It was not until 1851, when Dumas again took Up this idea of triads, that any interest was manifested ; but subsequent to this time many chemists began to investigate these relations between the

1 A large number of articles have recently been added to the already extensive literature. Among these recent contributions reference will be given to a few, such as that of Sir William Ramsay, Proc. Roy. Soc., A 92, 451 (1916) ; Parson, Smithsonian Publication, 2371 (1915) ; R. A. Millikan's recent book, The Electron (1917); G. N. Lewis, Jour. Am. Chem. Soc., 35, 1448 (1914), 38, 762 (1916) ; and Harkins, Ibid., 39, 856 (1917)-

THE PERIODIC SYSTEM

properties of the elements and the relation of their symbol weights.

Table VI, in which are given some of the more important triads, emphasizes the constant differences between the sym- bol weights.

TABLE VI

ELEMENTS

SYMBOL WEIGHTS

DIFFERENCES

MEAN OF EXTREME SYMBOL WEIGHTS

Lithium.

6 Q4.

•\f\ f\f\

Sodium Potassium

Chlorine Bromine Iodine

Sulphur Selenium Tellurium

23.00 39.10

3546 79.92 126.92

32.07 79.2 127 5

16.10

44.46 47.00

47-13 48.3

23.02 81.19 79.8

Calcium

40 o

Strontium

87 7

47-7

88.7

Barium

1-174

49-7

Phosphorus

-JT QA

Arsenic

74. Q6

43-92

75.62

Antimony . .

1 2O 2

45-24

In the following series of triads the symbol weights are practically the same :

Iron . . • 55.85 Ruthenium . 101.7 Osmium . 190.9 Cobalt . 58.97 Rhodium . . 102.9 Iridium . . 193.3 Nickel . 58.68 Palladium . . 106.7 Platinum . 195.2

J. P. Cooke (1854) pointed out that these triads did not include all of the members of the natural groups of the ele- ments, for example, fluorine was left out of the group of the closely related halogens. This idea of Cooke's emphasized the fallacy of trying to continue this method of grouping the elements into triads.

PHYSICAL CHEMISTRY

THE PERIODIC SYSTEM 69

Gladstone (1853) arranged the elements in the order of increasing symbol weights, but the values were so inaccurate that no relations were really apparent. Cannizzaro's more accurate values enabled Chancourtois a few years later (1862) to point out important and remarkable relations between the physical and chemical properties and the sym- bol weights. He arranged the elements in a spiral around a cylinder, which he divided into 16 vertical sections. The elements in any vertical section were found to have analogous chemical and physical properties. This arrangement is known as the Telluric Screw.

Newlands' Law of Octaves. — Newlands (1864-66) ar- ranged the elements in the increasing order of their symbol weights and announced his Law of Octaves as follows : " If the elements are arranged in the order of their equivalents with a few slight transpositions, it will be observed that ele- ments belonging to the same group usually appear on the same horizontal line ; members of the analogous elements generally differ either by seven or some multiple of seven. In other words, members of the same group stand to each other in the same relation as the extremities of one or more octaves in music."

The Periodic Law. — Mendele'eff (1869) and Lother Meyer (1869) independently and practically simultaneously formu- lated periodic systems which were very similar to that put forth by Newlands, but they were not familiar with it. Their generalization, commonly known as the Periodic Law, is expressed by the statement that the properties of the ele- ments are periodic functions of their symbol weights.

The Atomic Volume Curve. — Meyer paid special atten- tion to the physical properties and expressed the symbol weights as periodic functions of the specific gravities of the elements. He pointed out that the periodicity is more closely manifest in the so-called atomic volumes, which he defined as equal to the symbol weight divided by the specific

70 PHYSICAL CHEMISTRY

symbol weight

gravity, i.e. - ~- — = atomic volume. He plotted

specific gravity

these values of the atomic volumes against the symbol weights and obtained an atomic volume curve such as is represented in Fig. 5.

The whole curve is made up of a series of periods or waves. The summits (i.e. the crests) of the waves are oc- cupied by the alkali metals :

Cs = 135, Rb = 85, K = 39, Na = 23, and Li = 7 Differences 47.5 46.5 16 16

We have two short periods, one between Li and Na and the other between Na and K. Then follow two long periods, one between K and Rb and the other between Rb and Cs. The remainder of the curve is partly of a different form and is evidently incomplete, and there is no reason to suspect another alkali of higher symbol weight than Cs.

By a consideration of the troughs of the curve, differences between the long and short periods may be indicated. The elements of minimum atomic volume are :

Pt = 191, Rh = 102, Co = 59, Al = 27, B = n Differences 89 43 32 16

These differences between the symbol weights of the ele- ments at the trough of the curves are about 16 and some multiple of 16, and the same is true for the metals that occupy the crests or peaks of the curve. The elements with the smallest atomic volume do not form a group, as do those with the highest atomic volumes, but belong to two widely different groups, which do not show any chemical analogy. Other elements fall into (i) two short periods, beginning with Li and with Na ; (2) two complete long series, beginning with K and with Rb ; (3) a third long series, beginning with Cs followed regularly by Ba, La, and Cr and interrupted by the intrusion of closely related rare elements, followed again regularly by metals from Ta to Bi, and lastly by a small

THE PERIODIC SYSTEM 71

portion of a fourth long series. We thus have five maximum and six minimum sections of the curve.

The descending portion of the curve, representing the in- crease in symbol weight and decrease in atomic volume, is composed of the so-called base-f.orm.mg elements. The ascending portions are occupied by the acid-forming elements, while the minima portions represent the elements Al, Mn, Ru, Pd, etc., which are not decidedly acid-forming or base- forming.

The position of elements on the curve is closely connected with the physical as well as the chemical properties. Ele- ments chemically similar occupy corresponding positions on similar portions of the curve. At the maximum positions we find the light elements ; at the minimum positions the heavy elements.

The Periodic Table. — The Periodic Table presented by Mendel^eff illustrates the periodicity of chemical properties much better than the curve that we have just been consider- ing. The following modern Periodic Table given in Table VII is practically the same as the one presented by Mendele'eff, except that the symbol weights are more accurately known and the new group of the rare elements in Group III and Group 0 is added.

DISCUSSION OF THE PERIODIC TABLE

Arrangement. — All the elements are arranged in suc- cession in the order of their increasing symbol weights. Starting with Li next above H, we find that the one above fluorine, Na, has properties very similar to Li. If Na be placed in the same vertical column with Li and we then arrange the other elements in the increasing order of their atomic weights, the elements which fall in the same vertical column resemble each other very closely chemically. The set of seven elements starting with Li agree very closely with the second set in properties. The first of the next set, K,

Offi

offi

PHYSICAL CHEMISTRY

•

55 *

(J £

.«> q

2 1

s • *! o

C °0

M H

•^ *

M ON

•1 1

a 8

S -d

^ s

HH ^ 6 SN

.a.3

eres ries

THE PERIODIC SYSTEM 73

falls into the group with Li and Na, and the remainder have a striking analogy to the corresponding element of the other sets. After manganese we have one of the weakest points in the Periodic Law, but here also certain regularities are again manifest by the subsequent elements.

Chemical Properties. — The elements on the left are ele- ments present in the strongest alkalies, while those on the extreme right are the elements present in the acids and are the so-called acid-forming elements. Between, we have the gradation between acid properties and basic properties.

Valency. — Valency with respect to oxygen increases from unity for elements in the first column until it reaches seven, when the valency of one recurs and the other valencies are repeated. Valency with respect to H decreases from left to right.

Periods. — The first 14 elements (not counting Group 0 or H) arranged in the horizontal rows constitute what is designated two short periods, for the eighth of these, Na, has chemical properties analogous to the first Li ; the ninth, Mg, analogous to the second, Be, the tenth, Al, analogous to the third, B, and so on to the seventh, F, which has chemi- cal properties analogous to the i4th element, Cl. In the next elements we have to pass over 14 before we find one with properties similar to the i4th, K, which is the 28th element, Rb. That is, we have passed over a long period, and find the elements arranged in a long period, which is followed again by another long period of 14 elements. There are two short periods and five long periods. The last long periods are not completely filled out, and there are a number of vacant places. When the Periodic Tables were first pre- pared many of the elements known at present were un- known, and there were a larger number of vacant places in the table than at present. Notable among these were the spaces now occupied by gallium, scandium, and germanium. Mendeleeff predicted the chemical and physical properties

74 PHYSICAL CHEMISTRY

that the elements occupying these places should have. A short time afterward the above-named elements were dis- covered, and they were found to have the properties Mende- leeff predicted they should have. This fulfillment of proph- ecy brought the attention of the scientific world to Men- deleeff's classification and resulted in the rapid adoption of it. It was soon demonstrated that in such a system as this we had not only a means of prediction but also the only way by which the elements could be grouped together as a whole for the purpose of representing conveniently and con- cisely their interrelations. This was of great advantage. The elements in the atmosphere, the Argon Group, fall into a vertical column to the left of the strongly basic elements, Group I, and constitute the Zero Group, because they are inert and are said to have a valency of zero.

Physical Properties. — There are many other physical properties of the elements and of their compounds which manifest a periodic function of the symbol weights, and among these may be listed a few of the principal ones.

1 . Malleability.

(a) Light malleable metals occupy the points of maximum and contiguous portions of descending curves ; Li, Be, Na, Mg, Al ; K, Ca ; Rb, Sr ; Cs, Ba.

(b) The heavy malleable metals are found in the lowest points of the atomic volume curve and adjacent sections of the ascending curves ; Fe, Co, Ni, Cu, Zn ; Rb, Pd, Ag, Cd, In, Sn, Pt, Au, Hg, Tl, Pb.

(c) Less malleable metals are found just before the lowest points on the descending curves ; Ti, V, Cr, Mn ; Zr, Nb, Mo, Ru ; Ta, W, Os, Ir.

(d) Non-metallic and semi-metallic elements are found in each section on the ascending branches of the curves preced- ing the maximum.

2. Hardness of elements is inversely proportional to their atomic volume.

THE PERIODIC SYSTEM 75

3. Melting point data are shown diagrammatically in Fig. 5 and illustrate the periodic function of this property with increasing atomic weight.

(a) All gaseous elements, and all elements that fuse below a red heat are found on the ascending portions and at the maximum points of the atomic volume curve.

(6) All infusible and difficultly fusible elements occur at the points of the minima and descending portions of the curve. The periodicity corresponds to that shown by atomic volume and malleability. For those elements that are easily fusible the atomic volume is larger than that of the element with next smaller symbol weight. There are, however, some considerable variations : the melting point decreases with increase in symbol weight only in the follow- ing : (i) Alkalies, Li, Na, K, Rb, and Cs, (2) Alkaline earths, Mg, Ca, Sr, Ba, and in Cu, Cd, and Hg. The compounds of the elements also exhibit relations in their melting points. This has been worked out by Carnelley.

4. Volatility is intimately associated with fusibility. Easily fusible volatile metals ar.e found on the ascending portions of the atomic volume curve. Elements on ascend- ing portions of the curve are gaseous and easily volatile, but many elements of high atomic weight which occupy a similar position, however, require a strong red heat or even a white heat for volatilization.

5. Fizeau has shown that the volatile elements occurring on the ascending curve possess almost without exception a larger coefficient of expansion by heat between o° and 100° than the difficultly fusible elements occupying the minimum. Carnelley states that the coefficient of expansion of an ele- ment increases as the melting point decreases.

6. The refraction of light by the elements and their compounds is also essentially related to the symbol weight.

7. Conductivity for heat and for electricity of the ele- ments are dependent upon their ductility and malleability,

76 PHYSICAL CHEMISTRY

and hence are periodic functions of the atomic weights, the periodicity of which coincides with that of the atomic volume.

8. Magnetic and dimagnetic properties of the elements appear to be closely connected with their symbol weights and atomic volumes. Those elements the atomic volumes of which approach the minima are usually magnetic. Obser- vations differ so that it is difficult to tell whether there is a periodic relation between the magnetic and dimagnetic properties and atomic weights. However, from maxima to minima, the elements are entirely magnetic, and at minimum the magnetism exhibits its greatest intensity. This is true of the iron group. From the minimum to maximum, follow dimagnetic elements only. The magnetic susceptibility is a periodic function of the atomic weight, as is illustrated in Fig. 5-

9. Electropotential series is the arrangement of elements according to electropositive and electronegative character. These properties exhibit variations similar to those exhibited in malleability and brittleness.

The electrochemical character of the elements becomes more positive as the symbol weight increases. Cu is re- placed by silver. A strongly electronegative element Cl will displace a weaker one I. The electropositive character be- comes less marked with increase of symbol weight in the groups Cu, Ag, Au ; Zn, Cd, Hg. In the two short periods the elements become regularly less electropositive and more electronegative as the symbol weight increases, but in the long periods the change is less regular. The elements in the groups on the left-hand side of the table are electropositive and those on the right-hand side are electronegative.

Some of the other periodic properties are the following : The crystalline forms of various compounds of the elements, heats of chemical combination, ionic mobilities, distribution of the element in the earth, spectra of the elements, refrac-

THE PERIODIC SYSTEM

tive indices, ultra-violet vibration frequencies, solubility, electrode potentials, etc.

Advantages of the Periodic Law and Classification. — i . It affords the only known satisfactory method of classify- ing the elements so as to exhibit the relationship of the physical and chemical properties of the elements and of their compounds.

2 . The symbol weights of the elements may be determined by means of the periodic system when their equivalent weights are known. Many of the symbol weights used when Mendeleeff presented his periodic table did not allow plac- ing the elements in the position which corresponds to their properties, so he assumed that there had been an error made in the determination of the equivalent weight or that the incorrect multiple had been selected. For example, the sym- bol weight for uranium was thought to be 60 ; this was changed to 120, and finally to 240 (238.5).

3. The prediction of unknown elements, a statement of their properties and general chemical characteristics. As an illustration, in the following table, properties of the proph- esied elements are compared with those of the elements subsequently discovered.

PROPHESIED ELEMENTS

ELEMENTS DISCOVERED

Ek-aluminium

Symbol weight, 68 Specific gravity, 6.0

Gallium

Discovered by Lecoq de Bois-

baudran in 1875 Symbol weight, 69.5 Specific gravity, 5.96

Eka-boron

Symbol weight, 44 Oxide, Eb2O3, sp. gr. 3.5 Sulphate, Eb2(SO4)3 Double sulphate not isomor- phous with alum

Scandium

Discovered by Nilson in 1879 Symbol weight, 43.8 Sc2O3, sp. gr. 3.86 Sc2(SO4)3

Sc2(SO4)3 • 3 K2SO4 - slender prisms

PHYSICAL CHEMISTRY

PROPHESIED ELEMENTS

ELEMENTS DISCOVERED

Eka-silicon

Symbol weight, 72

Specific gravity, 5.5

Oxide, EsO2, sp. gr. 4.7

Chloride, EsCLj,, liquid, boiling point slightly under 100°, sp. gr. 1.9

Ethide, Es(C2H6)4, liquid, boil- ing point 160°, sp. gr. 0.96

Fluoride, EsF4, not gaseous

Germanium

Discovered by Winkler in 1887 Symbol weight, 72 Specific gravity, 5.47 Oxide, GeO2, sp. gr. 4.7 Chloride, GeCU, liquid, boiling

point 86°, sp. gr. 1.887 Ethide, Ge(C2H6)4, liquid, boiling

point 1 60°, sp. gr. slightly

less than that of water. Fluoride, GeF4 - 3 H2O, white

solid mass

Imperfections of the Periodic Law and Classification. —

We have seen that by this system not only all of the known elements can be classified, but also the unknown ones as well. It is not surprising then that from such a universal proposition there should be some variations and irregulari- ties, and so we do find in this classification a few weak points. When the Periodic Table was first presented there was a marked discrepancy in the arrangement in the case of the following elements, but according to the present accepted values for their symbol weights that has disappeared, as is shown in Table VIII.

TABLE VIII

ELEMENT

SYMBOL WEIGHT, 1870

SYMBOL WEIGHT, 1916

Osmium

108.6

IQO.Q

Iridium

1 06 7

iq^.l

Platinum

196.7

195-2

There has been an effort, due to imperfect knowledge of the law, to make too extensive an application, or to limit its

THE PERIODIC SYSTEM 79

sphere of activity, and hence because of insufficient and in- accurate data concerning certain elements erroneous con- clusions hare been drawn. However, there still remain a few remarkable exceptions to the Periodic Law. The fol- lowing are some of the most pronounced ones :

1. In Group I and in Group VII, the elements have a valency of one, and since the valency of hydrogen is unity, it could be placed in either. Owing to the fact that it has a low boiling-point and that its formula weight is represented (as many other gaseous elements) as diatomic, H2, it is in- cluded in Group VII by many chemists. Solid hydrogen does not resemble the alkali metals in physical properties, and it is typically non-metallic. Chemically, however, hydrogen acts very similarly to the alkalies, forming stable compounds with non-metallic elements, such as the halogens. Owing to this it is placed in Group I.

2. The symbol weight of argon, 39.88, is larger than that of potassium, 39.15, and so these two elements should change places. With argon between potassium and calcium we should have a decided discontinuity in the properties, and furthermore, this would bring potassium into Group 0, and the properties of potassium are decidedly unlike those of the other members of this group.

3 . The same holds for tellurium and iodine ; they should be interchanged according to their symbol weights, but according to their chemical properties iodine must be placed in Group VII.

4. In Group VIII we have iron, cobalt, and nickel, but from the symbol weights nickel and cobalt should exchange places. Since cobalt and iron form two series of salts, and nickel forms only the nickelous salts, the gradual variation in the properties is represented by placing cobalt between iron and nickel.

5. The three groups of triads in Group VIII are peculiar in that the triads are arranged in horizontal lines and con-

PHYSICAL CHEMISTRY

nect the members of the three long series. They destroy somewhat the symmetry of the whole system.

6. Between lanthanum, 139, and tantalum, 181, there are a large number of blank spaces, but it is not possible to fit the fifteen rare earth elements into these places, as the symmetry of the system is destroyed. Since these elements are triva- lent, they are grouped together in Group III.

Graphic Representations of the Periodic Table. — Many graphic representations of the periodic arrangement of the

FIG. 6. — Electro-Positive Elements, above plane of paper, black letters on white ground. Electro-Negative Elements, below plane of paper, white letters on black ground. Intermediate Elements, in plane of paper, black letters on sectioned ground.

elements have been devised, and these may be classified as plane diagrams and as space forms. They are designed to bring out more distinctly the relation of the properties of the elements and the atomic weights, but while some of them well express the relations to certain properties, others do not, but represent another group of properties better. Many of the later designs of the space forms are valuable aids in the study of the periodic functions of the atomic weights.

THE PERIODIC SYSTEM 8 1

Only one of the best of these will be presented here in Fig. 6, which is the space form according to Soddy, wherein the figure 8 design is employed.1

1 For other graphic designs the following references may be consulted, where full description of them may be found : (i) Crooks, Chem. News, 78, 25 (1898), employs a figure 8 form ; (2) Emerson, Am. Chem. Jour., 45, 1 60 (1911), places the elements on a helix; (3) Harkins and Hall, Jour. Am. Chem. Soc., 38, 169 (1916), give illustrations of a number of models, many of which are their own designs.

CHAPTER VIII THE KINETIC THEORY OF GASES

IN our preceding considerations we found it desirable to adopt Avogadro's Theory of the structure of a gas, wherein it is assumed that a gas is made up of molecules in motion, which in turn are aggregates of one or more atoms which may be alike or of different kinds. Bernoulli published in 1738 the fundamental notions of the Kinetic Theory of Gases, in which he pointed out that the pressure of a gas is due to the impact of the molecules on the walls of the con- taining vessel. The mathematical theory, however, was developed much later by Clausius, and it is due largely to his efforts and those of Maxwell that the theory as now accepted has been promulgated and developed.

The fundamental assumptions upon which the Kinetic Theory is based may be stated as follows :

1. Gases are made up of molecules of very small dimen- sions.

2. The space that the molecules occupy is small when compared to the volume of the gas itself.

3. The distance of the molecules apart is very large as compared to their size, i.e. they are so far apart that they have no marked influence on one another.

4. The molecules are in rapid motion in all directions, and are assumed to be perfectly elastic.

Deduction of The Gas Law from the Kinetic Theory of Gases. — The total pressure exerted by a gas on the walls of the containing vessel is due to the impacts of the gas

THE KINETIC THEORY OF GASES 83

molecules, which are moving in all directions, against the walls.

Let M be the mass of a given gas inclosed in a box, Fig. 7, whose parallel sides are all rectangles, the inside dimensions of which are b, c, and d. If m rep- resents the mass of one molecule,

— = n, the number of molecules. We

assume that these n molecules of the gas are moving about in all direc- FIG

tions. Let us assume that there is

but a single molecule of the gas in the box, and that it is moving with any velocity. The force that this molecule exerts on the different sides is found as follows : The velocity of the molecule, u, may be resolved into three components perpendicular to the faces of the box. Let x represent the component perpendicular to the face be ; y represent the component perpendicular to the face cd\ and z represent the component perpendicular to the face bd. Then the force exerted by the face, be, upon the molecule may be found by the formula F = ma, where F represents the force, m the mass of the molecule, and a represents the acceleration of the molecule in the direction

of the force. But acceleration a = — — , where v2 repre-

sents the velocity after impact with the face, and vi, the velocity before impact. Substituting, we have F = m^~v^ .

The molecule strikes the face be with the velocity x normal to the face, then rebounds from the face with a velocity — x. That is, vi = x and vz = — x. The effect of the force of impact upon one face is distributed over the period of time that it takes the molecule to travel the distance 2d, when

another similar impact occurs. This time, /, is equal to — •

84 PHYSICAL CHEMISTRY

Substituting these values, for vi, v%, and /, in the above equa-

„ m\ — x—x] mx2 TVT

tion, gives r = — * — -, or — . JNow, since the torce

2 d- d

exerted upon the face by the molecule is equal to that exerted by the molecule upon the face, but in opposite direc- tion, we may write the force exerted by one molecule upon

the face be, as F = ^-. The force exerted by the molecule

Ct n

2 Wt^C

upon the two parallel faces, be, then, is — r~- In the same way the force exerted by the molecule upon the two parallel faces cd, is 2 m^ , and similarly upon the two faces bd is 2 mz

b c

Let us assume that this force exerted by the one molecule is the mean force of all of the molecules ; then if there are n molecules the total force or pressure upon the two parallel

faces be will be 2 nmx • Similarly on the two parallel faces d

cd the pressure will be 2 nm/y , and on the two parallel faces

I-,-, M1i 2 nmz2

bd, it will be

If we designate the force on unit area by p, which is the intensity of pressure, then the pressure p on each face will be the same. The area of the two faces be is 2 be, and the

total force is 2nm% • hence the pressure p will be x •

d 2 oca

Similarly, for the pressures on the other faces we have

2 cdb

2 nmx'

2bdc P'

THE KINETIC THEORY OF GASES 85

• Adding these three equations, we have

2 bed

Simplifying and writing the mean square velocity for the sum of the squares of the three components, u2 = #2 + y2 + z2,

we have $p = ; but the product, bed, of the three

bed

dimensions of the box is the volume, hence, substituting V for bed, the equation becomes

3 V

Deduction of Boyle's Law. — We may define heat as the energy due to the position or velocity of the molecules of a substance. JHeat, due to the velocity of the molecules, we term Thermal Kinetic Energy. A measure of this Thermal Kinetic Energy is Temperature, then T = f(muz) .

For any constant temperature, u is a constant, and the mass, nm, of the gas, is also constant ; therefore, the right- hand member of the equation, J nmu2, is a constant. The equation may then be written pV = a constant. This is Boyle's Law, which we have deduced from the Kinetic Theory of Gases.

Deduction of Charles' or Gay Lussac's Law. — If we as- sume that T is a linear function of mu2, i.e. T = k(mu?),

then substituting in pV = - mnu2 we get pV — - n—t but

3 3 £

- T is a constant, hence pV = T X a constant or ^r= 0 3/2 1

constant. Thus, from the Kinetic Theory of Gases we have derived The Gas Law. From this equation we also have the conclusion that at constant pressure the volume of a constant mass of gas is directly proportional to the absolute temperature ; or, if the volume is constant, the pressure is directly proportional to the absolute temperature, i.e. the

86 PHYSICAL CHEMISTRY

coefficient of expansion of a gas is a constant, which is Charles' Law.

Deduction of Avogadro's Hypothesis. — Let us now apply the equation just obtained in the deduction of Boyle's Law to two different gases which are under the same conditions of temperature and pressure and which occupy the same volume. This equation for the two gases becomes re- spectively

pV = J miHiUj2 and pV = \ m^n^u^

Hence \ m\n\u? = J m^n^-. (i)

It has been shown experimentally that when two gases are under the same conditions of temperature and pressure they are in physical equilibrium and may be mixed without change in temperature. We conclude from this that the kinetic energy of the two molecular species remains unchanged, and further, that at the same temperature the kinetic energy of a molecule of one gas must be equal to the kinetic energy of a molecule of any other gas. Since the kinetic energy of a molecule is ^ mu2, then

, v

Dividing equation (i) by equation (2) we have f n\ — f HZ

That is, the equal volumes of all gases at the same tem- perature and pressure contain the same number of mole- cules. This is Avogadro's Hypothesis.

Molecular Velocity. — Solving equation pV = J nmu2 for

u, we have u* = or u = V or « = . (3)

nm w nm w p

This equation then gives us the velocity of the molecules of any gas, providing we know its volume and pressure and the quantity of gas present.

THE KINETIC THEORY OF GASES 87

Let us calculate the velocity of the hydrogen molecule at o° Centigrade when under one atmosphere pressure.

m X n = mass of gas.

One gram-molecular weight of a gas at o° and i atmosphere pressure occupies 22.4 liters. It will require 2.016 grams of hydrogen to occupy this volume under the conditions specified. Hence, substituting these values in the above equation, we have

^ /3 X 1033 X 980.6 X 22400

u — \

2.OIO

Solving for u we obtain u = 183,700 cm. per second, or 1.837 kilometers per second, as the velocity of the hydrogen molecule under the conditions of our problem.

Diffusion of Gases. — The molecules of a gas moving in an inclosed space bombard the walls. Now, if there is an opening in one side, the molecule will meet with no resistance and will continue in its path on through the opening and thus pass out. It will pass through with the original speed it possessed inside the vessel, and this speed of diffusion originated directly from the speed of the molecular motion, and we conclude that the mean speed of the issuing mole- cules must therefore be proportional to the mean speed of the molecules within the vessel. Since this speed is propor- tional to the pressure on the gas, the rate of outflow will be dependent somewhat on the resistance the gas meets in flowing out. If the gas flows through a very small aper- ture in a thin membrane into a vacuum, then the resistance is reduced practically to the minimum.

If we have two gases under the same conditions of pres- sure and temperature, from the equation u = \/— we

have ui'.uzi : Vp2 : V/^. That is, the molecular velocities are inversely proportional to the square roots of the densities of the gases.

88 PHYSICAL CHEMISTRY

This relationship may be deduced not only from the Kinetic Theory of Gases, but it has also been developed from flow of liquids through orifices, which fact is presented as an argument in favor of the kinetic theory. Bernoulli pre- sented a theory of the process of effusion by an extension to gases of Torricelli's Law, which states that the velocity with which a liquid issues through an orifice is proportional to the square root of the pressure, or the head of the liquid.

This law is expressed as follows : v = \ — , which gives us

—

the same relation as u = %- deduced from the Kinetic

Theory, which states that the pressure varies as the square of the molecular velocity.

The diffusion of gases through membranes and porous media as well as through cracks has been the subject of investigation since the time of Priestley. Graham (1833) recognized the similarity of diffusion and the passage of a gas as a whole through fine openings, which process he termed effusion in distinction from the passage of a gas through capillary tubes, which he designated transpiration. The latter process did not conform to the law of diffusion, while the process of effusion did conform to the diffusion law. Graham's Effusion Law is stated as follows : The times required for equal volumes of different gases to flow through an aperture is proportional to the square roots of their densities. This law is true for the flow of all liquids through a small orifice and was employed by Bunsen as a method for the determination of the specific gravity of gases. It has also been extended to the determination of molecular weights.

If ui : u* : : Vp2 : Vpi, and we assume the same volume of the two gases under the same conditions of temperature and pressure, then m\ : m^ : : PI : P2, since the molecular weights are in the same ratios as the densities of the gases. If we refer the densities to that of some standard, such as air,

THE KINETIC THEORY OF GASES

we have the specific gravities Si and 52. Substituting, we have ui : Uz : : Vs2 : Vsi. Since the times of efflux of equal volumes are inversely proportionaljto the velocity of effu- sion, then we have t\ : t% : : Vsi : Vs2. That is, the times re- quired for the e fusion of equal volumes of different gases under the same conditions of temperature and pressure are directly proportional to the square roots of the specific gravities of the gases. The molecular weights are proportional to the specific gravities ; substituting, we have

Table IX contains some of Graham's data arranged and recalculated by O. E. Meyer.

TABLE IX

GAS

SQUARE ROOT

OF THE

SPECIFIC GRAVITY

TIME OF EFFUSION THROUGH A

Drawn Out Glass Tube

Perforated Brass Plate

Hydrogen

0.263

0-745 0.984

0.985 0.986 I.OOO

1.051

1.237 1.237

0.277 0.756 0.987

0.276

Marsh gas

0.753

Carbon monoxide .... Ethylene

0.987

0.988

Nitrogen

0.984 I.OOO

1.053 1.199 1.218

0.984 I.OOO

1.050

Air . .

Oxygen

1.056

Nitrous oxide Carbonic acid

1.197

1.209

CHAPTER IX SPECIFIC HEAT OF GASES

THE amount of heat required to raise the temperature of a substance one degree is known as the heat capacity of the body and will be designated by q. If the amount of heat absorbed by a body when its temperature is raised from ti° to AJ° is H units of heat, then the mean heat capacity (qM)

would be qM=-~1?-

The specific heat capacity, C, usually called the specific heat, of a substance is the amount of heat required to raise one gram of the substance one degree. The unit of heat, the calorie, is defined as the amount of heat required to raise one gram of water one degree Centigrade. The amount of heat required to raise the temperature of one gram of water one degree is different at different temperatures. Therefore it is necessary to define very accurately the tem- perature used.

Table X illustrates the variation of the specific heat of water with the temperature as given by Callendar at 20° C. as the unit.

The unit employed is the calorie at 20° C., while the calorie at o° would be 1.0094 calories at 20°, and the mean calorie between o°-ioo° is equal to 1.0016 calories at 20° and the value at 15° is equal to i.oon calories at 20°.

The atomic heatoi an element is the specific heat multiplied by the atomic weight, that is, C times atomic weight = the atomic heat. Similarly, the molecular heat is the specific heat of the substance multiplied by the molecular weight.

SPECIFIC HEAT OF GASES TABLE X — SPECIFIC HEAT OF WATER

TEMPERATURE

SPECIFIC HEAT

TEMPERATURE

SPECIFIC HEAT

.0094

I.OOOO

.0085

0.9992

.0076

30 .

0.9987

.0054

0.9982

.0025

0.9987

.0011

I.OOOO

.OOO9

1.0033

.OOO7

IOO

1.0074

If a gas be subjected to compression, its temperature is raised thereby. On heating a gas the amount of heat re- quired to raise its temperature depends upon whether this is done under constant pressure or constant volume. To keep the volume of a gas constant when it is heated, an in- crease in pressure is required, because the kinetic energy of rectilinear motion of the molecules is increased. That is, the added energy is changed into energy of motion of the molecules, which produce additional pressure. If, however, the gas is allowed to expand when it is heated and the pres- sure kept constant, work must be done to move this external pressure as the gas expands. In the latter case we have what is designated the specific heat at constant pressure Cp, and in the first, the specific heat at constant volume C9.

The difference between these two specific heats is the work done against the external pressure. The relation between the two specific heats may be easily determined.

Let us assume that we have one gram-molecule of gas under standard conditions of temperature and pressure, and it will occupy 22.4 liters. If it is heated from o° to i° C, it expands -g-fg- of its original volume, or 2-7-3- °f 22-4 liters = 0.08204 liter. During this expansion, work is done in increasing the volume against the pressure. This work is

PHYSICAL CHEMISTRY

equal to 0.08204 liter atmosphere. But 0.08204 liter atmosphere per degree is the constant R of the Gas Law Equation. Therefore the difference between the molecular heat at constant pressure, mCp, and at constant volume, mCv, is R, that is, mCp = mCv + R.

R may be calculated in calories as follows : i calorie = 42 ,690 gram-centimeters ; R expressed in gram-centimeters is

1033.6X22400 = 84?8o and 84780 273 42690

= approximately 2 calories.

The molecular heats, mCv and mCp, of some of the more common gases are given in Table XI.

1.986 calories or R

TABLE XI

The values for mCp were determined experimentally and mCv by difference.

GAS

SPECIFIC HEAT CP

mCp

mCv

Helium

^lercury

2 Q6^

Hydrogen Oxygen .

3-409 O 2I7S

6.880 6 960

4.880 A Q6O

.412 4.O

Chlorine Hydrochloric acid . . . Nitrous oxide

O.I24I 0.1876

o 2262 .

8.810 6.85 Q QQ

6.810

4-85

7 QQ

.29 .409 I 24.7

Methane

0.893

9-51

7-51

1.266

The heat added to a substance may be utilized in (i) in- creasing the kinetic energy of rectilinear motion of the mole- cules, manifesting itself only in a rise of the temperature ; (2) in performing work against the external pressure in order to expand the gas, or (3) utilized within the molecule itself when it is an associated or polyatomic molecule ; and (4) in

SPECIFIC HEAT OF GASES 93

overcoming the mutual attraction of the molecules. In the case of ideally perfect gases the molecules are out of the sphere of action of one another, and consequently the effect of this last consideration is very small and therefore prac- tically negligible.

If the law pV=RT holds for the gas, the specific heat of the gas must be independent of the pressure and also of the volume. The whole work done during a change of volume will be external. If the volume changes from Vi to v2 under constant pressure p, the external work will be p(v2 — Vi). Now, as we have seen, the specific heat at constant pressure exceeds that at constant volume by the thermal equivalent of the work required to overcome the resistance offered to the expansion of the gas.

In equation mCp — mCv = R, substituting for R its value,

•2 — , we have 273

mCp — mCv = £ — 273

From the consideration of the Kinetic Theory of Gases we found that pV = J mnu2, and for the kinetic energy K = % (mn)u2.

Equating these, we have

or pV = %K,

which enables us to express the molecular energy in a form which can be readily determined. The pressure and kinetic energy of a gas are in an invariable ratio which is inde- pendent of the temperature. Substituting this value for pV in the equation above, we have

mCp - mCv = 2 K • 273X3

All of the energy, E, possessed by the substance is the heat required to warm it from absolute zero to the given

94 PHYSICAL CHEMISTRY

temperature at constant volume. This is increased by the heat required to warm the gas from o° to i°, that is, by •2^-5- of E. But this heat at constant volume is the specific

heat at constant volume, that is, mC9 = — ^— E. Then

273 dividing the above equation by this, we have

mCp — mCv

In case the total energy is the kinetic energy, then K = E and the equation becomes

which is the maximum value of the ratio of the specific heat at constant pressure to the specific heat at constant volume. This value has been obtained experimentally in the case of monatomic gases, mercury vapor, argon, and helium.

In the case of diatomic or polyatomic gases, an appreciable portion of the heat applied to raise the temperature is utilized in overcoming the mutual attraction of the molecules or in intermolecular work. It is possible to raise the tempera- ture of some substances to such an extent that this portion of the energy increases the speed of the atoms within the molecule whereby they are separated from their combination with the others, and the freed atoms thus become like inde- pendent molecules, the atomic energy going to increase the total molecular energy. This would lead us to the conclu- sion that the kinetic energy of the atoms would be decreased and the molecular energy increased, hence K < E. It is apparent that in the case where the amplitude of vibration of the atoms of the molecules has not been increased suffi- ciently to cause them to pass beyond the influence of the other atoms within the molecule, just before dissociation takes place, that we will have the maximum of heat energy

SPECIFIC HEAT OF GASES 95

being utilized in the atomic energy. The more atoms there are in the molecule, the greater will be the amount used in this way and consequently the greater the decrease in the kinetic energy and the less the value of the ratio :

molecular heat at constant pressure mCP _ molecular heat at constant volume mCv

Hence it follows that by determining y for a given gas or vapor, it would be possible to determine the complexity of the molecules.

There are a number of methods by which the value of y may be obtained, and it is not always necessary actually to determine both of the specific heats.

Laplace showed that the velocity of sound in a gas is

expressed as follows : v = \— , where v is the velocity, y is

1 P

the ratio of the two specific heats, p the pressure, and p the density. The method of Kundt and Warburg, which is usually employed, is a means of finding experimentally the value of v. The apparatus consists of a " Kundt 's dust tube," and as employed by Ramsay in the determination of the specific heat of helium consisted of a long tube of narrow bore, closed at one end, through which is sealed a glass rod extending for an equal distance inside and outside of the tube. Some lycopodium powder is distributed along the tube and dry air is introduced. The glass rod is set in vibra- tion by rubbing it with a cloth wet with alcohol. By mov- ing the clamp on the rubber tubing which closes the other end of the tube, the length can be adjusted till it resounds to the proper note. The interference of the waves deposits the lycopodium in piles at the nodes. The distance be- tween these nodes represents one half the wave length and can be readily measured. Air is then removed by evacua- tion, and the tube is refilled with the gas under investiga- tion and the wave length determined.

96 PHYSICAL CHEMISTRY

Let X represent the wave length of a sound of frequency n in any specified gas ; let p = the pressure and p its density, then from Laplace's formula we have for any two gases under the same pressure and temperature :

and % * pi pz vz pi yz

Since the densities are proportional to the molecular weights, we may write the equation

yz mi which becomes

Vz yz mi

Taking air as the standard gas, y\ = 1.408 ; the value of y for any other gas is then obtained by comparing the wave lengths of the same sound in the gas and in air, providing the molecular weight or density of the gas is known. The velocity is equal to the wave length times the number of vibrations (pitch) in a unit of time. If x is the distance between the nodes or ridges of dust, then X = 2 x and the velocity is 2 nx. Then we would have vi = 2 nx\, and vz = 2 nxzj which, substituted in the above equation, gives

Substituting the value for air, y\ = 1.408 and m\ = 28.9, the value for y2 can be obtained if the other values are known ; xz and x\ being obtained experimentally and mz being known.

CHAPTER X VAN DER WAALS' EQUATION

WE saw that the Laws of Boyle, Gay Lussac, and Avo- gadro are only strictly applicable to perfect gases. Under low pressure the deviation is small, but it is greater when gases are highly compressed. We considered that the ki- netic energy of rectilinear motion of the molecules is directly proportional to the absolute temperature under all condi- tions, and so certain modifications in the Kinetic Theory were suggested by van der Waals to explain the observed variations.

In the Kinetic Theory the pressure due to the bombard- ment of the walls of the vessel by the molecules of the gas is calculated on the assumption (i) that the actual volume occupied by the molecules is inappreciable compared with the total volume of the gas, and (2) that the molecules exert no appreciable attraction for each other. It is found that when the gas is greatly rarefied, this assumption is admissible, but when the molecules are brought close together by com- pression of the gas, it is not ; hence the Gas Law Equa- tion must be modified to take these facts into consideration. Many attempts have been made to correct the Gas Law Equation for this purpose, the most successful being that of van der Waals (1879).

According to the Kinetic Theory the total volume occupied by the molecules is small in comparison to the total volume of the gas. Van der Waals corrected for the volume actually occupied by the molecules thus :

98 PHYSICAL CHEMISTRY

Let b = volume occupied by molecules of gas v = volume of the gas

then (v — 6) = the actual or free space in which the mole- cules are free to move, and when the gas is subjected to pressure this is the part which decreases in volume.

In 1854 Joule and Thomson showed experimentally that strongly compressed gases are cooled by expansion. Then, on expansion, work is done against the molecular force, and we conclude that the molecules have attracted one another. Hence a certain cohesion is ascribed to the gases, which is more noticeable the greater their density. Under high pres- sure gases contract more than they should according to Boyle's Law, and this is explained on the supposition that in compression the molecules are drawn more closely together by their attractive force, and this tends to aid the external pressure in making the volume smaller. Therefore this factor should be added to the external pressure. This force must be proportional to the number of molecules attract- ing each other, that is, to the density of the gas, since the density of a given gas is proportional to the number of molecules per unit volume. Van der Waals concluded that the attraction is proportional to the square of the density

or inversely to the square of the volume, and gave -^- as the

expression for this correction.

Substituting these two values in the Gas Law Equation we have

+ -rk\(V-b)-RT

•which is known as van der Waals' Equation of Condition. This equation gives the behavior of the so-called permanent gases, of the easily condensed gases, and it is also claimed that it can be applied to the liquid state as well, although Tait has pointed out that it does not hold for any real liquid.

VAN DER WAALS' EQUATION

It is apparent that when the volume is large, the correct- ing factors, — and b, have no appreciable influence and the

equation is really pV = RT. When the pressure is very great, the factor b ceases to be negligible, and its influence

increases more rapidly than -^ • The product p V reaches a

minimum, and afterwards increases, and eventually becomes much greater than at low pressures.

For ethylene, which is readily liquefiable, Baynes calcu- lated the values of p V from the following formula :

( V - 0.0024) = 0.0037 (272.5 + 0

where pV = 1000 for p = i atmosphere at 20° C. The observed values in Table XII are from Amagat's results.

TABLE XII

Observed

Calculated

IOOO

31.6

914

895

72.9

416

387

110.5

454

456

176.0

643

642

282.2

941

940

398.7

1248

1254

Van der Waals assumed that the molecules of an ordinary substance undergo no alteration during the process of liquefaction, and his equation is intended to apply only to such substances. When association takes place, the rela- tion between pressure, volume, and temperature becomes complex.

100 PHYSICAL CHEMISTRY

If V remains constant, then

takes the form

(p + QC = RT

R where C and Cf are constants and k = ^ •

That is, the p is a linear function of the absolute tempera- ture when the volume of the mass remains constant.

The constants a and b in van der Waals' equation may be calculated from experimental data ; or from a number of iso- therms the pressure and temperature at a series of constant volumes may be read off and the values of the constants k and C in the formula p = kT — C calculated for each volume.

Clausius (1880) claimed that van der Waals' equation did not represent the facts with sufficient exactness and de- veloped an equation himself which allowed for the variation of molecular attraction with change in temperature.

RO r

The Clausius equation, p = — -- — - - — , contains

V — a B(v -\- B)

four constants, R, c, a, B, which necessitate four experiments on p and V at different temperatures to establish, and it is claimed to give greater range and better agreement than van der Waals' equation which contains only three con- stants.

APPLICATION OF VAN DER WAALS' EQUATION

The following quotation is Andrews' description (1863) of his experiments on the behavior of carbon dioxide when subjected to changes of pressure and of temperature : " On partially liquefying carbonic acid by pressure alone and gradually raising at the same time the temperature to 88° F.

VAN DER WAALS; EQ(JATIQ$) '„-•'', ;^ \\ \ \ SOI

the surface of demarcation between the liquid and gas became fainter, lost its curvature, and at last disappeared. The space was then occupied by a homogeneous fluid, which exhibited, when the pressure was suddenly diminished or the temperature slightly lowered, a peculiar appearance of moving or flickering striae throughout its entire mass. At temperatures above 88° F. no apparent liquefaction of car- bonic acid, or separation into two distinct forms of matter, could be effected even when a pressure of 300 or 400 atmos- pheres was applied. Nitrous oxide gave analogous results. "

Andrews plotted the results of his experiments, and the curves in Fig. 8 represent them.

The p-V curve of constant temperature, isothermal curve, for gases that obey Boyle's Law, should be a rectangular hyperbola, and the curve for CC>2 at 48.1° approximates this closely. At 35.5° the curve has a decided flexure, while at 32.5° this is more marked, and at 31.1° still more marked, when we have a double flexure. This curve runs for a short distance paral- lel to the F-axis and represents the critical temperature of CO2. The volume diminishes regularly with in- crease in pressure at this tempera- ture until a pressure of 73 atmos- pheres is reached, when the volume decreases very rapidly, about one

half of it disappearing. A steady increase in pressure is required to produce this change, and by the time 77 atmospheres are reached we have a homogeneous mass which responds to a regular change in volume with in- creased pressure. At 21.5° we have the volume gradually decreasing with increased pressure until about 60 atmospheres are reached, when there is a sudden break in the curve which

FIG. 8.

CHEMISTRY

runs parallel to the V axis, showing a marked decrease in volume without change in temperature. This is similar to the curve at 13.1°, which becomes horizontal at 49 atmos- pheres pressure, showing a change of about f the volume a perfect gas should occupy at this temperature.

Andrews from his experimental work insisted on the idea of the continuous passage of vapor into the liquid form on increasing the pressure, and Thomson, in an effort to explain the shape of the isotherms just above the critical tempera- ture, prescribed an hypothesis in confirmation of this idea as illustrated by Fig. 8.

FGH represents the isotherm above the critical tempera- ture and pressure, where van der Waals' equation assumes a continuous passage from the liquid to the vapor state or vice versa. The line ABC, which is a broken line, repre- sents the ordinary isotherm of a substance passing from the liquid to the gaseous state. The part A B refers to the liquid state, at B the vapor pressure is equal to the external pressure, and the substance begins to separate into saturated vapor and liquid. The horizontal portion BC shows that while this change is taking place the pressure remains con- stant and represents the isotherm of the mixture. The por- tion CD represents non-saturated vapor, and the isotherm approximates more nearly that of a perfect gas.

James Thomson suggested that A A' and CD are portions of the same continuous curve and are connected by some ideal branch, such as AMBNC, along which the substance might pass continuously from liquid to gaseous condition below the critical temperature, as it does above that tem- perature, without separation into two distinct states simul- taneously existing in contact with each other. Along AM we have the condition of superheated liquids, and along C N, supersaturated vapors. So the abnormal conditions of both liquid and vapor are represented by Thomson's curve AMB NC, as conditions of unstable equilibrium. The vapor

VAN DER WAALS' EQUATION 103

at A7 is supersaturated, it condenses when equilibrium is destroyed, and if the temperature be kept constant, a de- crease of pressure to the point n will take place. Similarly at M we have a superheated liquid which on disturbing the equilibrium assumes a condition of stable equilibrium with explosive violence and assumes the condition represented by m when the substance is partly liquid and partly vapor. Between N and M we have the volume and pressure in- creasing simultaneously, a condition difficult to realize in a homogeneous mass. It is apparent that the pressure curve cuts the Thomson hypothetical curve at three points, A, B, and C, which would correspond to three different values for the volume for the one value of the pressure. As the pres- sure increases it is apparent that the Thomson curve de- creases in length, the difference between the three values of the volumes becomes less ; and as we approach the critical point these values likewise approach this value of the critical volume as their simultaneous and limiting value.

Realization of Parts of Curve Experimentally. — i. Methyl formate (31.9° B. Pt.) was heated to 80° and the whole of the vapor condensed. Pressure was lowered below 800 mm. without boiling taking place ; at 80° the vapor pressure is 3500 mm., so that the pressure was reduced to less than one fourth of the vapor pressure ; in other words, it was more than 45° above its boiling point under 800 mm. and 80° C. Boiling finally took place with explosive violence.

2. Worthington showed that when a sealed tube, nearly full of pure liquid free from air, is gently warmed until the liquid fills the tube completely, a bubble of vapor will not form on cooling until a very large negative pressure is reached. The tubes collapsed in some cases.

3. Aitken showed that temperature of dust-free vapors could be lowered many degrees below the condensing point before liquefaction takes place.

It is therefore proved that part of the continuous isother-

104 PHYSICAL CHEMISTRY

mal (Fig. 8) from A to M and from C towards N may be realized experimentally. From M to N increase in vol- ume is attended with rise of pressure, and if it could be brought about, would take place with explosive rapidity.

CALCULATION OF CRITICAL CONSTANTS FROM VAN DER WAALS'. EQUATION

The Gas Law Equation pV = RT, when corrected for the volume b, actually occupied by the molecules and the

mutual attraction of the molecules, -^, gives us van der Waals' equation :

(i)

which, when rearranged in the order of the decreasing powers of V, gives

p J p p

Under normal conditions of temperature, when V = i, p = i, and T = 273, equation (i) becomes

(i + a) (i - 6) = 273 R (3)

Solving for R, we have

R _ d + a) d - b)

273 Substituting this value of R in equation (2), we have

2 + av_a = Q ( }

273 £ p p

This is a cubic equation with respect to V, if p is con- stant, with three roots, one or all of which may be real. We saw that there is one temperature at which the three values of V for one value of p become equal and that is at the Crit- ical Temperature. But at this temperature the pressure is

VAN DER WAALS' EQUATION 105

designated the critical pressure and the volume the critical volume. Let us designate these critical values for V, p, and T respectively as follows : Ve, pn and Te. If the three roots are equal, they become the critical volume Ve, and the cubic equation becomes ( V — Ve)3 = o, which, on expanding, becomes

which is equivalent to our equation (4).

Equating 1 the coefficients of equations (4) and (5), where Vc is the critical volume, and remembering that the corre- sponding values for T and p are their critical values, we then have

3V. = b + (l+a)^-b)Tt (6)

273ft

3^2 = (7)

From these three equations we can calculate the critical values in terms of a and b, the constants of van der Waals* equation.

Dividing (8) by (7), we have

3V.1 P. <*

^=b

1 Wells states the Theorem of "[Indeterminate Coefficients as follows : If the series A + Bx + Cxz + Dx*+ ... is always equal to the series A ' + B 'x + C'x2 + D 'x3 + . . . where x has any value which makes both series convergent, the coefficients of like powers of x in the two series will be equal; that is, A = A', B = B', C = C', D = D', etc. From this we have the following rule : If two equations represent the same locus and one term of one equation is exactly the same as one term of the other, then the coefficients of like powers of the variable are equal.

106 PHYSICAL CHEMISTRY

Then Ve = 3 b (critical volume). (9)

Substituting this value in (7), we have

Solving for pe

pe = — (critical pressure). (10)

Substituting these values of Ve and pe in equation (6) we have

If we desire to retain the value of the gas constant R in the equation, instead of expressing the initial standard con-

ditions as P° ° and defining them as po = i , V0 = i , and TO

To = 273, we could have kept this as R, and equation (4) would take the form

RI]V*+aV-ri=0 (12)

P ) P P

and equation (6) would become

3 f. = &+££ (13)

From which Te can be calculated by substituting values of Vc and pc from equations (9) and (10) respectively, and we have

VAN DER WAALS' EQUATION 107

RTe

a 8 a

Conversely, we may express the values of the constants a, b, and /? in terms of the critical values. From equation (9),

Solving for 6, we have

b =-7 (i5)

From equation (10),

*---^

27 62

Solving for a, we have

a = 27 62£c (16)

Substituting the value of b from (15), we have

'-^t'-sV-'P- (,7)

Solving equation (14) for R, we have

and substituting the value of a from (17) and b from (15), we have

R - 8 • 3 Vfp.

108 PHYSICAL CHEMISTRY

which simplifies to

THE REDUCED EQUATION OF STATE

If we substitute in van der Waals' equation the values of critical values of the pressure, volume, and temperature, we have

This may be simplified if we divide each side of the equa-

tion by -^-*" ; dividing the first factor of the left member

by pe and the second by — e- , we have

«X- (22)

It is apparent that the values of the pressure, volume, and temperature are expressed as factors of the critical values, hence if we substitute for these fractions

we have

(3 * ~ i) = 8 6.

Therefore, expressing V, p, and T respectively in frac- tions of the critical volume, pressure, and temperature, the equation of condition assumes the same form for all sub- stances, or if two liquids be taken under the conditions of temperature and pressure which are the same fractions of

VAN DER WAALS' EQUATION

109

their respective critical values, such conditions are known as corresponding conditions; the law is called the Law of Corresponding States, and the equation is the Reduced Equa- tion of State. •

This equation is independent of the substance and of the physical state of the substance, as there are no arbitrary constants, provided that molecular association or dissocia- tion does not take place. Young investigated this relation- ship and showed that the value for the reduced pressures is the same for all substances and is 0.08846. The substances at their boiling point are under corresponding states, and the value of the ratio of the boiling temperature to the critical temperature is about 0.75. If the substance is under cor- responding pressure and temperature, the volume is also a corresponding volume. This is emphasized by the data given in Table XIII.

TABLE XIII — REDUCED VALUES IN CORRESPONDING STATES

(COMPILED FROM YOUNG'S STOICHIOMETRY) Ratio of Pressure to Critical Pressure = 0.08846

SUBSTANCE

£-•

V "quid = »

Hi!*.*

Acetic Acid Benzene

0.7624

o 7282

0.4100

OAf)f\C

254

?8 i

Carbon Tetrachloride . . . Ether

0.7251

o 7380

O.4O78

O J.O^O

20.3

2745 28 a

Ethyl Acetate Ethyl Alcohol

0.7504

O 77Q4.

0.4001 o 4.061

4O.J

30.25

Ethyl Formate

O 7^8^

O AOO1

o^-1 o 2Q 6

Methyl Acetate .... Methyl Alcohol Methyl Formate .... Stannic Chloride ....

°-7445 0-7734 0.7348

0-7357

0.3989

0-3973 0.4001 0.4031

30.15

34-35 29-3

28.15

The data confirm van der Waals' generalization that : " When the absolute temperatures of two substances are

*'. 1 10 PHYSICAL CHEMISTRY

proportional to their absolute critical temperatures, their vapor pressures will be proportional to their critical pres- sures, and their orthobaric (the volume of a liquid at a given temperature and under a pressure equal to the vapor pres- sure) volumes, both as a liquid and vapor, to their critical volumes."

CHAPTER XI THE PHYSICAL PROPERTIES OF LIQUIDS

MOLECULAR VOLUME

KOPP (1858) showed that it is possible to calculate the volume of one gram-molecule of a liquid organic substance at its boiling point from its composition.

Molecular volume equals the specific volume times the molecular weight ; that is,

•A, j 7 r Molecular weight

Molecular volume = —

density

or mol. vol. = —

Kopp selected their boiling points as his condition for comparing substances. The question arises, was he justified in selecting this particular condition, and if so, then the boiling temperatures must represent corresponding states and consequently corresponding temperatures. If the boil- ing points are reduced temperatures, his selection of the boil- ing temperatures has been justified. •

Guldberg .(1890) and Guye (1890) both showed that the boiling temperature at atmospheric pressure is about two thirds of the critical temperature expressed on the absolute scale. We have just seen that the work of Young presented in Table XIII confirms this and that the boiling tempera- ture of liquids is a reduced temperature and that the sub- stances at their boiling points are at corresponding states.

112

PHYSICAL CHEMISTRY

Kopp determined the molecular volume of a number of liquids at their boiling points and drew the following con- clusions :

1. Among homologous compounds, the same difference of molecular volume corresponds to the same difference of com- position.

2. Isomeric liquids have the same molecular volume.

3. By replacing two atoms of hydrogen by one atom of oxygen the molecular volume is unchanged.

4. An atom of carbon can replace two atoms of hydrogen without change of volume.

The first conclusion stated above is illustrated in Table XIV, where m = molecular weight, v the specific volume,

v = - , where p = the density. The molecular volume P

TABLE XIV

DIFFERENCE

Methyl alcohol

CH3OH . i

39-4

Ethyl alcohol

CaHsOH . .

57-1

177

,i •,

Propyl alcohol

C3H7OH . .

73-4

10.3

if. e

Butyl alcohol

C4H9OH . .

89.9

10.5 if. ?

Amyl alcohol Hexyl alcohol

C5HnOH . CeHiaOH .

102

1 06. i 122.5

16.4 1-2

Heptyl alcohol

C7H15OH .

116

138.7

Octyl alcohol

C8Hi7OH .

130

154-9

lf\ ?

Nonyl alcohol

C9H19OH ' .

144

171.1

The difference in composition of these compounds is CH2, which makes a difference in the molecular volume of 16.2 units, under the given conditions, while under other condi- tions the value for a constant difference in composition may be different.

THE PHYSICAL PROPERTIES OF LIQUIDS

In his later more accurate investigations Kopp found the value for CH2 in two homologous series as given in Table XV.

TABLE XV

MOLECULAR VOLUME

DIFFERENCE

Formic acid H COOH . . .

41.8

Acetic acid CH3 COOH . .

63.5

21.7

Propionic acid C2H5 COOH . .

854

21.9

O T O

Butyric acid C3H7 COOH . .

106.6

£ 1 *£

Valeric acid C4H9 COOH . .

130.3

237

Ethyl formate H COOC2H5 . .

854

oo o

Ethyl acetate CH3 COOC2H6

107.6

yy»m

TQ ?

Ethyl propionate C2H5COOC2H5

125.8

1 O.^

Ethyl butyrate C3H7COOC2H6 .

149.1

23-3

From this he concluded that the value of CH2 is equal to 22. He also found that by replacing 2 C by 4 H, or C by 2 H, the molecular volume did not change. That is, CH2 would be equivalent then to 2 C = 22, therefore C = ii and 2 H would = n and H = 5.5. In this man- ner the atomic volumes of other elements were obtained and the following values have been assigned :C=n;H = 5.5; O = 1 1 . It would follow from this that the molecular vol- ume would be the sum of the atomic volumes just as the molecular weight is the sum of the atomic weights. Hence, it follows that isomeric bodies would have the same molec- ular volume. Methyl acetate, CH3COOCH3, Boil. Pt. 57.1°, has a molecular volume of 84.8, while for ethyl formate, HCOOC2HB, Boil. Pt. 54.3°, the molecular volume was found to be the same, 85.4. Hence the molecular volume is an additive property. However, in attempting to calcu- late the molecular volume from the atomic volumes it was found that for compounds of different types there was a marked consistent discrepancy between the observed and

*;•, 114 PHYSICAL CHEMISTRY

the calculated volumes. This fact led Kopp to assign dif- ferent values to the same element, depending upon the influence of the nature of the atom and its linking or archi- tectural relation to the other atoms. Hence there was a constitutive relation which had to be taken into consideration which demonstrated that this property is not strictly additive. Kopp found that for oxygen singly linked, as in the hy- droxyl group (OH), the value of the atomic volume is 7.8, while for doubly linked oxygen, in the carbonyl group (CO) it is 12.2. On this basis, the calculated values for forty-five different compounds did not vary more than four per cent. Kopp gives the following values for the elements :

C . n.o Cl 22.8

O (OH) 7.8 Br . . .. , ". . . 27.8

O (CO) 12.2 I ... V. .'".;' 37.5

H 5-5 S , . , . , . . 22.6

Sulphur and nitrogen show variations similar to oxygen; they have different values in some different types of com- pounds; in ammonia, N = 2.3, in the cyanogen group, CN, it = 28, and in the nitro group, NO2, it = 33, which, shows great variations in the value of the nitrogen.

Schroeder, as well as Kopp, suggested that the atomic volume of different elements is the same or some multiple of the same number, which unit is called a stere, the value of which was between 6.7 and 7.4. Later Buff (1865) showed that unsaturated elements gave higher values than saturated ones ; that is, a correction had to be made for the double bond, which was estimated at about fojir units. But in the case of the paraffins aaid their corresponding defines this value of the double bond is practically nil.

The formation of ring compounds results in the decrease in the molecular volume. By comparing the values in Table XVI for the homologous series of paraffins with the cyclo- paraffins, which differ by 2 H, Willtstatter (1907) showed the effect of the ring structure.

THE PHYSICAL PROPERTIES OF LIQUIDS 115

TABLE XVI

PARAFFIN

Vm AT 0°

CYCLOPARAFFIN

Vm AT 0°

DIFFERENCE

Butane .

96.5

Cyclobutane . . .

17-5

Pentane .

112.4

Cyclopentane . .

91.1

21-3

Hexane . . .

127.2

Cyclohexane . . ...

105.2

22.O

Heptane .

142.5

Cycloheptane

118.0

24-5

Octane

158.3

Cyclooctane . . .

130.9

27.4

Nonane . . .

174-3

Cyclononane . * *

159-5

14.8

If the value for 2 H be deducted from the differences, it is apparent that the ring formation is accompanied by a marked contraction.

More recently Ramsay, Thorpe, and Lessen, as well as Schiff, have worked over the old data and collected new evidence which confirms in general Kopp's law and his first approximations.

SURFACE TENSION OF LIQUIDS

Within a liquid a molecule is attracted equally in all di- rections by those near it, and this force diminishes rapidly as the distance from the molecule increases. It is apparent that this attractive force must be uniform, since there is no accumulation of the molecules of the liquid in one portion ; i.e. the densities of all portions of the liquid are the same.

As we approach the surface of a liquid the attraction from above diminishes and the tension from the sides increases. This increased tension along the surface in all directions is much greater than that between the molecules in the in- terior of the liquid. The resultant of these forces is normal to the surface inward and not outward, which results in a tendency for the molecules to be drawn into the liquid with a corresponding decrease in the surface. This force acting along the surface and tending to decrease the volume is

Il6 PHYSICAL CHEMISTRY.

designated the surface tension, and hence the unit surface tension, y, of a liquid is the force acting at right angles to a line one centimeter in length along the surface of the liquid. The molecules on the surface must have more en- ergy than those on the interior, and this increase in energy expressed in ergs per square centimeter of surface is nu- merically equal to the surface tension expressed in dynes per linear centimeter.

The surface tension may be determined from the height to which the liquid will rise in a capillary tube.

Let h = height in centimeters that the liquid rises, r = radius of the capillary tube, y = surface tension, expressed in dynes per centimeter.

The length of contact of the surface of the liquid with the inner surface of the tube, multiplied by the tension per centimeter, gives the total force acting, i.e. = 2 wry; but this is equivalent to supporting a column of liquid of height h, and density p, against the force of gravity. Therefore we have

7rr2gph = 2irry

Solving for y we then have

which is expressed in absolute units.

The surface tension decreases with the rise in temperature, and vanishes at the critical point.

Ramsay and Shields (1893) employed the surface tension of liquids for the determination of molecular weights of pure substances in the liquid state, which was an extension of the earlier work of Eotvos (1886).

In the gas equation pV = RT, pV may be termed the volume energy of the gas, and it was shown by Eotvos that a similar equation expresses the relation, within certain

THE PHYSICAL PROPERTIES OF LIQUIDS 117

limits, between the surface energy of the liquid and the temperature, which is

yV* = k(tQ-t)

in which y = surface tension, tQ = temperature at which yV% = o, / = temperature of observation, and V = molec- ular volume which is equivalent to mv. If mv = volume of a cube, then the area of one of the faces is (mu)*, and since the molecular volumes contain the same number of molecules, the molecular surface (w»)» or V* would have an equal number of molecules distributed on it.

Experimentally the temperature, /0, was found to coin- cide practically with the critical temperature, i.e. to = te. If we define r = tc—t, then it is apparent that r is the temperature measured downward from the critical temper- ature. We may then write our equation

yV* = kr

and as V* = surface (s) over which a definite number of molecules are distributed, substituting we have

y • 5 = kr.

Ramsay and Shields, from carefully determined surface tension measurements over the whole range of temperatures up to the critical temperature, showed that this equation holds only approximately. By plotting the values of y • 5 against temperatures (t) we have the curve represented in Fig. 9. At tc = t, r = o and y • 5 = o ; but at lower temperatures, T increases and the values of y • 5 are represented by

ABC, a portion, AB, being curved

and the remainder, BC, being a straight line. Hence at

temperatures represented by A A' the equation does not

Il8 PHYSICAL CHEMISTRY

hold, but beyond a certain distance from the critical point it does hold.

Ramsay and Shields suggested that a correction for this be introduced and that we begin to count from a point A'. Making this correction for the distance d represented by A — A', the equation becomes

y . s = k(r-d).

The value of d is usually 6.

This formula may be rewritten thus :

y(mv)% = k(r-d).

In order to obtain the value of the constant k, measure- ments of the surface tension will have to be made at two temperatures. Then for simultaneous values we have

yi(mvi)% = kfa—d) and y2 ( Solving for k we have

Substituting the values obtained by Ramsay and Shields and solving for k, the following results were obtained :

Ether . . .".'.. ....... 2.1716

Methyl formate .......... 2.0419

Ethyl acetate ....'• ...... 2.2256

Carbon tetrachloride ........ 2.1052

Benzene ............ 2.1043

Chlorbenzene ..... x ..... 2.0770

Average ........... 2.1209

Hence, using the molecular weight, m, of the substance in the gaseous state, they conclude that the constant k is 2.12 (C.G.S. units) for normal liquids whose molecular aggre- gate is the same in the liquid as in the gaseous state. That

THE PHYSICAL PROPERTIES OF LIQUIDS 1 19

is, it holds for non-associated liquids. It follows that if a liquid gives a value of the constant 2.12, or more, it is non- associated, and if less, it is associated ; hence we have a method of determining the degree of association by deter- mining the relation of the found value of k and the value 2.12 for normal liquids.

If x = the number of molecules in the associated molecule, m% = number of times the mass of the associated molecule is greater than that of the unassociated molecule. Our equation would then be

y (mxv)* = 2.i2(r — d) (l)

but from the data we would obtain

y(mv)\ = k^r-d). (2)

Dividing (i) by (2) we have

) (3)

in which x is termed the association factor and represents the number of gaseous molecules combined to form the liquid molecule.

Morgan has worked out the practical details by means of which the proportionality of the surface tension of a liquid to the weight of a falling drop of it can be determined. This relationship is known as Tale's Law. Morgan substi- tuted the weight of the drop, falling from a fine capillary tube, for the surface tension of the drop and obtained the following equation :

w(mv)% = k(r—d)

where k is established by using the non-associated ^liquid benzene.

Walden makes use of the term' specific cohesion (a2) which

he defines as a2 = ^ , where y is the surface tension and P

120 PHYSICAL CHEMISTRY

p, the density. If the surface tension is measured at the boiling point of the liquid, Walden finds a relation existing between the latent heat of vaporization and the specific

cohesion, which is expressed thus : — -= constant, where L9 is

the latent heat of vaporization at the boiling point. The average value of this constant is given as 17.9. Trouton showed that the latent heat of vaporization, L,, multiplied by the molecular weight, m, was proportional to the boil- ing 'point of the liquid measured on the absolute scale; i.e.

^— * = constant. This is known as Trouton's Law, which

emphasizes that the boiling points of liquids are correspond- ing states, and hence we are justified in using these tem- peratures as comparable temperatures, and as the boiling points are approximately the same fraction of the critical values, they are reduced temperatures. Walden empha- sized this, too, when he obtained for a large number of liquids 20.7 as the value of the constant for the equation repre- senting Trouton's Law.

As — * = constant =17.9 (i)

and = 20.6 (2)

solving for m we have

_ 20.6 T _ 1.16 T 17.90? a2

from which the molecular weight can be calculated.

Using this formula Walden has calculated the molecular weight of a large number of substances and found the usual formula to represent the substance in the liquid state, such as SnCl4, SiCl4, CC14, PC13, CSs, etc.

He extended his formula and showed that it is applicable to the melting point of substances and that this temperature

THE PHYSICAL PROPERTIES OF LIQUIDS 1 21

is also a reduced temperature and consequently a com- parable temperature. The formula takes the form

From this fused salts appear to be highly associated, for he obtained for sodium chloride (NaCl)io, for sodium bromide (NaBr)g, and for sodium iodide (Nal)6.2, as the respective formulae representing the molecules in the solid state.

NOTE. — See Appendix for further discussion of the relative surface tension and association factors.

CHAPTER XII REFRACTION OF LIGHT

THE refraction of light furnishes, for transparent liquids, a set of physical constants which may be conveniently and accurately measured. When a ray of light passes from one medium into another, the direction of the entering ray (the incident ray) changes at the surface separating the two media, and will pass into the other medium as the refracted ray. The angle this refracted ray makes with the normal to the surface of separation is called the angle of refraction, and the angle the incident ray makes with the normal to the surface is termed the angle of incidence. The refracted ray lies in the plane of incidence and on the opposite side of the normal to the incident ray.

Let the surface of separation of the two media be repre- sented by AB in Fig. 10, the incident ray by bo, the re- fracted ray by oc and the normal to the surface by aod, while i is the angle of incidence, and r is the angle of re- fraction. Then sin i = -^ and sin r =

£dj0r*™A = ri, Since bo and co are co sin r cd

radii of the circle. This ratio, which is termed the relative index of refraction, is designated by «,

j sin i

and we have n~ - — .

sin r

That is, the sine of the angle of refraction bears a constant

REFRACTION OF LIGHT 123

ratio to the sine of the angle of incidence. This is Snell's Law. The numerical value of this ratio depends on the nature of the two media and on the character of the incident ray.

According to the wave theory of light, this ratio of the sines of the angles of incidence and of refraction is the same as the ratio of the velocities with which the light wave trav- erses the two media. The absolute index of refraction is the value for light passing from a vacuum and would be slightly higher than the value for air ; but this correction is rarely made.

In the determination of the index of refraction of liquids, we have the passage of a ray of light through the liquid into the glass prism and then into the air, that is, we have the passage of the ray through the glass prism. In the Pulfrich refractometer, which is one of the principal ones in use, the entering ray of light is adjusted so as to pass horizontally between the liquid and the prism, and the angle of incidence then becomes

90°. If a ray of light be allowed to enter the prism as is indicated in Fig. n, it will be refracted as it passes into the glass from the liquid and again as it passes from the glass into the air, where it is observed by means of the telescope of the instrument. We desire an expression for the index of refraction between the air and the liquid as it is customary to define the ratio when the ray passes from air into the denser medium. For these three media we would have the following relations :

liuid ,r air .-, N air ; N = — - , then — =

glass ' glass ' n\ liquid

which we shall designate by n.

•••

124 PHYSICAL CHEMISTRY

Now we have

and

glass sin r glass sin r'

and remembering the angle of incidence is 90°, then we have

sin 90° f x

«i = . , (2)

sin r

Since sin 90° = i, this becomes

sin r' But sin r' = cos r = Vi — sin2 r. (4)

Transposing (i) we have sin r = ^P~^ (5)

Substituting in (4)

Substituting this value in (3), we have

i N

N Substituting in n = — , we have

n = VjV2 - sin2 i. Therefore the index of refraction, n = V N2 — sin2 i.

The value of N is usually furnished with the instrument, and tables are provided for obtaining the value of n for any observed value of the angle *".

It is necessary to use monochromatic light, as light of different wave lengths is differently refracted and conse- quently gives different indices of refraction. It is cus- tomary to use sodium light, the D line, but the light of other elements is also used, such as that of lithium, strontium, or the three rays of the hydrogen spectrum : the red line Ha, the blue line H/s, and the violet line Hy.

REFRACTION OF LIGHT

125

METHODS OF EXPRESSING REFRACTIVE POWER

The index of refraction varies with the temperature and with the pressure, in general, with all conditions that in- fluence the density, and hence efforts have been1 made to find an expression which will be independent of these various physical factors and which is dependent only upon the chemi- cal nature of the substance. Gladstone and Dale developed

the empirical formula r

, and named this r, the

specific refractive index or specific refractivity.

Lorentz of Leyden proposed (1880) a formula deduced from the electromagnetic theory of light,

*r —

r =

Lorenz of Copenhagen simultaneously derived the same formula deduced from the undulatory theory of light. This formula is independent of temperature, pressure, and change of; state. Table XVII represents the specific refractivity of water at different temperatures as calculated from both formulae. The n2 formula, as it is termed, apparently gives more constant values :

TABLE XVII

GLADSTONE AND DALE

LORENTZ

TEMPERATURE

n— i

«2-I £

»*+2 p

0°

0.3338

0.2061

0.3338

0.2061

0.3336

0.2061

0.3321

0.2059

IOO

0.3323

0.2061

The effect of the change of state is shown in Table XVIII. The w2 formula gives more uniform values, there not being

126

PHYSICAL CHEMISTRY

such great differences between the value of the vapor and liquid as by the Gladstone-Dale formula.

TABLE XVIII

SUBSTANCE

»-

-i

«2-I i

nH-2 p

Temp.

Vapor

Liquid

Dif- ference

Vapor

Liquid

Dif- ference

Water - .

10°

'i TOI

-J-2-jg

O O2^7

o 2068

o 2061

OOO7

Carbon bisulphide

•4347

•4977

.0630

.2898

.2805

•0093

Chloroform . .' .

.2694

.3000

.0306

.1796

.1790

.0006

Molecular refractivity is obtained by multiplying the specific refractivity by the molecular weight (m) of the substance. Our formulae then become

mr =

n — i

2 _

From the above data it would appear that there is no question as to which of the two formulas is the more trust- worthy, but all data do not give such conclusive evidence, hence there is still a difference of opinion, and the workers in Continental Europe use the formula of Lorentz-Lorenz, while in England the Gladstone- Dale formula is employed. Most of the data have been calculated by means of the Lorentz-Lorenz formula, and hence this is the one more generally used.

The first systematic study of the refractivity of organic compounds was made by Gladstone and Dale (1858-63). They showed that " Every liquid has a specific refractivity energy composed of the specific refractivity energies of its component elements modified by the manner of combination

REFRACTION OF LIGHT

I27

and which is unaffected by change of temperature." Lan- dolt (1864), from extensive data, confirmed the refractive values for the elements carbon, hydrogen, and oxygen, and showed that the constitution had an effect on the refractivity. Bruhl (1891) extended the work of the previous investi- gators and tabulated the following values for the refractivity constants.

The refractivities of the commoner elements are given in Table XIX for the D line, and the hydrogen lines, Ha, Hp, Hy, and also the dispersive power for H/s — Ha and Hy — Ha. These are the recalculated values of Eisenlohr and are prac- tically the same as the original values of Bruhl and Conrady.

TABLE XIX

ELEMENT

Na D LINE*

Hv-Ha

Carbon C

2 4.2

2 4.1

2 4.4.

2 4.6

o 025

oo 6

Hydrogen H Oxygen O' in hydroxyl . . Oxygen O< in ether . Oxygen O" in ketone . . Chlorine Cl . •.'.'.

1. 10 1.52 1.64 2.21 5 Q6

1.09 1.52 1.64 2.19

C Q'J

i. ii

1-53 1-65 2.24 6 04

1. 12

1-54 1.66 2.26 6 10

0.023

0.006

0.012 0.057

o 107

0.029 0.015 0.019 0.078 o 168

Bromine Br

8 86

8 80

Q OO

QIC

O 21 1

o ^4.0

Iodine I . . . . . . . Double Bond = . . ' .. .- Triple Bond =

13.90

i-73 2.40

13-75 1.68

2-33

14.22

.1.82 2.50

14-52

1.89

2.53

0.482 0.138 0.139

0-775

0.20O O.I7I

Homologous series of paraffin compounds with a difference of CH2 have a difference in the molecular refractivity of 4.57, therefore the value of CH2 = 4.57. Landolt found 4.56. The value fluctuates between 4.58 and 4.61 for dif- ferent series, while individual values show even greater vari- ation, 4.11 to 4.86.

The data in Table XX show the value for CH2 in a number of different types of compounds with the number of sub- stances investigated in each series ;

128

PHYSICAL CHEMISTRY

TABLE XX

(After Cohen)

Na D LINE

DISPERSION

H)8-H«

Hv-Ha

Hydrocarbons . . Aldehydes and ketones Acids

66 92

74 81 190 503

4.6O 4.60 4-58 4.6l

4-58

4-59

4.62 4.62 4.61 4-63 4.60 4.62

4.67 4.67 4.66 4.68

4-65 4.66

4.72 471 471 472 4.69 471

0.072 0.069 0.070 0.070 0.069 0.071

O.II8

O.II2 O.II5 O.II2 O.I 1 1 O.II3

Alcohols .... Esters . . : . .

Mean . «

Since the refractivities of the individual elements are constant, it follows that the molecular refractivity (M«) of isomeric substances should be identical. The data in Table XXI show this to be the case :

TABLE XXI (After Cohen)

SUBSTANCE

FORMULA

My-Ma

Propyl alcohol .... Isopropyl alcohol

C3H7(OH) C3H7(OH)

0.2903 0.2907

1742 1744

0.41 0.42

Propyl aldehyde .... Acetone

C3H6O C3H6O

0.2747

o 2767

15-93 I6.O5

0.41 O d.'l

Propionic acid .... Methyl acetate .... Ethyl formate ....

C3H602 C3H602 C3H602

0.2354 0.2437 0.2423

1742 18.03 17-93

0.42 0.44 0.44

Butyl alcohol Isobutyl alcohol .... Trimethyl carbinol . Ethyl ether

C4H9(OH) C4H9(OH) C4H9(OH) (C2H5)2O

0.2974 0.2967 0.2985

O^OI 5

22.01 21.96 22.09 22 "*I

0.52 0.51 0-53 O.55

Butyl iodide

C4H9I

0.1807

-i-i 25

1.26

Isobutyl iodide ....

C4HJ

0.1807

33-25

1.26

REFRACTION OF LIGHT

I29

TABLE XXI — Cont.

SUBSTANCE

FORMULA

My-Ma

Isocaproic acid ....

C6H1202

0.2691

31-22

0-77

Isoamyl formate . . . ".

C6H1202

0.2729

31.66

0.77

Ethyl butyrate ....

C6H1202

0.2690

31.20

0-75

Methyl isovalerate . . .

C6H1202

O.27I2

31.46

0.78

Ortho xylene

C H

O 77^O

'IC CJ

Meta xylene

O ^70

-ZZ.JT.

.54.

Para xylene

C8H10 *•

0.3368

35-70

•56

Ethyl benzene . . . .

CgHio

0-3343

3544

•50

Pseudo cumene ....

CgHi2

0.3363

40.35

.69

Mesitylene .....

CgHi2

0.3361

40.33

•63

Determination of the doubly linked oxygen, O", was ob- tained by subtracting from the molecular refractivity of a series of aldehydes or ketones (CnH2nO), the calculated value of (CH2)n. The value obtained was 2.32. The dif- ference between the molecular refractivity of aldehydes and acids gave the value for hydroxyl oxygen (O'). The calculated value for (CH2)nO" subtracted from the observed values for the aliphatic esters gave a mean value of 1.65 for the ether oxygen (O<). Briihl and Conrady obtained the value for the double bond by deducting the constant for a saturated carbon from the observed values and obtained 1.63 to 2.17 with a mean value of 1.83.

The following, Table XXII, according to Eykman, gives the values for a number of different types :

TABLE XXII

No radicals

CH2 • CH2

i 5i

One radical

RCH : CH2

i. 60

Two radicals

RCH • CHR

I 75

Three radicals

R2C • CHR

i 88

Four radicals

R2C • CR2

2 OO

130

PHYSICAL CHEMISTRY

The effect of simple ring formation gives very small values, not much greater than the variations due to experimental error. Tschugaeff from a large amount of data found a value of about MD = 0.67, while Oesterling found nearly the same value (MD = 0.71). These values were used to establish the cyclic structure of various compounds.

Upon the basis that benzene has three double bonds, the value for the molecular refractivity may be calculated as follows, from the atomic refractivities given in Table XIX, for the red H line, Ha.

. •

6 C atoms 6 X 2.41 = 14.46

6 H atoms 6 X 1.09 = 6.54

3 double bonds 3 X i .68 = 5.04

Sum of atomic refractivities 26.04

Experimentally at 20°, n = 1.4967, p = 0.8799, and the molecular weight is 78.

Substituting in the n2 formula we have

i.4o672 — i . 78

- x — r-* = 25.93

I.49672 + 2 0.8799

which is a close agreement.

Similarly, some of the other simple benzene derivatives give the following values according to Cohen.

Observed

Calculated

Benzene ... .

2^ Q-l

26 O4.

Toluene ....

T.Q 7Q

iO.8q

Ethyl benzene '. '. Phenol . „ .-' * . . -\' .- t .

3544

27 75

35-37

27 82

Benzyl alcohol i- .

^2.2^

32.^1

Chlorobenzene '- .

30.90

31.22

REFRACTION OF LIGHT 131

The following complex compounds do not show such a close agreement :

C - C-T* VT^T.

Observed

Calculated

Naphthalene

4.-I.Q-Z

4.1.65

Anthracene .

61.15

55-15

Phenanthrene

61.59

56.99

The refractivity is employed as an aid in deciding the structural relation of compounds.

The refractive index is used as a means of identifying sub- stances, determining the purity or presence of adulterants, and also the strength of solutions or concentration. For analytical purposes, then, the index of refraction is a property that is coming into very general use. A number of special types of instruments are being employed for this purpose, among which may be mentioned, in addition to the Pulfrich refractometer :

(1) The Abbe refractometer, which has a scale giving the index of refraction direct. This is employed extensively for the analysis and identification of oils.

(2) The butyrometer is employed for analysis of butter fat and has an arbitrary scale.

(3) The Immersion refractometer is employed in analy- sis of milk serum to determine whether the milk has been watered, and in the analysis of various other types of solutions. These are also provided with an arbitrary scale, which is divided into 100 arbitrary divisions comprising indices from 1.325 to 1.367.

(4) The Zeiss refractometer is particularly adapted to determination of alcohol.

The greater the wave length of light, the less the refractive

132 PHYSICAL CHEMISTRY

index, and hence the index of refraction varies with the kind of light employed. The difference between the spe- cific refractivities for light of greatly different wave lengths is called the specific dispersive power or dispersivity. This is obtained by using either of the -formulae and subtracting the specific refractivities.

2 _

The molecular dispersivity is the molecular weight (m) times the specific dispersivity.

z p

The dispersivity values have been determined in a man- ner similar to the method for obtaining the refractivity con- stants for the elements and the different linkages. Bruhl concludes that dispersivity is preeminently a constitutive property and is much more valuable as an aid in establish- ing structural relations than the refractivity. Eykman has shown that dispersivity affords a valuable indication of the position of the double bond. Auwers and Ellinger have shown that dispersivity is increased by the double bond in the side chain as compared with it in the nucleus. In Table XIX is given the atomic dispersive power of a number of ele- ments using the hydrogen lines and in Table XXI is given the molecular dispersive power of a few isomeric compounds.

CHAPTER XIII OPTICAL ROTATION

ORDINARY light consists of transverse vibrations which take place in all directions at right angles to the direction of the ray. If a ray of light is allowed to pass through a piece of tourmaline (an aluminium boron silicate) cut parallel to the crystallographic axis, a part of the light will pass through. If another similar piece of tourmaline is placed with its axis parallel to the first, the ray of light will pass through this second piece also. If this second piece be rotated in a plane perpendicular to the ray of light, the intensity of the light will gradually diminish with the rotation, and when the axes are at right angles the light which passes through the first tourmaline plate will not pass through the second when in this position. Transverse vibrations in only one plane pass through the first plate of tourmaline, and the light which comes through is said to be plane polarized.

If a ray of light be allowed to pass through a piece of Iceland spar normal to one of the faces, it will be broken up into two rays which are differently refracted. This phe- nomenon is termed double refraction, and the two rays are designated the ordinary ray, which follows the laws of refrac- tion, and the extraordinary ray, which does not follow these laws. These two rays are polarized at right angles to each other. Hence Iceland spar can be used for the purpose of obtaining plane polarized light, but in order to do this it is

133

134 PHYSICAL CHEMISTRY

necessary to intercept one of the rays, and thus permit only one to pass through. This may be done by taking a long crystal of Iceland spar, grinding the ends so as to change the angle about three degrees, thus making the angle (Fig. 12) DAB > 68°, and then cutting it in two along the line DB perpendicular to the new face AD, thus making the angle ADB a right angle. These cut surfaces are then polished and cemented in their original position by Canada balsam. £ The ray of light entering

at R is doubly refracted, the ordinary ray following the law of refraction is refracted and meets the surface of Canada balsam,

which has an index of refraction of 1.55, which is greater than that of the Iceland spar, 1.48, for the ordinary ray. If it strikes the Canada balsam at an angle greater than the critical angle, it will be totally reflected at the surface. The extraordinary ray, RE, is refracted less than the ordinary ray. Its index of refraction in the medium is greater than that of the Canada balsam, consequently it can never be reflected at that surface and so will pass through the prism as indicated by REE'. At the point of entrance, R, and also at the surface where the two pieces are cemented together, the extraordinary ray is refracted, but the amount is so small that on a diagram of this size, it can hardly be represented in any other way than by a straight line through both sections of the prism. This prism is known as a Nicols prism, and since it produces plane polarized light it is known as a polarizer. The plane in which the plane of polarization is located can be ascertained by means of a second Nicols prism ; when it is used in this manner it is designated an analyzer.

Method of Measuring Optical Rotation. — The amount of rotation can be measured by placing the substance be-

OPTICAL ROTATION 135

tween two Nicols prisms, one a polarizer to produce the polarized light, and one an analyzer to determine the amount the plane of polarization has been rotated. This is meas- ured by having a scale divided into degrees and fractions thereof attached to the analyzer so as to determine the angle through which the analyzer has to turn in order to permit the light to pass through. Such an instrument is called a polarimeter. The light which comes through would produce either a bright field or total darkness ; in either case it would be difficult to read accurately. In order to obtain a field which can be read easily a number of devices have been designed and are now employed, such as the bi-quartz disk, the quartz wedge compensator, and the Lippich half- shadow apparatus consisting of small Nicols.

The angle of optical rotation is proportional to the thick- ness of the liquid through which the light passes. The specific rotation is the angle of rotation, «, divided by the length, I, of the column of liquid times its density, p. Since the rotation varies with the temperature, it is customary to state the temperature of the solution at which the deter- mination is made as well as the kind of light used. The equation for the specific rotation is

' P

in which /° represents the temperature and D, the spec- trum line, sodium in this case.

For solutions when the concentration is expressed in grams, g, in definite volume, v, we have

[a] = ~ or, for concentration in

per cent, p,

136 PHYSICAL CHEMISTRY

The molecular rotation of liquids would be expressed

r i'° a • m m[« = 7-

J> / • p

or it is sometimes written

and owing to the large value of the rotation it is customary to divide the result by 100.

Asymmetry. — It was early recognized by Biot that many substances in aqueous solutions had the power of rotating the plane of polarized light, while an explanation was offered through the classic researches of Pasteur. One peculiarity of compounds and their solutions which manifest optical activity is that the compounds contain one or more asym- metric atoms of either carbon, nitrogen, sulphur, selenium, tin, silicon, etc. In fact, there is no authentic case in which an active compound has been found that does not contain an asymmetric atom. That is, a carbon atom is said to be asymmetric when all four of the valences are satisfied by groups which are different chemically or structurally. For example, amyl alcohol, which is optically active, may be represented by the formula designated active. If, however, the OH group be replaced by hydrogen, we obtain the formula

CH3 H CH3 H

X • X

C2HB CH2OH CsHg CH3

ACTIVE INACTIVE

designated inactive, and the groups attached to the carbon atom are not all different, as they are in the formula marked active. In the substitution, however, it is necessary to destroy the asymmetric character of the carbon atom be- fore the substance will become inactive. In the case of

OPTICAL ROTATION 137

malic acid (monohydroxysuccinic acid) and of tartaric acid, there are four different groups attached to the asymmetric carbon atoms as the following formulas indicate :

H H

I I

OH— C— COOH OH— C— COOH

I I

H— C— COOH OH— C— COOH

i i i

MALIC ACID TARTARIC Acir

These active compounds have isomers which have anal- ogous properties, and while they are both optically active, and the rotation is of the same magnitude, it is in opposite directions for the two compounds, one rotating the plane of polarized light to the right, and the other rotating it to the left. Those that rotate the plane of polarized light to the right are termed dextro-rotatory, and those that rotate the plane of polarized light to the left are termed Icevorotatory.

In 1867, Kekule proposed that the carbon be conceived as located at the center of a regular tetrahedron and that the four affinities be represented by lines drawn to the four vertices. For convenience of writing, the symbol for car- bon is omitted and the elements or groups in combination with the carbon are indicated at the vertices, as shown in the following figures. In order to explain isomerism, Le Bel and van't Hoff simultaneously (1874) and independently made use of the idea of the tetrahedron carbon atom and grouped the elements or groups in combination with the carbon atom around the base of the tetrahedron in one di- rection to represent one isomer and in the opposite direction to represent the other isomer. This is illustrated in Fig. 13, where we have in I the symbols acd arranged from right to left, while in II they are arranged from left to right. The rotation would be represented as — or laevorotatory

138

PHYSICAL CHEMISTRY

FIG. 13.

in I and + or dextro-rotatory in II. These two figures, 1 and II, are the mirrored images of each other, and while they are alike, they cannot be superposed ; that is, they are

right-handed and left-handed. It is known that solutions of two isomeric compounds can be mixed in equal quantities so as to produce an inactive mixture, and such mix- tures are termed racemic mixtures. There are, however, certain forms of isomeric active compounds which are inactive, and this property is explained upon the assumption that by an internal compensation the compound is rendered inactive. Such in- active compounds are designated the meso form. Here we have an illustration of a compound containing an asymmetric carbon atom without rendering the compound optically active. In the case of tartaric acid we have the example of a compound existing in these three forms, and in Fig. 14 is illustrated the structural arrangements by means of which they are explained.

COOH COOH COOH

H— C— OH OH— C— H

H— C— OH

I CQOH

H— C— OH

HO— C— H I COOH

MESOTARTARIC ACID

L^VOTARTARIC ACID FIG. 14.

DEXTROTARTARIC ACID

OPTICAL ROTATION 139

The meso form manifests no rotation, the laevotartaric acid rotates the plane of polarized light to the left, and the dextro- tartaric acid rotates the plane of polarized light to the right. In addition, we have the racemic acid, which is a mixture of equimolecular parts of /- and of d-tartaric acids.

Many substances are optically active, and the specific rotation of these is listed in tables of physical constants. The use of this property is one of the principal methods employed in identifying, testing the purity, as well as making quantitative determinations of such substances as sugars ; essential oils, including lemon, wintergreen, peppermint, etc. ; the alkaloids, nicotine, brucine, strychnine, etc. ; tur- pentine, camphor, and a long list of others. In the case of sugars, this method is generally employed, as the rotation is proportional to the concentration :

in which c equals concentration in 100 cc. of solution. Then a = [a]/ • c, and since a tube of constant length, /, expressed in decimeters, is employed, and the specific rotation of cane sugar is constant, [a] = (66.5, / = one decimeter) ; substituting we have a = 66.5- /• c, but 66.5 / is a constant, fc, then a = kc, the rotation is proportional to the concen- tration. In Table XXIII are given the values of the specific rotation, [a]2°, at 20° for sodium light, the D-line of the spectrum, for the carbohydrates commonly occurring in foods. These values are the ones usually employed in ana- lytical work and are sufficiently exact for that purpose.

Effect of Temperature. — We have seen that the temper- ature affects the specific rotation, and the formula contains a term designating the temperature at which the deter- mination is made. The rotation may increase or decrease with the change of temperature. Methyl tartrate is prac- tically inactive at o° C., while below this temperature it is

140

PHYSICAL CHEMISTRY

laevorotatory, i.e. negative. Many of the esters of tar- taric acid pass through a maximum value for the specific rotation with change of temperature, while some of those with large negative rotation change but little with a large change in temperature. For most sugars the specific ro- tation is practically constant for all temperatures. In general, however, the specific rotation decreases with the temperature, as is shown by laevulose and arabinose, par- ticularly while xylose increases and dextrose remains prac- tically constant for temperature changes up to 100°. It is necessary to determine the temperature accurately in all sugar analysis and to make the necessary corrections. Browne has compiled formulae by which such corrections can be made and these are given in Table XXIII.

TABLE XXIII

WOOD-

BROWNE'S SUGAR ANALYSIS

MAN'S

SUGAR

FOOD ANALYSIS

CONCENTRATION

MST

Arabinose

+ 6

+ 104.5

Dextrose

+ 52.50 -f- 0.018796 p + 0.00051683 p2

+ 52.5

p = o to 100 per cent

Laevulose

+ [101.38 — 0.56 / -f o.io8(c — 10)]

- 92.5

Invert sug.

— [27.9 — 0.32 /]

— 20.0

Lactose

+ 52.53 —0.07 (1 — 20)

+ 52-5

[/ = 15° to 25° C.]

Galactose

52.53 = constant

+ 80.5

c = 24 to 40

Maltose

140-375 — 0.01837 p — 0.095 t

+ 138.5

Sucrose

+ 66.435 + 0.00870 c — 0.000235 c-

+ 66.5

0-65 gr. per 100 cc.

Xylose

+ 19-0

Effect of Concentration. — That the specific rotation of sugar solutions is practically constant for all concentra- tions is illustrated in Table XXIII. Biot (1834) found that for aqueous solutions of tartaric acid the specific rotation increases with the dilution. The specific rotation of al- coholic solutions of camphor decreases with the dilution.

OPTICAL ROTATION

141

Effect of Varying the Solvent. — The rotation of optically active substances is very different in solution from the rota- tion of the pure substance, and the nature of the solvent has a marked effect upon the magnitude of this rotation. Table XXIV shows the change in the specific rotation of ethyl tartrate and of nicotine when dissolved in different solvents, the specific rotation of the pure substances being respectively +7.8 and —161.5.

TABLE XXIV

(Thorp's Dictionary)

SOLVENT

[a]^ Ax INFINITE DILUTION

ETHYL TARTRATE

NICOTINE

Formanide * . Water

+ 30-4° 26.85

u-5 9-13 6.1 - 19.1

- 70° 77-4 129.4 140.1 163.5 183-5

Methyl alcohol -•"•'•

Ethyl alcohol Benzene

Ethylene bromide . . ,

The order of rotation is the same for these two active compounds in these various solvents, and Walden has found this to be true for a number of other substances and solvents.

When mixed solvents are employed, various results are obtained as is illustrated in the case of J-tartaric acid, which, when dissolved in a mixture of acetone and ether, rotates the plane of polarization to the left, while in aqueous solutions it is dextro-rotatory.

Muta-rotation. — In the case of freshly prepared solutions of certain substances the specific rotation undergoes a change when the solution is allowed to stand, but finally a constant value is obtained. This change may be either an increase or a decrease. This phenomenon is known as muta-rotation, and is also called birotation, multirotation, etc. This change

142 PHYSICAL CHEMISTRY

in the specific rotation is very pronounced in the case of the reducing sugars, certain oxy-salts, and lactones. Dextrose gives a value of 105.2 for freshly prepared solutions, which finally gives the constant value of 52.5. This phenomenon is explained by Landolt and others on the assumption of dif- ferent molecular arrangements of active forms in the freshly prepared solutions which gradually break down into mole- cules of lower rotation. This change to a constant rotation can be produced by allowing the solution to stand for sev- eral hours, by boiling the solution, or by the addition of a small quantity of alkali or acid.

Electromagnetic Rotatory Power. — Optical activity is due to the inner structure, and not many substances possess this property. Electromagnetic rotatory power is possessed by all substances. This property was discovered by Fara- day in 1846. He placed glass between poles of a magnet and found that the plane of polarized light was turned. This phenomenon lasts only while the current is passing.

The electromagnetic rotatory power is a function of the temperature, depends upon the strength of the magnetic field, and, as in the case of optically active substances, is dependent upon the density of the solution and length of the observing tube. If polarized light which passes through a solution in the electric field is reflected back through it, the plane will be turned back to its original position ; while in case of an optically active compound, if the ray be sent back through it, the amount of rotation will be doubled.

The formula for the magnetic rotation is similar to that for the specific rotation of optically active substances. The specific magnetic rotation is, however, the ratio of the rota- tion of the given substance to the rotation of water which

Perkin used as the standard, i.e. - -r- -^- = , where

lp I0pn

—• refers to water. The molecular magnetic rotation is the

OPTICAL ROTATION

specific rotation multiplied by the molecular weight of the substance divided by the molecular weight of water, i.e.

uiQpQm _ moiecuiar magnetic rotation. lp<i>o 1 8

The molecular magnetic rotatory power is an additive as well as a constitutive property. The value for CH2 is obtained from homologous series such as the following:

CH,

Paraffins 1.051

Alcohols 1.057

Aldehydes 1.022

Fatty acids 1.021

Esters 1.023

SERIES

Alkyl chlorides Alkyl bromides Alkyl iodides Phenyl esters

I.OI5 1.031 1.031 1-053

The individual values vary ; as in the case of alkyl iodide they range from 1.005 to 1.066. Perkin takes as the mean value, CH2 =1.023. If there are a number of carbon atoms in the molecules of a particular group of compounds, then by deducting n times the value of CH2 from the total magnetic rotation, a value is obtained which is called the series constant (5) . In the fatty acid series we have :

ACID

MOLECULAR MAGNETIC ROTATION

»Xi.023

Propionic

3.462 4.472 5.513 7.552 8-565 9-590

3 X .023 4 X .023 5 X .023 7 X .023 8 X .023 9 X .023 Mean val

0-393 0.380

0.398 0.391 0.381 0.383 ue 0.393

Butyric Valeric CEnanthylic

Caprylic

Pelargonic

in which n is the number of carbon atoms belonging to the CH2 group, and S is the series constant which is obtained by subtracting the value of wCH2 from the molecular magnetic rotation. In a similar manner the series constant for a

144

PHYSICAL CHEMISTRY

large number of series of organic compounds has been worked out, and in Table XXV a few of these are given.

TABLE XXV

SERIES

FORMULA

Paraffins normal

CnH2

o 508

Alcohols, primary Alcohols iso

CnH2re+20 CnHan+20

0.631 o 600

Aldehydes

CnH2nO

o 261

Ketones . ' '. .- Fatty acids

C»H2nO

CnH2nO2

0-375

O 1QT>

Unsaturated acids .... Dibasic acids Formic esters Acetic esters

OH»^Qi

CnH2n_2O4

CnH2n02

CnH2nO2

I-45I 0.196

0-495 O ^7O

Ethyl esters

CnH2nO2

O "^7

Alkyl chlorides

I 988

Alkyl bromides

CreH^+iBr

3.816

By means of these series constants, the value for the elements may be determined as well as the effect of the linkage and the establishment of the value of the double bond. Having these different values, and knowing the molecular magnetic rotation, these may be employed in determining the structure of organic compounds. One illustration of the method will suffice.

The molecular magnetic rotation of acetoacetic ester was observed to be 6.510, and checking by this method we have :

For acetic ester the series constant is 0.370

For ketone the series constant is . . . . . . . 0.375

Giving as the mean of these values 0.372

Since w is 6 we have 6 X i .023 = 6.138

or 6.510

as the calculated value which checks the observed value closely and indicates the ketonic form of the ester. Hence we conclude that the structure of ace,toacetic ester is ketonic.

CHAPTER XIV SOLUTIONS

IT is a familiar fact that the physical form in which matter exists is dependent on temperature and pressure. Water exists in three physical forms which can be changed one into the other by slight variations in the temperature without changing the pressure. This is true of a very large number of substances ; but in many cases, these changes in form can be much more easily accomplished by changing the pres- sure also, whereas some substances which exist ordinarily in the gaseous form cannot be changed to the other forms unless there is a change in the pressure as well as in the temperature. Theoretically matter exists in all three forms, — solid, liquid, and gaseous — and to these forms of matter we are to apply the term phase, a concept which was cre^- ated by Willard Gibbs and which he defined as follows: " We may call such bodies as differ in composition or state different phases of the matter considered, regarding all bodies which differ only in quantity and form as different examples of the same phase." This is analogous to our conception of form of matter, physical modification, or state. By the term phase we understand a mass that is chemically and physically homogeneous. Any mass of matter under con- sideration which may exist in one or more phases is termed a system.

The homogeneity of a system results from the system being in a state of equilibrium which is independent of the time. For in heterogeneous (non-homogeneous) systems, such as a salt in contact with a solvent, or two gases that

145

'••

146 PHYSICAL CHEMISTRY

have just been brought into contact, the concentration is different at different places, and the mixtures are of different composition in different parts of the systems. The systems not being in equilibrium will change simultaneously into homogeneous systems, and equilibrium will result. This would also take place if different parts of the same system were at different pressures or different temperatures. Hence, our considerations are limited to the state of equilibrium of bodies or systems of bodies and consequently to homo- geneous systems. The existence of water in contact with water vapor might be considered contradictory to the idea of physical homogeneity, yet when the system is of uniform temperature and pressure, equilibrium exists, although we have it consisting of more than one homogeneous body, for the water is itself homogeneous and the water vapor too. In such systems we must have the same temperature and the same pressure throughout, for otherwise there would not be equilibrium and consequently a change would occur in the volume energy of the bodies that constitute the sys- tem. Such a system is said to be a one-component system because it consists of only one chemical individual, species, or compound.

Now this system — water and water vapor — consists of two phases, the liquid and the vapor. It is not necessary that a phase consist of only one body, for it may be dis- tributed among a large number ; or, in other words, a very large number of bodies of one particular chemical individu- ality may constitute a phase, as the vast number of globules of butter fat in milk all constitute one phase. Or, a large number of different chemical individuals may constitute one phase, as the casein and milk sugar in the water solution constitute the second liquid phase in milk. This last case is an example of a multiple component system. This then would give a two -phase system for milk. If to distilled water sodium chloride is added, we obtain a solution which

SOLUTIONS 147

is physically as well as chemically homogeneous and there- fore constitutes one phase. If we continue to add salt, we reach a point beyond which no more salt will go into solu- tion and the solid added will remain undissolved and be eventually in equilibrium with the solution. We now have an additional phase — one solid phase ; but if we were to decrease the;, temperature of the system sufficiently, there would appear solid water (ice) as a second solid phase, and we should have with the vapor above the solution a four- phase system. It is possible to make our selection such that the solid substance used is capable of existing in two solid modifications, and with the appropriate solvent we could then have five phases : two solid phases of the dissolved substance, the solid phase of the solvent, the liquid phase (solution), and the vapor phase of the pure solvent. If we select two non-miscible substances, we should then have two liquid phases ; the vapor phase, and, if the temperature is very low, possibly a solid phase. So by the judicious selec- tion of substances we can make any complexity of phases we desire.

Components. — As in the case of physical homogeneity, so also with chemical homogeneity, it is necessary that the system be in a state of equilibrium, otherwise there may be a gradual transformation of one of the chemical individuals into the other, or vice versa, and it is not with the process of change that we have to do, but with the state of equilib- rium to which the subsequent considerations apply. The determination of the number of components that constitute a system is not always an easy matter, hence it is necessary that the idea of components be clearly in mind. In the water system consisting of the three phases, — solid, liquid, and vapor, — an analysis of all the phases would show that they are composed of oxygen and hydrogen and that the proportion is the same in all three phases, and further, that this proportion is that in which oxygen and hydrogen com-

148 PHYSICAL CHEMISTRY

bine to form water. The system is said to consist of one chemical individual or substance and consequently is desig- nated a one-component system. The same is true of sulphur ; there would be four phases, but all of them would show the same composition by analysis. In the case of water, how- ever, if the temperature was raised very high, it would be found that the water was decomposed into its constituents, hydrogen and oxygen, arid that they existed as the elemental substances in equilibrium with water vapor. Here we should have a somewhat different state, as they would then be considered as components, because they take part in the equilibrium. Hence, a change in the conditions of the system may necessitate a change in the number of com- ponents. We therefore distinguish the components of a phase or system as the constituents of independently variable concentration, and they may be either elements or compounds. Therefore we define the components or " individuals of any reacting system as the separate chemical substances undecomposed in the reactions concerned, which are neces- sary to construct the system. The number of such (com- ponents or) individuals to be chosen is the smallest number necessary to construct the system." (Richards.)

This may be illustrated by the system CaCO3 ^ CaO + CO2, wherein only two of the three constituents, CaO and CO2, are " undecomposed in the reaction concerned." Conse- quently the system is a two-component system.

The composition of Glauber salt is Na2SO4 • ioH2O, that of its solution Na2SO4 and H2O, and that of the vapor of the solution is H20, so that, varying the ratios of Na2SO4 and H2O, the constituents of the solution, we can produce all of the three phases, therefore this is a two-component system. Similarly other hydrates can be obtained by variation of two components. This is also true for double salts, such as K2SO4 • MgSO4 • 3H2O (Schonite), K2SO4 • CuSO4 • 6H2O, etc., where the components are the undecomposed single salts

SOLUTIONS 149

and water, therefore a three-component system, such as they are, is sufficient to form all modifications that can exist.

Separation of Phases. — The tests employed by the or- ganic chemist for the identification and purity of substances are by means of phase transformations with a record of the accompanying heat change. If he desires to determine the purity of a beautiful crystalline product, he determines its so-called melting point. This .consists in nothing more than determining at a constant pressure at what temper- ature the solid and liquid phases are in equilibrium. On the other hand, if the substance is a liquid, he determines at constant pressure the temperature at which the liquid and vapor phases are in equilibrium, that is, the boiling point. If either is constant, the substance has the same composition in both phases, and he is working with a one- component system and concludes that the substance is pure. (This is true except in some special cases that will be con- sidered in detail subsequently.) Not only in the preparation and identification of substances do we make use of the phase conceptions, but in the preparation and purification of the same.

Our gravimetric methods are based on the separation of the pure solid phase which is one of the components of our multiple component system. In fractional crystallization we have the separation of a solid phase, while in the process of fractional distillation we make use of the vapor phase for the separation of 'components. So in a large majority of our chemical manipulations we have to do with the separation of phases. When these phases are alike, both solid, both liquid, or both vapors, the operation becomes much more difficult and particularly is this true in the separation of vapor phases. In the separation of these latter we have not as yet made very rapid progress.

When the components are increased, the complexity of some of the systems is very much increased, for there are

150 PHYSICAL CHEMISTRY

a great many possibilities in multiple component systems. These compounds may be so selected that they form a phase which conforms to the laws of Definite and Multiple Pro- portions. Then the phase is known as a chemical compound. If, however, the components do not conform to this law, the phase is called a solution. A solution may better be de- fined as a phase in which the relative quantities of the components can vary continuously within certain limits, or as a phase of continuously varying concentrations. There is, however, no stipulation as to the particular phase of which a solution may be formed, therefore it is possible that a solution may be of any of the three phases — solid, vapor, or liquid.

In the case of solutions that are in the form of liquids, one of the components is called the solvent and the other the dis- solved substance or solute. We are familiar with many examples of solutions wherein the solvent is liquid and the dissolved substance is a solid, a liquid, or a vapor (or gas). Where solids act as the solvent and the so-called solid solu- tions result, we have a conception which is perhaps not quite so well known but which is very common. Examples of solid solutions include such double salts as potassium and ammonium alum, ammonium and ferric chlorides, po- tassium and thallium chlorates, etc. ; the occlusion of gases by metals, such as hydrogen by palladium ; and the absorp- tion of oxygen and carbon dioxide by glass at a temperature of 200° under 200 atmospheres pressure. Copper diffuses into platinum and into zinc. For the same reason hot platinum crucibles should not be handled with brass tongs. Another very interesting case is the passage of sodium through sodium glass without any visible change. If electrodes of lithium amalgam are used, the sodium is re- placed by lithium and the glass becomes opaque and crumbly, owing to the fact that there was a contraction. It has, however, been found impossible to electrolyze a sodium glass

SOLUTIONS 151

between electrodes of potassium amalgam. Many other ex- amples of solid solutions will be met in the course of our work.

GAS AS SOLVENT

When hydrogen is introduced into a vessel containing oxygen at ordinary temperature, after a short time the two gases will be mixed thoroughly. It is immaterial what relative quantities of the two are brought together, there will be produced a homogeneous mixture of the two. This is true of any other gases that do not react chemically. So it may be stated that gases are miscible in all proportions. Here we have a simple intermingling of the gases, and as a result we should expect the properties of the mixtures to be the summation of those of the individual constituents, and in fact this is the case, each individual gas conducting itself as though the other were not present. The pressure of the gas mixture is the sum of the individual pressures. The specific heat, the power of absorbing and refracting light, the solubility, in fact all of the physical properties of the gases remain the same when they are mixed.

Dewar has shown that a vessel containing air is more highly colored by iodine than when the iodine is introduced into one from which the air was removed. This is also true of a number of gases, thus showing that the gas present exerts a solvent action on the iodine and more of it is there- fore present. Villard (1895) nas shown that iodine is dis.- solved by CO2, as the spectra of the vapor do not show the least characteristic of gaseous iodine. That iodine and bromine are soluble in CS2 above its critical temperature, and that KI is soluble in alcohol vapor, have been fully demonstrated by Pictet, Wood, Hannay, and Hogarth, and others. While the question of a gas acting as a solvent has been quite fully demonstrated in cases where the solute is a gas, liquid, or solid, the subject does not present any- thing of importance in our present consideration further

152 PHYSICAL CHEMISTRY

than the fact that a gas may be considered as a solvent, thus illustrating our second group of solvents.

LIQUID AS SOLVENT

Gas as Solute. — When a gas is brought into contact with any selected liquid, the gas is absorbed by it ; but the quantity absorbed varies greatly with the liquid employed, with the gas used, as well as with the temperature and pressure. In the case of oxygen, hydrogen, nitrogen, and many other gases, the quantity of the gas dissolved is very small whatever the liquid employed. In any case when the maximum amount has been absorbed under the prevailing conditions, there results a state of affairs such that the same number of molecules of the gas pass into the liquid and pass from the liquid into the gaseous space above, in unit time. The system consisting of the gas and the liquid is said to be in a state of equilibrium.

It was shown by Henry (1803) that the mass of any gas that dissolves in a selected solvent is in direct ratio to the pressure of the gas. For example, at three atmospheres pres- sure three times as much can be dissolved by a liquid at a con- stant temperature as is dissolved at one atmosphere pressure. This law of Henry may be expressed in a number of ways.

Statement of Henry's Law. — i. If we designate the mass of the gas in unit volume of the liquid as the concen- tration of the gas in the liquid, Ct, and represent the concen- tration of the gas in the space above the liquid by Cv, then

the ratio of these two concentrations remains constant for

£ all values of the pressure, i.e. — =k.

2. The total quantity of a gas absorbed is always pro- portional to the pressure on the gas. As we usually express the quantity as the mass (i.e. the weight) then the mass of the gas per unit volume, i.e. the concentration (Ci) is pro- portional to the pressure. We then have Ct = k'p.

SOLUTIONS

153

3. If the quantity be expressed in terms of volume, then it follows from Boyle's Law that twice the mass occupies the same volume under twice the pressure, and as Henry 's" Law states that the quantity of gas absorbed is propor- tional to the pressure, it follows that the same volume of gas is dissolved in a specified quantity of a liquid at all pressures.

Confirmation of Henry's Law. — Henry's Law has been subsequently confirmed by a number of workers, particu- larly by Bunsen and by Khanikof and Luginin, the results of whose experiments on the solubility of CO2 in water are given in Table XXVI.

TABLE XXVI

-f

k^ P

69.8

0.9441

0.01352

218.9

3-1764

0.01451

80.9

I.I6I9

O.OI436

236.9

34857

0.01472

128.9

1.8647

0.01447

255-4

37152

0.01455

147.0

2.1623

O.OI47I

273.8

4.0031

0.01463

200.2

2.9076

O.OI45I

3II.O

4.5006

0.01447

It is apparent that the value for k is a constant and that the ratio of C, : p is independent of the pressure. In other solvents this law has been shown to hold for nearly all of the gases that have been studied, which include N2, H2, 02, C02, CO, N20, CH4, H2S, NO, C^o, C^, C,R6.

Exceptions to Henry's Law. — In the case of a number of gases, the amount of the gas absorbed has no relation what- ever to the pressure. For example, HC1, NH3, SO2, HI, etc., are very soluble in water, and their properties in solution are different from those in the gaseous state. There appears to be a reaction between the solvent and solute, for in the case of HC1 and water at atmospheric pressure, a mixture of a definite composition distills over at 106°, and in the case of HBr and H2O, a mixture of definite composition comes

154

PHYSICAL CHEMISTRY

over at 126°. These gaseous substances which are so very readily soluble in water do not follow Henry's Law.

Coefficient of Absorption is defined as the number of cubic centimeters of the gas absorbed by one cubic centimeter of the liquid at o° C. and 760 mm. pressure. This coefficient for the so-called permanent gases is very small and varies from o.o i to 0.05, while in the case of those gases which are exceptions to Henry's Law the coefficient is much larger. The solubility of gases decreases with an increase of tem- perature, as is illustrated in Table XXVII.

TABLE XXVII — COEFFICIENT OF ABSORPTION

GAS

10°

20°

30°

50°

100°

Oxygen ....

0.04890

0.03802

0.03102

0.02608

0.02090

0.01700

Hydrogen . . .

0.02148

0.01955

O.OI8I9

0.01699

0.01608

0.0160

Nitrogen

0.02348

0.01857

0.01542

0.01340

0.01087

0.00947

Carbon dioxide

1.713

1.194

0.878

0.665

0.436

Ammonia . . .

1305.0

915-5

7154

Hydrochloric acid

506.9

474-3

442-3

411.8

361.9

Sulphur dioxide .

79.789

56.647

39-374

27.161

When the temperature is raised, the gas can be entirely removed from the liquid, except in some cases in which the solubility does not conform to Henry's Law. The removal of the gas can also be accomplished by diminishing the pressure. A solution of sodium bicarbonate under greatly reduced pressure loses one half of its carbon dioxide. By diminishing the pressure the blood loses the carbon dioxide and oxygen dissolved in it.

Dalton's Law. — When two different gases are mixed, if there is no chemical reaction between the gaseous particles, it has been found that each gas conducts itself as though the other gas was not present. In fact, all of the physical prop- erties, such as the pressure exerted on the walls of the

SOLUTIONS 155

containing vessel, the specific heat, etc., experience no change. Hence, if we have a mixture of gases in contact with a liquid, each individual gaseous species exerts its own individual pressure, and according to Henry's Law the amount of this particular gas absorbed should be proportional to this pressure. In fact, it has been shown by Dalton (1807) that the solubility of a gas is unaffected by the presence of other gases and that the amount of each absorbed is pro- portional to its own partial pressure. This is known as the Absorption Law of Dalton. By the partial pressure of a gas we mean the pressure exerted by that particular gas. For example, if we have a mixture of two gases, oxygen and nitrogen, the total pressure, p, which would be required to keep them at a certain volume would be the pressure of one atmosphere. Now the oxygen in this volume would exert its own pressure, po, and the nitrogen its own pressure, pNt the sum of which would equal the total atmospheric pres- sure exerted upon the mixture, i.e. p = po + py, which is the expression for Dalton 's Law that the total pressure is equal to the sum of the partial pressures of the individual species of a gaseous mixture.

Water exposed to air becomes saturated at the given temperature and pressure. Let us assume that the pres- sure is 760 mm. This is the total pressure, and since the oxygen constitutes 20.9 and the nitrogen 79.1 per cent by volume of the air, then the partial pressure of the oxygen

will be 20'9 of 760 mm., or 158.84 mm., and that of nitrogen 100.0

will be '9>I of 760 mm., or 601.16 mm. At 18° the solubility 100.0

of oxygen is 0.0324 and of nitrogen is 0.01605 under 760 mm.

1^8.84. - ••* , ,, 601.16 v

-* — -X 0.03242 = 0.006776; X 0.01605 = 0.01269.

760 760

0.006776 : 0.01269 : : 34-8 : 65.2 per cent of oxygen and of nitrogen respectively.

CHAPTER XV SOLUTION OF LIQUIDS IN LIQUIDS— I

SOLUBILITY

WHEN liquids mix in all proportions they are termed con- sulate liquids. Water and alcohol are miscible in all pro- portions. They are termed a pair of consulate liquids. Mercury and water do not mix in any proportion, neither do kerosene and water. These are non-miscible liquids. In- termediate between these two types of pairs of liquids we have a very large number of liquids which manifest a partial solubility of the one in the other. These pairs of liquids are termed partially miscible liquids.

If we add ether to water, there is formed a solution of ether in water, and this becomes more and more concentrated as ether is added. Finally a concentration is reached in which a second liquid layer appears. We have saturated the water with ether ; we have two liquid layers that are non-miscible. If we were to add water to ether, the same result would be obtained, — the formation of two non-miscible layers. If we continue to add ether in the first case, the relative volumes of the two layers would change, the lighter one increasing in volume and the lower one decreasing until finally it would disappear, when we should have water dissolved in ether. If we were to add water to ether, we should have practically the same result, the water dissolving, two liquid layers formed, the volume of the layers changing until one (the lighter in this case) disappeared with the formation

156

SOLUTION OF LIQUIDS IN LIQUIDS 157

of a homogeneous solution of ether in water. This may be represented graphically by Fig. 15.

If A = 100 per cent of water and B = 100 per cent ether, then AB will represent all possible concentrations of water and ether.

Let the concentration of the liquid layers be represented by the vertical axis A C. Ethly EUur

If we start out with pure water, at A , and add ether, the concentration of the solutions would be represented by the line AE. At the concentration represented by E the second liquid layer would appear. The two liquid layers would have the concentrations repre- sented by E and E' respectively, E' being

the concentration of the upper layer. FIG. 15.

Now as more ether is added, the concentra- tion of the two liquid layers when in equilibrium would remain constant, as represented by the lines E'F' and EF. By the continued addition of ether a point, F, would finally be reached at which the lower layer would disappear, and we should have a homogeneous solution of water in ether, the concentration of which would be represented by F'. As the addition of ether is continued, solutions of water in ether would be formed, which are represented by the line F'D. EF and E'F1 rep- resent the two non-miscible liquid layers, and since these are in equilib- rium, they represent saturated solutions ; EF saturated with respect to ether and the lighter layer E'F' saturated with respect to water.

Hence it is apparent that the two non-miscible liquids formed from the partially miscible liquids are saturated solutions, and these saturated solutions are themselves non- miscible liquids, so we may consider the pair of saturated solutions formed from partially miscible liquids in the class of non-miscible liquids.

The determination of the mutual solubilities of this system at different temperatures would give us the different concentration in the two layers. So a study of the be- havior of a pair of partially miscible liquids resolves itself into the determination of the solubility at different tem- peratures. Alexejeff (1886) took a definite weight of water

PHYSICAL CHEMISTRY

and of aniline, put them into a tube, sealed it, and determined the temperature at which the mixture became clear. He did this for a number of concentrations and obtained the following data:

TEMPERATURE

1 6°

55°

77°

142°

156°

164°

157°

68°

39°

25°

8.4°

Aniline per

cent .

3-i

3-8

5-3

94-5

95-4

Let us represent on the horizontal axis the concentration of aniline and water in Fig. 16 by the line AB, and on the vertical axis the tem- perature, then A represents 100 per cent of water and B represents 100 per cent of aniline, and AB represents all possible concentrations of water and aniline. Plotting the above data we obtain the curve DCE. The point D represents the solubility of aniline in water and E the solubility of water in aniline at o° C. It is apparent then as the tempera- ture increases the solubility of aniline in water increases, and DC repre- sents this. Similarly the part of the curve EC represents the increased solubility of water in aniline with the increase in temperature.

Above the temperature represented by C (164°) aniline and water are miscible in all proportions, i.e. they are consulate liquids above this temperature, which is termed the critical

I64.i v solubility temperature. The area outside and

above the curve represents those concentra- tions and temperatures where aniline and water are mutually soluble forming one liquid layer. Within the solubility curve DCE we have the concentrations and temperatures where two liquid layers are found. If quanti- ties of aniline and water represented by any FIG. 16. point within this area, as ra, be mixed and al-

lowed to come to equilibrium at any tempera- ture below C, the mixture will separate into two liquid layers, the com- position of the layers will be represented by the two points x y on the curve DCE. The point x represents the upper water layer and y the lower aniline layer, and the relative quantities of the layers are repre- sented by the distances xm and my respectively, i.e. the weight of the layer x is to the weight of the layer y as the length xm is to the length my.

A 100* Water

100* B Aniline

SOLUTION OF LIQUIDS IN LIQUIDS

159

Most partially miscible liquids become consulate at high temperatures, but there are a number of interesting excep- tions to this. A mixture of di- or trimethyl amine and water separates into two liquid layers when the temperature is lowered, the mutual solubility increases, and if the tem- perature be lowered sufficiently the liquids become consu- late. This decrease in solubility with rise of temperature has been observed in many other cases, such as butyl al- cohol in water, and also paraldehyde in water.

In Fig. 17 we have minimum solubility, while with de- crease in temperature the solubility increases and finally reaches a temperature below which the liquids are consulate.

Many ketones and lactones show a peculiar characteristic in that they have a minimum solubility at an intermediate temperature, and the solubility increases with either an increase or a decrease of temperature. In Fig. 18 we have

ISO"

100% JVator

FIG. 17.

100* Triethylamine

100 * Water

100*

Methylethylketone

FIG. i 8.

represented the temperature of minimum solubility, and either above or below this temperature the solubility in- creases.

It is conceivable that the solubility curve may be a closed curve as these figures represent the three different portions of a closed curve. Recently Hudson found this to be real- ized in the case of nicotine and water. Figure 19 represents the effect of temperature on the solubility of nicotine in water.

i6o

PHYSICAL CHEMISTRY

150"

JOO* Water

1009 Nicotine

By heating mixtures of non-miscible liquids, we saw that above a certain temperature for all concentrations they become consulate. If, however, we keep the temperature constant, we can accomplish practically the same result by adding a liquid which is consulate with both the components. So if we have three liquid components A, B, and C, and if

Cis consulate with A and B, then the mutual solubility of A and B is increased, and by addition of a sufficient quantity of C one liquid layer can be produced. It is con- ceivable, however, that if C is consulate with A, but only par- tially miscible with B, the addi- FlG I9- tion of C to a mixture of A and

B would increase the solubility of A but might decrease the solubility of B. By the proper selection of the three com- ponents we could obtain combinations which would result in the formation of these three classes of reactions :

1. The three components form only one pair of partially miscible liquids.

2. The three components form two pairs of partially mis- cible liquids.

3. The three components form three pairs of partially miscible liquids.

Triangular Diagram. — In representing the relation of the mutual solubility to the change in temperature we used the horizontal axis to represent the concentration and the vertical axis to represent the temperature. To represent the concentration of three liquid components use is made of the triangular diagram, and since this is on a plane sur- face it represents the concentration at one temperature. There are two methods of representing the concentration by means of a triangular diagram, and we shall use the method of Roozeboom, and only refer to that of Gibbs indirectly.

SOLUTION OF LIQUIDS IN LIQUIDS

161

Construct an equilateral triangle, A CB, Fig. 20. We saw that a line such as AB would represent all possible concentrations of A and B. Similarly let BC represent all possible concentrations of B and C, and AC represent all possible concentrations of A and C. The concentra- tion of any mixture of A , B, and C will be represented by some point within the triangle. Assume the ends of the lines, i.e. the corners of the

100%

100% 0

70 60 50 40 30

30 40 60 €0 70

FIG. 20.

zo 10 o*

80 90 100 1

triangle, to represent 100 per cent respectively of A, B, and C; then divide the sides into 10 equal parts and draw lines parallel to the sides of the triangle. Then from the intersection of these lines the composi- tion of a mixture represented by any point, such as O, can be readily ascertained. Counting the composition of A on the lines parallel to the side opposite A, we have 4, i.e. 40 per cent; counting similarly for B, we find i.o or 10 per cent, and since O is on 5th line from the side opposite C, then the concentration of C is 50 per cent, and that of our mixture is A =40 per cent, B = 10 per cent, and C = 50 per cent.

162

PHYSICAL CHEMISTRY

Ether and alcohol are miscible in all proportions (and also water and alcohol), but water and ether are only partially miscible. So if a mixture of ether and water be taken in known proportions of about equal quantities and shaken with a little alcohol and allowed to come to equilibrium, two

FIG. "2i.

liquid layers will be formed. By repeating this with suc- cessive additions of alcohol a concentration will eventually be reached at which but one liquid layer is formed. If the point of concentration be established where just one drop of the alcohol will cause the disappearance of one of the two liquid layers, we have a point of saturation. Similarly suc- cessive points of saturation could be established syntheti- cally for all concentrations of ether and water. Then by

SOLUTION OF LIQUIDS IN LIQUIDS 163

plotting these results on a triangular diagram, we would have a curve similar to x y z y\ %i in Fig. 21.

Let W represent water, E ether, A alcohol ; then the sides of the triangle will represent all possible mixtures of the three pairs of liquids, taken two at a time. Since ether is partially soluble in water, x repre- sents the saturated solution of ether in water, similarly Xi represents a saturated solution of water in ether. The line Wx would represent solu- tions of ether in water and Exi solutions of water in ether.

The series of saturated solutions of water, ether, and alcohol at con- stant temperature may be represented schematically by the isotherm x y z yi XL If one starts with the liquid phase designated by x and varies the three components, the line xyz would represent one series of saturated solutions. From Xi the same point z would be reached, and the curve Xiyiz would represent the composition of the other series of saturated solutions. So by starting with the concentration designated by either x or Xi and varying the composition, the same concentration of saturation as represented by the point z would be reached, where the two solution phases become identical. Hence the isotherm x y z yi x\ represents the series of saturated solutions of the three components which are in equilibrium at a definite constant temperature.

Above and outside of this isotherm is the field of unsaturated solu- tions, and the portion of the figure included by the curve represents the field of mixtures which separate into two liquid phases, the compo- sition of which is given by some two points on the isotherm. Since the isotherm represents the composition of these saturated solutions in equilibrium, the addition of the component W or E will cause clouding. Now let us inquire whether it makes any difference which of the con- stituents is added. We saw that the location of x was due to the saturation of W by E, so any further addition of W would not cause clouding of this solution, but as we follow up the isotherm there must come a point at which the addition of W will cause clouding. Such a point, y, is where the line WH drawn through W is tangent to the curve. The same is true for the addition of the component E, the line EK through E being tangent to the curve at yi. It has been shown ex- perimentally that if to a mixture of A and E containing more of E than indicated by H, W be gradually added, clouding will eventually take place and the mixture separate into two liquid phases ; but if W be added to a mixture of E and A containing less of E than indicated by H, no clouding will result. The same reasoning may be applied to the addi- tion of E to solutions of W and A containing more or less of W than indi- cated by K, clouding occurring in the first case and not in the second.

1 64 PHYSICAL CHEMISTRY

It is therefore apparent that the isotherm is divided into four parts which correspond to the following four distinct sets of equilibria :

1. The solutions represented by the line xy are saturated with respect to E, and an excess of W does not produce a precipitate.

2. The solutions represented by the line yz are saturated with respect to £, and an excess of W or E produces a precipitate of E.

3. The solutions represented by the line zy\ are saturated with respect to W, and an excess of W or E produces a precipitate of W.

4. The solutions represented by the line yix\ are saturated with respect to W, and an excess of E does not produce a precipitate.

Above the solubility curve we have the area of unsaturated solutions, while within the curve all possible mixtures of water and ether and alcohol which will separate into two liquid layers may be represented. Any point, such as d, represents the proportions of water, ether, and alcohol which when shaken together and allowed to come to equilibrium would separate into liquid layers ; the composition of the lower heavier liquid layer would be represented by some point, as m, on the solubility curve and the upper liquid layer by n on the other side of the solubility curve. The straight line passing through the point d and connecting these two points is designated the tie line. If any other mixture, rep- resented by a point k on this line, was to be prepared and allowed to come to equilibrium, the composition of the two layers would also be represented by the same two points m and n on the solubility curve. That is, if we were to take a number of mixtures represented by points on this tie line and allow them to come to equilibrium, the upper layers on analysis would all be found to have the same composition represented by n, while the lower layers would all have the composition represented by the point m on the solubility curve.

Another case similar to the water-ether-alcohol system is that of silver, lead, and zinc. Molten lead and silver are miscible in all proportions, silver and zinc are also consu- late, but lead and zinc are only partially miscible. This system has been worked out by Wright, who obtained the data given in Table XXVIII.

The values given in the horizontal rows represent com- position of upper and lower layers in equilibrium at the particular temperature. These would compare to such points as n and m in Fig. 2 1 , which are designated conjugate points, and the liquids are termed conjugate liquids. The

SOLUTION OF LIQUIDS IN LIQUIDS

composition of the upper layer is much richer in silver than is the lower layer. So by this means silver can be sep- arated from lead and the upper layer rich in silver can be

TABLE XXVIII

UPPER LAYER PERCENTAGE AMOUNT or

LOWER LAYER PERCENTAGE AMOUNT OF

Silver

Lead

Zinc

Silver

Lead

Zinc

40.89

3.38

55-73

1-54

96.28

2.18

47.68

379

48.53

2-39

9578

1-83

52.80

4.09

43.11

4.18

94-43

1-39

60.14

9.00

30.86

10.22

88.02

1.76

65.34

13.67

20.79

15.69

81.88

2-43

60.35

28.42

11.23

29-53

68.03

2.44

skimmed off from the lower liquid layer. This method constitutes the Parkes' Process for the desilverization of lead. In fact, this process is simply an example of the dis- tribution of a substance between two liquid layers.

Saturated solutions are non-miscible and so this is a special case of two non-miscible liquids ; and if we have a third component soluble in both the liquid components, this third component will be distributed between the two liquid phases. We saw according to Henry's Law that the ratio of the concentration (Cv) of a gas in the gaseous space and

the concentration (C/) in the liquid at equilibrium is always

£ equal to a constant — - = k. Now if we apply this law to

the distribution of a substance between two liquid layers, then the coefficient of distribution is constant if the molec- ular species are the same in both liquids. For the equilib- rium between two non-miscible liquids in which the third component is dissolved we find that the ratio of the concen- trations, C\ of the third component in the one liquid and

1 66 PHYSICAL CHEMISTRY

the concentration Cz in the other liquid, is a constant, i.e.

-r = k. That is, the ratio of distribution between two liquids C\

is a constant. This is known as Nernst's Distribution Law.

This law has its application, as we have seen, to metal- lurgical processes, and it is apparent that the greater the constant the more of the dissolved substance (Ag, for ex- ample) can be removed from the liquid by adding zinc. As the solubility of silver is greater in aluminium than in zinc, the substitution of aluminium for zinc would give a larger value for the constant, and consequently a greater quantity of silver would be found in the upper layer, and therefore a greater percentage extraction. So the practice consists in adding a considerable quantity of aluminium to increase the efficiency of the desilverization of the lead.

Shaking Out Process. — The ordinary shaking out pro- cess employed in the organic laboratory is nothing more than the application of this principle. If a compound is prepared in an aqueous solution and this solution shaken with ether, in which the substance is more soluble, and the ether is then removed by means of a separatory funnel and evaporated, the separated material is obtained in the free state. The greater the distribution ratio the more efficient the extraction, and it is better to extract with successive small quantities of the solvent than to use the total quan- tity at one time, as the following consideration will show.

Let us assume that we have' 12 grams of a substance dis- solved in 100 cc. of water and that it is twice as soluble in benzene as it is in water. If we add an equal volume of benzene to the 100 cc. of water, then the substance dis- solved will distribute itself between the benzene and water in the ratio of 2:1, and f of 12, or 8 grams, or 66 f per cent, will be contained in the benzene, and ^ of 12, or 4 grams, or 33^ per cent, will remain in the water. Hence, by extracting with equal quantities of the benzene, 66 f

SOLUTION OF LIQUIDS IN LIQUIDS 167

per cent of the substance could be extracted. Now as- sume that we divide the benzene into two portions of 50 cc. each and extract the 100 cc. of aqueous solution with them successively. Since the substance is twice as soluble in benzene as in water, 50 cc. of benzene will dissolve as much of the substance as the 100 cc. of water, and so after shaking 100 cc. of water with 50 cc. of benzene the substance would be equally divided between the two solvents or in the ratio of i : i, and one half of the substance would be extracted, i.e. 50 per cent. By extracting again with 50 cc. of benzene it is apparent that 50 per cent of the remainder would be extracted, or 25 per cent of the original quantity. Hence, by extraction with 100 cc. of benzene, using successively 50 cc. portions, the total amount of the dissolved substance removed is 75 per cent as against 66 f per cent when it was all used at once. It is better, therefore, to extract several times with small quantities of the liquid than to extract once with a volume equal to the aggregate of the volumes used.

CHAPTER XVI

SOLUTION OF LIQUIDS IN LIQUIDS — H VAPOR PRESSURE

WATER boils at a lower temperature on a high mountain than it does in a valley. This is commonly explained by saying that the pressure exerted by the atmosphere on the surface of the water is less at the higher altitude, or that the liquid water passes into the vapor phase at a lower tem- perature when the pressure is diminished. This fact is made use of in organic chemistry when we carry on the operation known as distillation under diminished pressure. At these respective temperatures under their correspond- ing pressures there exists a state of equilibrium between the vapor and the liquid, and the liquid will all pass over into the vapor phase without change in temperature, if heat be continuously supplied. If at these various temperatures of equilibrium the corresponding pressures be determined and represented diagrammatically so that the ordinates repre- sent the pressures and the abscissae the temperatures, and if the points are connected by a curve, we should have the values for all intermediate temperatures and pressures. Such a curve is known as the Vaporization Curve and repre- sents all possible temperatures and pressures at which the liquid and vapor are in stable equilibrium. It can there- fore be designated an Equilibrium Curve. The pressure that the vapor exerts under these conditions of equilibrium is designated the Vapor Pressure of the substance.

Methods of determining vapor pressures of substances are usually classified as the static method and the Ramsay

1 68

SOLUTION OF LIQUIDS IN LIQUIDS

169

and Young or dynamic method. By the static method the substance is placed in a Torricellian vacuum above a column of mercury, is heated, and the pressure determined by change in height of the column of mercury.

By the Ramsay and Young method the pressure is kept constant and the temperature is varied until equilibrium at that pressure is established.

We shall consider the vapor pressure determinations of two substances, benzene and water, and represent them dia- grammatically. When the pressures are represented as ordinates and the temperatures as abscissae, the diagram is known as a p-t diagram, that is, a pressure-temperature diagram.

The following values for benzene have been found by Ramsay and Young, and subsequently confirmed by Fischer :

TABLE XXIX — VAPOR PRESSURE OF BENZENE

p IN MM. HG.

p IN MM. HG. ,

p IN MM. HG.

0°

26.54

5°

34.80

40°

180.20

28.04

36.69

268.30

29.61

45-19

388.51

31.26

74-13

548.16

32.99

117-45

755-00

The curve, AB in Fig. 22, represents the vapor pressure curve of liquid benzene, and is an equilibrium curve, as it represents the pressures and the corresponding temperatures at which the liquid and vapor of benzene are in equilibrium. The curve AB divides the area into two parts, and is then the boundary between the area above the line representing the liquid phase and that below which represents the vapor phase. The area between the curve AB and the tem- perature axis represents the pressures and tem- peratures at which benzene exists as a vapor, while the area above and bounded by AB and FIG. 22.

170

PHYSICAL CHEMISTRY

the pressure axis represents the pressures and temperatures at which benzene will exist as a liquid.

In a like manner we give values for the vapor pressure of water :

TABLE XXX — VAPOR PRESSURE OP WATER

p IN MM. HO.

P IN MM. HO.

- 10°

2.144

120°

1484

4-58

130

2019

+ 20

17-54

150

3568

55-34

20O

11625

149.46

250

29734

355-47

270

41101

IOO

760.0

364.3

147904

(194.6, atmos-

pheres C. P.)

In Fig. 23 AB represents the vapor pressure curve for water and is an equilibrium curve as well, for it represents the equilibrium between liquid water and vapor for all intermediate temperatures. It likewise represents the boundary between areas where the liquid and the vapor phases of water exist.

These two examples are sufficient to illustrate the method of representing the condition of equilibrium in a two-phase

; liquid- vapor one-component system, and

FlG" 23' this method is general in its applica-

tion. With a constant mass the state of a system is defined by arbitrarily fixing one of the variable factors. For if the temperature is fixed, then the pressure at which the liquid and vapor coexist is also fixed, and is represented by a point on the curve A B at which a line perpendicular to the t axis at that particular value for the temperature cuts the curve A B. If we fix the pressure, the temperature at which the vapor and liquid coexist is also fixed.

SOLUTION OF LIQUIDS IN LIQUIDS 171

The mass of the phase or phases does not influence the equilibrium of the system, for if we increase the pressure, the vapor phase will disappear. The pressure is independent of the relative or absolute volumes of the vapor and liquid phases. If the pressure and temperature are maintained con- stant, it does not matter whether we have 500 or 50 cc. of the liquid present, the equilibrium will be preserved and we could remove most of the liquid without disturbing the equilibrium.

Limits of the Vapor Pressure Curve. — It is natural to inquire to what pressure and temperature it is possible to subject a two-phase liquid- vapor one-component system, such as water or benzene, and still obtain a condition of equilibrium between the two phases. The vapor pressure curve is a boundary curve and separates the area of the diagram into the areas of pure liquid and pure vapor ; hence, if we follow this curve to a sufficiently high temperature with its corresponding pressure, we reach the point at which there is no distinction between the liquid and the vapor phases, and the system ceases to be heterogeneous and is a homogeneous single phase. This would occur at the temperature at which there is no distinction between the vapor and liquid, that is, at the critical temperature, and the corresponding pressure, called the critical pressure. Hence, the vapor pressure curve must end at the critical point, and above this temperature there is no pressure great enough to produce the liquid phase. In the case of water the vapor pressure curve would terminate at a temperature of 633° absolute, and a pressure of 195.5 atmospheres, which are called respectively the critical temperature and critical pressure of water. For benzene the critical values are 561.5° absolute and 47.89 atmospheres pressure.

It is a familiar fact that if the temperature of a liquid, as water, is lowered, there occurs a time when the substance ceases to exist in the liquid phase and a new phase appears — the solid phase. Hence, it follows that there must be a

172 PHYSICAL CHEMISTRY

lower limit to the vapor pressure curve for liquid water, that is, to the vaporization curve. It is also a familiar fact that when clothes are placed on the line in winter, they freeze, thus becoming stiff and hard. Later they are all found to be soft and dry. This is due to the fact that the water on exposure to the cold becomes ice and later disap- pears in the form of vapor. That is, the solid water (ice) passes directly from the solid to the vapor phase without passing through the intermediate liquid phase. This happens in the case of a large number of substances, for exam- ple, if mercuric chloride is heated at ordinary atmospheric pressure, it liquefies, and if the heat be increased, the liquid passes into the vapor phase. If, however, the pressure is diminished to 200 or 300 mm. and heat applied, it is found that the solid passes over into the vapor phase without passing through the intermediate liquid phase. This pas- sage of a substance from the solid to the vapor phase with- out passing through the intermediate liquid phase is desig- nated sublimation. The solid like the liquid has a certain tendency to pass into the vapor phase, and as this can be measured as a pressure, we speak of the vapor pressure of solids. This tendency to sublime can be measured in a manner somewhat analogous to the determination of the vapor pressure of liquids, and it may be represented on thep-t diagram ; the curve representing the vapor pressure of a solid is an equilibrium curve and represents the equilibrium between the solid (ice) and vapor, and is called the Sublimation Curve.

FiG^J In the case of benzene the vapor

pressures are given in Table XXIX.

Representing these data on the p-t diagram, Fig. 24, we have

CD, which terminates at the melting point of benzene, that is,

where the sublimation curve intersects the vaporization curve.

SOLUTION OF LIQUIDS IN LIQUIDS

In the case of water we have the following values for the vapor pressure of ice :

TABLE XXXI — VAPOR PRESSURE OF ICE

p IN MM. OF MERCURY

-50°

O.O29

- 8°

2.322

- 40

0.094

- 6

2.762

-30

0.280

-4

3-277

— 20

0.770

— 2

3-879

~ 15

1.237

— I

4.215

— IO

1.947

— 0

4-579

Water

FIG. 25.

Representing these values on the p-t diagram, Fig. 25, we have CD, which intersects the vaporization curve CB at C. This is the melting point of ice and is therefore the upper limit or termination of the sublimation curve, which is an equilibrium curve between the vapor and solid phases, thus dividing the area represented by the p-t diagram into still smaller divisions.

In systems composed of two miscible liquids, the vapor pressure of the one liquid phase is found to depend on its concentration and on the temperature. At constant temperature the variation of the vapor pressure with change of con- centration may be represented on a p-conc. diagram, and three different types of curves are found to represent the vapor pressure of mixtures of dif- ferent pairs of miscible liquids.

Let us represent on a pressure-con- centration diagram, Fig. 26, the con- centration of mixtures of two miscible liquids and by A and B the vapor pressures at a given temperature.

FIG. 26.

100 % B

PHYSICAL CHEMISTRY

If the vapor pressures of all mixtures of A and B are inter- mediate between the vapor pressures of A and B, then the curve AB represents the vapor pressures of all mixtures, and the total pressure is the sum of the partial pressures of the vapor of the two components. The addition of a second component to a solvent may affect the vapor pressure in one of three ways : (i) it may lower the vapor pressure, (2) it may raise the vapor pressure, or (3) it may not affect it.

In the pressure-concentration diagram, Fig. 27, let C and D represent the vapor pressures of two miscible liquids, then as we add D to C the vapor pressure of C is raised. If we take D as the solvent and add C, the vapor pressure will be raised, and if we plot these results we obtain a curve represented by COD which indicates a maximum vapor pressure for some mixture of these two miscible liquids.

C 100%

FIG. 27.

100%

FIG. 28.

In the pressure-concentration diagram, Fig. 28, let E and F represent the vapor pressures of two miscible liquids. Let us assume that the addition of the second ^component diminishes the vapor pressure of the solvent ; then by adding F to E the vapor pressure will be decreased, and similarly by adding E to F the vapor pressure of the mixture will be less than that of F. By plotting such results we obtain the curve EMF, which represents a minimum vapor pressure ; while in the first case, where the vapor pressures of the mixtures were intermediate between the vapor pressures of the

SOLUTION OF LIQUIDS IN LIQUIDS 175

two components, we have neither maximum nor minimum pressures.

We have already seen that the vapor pressure is the pres- sure which is necessary to balance the tendency of the sol- vent to pass into the vapor phase, and at a given temperature this tendency is much less than it was before the solute was added. It will be necessary to raise the temperature con- siderably to form the amount of vapor sufficient to produce the pressure equivalent to the pressure of the vapor of the pure solvent. Therefore, the liquid with the lower vapor pressure at a given temperature is the liquid with the higher boiling point. Representing the pairs of liquids A and B on a temperature-concentration diagram, Fig. 29, we would have the boiling point of A higher than that of B, and since the vapor pressure of

mixtures of the two liquids is inter- FlG 2g

mediate between that of the liquids

themselves, the boiling point of their solutions is intermediate between the boiling points of the pure liquids, as is shown by the line A B, which represents the boiling points of all mixtures of A and B.

To produce the same amount of vapor from solutions of two miscible liquids which can have a minimum vapor pressure, requires a larger expenditure of energy in the form of heat than to produce the same pressure from the pure solvent. So if we take different mixtures of two miscible liquids which manifest minimum vapor pressures and de- termine the boiling points and plot them on a temperature- concentration diagram, as in Fig. 30, we obtain the curve EMF, which shows that as we add the component F to the solvent E the boiling point is raised, and the rise is greater the greater the concentration within certain limits. The same is true if we use F as the solvent, and as we add

i76

PHYSICAL CHEMISTRY

E the boiling point of the solutions increases with the in- creased concentration of E. We obtain the curve EMF which shows a maximum boiling point for mixtures of E

100*

FIG. 30.

FIG. 31.

and F. Pairs of miscible liquids which have a minimum vapor pressure curve also have a maximum boiling point curve.

Similarly it may be shown, as represented in Fig. 3 1 , that two miscible liquids which have a maximum vapor pressure curve (Fig. 27) have a minimum boiling point curve, COD.

COMPOSITION OF THE VAPOR PHASE

The vapor phase under constant pressure and temper- ature will be in equilibrium with the liquid phase, and we have just seen that the pressure of the vapor phase is due to the vapor pressures of the individual components of the vapor, i.e. p = pi -\- pz, which is Dal ton's Law. The con- centrations in a gas are proportional to the partial pres- sures, and hence we could determine the concentration of the components in the vapor phase if we knew the partial pressures. The determination of the partial pressures is difficult, and satisfactory methods have not been devised. But we can determine the concentration by distilling over fractions, collecting, and analyzing them.

Let us consider a pair of liquids whose mixtures have boiling points intermediate between the boiling points of

SOLUTION OF LIQUIDS IN LIQUIDS 177

the two components. In Fig. 32 let A and B represent the two components and AyB represent the boiling points of the mixtures. Let us consider* a mixture represented by ' the point p, the composition of which is, say, 80 per cent A and 20. per cent B. If we heat this mixture and continue to raise" its temperature until we intersect the boiling point curve AB at z, the liquid will boil at this temperature, /„ and the vapor which passes off will be richer in B than in A. The temperature of the. liquid in the flask will rise and pass along the line zA, and the concentration of the liquid in the flask will approach the composition of pure A. The distillate which passes off at z is richer in B than the liquid from which it was dis- tilfed, and may be represented by some point as x. If the vapor of this composition is condensed and then heated to its boiling point, IT it will be found to boil at the temperature ty. This will boil, and the vapor will be richer in B than is represented by the concentration y, i.e. some concentration such as w. The vapor w, if con- densed, would be found to have a boiling point /„, and the vapor of this would be richer in B. By this, process of redistillation we are obtaining distillates successively richer in B, and it is apparent that if this be continued a suf- ficient number of times we approach B and thus com- pletely separate it from A. From the liquid remaining in the flask we obtain A and from the distillates pure B, and therefore can completely separate them by this means, which is termed fractional distillation. Any point on the curve BwxA represents the composition of the vapor phase, i.e. of the distillates, at the boiling point of the mixture from which it was obtained. This curve is called the Vapor Composition Curve.

178 PHYSICAL CHEMISTRY

In Fig. 33, where we have a maxiiattm boiling point, the vapor composition curve is represented by the dotted curve CcOdD. If we take any mixture richer in D than the maximum boiling mixture, and fractionate it, the distillate will be richer in D than in C, and the composition of the liquid in the flask becomes richer in C. For mixtures richer in C than the maximum boiling mixture, the vapor will be richer in C and the composition of the liquid remaining in the flask becomes richer in D. For any mixture the concentration of the liquid in the flask tends to become of the concen- tration as represented by the con- centration 0, at which the boiling

100*.

• j • j 1 1*1 j r • j

c D point is the highest or any mixtures

FlG' 33' of C and D, and the composition

of the vapor is the same as that of the distilling liquid, i.e. we have a constant boiling liquid, and all of. the liquid passes over without change in temperature.

This phenomenon is the same as in the case of pure sub- stances. The boiling point is used as a means of deter- mining whether a substance is pure. If the boiling point is constant, we conclude that the substance is a pure one and that the composition of the vapor and of the liquid are the same. If this criterion be applied to this boiling mix- ture, the conclusion would be that it is a pure chemical compound. For a long time such mixtures were considered as chemical compounds. In the case of pure substances the composition of the liquid and vapor phases is the same, irrespective of the pressure at which the boiling point is determined. If, however, these constant boiling mixtures of pairs of miscible liquids be determined at different pres- sures, vapors of different composition will be obtained. This proves that they are not chemical compounds but mixtures.

SOLUTION OF LIQUIDS IN LIQUIDS 179

In Fig. 34, EeMfF is the vapor composition curve of the distillates from the mixtures of pairs of liquids with a jniai- mum boiling point. The distillates of mixtures whose boil- ing points are represented by EM are richer in F than the mixtures from which they were obtained, and as these dis- tillates are continuously fractionated by distillation the com- position of the distillate approaches M. Similarly, for the liquids whose boiling points are < represented by MF the composition E of the distillates obtained by frac- tional distillation approaches M as the final value. That is, the dis- tillates of all mixtures upon frac- tionation give as final values the

composition represented by M, which -jr '" *

is that mixture with the lowest FlG> 34'

boiling point. At this temperature the mixture of this composition distills at constant temperature and the vapor and liquid have the same composition. What was stated with respect to the point 0 of the maximum boiling liquids applies to the point M of the minimum boiling liquids ; the composition varies with the pressure and therefore they are not pure chemical compounds.

Mixtures of the type illustrated in Fig. 32 are not very common. In the case of methyl alcohol-water and acetone- water mixtures, approximate separation by fractional dis- tillation can be obtained.

Mixtures of the type illustrated in Fig. 33 are repre- sented by a number of solutions of acids in water where maximum boiling points are obtained as illustrated in Table XXXII.

Mixtures of the type illustrated in Fig. 34 are common, and a few of the more common pairs of miscible liquids that have a maximum vapor pressure and a minimum boiling point are given in Table XXXIII.

180

PHYSICAL CHEMISTRY TABLE XXXII

TEMPERA-

PER CENT

SOLVENT

BOILING POINT

SOLUTE

BOILING POINT

TURE OF MAXIMUM

WEIGHT

BOILING

POINT

SOLVENT

Water. . . .

100°

Nitric acid . . .

86°

120.5°

32.

Water. . . .

100.

Hydrochloric acid

-82.9

1 10.

79.76

Water. . . .

IOO.

Hydrobromic acid

-68.7

126.

52.5

Water. . . .

IOO.

Hydriodic acid .

-35-7

127.0

43-0

Water. . . .

IOO.

Hydrofluoric acid

19.4

120.

63-

Water. . . ._

IOO.

Formic acid . .

99.9

I07.I

23.0

Perchloric acid .

IIO.O

Water ....

IOO.

203.

71.6

Chloroform . .

61.2

Acetone

56.4

64.7

80.

Chloroform .

61.2

Methyl acetate .

56.0

64-5

78.

Propionic acid .

140.

Pyridine . . .

117-5

149.

TABLE XXXIII

SOLVENT

BOILING POINT

SOLUTE

BOILING POINT

TEMPERA- TURE OF MINIMUM BOILING POINT

PER CENT

SOLVENT

WEIGHT

Water. . . .

100°

Ethyl alcohol . .

78-3°

78.15°

4-43

Water. . . .

IOO.

Isopropyl alcohol

82.45

80.35

12.10

Water. . . .

IOO.

n Propyl alcohol .

97-2

87-7

28.31

Butyric acid

159.

Water ....

IOO.

99.2

20.

Pyridine . . .

115-

Water ....

IOO.

92.5

59-

Benzene . . .

80.2

Methyl alcohol .

64.7

58.35

60.

Benzene .

80.2

Ethyl alcohol . .

78.3

68.25

67.64

Tertiary butyl

alcohol

82.55

Benzene . .

80.2

73-95

36.6

Allyl alcohol .

95-5

Benzene

80.2

76-5

20.O

Toluene . . .

109.

Allyl alcohol . .

95-5

9i-5

50.0

Ethyl alcohol .

78-3

Normal hexane .

68.95

58.65

2I.O

Carbon tetra-

chloride

76.75

Methyl alcohol .

64.7

55-7

794

Ethyl iodide .

72.9

Methyl alcohol .

64.7

55-0

83-

Ethyl alcohol .

78.

Ethyl iodide . .

72.0

63.0

14.

Acetone . . .

56.4

Carbon bisulphide

46.2

39-25

34-0

Methyl acetate

56.0

Carbon bisulphide

45-6

39-5

29.0

SOLUTION OF LIQUIDS IN LIQUIDS 181

FRACTIONAL DISTILLATION WITH STEAM

In the case of a one-component system of a liquid and vapor, the vapor pressure of the pure liquid at the boiling point under atmospheric pressure is equal to 760 mm. pres- sure. That is, the vapor exerts a pressure of this amount against the tendency of the liquid to vaporize. In the case of two non-miscible or partially miscible liquids, the vapor pressure of these at the boiling point of the mixture will be the sum of the partial vapor pressures of the two liquids. This will be equal to the external or atmospheric pressure, if boiling under atmospheric pressure. If carbon bisulphide boils at 50° C. the vapor pressure at this temperature is balanced by the atmospheric pressure, and if we have water mixed with it at this temperature the vapor pressure of the water is appreciable, as p = pcs, + PH&, hence the vapor pressure of CSz does not have to equal the atmospheric pressure, as the combined pressures of the carbon bisulphide and of the water are equal to the external pressure. It is, therefore, apparent that the aggregate pressures of the two vapors will equal the atmospheric pressure at a temperature below 50°, the boiling point of the lower boiling liquid. That is, the mixture will boil at a temperature below that of the lower boiling liquid. The quantities of the substances in the vapor phase will, of course, depend upon the vapor pressure of the substances at that temperature. This may be illustrated by a specific case.

In the distillation of nitrobenzene by steam the mixture boils at 99° C. at a pressure of 760 mm. At this temperature the vapor pressure of water is 733 mm. and that of the nitrobenzene would be the difference 760 — 733 or 27 mm. Since 22.4 liters, the gram-molecular volume, would contain 1 8 grams of water vapor under the standard conditions, an equal volume under 760 mm. pressure and at o° would contain 123 grams of nitrobenzene. Since the volumes

182 PHYSICAL CHEMISTRY

are indirectly proportional to the pressures we would have, as the weights are proportional to the pressures, 1 8 gr. : % gr. : : 760 mm. : 733 mm. (the vapor pressure of

water at 99° C.). This gives - — 733 grams of water

760

which would pass over. In a like manner we find *

760 grams of nitrobenzene in the distillate. These give us the

ratio of I23 X 2? : l8 X 733 or 367 : 1466 or i : 4 as the 760 760

relative weights of the distillates. As the water is much lighter than the nitrobenzene, the volume of water is much larger relatively to that of the nitrobenzene that passes over. If the molecular weight of the substance being distilled with steam is not known, it can be readily calculated by measuring the volume of the liquids distilled over, and from their specific gravities the weight could be determined and from this ratio the value of m in place of the molecular weight of nitrobenzene vapor could be calculated.

CHAPTER XVII PHASE RULE

SINCE we know that the existence of water in the vapor, liquid, or solid phase depends upon the conditions of tem- perature and pressure, the limiting value for any particular phase is a question merely of the relation of these factors. In a consideration of the subject of phases and of the problems of equilibrium from this point of view, we practically take into consideration the heat and volume energy and leave out of consideration the force of gravity, electrical strains and stresses, distortion of the solid mass, capillary tension, etc., and thus confine ourselves to those systems wherein there exists only uniform temperature, pressure, and chemical potential.

In a system that contains only one phase, unless we have both the pressure and temperature designated, the con- centration is not known. Both of these factors are needed to establish the system. We know that both of these in- dependent variables can be changed within certain limits and the system still be maintained as a one-phase system. Then the question arises : What are the limits to which these independent variables can be varied and yet retain the system as a one-phase system ? That is, What are the boundaries of any of these different possible one-phase systems such as water, and what will happen to the system when these limits are exceeded? If the pressure and temperature are varied in the proper direction, a vapor can be made to condense into a liquid, — the greater the pressure the more of the vapor will disappear and the greater the liquid phase will become. The

183

1 84 PHYSICAL CHEMISTRY

concentration of the system has increased and we have a two-phase system. If, on the other hand, the pressure is diminished and the temperature increased sufficiently, it may break up and become disintegrated by the decomposition of the components. So that the boundary limits in all directions are not accessible and hence not easily established experimentally.

By decreasing the temperature of the two-phase system of water — liquid and vapor — a new phase appears. This is the solid (ice). When this occurs we have the system more securely fixed, as it were, for none of the variables can now be changed without causing the disappearance of some of the phases — ice, if the temperature is increased, or liquid, if the temperature is decreased. Every phase of a system has its boundaries or limitations on all sides, that is, its sphere of existence. These boundaries are represented by the in- dependent variables — the temperature, pressure, and con- centrations. We see then that every system has a certain amount of freedom in the variation of its variables in so far as the identity of the system is not destroyed, and we have also seen that this sphere of freedom is not necessarily bounded on all sides by other phases. This "sphere of existence " is spoken of as the number of degrees of freedom of the system and is defined as " the number of the variable factors — temperature, pressure, and concentration of the components — which must be arbitrarily fixed in order that the conditions of the system may be perfectly defined. " — Findlay's Phase Rule, p. 16.

A gas would have two degrees of freedom because, in order to determine its concentration, we should have to define both the pressure and temperature.

A system, liquid-vapor, has one degree of freedom, while a system, solid-liquid-vapor, has no degree of freedom, because a change of any of the variables would cause one of the phases to disappear and the equilibrium to be disturbed.

PHASE RULE 185

In speaking of the amount of variance or variation of the system, we say that the system is non variant (invariant), monovariant, divariant, multivariant, etc., when the number of degrees of freedom is respectively zero, one, two, three, etc. This relation between the number of degrees of freedom, the number of independent variables, and the number of components of the system has been expressed by Gibbs in his celebrated Phase Rule, which defines the system completely. This Phase Rule may be stated as follows : The number of degrees of freedom of a system is equal to the number of com- ponents plus two, minus the number of phases. This may be expressed by the following equation :

JV + 2 - P = F

in which N is the number of components, P the number of phases, and F the number of degrees of freedom, or the variance of the system.

The concept of phases has been of great importance in aiding the classification and correlation of a large number of isolated facts, in the interpretation of new phenomena, and in guiding us in the discovery of new phenomena and their relations. In this respect the Phase Rule as a system of classification of interrelated phenomena is to chemistry in general what the periodic law is to inorganic chemistry. It is really a basis of classification of the phenomena of chemistry rather than a separate division of the subject.

Ostwald goes even farther and states that it is possible from the principles of chemical dynamics - (the theory of the progress of chemical reaction and the theory of chemical equilibrium) to deduce all of the stoichiometrical laws, the laws of constant proportion, the laws of multiple proportions, and the law of combining weights. Through this conception of the phase introduced by Gibbs and amplified by himself and Franz Wald, Ostwald proceeds to deduce these laws in his Faraday Lecture (Jour. Chem. Soc., 85, 506 (1904)).

FIG. 35.

1 86 PHYSICAL CHEMISTRY

SYSTEM OF WATER

The p-t diagram, Fig. 35, represents the whole range of temperatures and pressures of the system water, and this area is divided into three areas representing the ranges of temperature and pressure at which water can exist as vapor, as liquid, and as solid. Each of these three systems consists of one phase, hence, according to the Phase Rule N + 2 — P = F, we have 1 + 2 — 1 = 2; i.e. two degrees of freedom or a Divariant System. The three divariant systems then are:

1. The area DCB-t-axi$ representing the vapor phase,

2. The area ECB representing the liquid phase,

3 . The area DCE-p-axis representing the solid phase.

It is apparent, as in the case of the liquid phase, that at a point such as G, if the temperature be kept constant, there are a large number of pressures to which the liquid can be subjected without introducing a new phase or causing the liquid phase to disappear. Likewise, if the pressure at G be kept constant, there are a large number of temperatures at which the liquid phase persists, i.e. the liquid phase is capable of existing at various temperatures at the same pressure. This is true of any other phase ; each pressure has a number of temperatures and each temperature a number of pressures at which the phase exists.

The boundary between the vapor area and the liquid area is represented by the curve CB, which is the Vaporization Curve and represents the equilibrium between the liquid and vapor phases. Since we have two phases in equilibrium, according to the Phase Rule we should have 1 + 2 — 2 = 1, or a Monovariant System. The same is true of the equilibrium curve between vapor and solid, represented by the Sublima-

PHASE RULE 187

tion Curve, DC, and the equilibrium between the solid and liquid represented by the Fusion Curve, EC. Hence we have three monovariant systems represented by the following curves :

1. CB, representing equilibrium between the liquid and vapor phases,

2. CD, representing equilibrium between the vapor and solid phases,

3. CE, representing equilibrium between the liquid and solid phases.

The three curves representing the monovariant systems intersect for water at a point known as the triple point. This point represents the only temperature and pressure at which the three phases — solid, liquid, and vapor — can exist in equilibrium ; for water this is at 4.6 mm. pressure and at + 0.0075°. According to the Phase Rule, since we have three phases present we should have 1-1-2—3 = 0; i.e. the system is a Nonvariant System.

We have just denned the boundaries of the various phases when in equilibrium, but it is natural to inquire if any particular phase can exist under any other conditions than those represented by the diagram. It is known that if vapor is cooled very carefully, it can be obtained at a tem- perature much below that at which it should condense and become a liquid. In the diagram, Fig. 35, let F represent some temperature and pressure of the vapor. By cooling the vapor very carefully it may be made to follow the conditions represented by the line FG, and at G, in the liquid area, the vapor phase still exists. That is, the vapor is capable of existing under other conditions than that rep- resented by the area designated vapor, but under such conditions the system is said to be in a state of labile equilib- rium ; and if a minute trace of the liquid phase be introduced, some of the vapor will become liquid and assume a condition of stable equilibrium with the vapor represented by a point

1 88 PHYSICAL CHEMISTRY

H on the equilibrium curve CB. If we continue to cool the monovariant system, liquid-vapor, it is possible to con- tinue the curve CB into the solid area to A , without the ap- pearance of the solid phase. That is, we have undercooled the liquid below its freezing point. If, however, a portion of the solid phase is introduced, the liquid phase will dis- appear and the system will become a system composed of solid and vapor in equilibrium. We have not been able to obtain the solid phase under such conditions that a liquid or vapor exists, but a liquid can be heated above the temperature at which it is in equilibrium with the vapor phase and be rep- resented in the vapor phase area. It is claimed that water has been heated to about 200° C. and still remained in the liquid phase.

At the triple point C we have the three phases in equi- librium. If the system, solid-liquid-vapor, be heated, the solid phase will disappear first and the equilibrium between liquid- vapor will be produced ; and if heat be continually added, the system will take the direction represented by the curve CB. If the system be cooled, the liquid water will disappear and the equilibrium will be described by the curve CD, which represents the equilibrium between ice and vapor.

The triple point C for water is not exactly o° C., as the melting point is defined as o° under a pressure of 760 mm. This ice is under its own vapor pressure, which is nearly 4.6 mm., or practically one atmosphere less. From Table XXXIV, which gives the fusion pressure of ice for pressure as high as about 2000 atmospheres, it is found that an in- crease of one atmosphere lowers the melting point of ice 0.0075°, *"•£• it would require 134 atmospheres to change the melting point i° C.

PHASE RULE 189

TABLE XXXIV — FUSION PRESSURE OF ICE

TEMP.

PRESSURE IN KILOGRAMS PER SQ. CM.

CHANGE OF MELTING PT. PER INCREASE OF i KILOGRAM PER SQ. CM.

o°C.

- 5

o (4.6 mm.) 610

0.0072 0.0087

— IO

- 15

1130 1590

O.OIO2 O.OIlS

— 20

1970

0.0135

Polymorphism. — We have been considering the physical forms of matter, i.e. the different phases due to the change in pressure and temperature. Whether water exists in the solid, liquid, or vapor phase depends upon the pressure and temperature to which it is subjected. It is known that certain substances exist in only one vapor, one liquid, and one solid phase ; but many other substances exist in four or more different phases. For example, sulphur exists in at least four phases : two solid, one liquid, and one vapor. The same is true of a large number of other substances. The solid phases are always different in crystalline form, the melting points are different, as well as the specific gravity and a number of other physical properties. This phenom- enon is known as polymorphism and was recognized by Mitscherlich as early as 1820 in the cases of disodium hydrogen phosphate and of sulphur. Formerly polymor- phism was considered a very rare thing, but so many cases have now been observed that it is considered the rule rather than the exception. When an element exists in more than one form or modification it is said to exhibit allotropy, and the forms or modifications are termed allotropes or allotropic modifications. When compounds exhibit this phenomenon it is termed polymorphism, and depending on the number of crystalline forms, the compound is said to be, for two forms,

190 PHYSICAL CHEMISTRY

dimorphous ; for three, trimorphous ; for four, tetrarhor- phous. The term polymorphism is frequently applied to both compounds and elements, but does not include the allotropy of amorphous substances, such as ozone, or of liquid sulphur.

Types of Polymorphism or Allotropy. — The different allotropic modifications of substances have different and distinct physical properties : crystalline form, melting point, rate of expansion, conductivity of both heat and electricity, color, etc.

The transformation of a substance from one phase into another takes place at constant temperature for a given pressure. This is illustrated by the change of liquid water into ice, where we have the appearance of a new phase and the two phases coexisting in equilibrium ; or at very high pressures the reverse change may occur. The conditions of temperature and pressure under which the change of one phase into another occurs or where a new phase appears and coexists in equilibrium with the others is termed the transition point. The temperature at which this occurs is the transition temperature, and the pressure, the transition pressure, which, however, may vary over wide ranges without appreciably affecting the temperature of equilib- rium, and as a result is many times neglected, particu- larly in the case of such transitions as that of a iron into /3 iron. The transition point is also called the inversion point.

The three following types of polymorphic or allotropic substances exist :

I. Enantiotropic substances are those whose polymorphic forms may be directly transformed one into the other, and the transition point lies below the melting point of each of the forms.

In Table XXXV are listed a few well-marked examples of enantiotropic polymerization among inorganic substances.

PHASE RULE TABLE XXXV

191

SUBSTANCES

FORMS

TRANSITION TEMPERATURE

/ a^P

\ ^^±T

780° 920

Rhombic ^f. Monoclinic

95-5

J Gray ^ Tetragonal I Tetragonal ^ Rhombic

18 '161

f «^t/3 I /3^±T

170 340

Agl

Hexagonal ^fH Regular

AgN03

Rhombic ^ Rhombohedral

159-5

As2S2

Red ^± Black

267

Ca2SiO4

7^/3

675

/^«

1420

HgI2

Tetragonal ^ Rhombic

126

KNO3

Rhombic !^ Rhombohedral

129.5

K2SO4

Rhombic ^ Hexagonal

599

Tetragonal ^ a rhombic

-16

a rhombic ^ 0 rhombic

NH4N03

/3 rhombic ^ Hexagonal rhombohedral Hexagonal . rhombohedral Ze^ Regular

85-4 125

SiO2

Quartz <* Tridymite

800

T1NO3

[ Rhombic <* Rhombohedral 1 Rhombohedral <* Regular

728 142-5

II. Monotropic Substances, Iodine monochloride is known in two forms : a-ICl which melts at 27.2°, and /3-IC1 which melts at 13.9°, the a form being the stable form at ordi- nary temperature. These do not exhibit a transition period nor are they directly transformable one into the other. A number of substances manifest this phenomenon of not

I Q2 PHYSICAL CHEMISTRY

being reversibly transformable and polymorphism of this irreversible kind is termed monotropy.

III. Dynamic Allotropy. It is known that two of the liquid forms of sulphur, S\ and SM, can exist together in definite proportions, which depend on the temperature. This phenomenon is termed dynamic allotropy. The various solid polymorphic forms cannot exist together except at the transition point, but those manifesting dynamic allotropy can do so, and this is explained on the basis of the existence of molecules of different complexity.

Smith and his colaborers have shown that the two liquid phases of sulphur, SA and SM, have different solubilities in a number of different solvents : diphenylmethane, di- phenyl, /?-naphthol and triphenylmethane ; SA dissolves in these solvents with an absorption of heat as shown by the ascending curve of solubility, while S^ dissolves with evolu- tion of heat as shown by the descending curve of solubility.

Many substances that manifest polymorphism have labile modifications that exist at temperatures far below the transi- tion point or inversion temperature as in the case of calcite and aragonite, the two solid modifications of calcium car- bonate. On heating, aragonite changes to calcite, but at ordinary temperatures the two forms exist in apparent stable equilibrium. In the case of carbon the three modifi- cations exist together under ordinary conditions of tem- perature and pressure, which is possibly due to the high inversion temperature. The same is probably true in the case of titanic acid and many others.

ONE COMPONENT SYSTEM — SULPHUR

The p-t diagram for sulphur is represented in Fig. 36. Sulphur exists in two solid crystalline forms, the rhombic, stable below 95.5°, and the monoclinic, the stable form, between 95.5° and 120°.

PHASE RULE

193

Vapor

IlA 120*151*

Sulphur

FIG. 36.

This figure will probably be more readily understood if it is redrawn, first drawing the p-t diagram for rhombic sulphur and then drawing the p-t diagram for monoclinic sulphur superposed upon this with the melting point of monoclinic sulphur (120°) located upon the vapor pres- sure curve for rhombic sulphur.

Applying the phase rule to the various systems represented by the areas, lines, and points as we did in the case of the p-t diagram for water we would have :

I. Fields or areas. Here we have one phase. Then from the

Phase Rule, N — P + 2 = F, substituting, we have i — i + 2 = 2. Therefore the areas represent divariant systems. There are four of these :

1. Area under line EFCB — sulphur vapor

2. Area to the right of BCGH — liquid sulphur

3. Area to left of EFGH — rhombic sulphur

4. Area of the triangle GFC — monoclinic sulphur

II. Curves. According to the Phase Rule we have, 1 — 2 + 2 = 1, therefore monovariant systems:

1 . Curve EF — rhombic-vapor

2 . Curve FC — monoclinic -vapor

3. Curve CB — liquid-vapor

4. Curve CG — monoclinic-liquid

5. Curve GH — rhombic-liquid

6. Curve FG — rhombic-monoclinic

III. At the intersection of some of these curves we have three phases in equilibrium, and according to the Phase Rule we have 1—3 + 2=0; therefore nonvariant systems. These are called triple points.

1 . Point F — rhombic-monoclinic-vapor

2 . Point C — monoclinic-liquid-vapor

IQ4 PHYSICAL CHEMISTRY

3 . Point G — rhombic-liquid-monoclinic

4. Point A — rhombic-monoclinic-vapor is a condition of labile equilibrium and is not readily realized.

The intersection of the two sublimation curves at F represents the transition point 95.5° at which rhombic and monoclinic sulphur are in equilibrium. Below this tempera- ture rhombic sulphur has the lower vapor pressure and is the stable form, while above this temperature monoclinic sul- phur is the stable form.

CHAPTER XVIII

SOLUTION OF SOLIDS IN LIQUIDS— I

THE solubility of a solid in a liquid depends upon the nature of the solvent as well as upon the solute. The solu- bility is also usually greatly affected by the temperature, but the pressure does not have such a marked effect.

In Figs. 37 and 38 we have represented the change in the solubility of solids in water with changes in temperature. These are termed temperature-concentration diagrams.

Generally speaking, the analogous compounds of the ele- ments of the same family, if arranged in the order of their

FIG. 37-

FIG. 38.

solubility, will be found to be in the increasing or the de- creasing order of their atomic weights.

Cs, Rb, K, Na, Li, with decreasing order of atomic weights, have increasing solubility of their chlorides and nitrates. This does not hold absolutely.

These solubility curves are equilibrium curves and rep- resent the equilibrium between the solid salt and the solu- tion, which is saturated with respect to the solid phase separating. A saturated solution is then a solution, at a specified temperature, in equilibrium with the solid phase.

196 PHYSICAL CHEMISTRY

If we have two curves, as in Fig. 37, A B must represent the solubility of one chemical individual and BC that of another. That is, along the line A B a different solid phase separates than along the line BC. Below the curve A B we have un- saturated solutions, and on the curve, saturated, and above, supersaturated solutions. In all solubility work we must consider what solid is in equilibrium with the solution, and since many salts separate with water of crystallization, we may have the same solubility at different temperatures. It must be remembered that a solution is saturated with respect to a particular substance only when it is in equilib- rium with that particular substance at the specified tem- perature.

The solubility of organic substances, likewise, depends upon the solvent and the solute, that is, upon the chemical character of both. In water, almost all substances con- taining the hydroxyl group (OH) dissolve more or less readily, e.g. the alcohols. In the case of organic acids, the solubility of the members of a homologous series decreases as the carbon content increases (e.g. formic, acetic, propionic, butyric). The solubility of the higher members of the series is small. Benzene, C6H6, is insoluble in water ; phenol, C6H6OH, is soluble to the extent of about two per cent in water ; while dihydric phenols, C6H4(OH)2, are very soluble, and trihydric phenols, C6H3(OH)3, are miscible in all propor- tions with water. Following the analogy, practically all alcohols are soluble in alcohol and all acids in acetic acid, all hydrocarbons in benzene, etc. An effort has been made by Carnelly and Thomson (Jour. Chem. Soc. 53, 782 (1888)) to formulate some rules for the solubility of substances, and they make the following general statements :

i. That for any series of isomeric organic compounds the order of solubility is the same as the order of fusibility : the most fusible is the most soluble. Taking all solvents into account, 1755 out of 1778 cases hold.

SOLUTION OF SOLIDS IN LIQUIDS 197

2. In any series of isomeric acids not only is the order of solubility of the acids themselves the same as the order of fusibility, but the same order of solubility extends to all the salts of the second acids, so that the salts of the more soluble and more fusible acids are also more easily soluble than the corresponding salts of the less fusible and less soluble acids. Five exceptions out of 143 cases were found.

3. For any series of isomeric compounds the order of solubility is the same no matter what may be the nature of the solvent. No exception to this was found out of 666 cases.

4. The ratio of the solubilities of the two isomerides in any given solvent is very nearly constant, and is therefore independent of the nature of the solvent.

Pitch of Solubility Curve. — In the pitch of the solubility curve one has some criterion as to the true heat of solution of the particular substance. By inspecting a solubility curve the sign of the heat effect involved in the solution of the substance can be ascertained. If the substance dissolves with an absorption of heat, it will dissolve in greater quan- tity as the temperature is increased. Most inorganic salts dissolve in water with absorption of heat, and their solu- bility increases with an increase in the temperature. Ex- amples are NH4NO3 and NH4CNS. A number of salts dissolve with the evolution of heat, and their solubility de- creases with increase in temperature; examples are most anhydrous sulphates, calcium isobutyrate, etc. We have a large number of salts, intermediate between these two classes, which dissolve with practically no heat effect, and the solubility of which is nearly constant for wide ranges of temperature. Common salt, NaCl, is an example of this class.

We must not fail to distinguish between the heat of solu- tion usually determined in thermo-chemistry and the true heat of solution, or perhaps it had better be called the

198 PHYSICAL CHEMISTRY

heat of precipitation, which has the opposite sign. By heat of solution or heat of precipitation we mean the heat effect when the solute is added to an almost saturated solu- tion. The heat of solution in the thermo-chemical sense is the heat effect when the solute is dissolved in a large amount of water and is very much more easily measured than the heat of precipitation. Calcium isobutyrate below 80° dissolves in a large quantity of water with evolution of heat, in a little water with absorption of heat. Cupric chloride dissolves in a large amount of water with evolu- tion of heat, and this heat effect decreases as the quantity of water used is decreased. In nearly saturated solutions the heat of solution changes sign and we have an absorption of heat.

It follows then that there must be some quantity of water in which a definite quantity of the salt will dissolve without either evolution or absorption of heat. This has been veri- fied experimentally in the case of the hydrates of FeCla. The heat of precipitation of NaCl is very nearly zero, and consequently the change in the solubility of this salt with the increase in temperature is very slight. So one can tell very readily the sign of the heat effect from the solu- bility curves, providing they are continuous curves. But if a curve has a break in it at some point, a discontinuity, we know that some change has taken place, — probably in the phases in contact with the solution. Hence any such sharp discontinuity will lead us to suspect that there is a change in the phase relations. As we have a number of such cases coming under the head of hydrates we shall defer their treatment.

THEOREM OF LE CHATELIER

We have seen that the results of the determinations of the effect of pressure on the fusion point of ice show that the temperatures at which the solid and liquid are in equilib-

SOLUTION OF SOLIDS IN LIQUIDS 199

rium are below the triple point. Ice has a lower density than liquid water, showing that the most dense phase of water is liquid water, hence when the system is subjected to pressure it will tend to compensate for this external pres- sure by readjusting itself so as to occupy a smaller volume, and if we have ice present this increased pressure will result in liquefying the ice, and the system will occupy a smaller volume. If, however, the temperature at which the solid and liquid are in equilibrium is above the temperature of the triple point, the substance has a greater density in the solid than in the liquid state, and increased pressure will tend to cause the system to pass into the solid state which is the most dense. For substances in general, the solid is the most dense phase. Water is one of the few exceptions to this general rule.

In the case of benzene the most dense phase is the solid. Hence an increase in the pressure will cause the freezing point to rise, and the fusion curve will slant away from the pressure axis toward the right. If benzene is subjected to 3742.7 mm. pressure, the melting point will be raised 0.143°.

This fact, that by means of an increase in pressure the most dense phase of the substance tends to form, represents one of the most fundamental laws. This law has its coun- terpart in the Law of Motion, that action and reaction are equal and in the opposite direction. This is known in chemistry as the Theorem of Le Chatelier and may be ex- pressed as follows : " Any change in the factors of equi- librium from outside is followed by an inverse change inside the system ; " i.e. there is a change in the factors of equilib- rium tending to restore equilibrium.

Hence by increasing the external pressure on a system there would be an increase of that component or phase occupy- ing the least volume ; or if heat is added, we have an increase of that component or phase which involves an absorption of heat. Hence a system in equilibrium tends to return

200 PHYSICAL CHEMISTRY

to equilibrium by eliminating the disturbing element. Ammonium chloride dissolves with expansion, and the solubility is diminished about one per cent by increasing the pressure to 160 atmospheres. Copper sulphate dis- solves with contraction, and the solubility increases 3.2 per cent on increasing the pressure to 60 atmospheres. Sodium sulphate with 10 molecules of water of crystallization dis- solves with absorption of heat, hence the solubility increases with an increase in temperature. All of these facts are in accord with the Theorem of Le Chatelier.

If a system is in equilibrium at a specified temperature and heat be applied, there will be a tendency to compensate for this heat added to the system by a readjustment within the system either through a physical adjustment, such as increase of the volume if the pressure remains constant, or by an increase of pressure in order to maintain the volume constant. Or if this addition of heat results in the com- pensating change through a chemical reaction, such as the formation of ozone from oxygen, or in the preparation of nitric oxide, carbon bisulphide, acetylene, etc., or the dis- sociation of calcium carbonate, we shall have either an ab- sorption of heat or an evolution of heat, depending upon the particular type of reaction that is taking place under our specified conditions. In most cases of dissociation the in- crease in dissociation is associated with an absorption of heat, that is, it is an endothermic reaction. For as heat is applied the reaction proceeds, and being accompanied by an absorption of heat, the heat from the outside of the system has to be applied to maintain the system at a con- stant temperature, so that a rise in temperature favors the formation of the products of the reaction. Ozone is pre- pared according to the equation 3 O2 = 2 O3, and the re- action is accompanied by an absorption of heat. It is an endothermic reaction, and therefore the percentage of ozone formed increases with the rise in temperature. If

SOLUTION OF SOLIDS IN LIQUIDS 2OI

the reaction evolves heat it is said to be exothermic and takes place best with a decrease in temperature.

The inversion temperature at which the rhombohedral form of NH4NO3 can be transformed into the /?-rhombic form can be changed from 85.45° under a pressure of one atmosphere to 82.29° by increasing the pressure to 250 at- mospheres.

The following geological application of the Theorem of Le Chatelier worked out by Van Hise is a marked confirma- tion of this principle. In the outer zone of the earth's crust there takes place the metamorphic changes of the minerals, such as the alteration of the silicates by means of hydration, carbonation, and desilicification, which are accompanied by a liberation of heat, decrease in the density, and an in- crease in the volume. This region is known as the Zone of Katamorphism, and in it the average specific gravity of the minerals is 2.948. In the inner zone of metamorphism, a few thousand feet from the surface of the earth, where there is an increased pressure due to the overlying rocks, there is also a much higher temperature than in the outer zone of metamorphism. This inner region is known as the Zone of Anamorphism, and we have the alteration of the minerals due to dehydration, decarbonation, and silicifica- tion, which are accompanied by an absorption of heat and condensation of volume, which are the typical changes. The average specific gravity of the minerals in the Zone of Anamorphism is 3.488, which is about 18 per cent higher than that of the minerals in the Zone of Katamorphism. This is a fair approximation and shows that a given mass of material occupies a much larger volume in the Zone of Katamorphism than in the Zone of Anamorphism.

A few special examples will serve to illustrate this. The change of hematite into limonite may be represented by the equation 2 Fe20s + 3 H2O = 2 Fe2O3 • 3 H2O. This reaction takes place in the Zone of Katamorphism and is one of

202 PHYSICAL CHEMISTRY

hydration. The specific gravity of hematite is 5.225 and of limonite 3.80, which change represents an increase in volume of 60.7 per cent. One of the most common and best known alterations is hematite into siderite. This may be represented as follows :

Fe2O3 + 2H2S + CO2 = FeSa + FeCO3 + 2 H2O + k cal. If the products of alteration are pyrite (isometric, sp.gr. 5.025) and siderite (sp.gr. 3.855), the increase in volume is 76 per cent ; but if marcasite (orthorhombic, sp.gr. 4.875) is formed instead of pyrite, the increase in volume of mar- casite and siderite over the -hematite is 78.7 per cent. The most marked case known in which minerals are concerned is the alteration of magnetite into siderite. The equation Fe304 + CO + 2 CO2 = 3 FeCO3 represents the alteration which gives a change of specific gravity from 5.74 for mag- netite to 2.83 for siderite, which represents the enormous increase in volume of 101 per cent. These changes all take place with the liberation of heat, expansion of volume, and decrease in symmetry.

As a typical example of deep-seated reactions under great pressure and high temperature, the change of calcite into wollastonite is one that is well known, CaCO3 + SiO2 = CaSiO3 + CO2 — k cal. Here we have a change in specific gravity from 2.713 for calcite and 2.655 f°r SiO2 to 2-&5 for wollastonite, which represents a decrease in volume of 31.5 per cent provided the silica is solid and the carbon dioxide escapes. We have, as in all other deep-seated reactions, an absorption of heat and condensation of volume as the typical changes in the Zone of Anamorphism.

The same principles are clearly illustrated in the case of the alteration of silicates, which are brought up by means of some erogenic movement to the surface of the earth or near to it. This alteration of the silicates by hydration, carbonation, and desilicification is attended with the con- comitant liberation of heat, a decrease in the specific grav-

SOLUTION OF SOLIDS IN LIQUIDS 203

ity, and a marked increase in the volume. The alteration of garnets into different combinations of the following minerals is well known: serpentine, talc, chlorite, epidote, zoisite, magnesite, and gibbsite.

The following equation, which is typical of these trans- formations, will suffice to illustrate the marked change which amounts in this case to an increase in volume of 76 per cent :

+ 15 H2O + 3 C02

pyrope sp.gr. 3.725

3 H2Mg3Si4012 + 3 MgC03 + 8 A1(OH)3 + k cal.

talc magnesite gibbsite

sp.gr. 2.75 sp.gr. 3.06 sp.gr. 2.35

CHAPTER XIX SOLUTION OF SOLIDS IN LIQUIDS — II

THE SOLVENT AND SOLUTE CRYSTALLIZE TOGETHER AS A MIXTURE OF THE PURE COMPONENTS

IN the two component systems in which we have a liquid solvent, and a solid solute, we assume that the vapor pressure of the solid is so small that it is negligible, so that in the systems we are to consider one of the components is non- volatile and one volatile. There are three general types of such systems :

Type I. The solvent and solute may crystallize together as a mixture of the pure components.

Type II. The solvent and solute crystallize in accordance with the Laws of Definite and Multiple Proportions.

Type III. The solvent and solute crystallize together not in accordance with the Laws of Definite and Multiple Pro- portions, but as solid solute dissolved in a solid solvent in varying proportions, within certain limits.

TYPE I — SYSTEM WATER AND SODIUM CHLORIDE

At the intersection of the vapor pressure and sublimation curves for pure water, the solid, liquid, and vapor phases are in equilibrium, and we designate this the fusion point of ice, or the transition point. As these phases are in equilib- rium under the pressure of the vapor of the system, it is a pressure of 4.6 mm. and at the temperature + 0.0075° C. The freezing point of liquids is the temperature at which the

204

SOLUTION OF SOLIDS IN LIQUIDS 205

solid and liquid phases are in equilibrium under atmospheric pressure, which in the case of water would be under nearly one atmosphere pressure more than at the transition temper- ature. As an increase in pressure of one atmosphere lowers the melting point of ice 0.0076°, it is apparent that the fusion point, freezing point, and transition point may be considered the same. On thep-t diagram, Fig. 39, let us represent the one-component systems by the following dotted lines.

A B is the vapor pressure curve

AC is the sublimation curve

AD is the fusion curve

A is the triple point and represents

the melting point of ice and the freezing pIG 39<

point of water.

If a second component, solid salt, NaCl, be added to water, the vapor pressure of the solution produced is lower than the vapor pressure of the pure solvent water, and the amount of the lowering of the vapor pressure is proportional to the concentration. By adding successive amounts of NaCl the vapor pressures of the solutions would be rep- resented by vapor pressure curves parallel to AB, but successively lower until we would reach a concentration representing the maximum amounts of salt that are soluble at the different temperatures, when we would have saturated solutions, the vapor pressures of which we represent by CF. This represents the maximum lowering of the vapor pressure of the pure water. If these vapor pressure curves are pro- jected until they intersect the freezing point curve, we have the point A, the intersection of the vapor pressure curve and the sublimation curve, passing down successively to the point C, its lowest limit. Similarly, the curve AD, the fusion curve, would pass over the space to the left of its original position and take up as its final position, CE. A, the freezing point of pure water, has been lowered from the

206 PHYSICAL CHEMISTRY

temperature o° to the temperature tc, and the distance along the temperature axis represents the maximum lowering of the freezing point.

The degree of variance of this two-component system may be obtained by applying the Phase Rule as follows :

I. Areas. (N — P + 2 = F), 2 — 2 + 2 = 2.'. Divariant systems :

1 . Salt-vapor below GCF and above /-axis.

2. Solution- vapor between BACF.

3. Solution-ice between DACE.

4. Ice-salt between ECG and £-axis.

II. Curves. (N - P + 2 = F), 2 - 3 + 2 = i .'. Mono- variant systems :

1. CF Solution-vapor-salt.

2. CE Solution-ice-salt.

3. CG Ice-salt-vapor.

-4. CA Solution-ice-vapor.

III. Point C. (N - P + 2 = F), 2 - 4 + 2 = o /. Non- variant system.

At point C the four phases, solution-salt ice-vapor, are in equilibrium. This is known as a Quadruple Point.

If a body in the liquid state be allowed to cool without change of state, and measurement of the temperature be made at different times, and these results plotted on a temperature-time axis, the curve has a regular form — a logarithmic curve when the cooling takes place for constant temperature surroundings. But if a change of state occurs, there is a decided change in the shape of the curve. In all cases observed the passage of a liquid to a solid is accom- panied by the evolution of heat. This heat liberated com- pensates for loss of heat by radiation and maintains the temperature constant, the solid separating and the process continuing until the whole of the liquid has changed to the solid state, when the temperature changes become regular again.

SOLUTION OF SOLIDS IN LIQUIDS

207

In Fig. 40 we have an illustration of the continuous cooling curve without change of state, while Fig. 41 illustrates the cooling curves of a number of pure substances. These show a marked break at the temperature of the melting point of

Time

FIG. 40.

Time

FIG. 41.

the substance ; above and below this the temperature falls regularly, but at this point the temperature remains con- stant until all of the substance has solidified.

The cooling curves for two component systems, such as solutions of sodium chloride in water, differ from that of a pure substance. For when solidification begins, either of the two components may separate, depending upon the concentration of the solution. At the point of solidification we have a marked break in the cool- ing curve, the separation of the pure component, which results in a change in the concentration of the solution with a lowering of the freezing point. Hence, on a t-time diagram for a solution of the concentration of ten per cent of sodium chloride, we should have the regular cooling of the solution, as represented by ab in Fig. 42, until at the point 6, the solid water (ice) begins to separate, and we have a change in the slope of the cooling curve. This separation of the ice continues until the point c is reached, when the remainder of the solution solidifies completely.

Time

FIG. 42.

208

PHYSICAL CHEMISTRY

a a

FIG. 43-

During the time indicated by cd, the temperature remains constant. On further cooling a regular cooling curve is obtained, as represented by de.

By this method the cooling curves of solutions over the whole range of concentrations desired may be obtained. The

temperature, b, at which these solutions begin to solidify has thus been determined. So if these values of the freezing points are plotted on a temper- ature-concentration diagram against their respective con- centrations and the points connected, we obtain the curve represented by a dotted line, the freezing or solidification curve. If on this diagram the cooling curves be superposed so that the freezing points, 6, are placed on the freezing curve at the point corresponding to their proper concentration, we have the diagram repre- sented by Fig. 43.

The first curve at the left is the cooling curve for pure water, and we have the usual curve for a pure substance, with the break occurring at b when it begins to freeze, and the temperature remaining constant until the liquid has all disappeared (be), when the cooling again becomes regular, as shown by the section ce. It will be noticed that the cool- ing curve for a solution containing 23 per cent of sodium chloride is exactly like this and is analogous to the cooling curve of a pure substance as shown in Fig. 41. That is, at the temperature designated /„ the solidification begins, and the temperature remains constant until the whole mass has solidified. This takes the time indicated by cd. This freezing point is different from the freezing point of any of these solutions in so far as the solidification takes place at constant temperature, and the composition of the solid

SOLUTION OF SOLIDS IN LIQUIDS 209

phase separating is the same as that of the solution from which it separates. This temperature is the lowest tem- perature at which any solution of these two components can exist. It is also the lowest melting point of any mixture of the two components. This temperature is called the eutectic temperature ; the solid which separates the eutectic and the point C, Fig. 44, is called the eutectic point. When water is one of the components, this point is also termed the cryohydric point, the mixture the cryohydrate, and the tem- perature the cryohydric temperature.

For all solutions in which the concentration of the sodium chloride is less than that represented by the point C, the solid phase separating is pure water, while for all concentra- tions greater than C, the solid phase is pure sodium chloride.

The curve ACB, Fig. 44, represents

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