Physical chemistry : its bearing on biology and medicine

Preface

The conceptions and methods of physical chemistry have been extensively utilised during recent years in attacking biological and physiological problems, and the results which have followed this application of physico-chemical principles are not only of very great interest in themselves, but are full of promise for the future. Students of biology and medicine, however, cannot truly appreciate or co-operate in this work unless they are familiar with the underlying principles. It is as a sketch of the physico-chemical basis for this modern treatment of biological and physiological problems that I have written the present volume.

The book originated in a course of lectures delivered to biological students at the University of London in 1909, but since then much fresh material has been incorporated. I have endeavoured to give a systematic exposition of physical chemistry so far as it has a bearing on the problems in question, and to illustrate the application of physico-chemical principles by examples taken from the fields of biology, physiology, and medicine. Since the book is intended chiefly for students of these sciences, the use of mathematics has been avoided as far as possible, and the reader is assumed to have only an ordinary acquaintance with physics and chemistry. Numerous refer-

I vi PREFACE

ences to original papers are given for the use of those who may desire to follow up any particular line.

Of larger works which have been frequently consulted in the preparation of this volume, the following may be mentioned : Physilcalische Chemie der Zelle und der Gewebe, by R. Hober ; Physilcalische Chemie und Medizin, by Koranyi and Richter; Grundriss der Kolloid- chemie, by Wo. Ostwald. I desire to thank Professor Benjamin Moore for permission to reproduce Fig. 22, and Herr W. Engelmann for permission to reproduce Figs. 4, 6, 10, and 14. I must also express my indebtedness to Professor Groom, Dr. Harden, and Dr. Senter, who very kindly read parts of the MS. or proofs, and made many valuable suggestions.

J. C. P.

London, June 1910.

Preface To The Second Edition

The chief new feature of this edition is the addition of a chapter on electromotive force. The treatment of permeability in Chapter Y has been extended by a short account of Czapek’s researches on the surface tension of the cell membrane, while references to recent work have been inserted throughout.

J. C. P.

London, October 1913.

Contents

CHAP. PAGE

I. Gases from the Standpoint of Experiment and

Theory. Diffusion Phenomena 1

Chapter I

GASES FROM THE STANDPOINT OF EXPERIMENT AND THEORY. DIFFUSION PHENOMENA

The recent development of physical chemistry has been characterised very specially by the elaboration and application of new methods for the study of the phenomena exhibited by solutions. These methods are closely related to a theory of solution, which in its turn is rooted in the analogy existing between the behaviour of solutions and that of gases. Any attempt, therefore, to expound the properties of solutions, and the interpretations of these properties that have been proposed, must be preceded by a glance at certain features which characterise the gaseous state, and at various theories which bear on the nature of gases.

Fundamental Experimental Laws. — For physico-chemical purposes the fundamental facts in which the behaviour of gases is revealed are summed up in three laws, two of which are purely physical in character, while the third is more accurately described as chemical. It is perhaps necessary to emphasise the fact that these three laws are absolutely independent of any theories regarding the nature of gases ; they are simply the integrated expression of experimental results.

(a) Boyle’s Law. — According to this law, the volume |

A

I occupied by a, given mass of gas varies inversely as the pressure to which it is subjected, provided the temperature is kept constant. The algebraic expression of this relationship is pv = G, where p is the pressure, v is the volume, and G is a constant. This is the equation to a hyperbola, and the curve therefore representing the corresponding changes of pressure and volume for a given quantity of a gas at constant temperature belongs to this type. If we represent by vx the volume occupied by a given quantity of gas under the pressure pv and by v2 its volume at the same temperature under the pressure p2, then we may express Boyle’s law by the formula V\v\—V2°i‘ ^-s an instarice of the extent to which this

law has been verified in work of the most accurate kind, Lord Rayleigh’s figures for hydrogen, oxygen, and carbon dioxide may be quoted.1 He has shown that if the value of pv obtained for p= 1 atmosphere is taken as unity, then the value of pv for p — 0'5 atmosphere, instead of 1*0000, is found to be 099974 in the case of hydrogen, 1-00038 in the case of oxygen, and 1-00279 in the case of carbon dioxide. For ordinary gases and under ordinary conditions, therefore, Boyle’s law may be taken as an accurate statement of the corresponding variation of pressure and volume.

Under certain conditions, however, the formula pv = C ceases to represent accurately the behaviour of a gas at constant temperature, and hence it must be regarded as of only limited validity. Such deviations from strict obedience to Boyle’s law occur (1) when the pressure applied to the gas is very high, and (2) when the gas is near its point of condensation. Amagat, for instance, in his experiments 2 on the compressibility of nitrogen at 22°, found that if the value of pv for p= 1 atmosphere is taken as unity, the value for p = 62 atmospheres is as low as 0’986, while for p = 373’3 atmospheres it is as high as L207. Such deviations from Boyle’s law, however, become in all cases less marked at liighei temperatures.

(b) Gay-Lussac' s Law. — The volume occupied by a given mass of gas, kept under constant pressure, increases as its temperature is raised, and the relative expansion is approximately the same for all gases. It is found that for 1° C. rise of temperature the volume of a gas increases by -2-fs- of the volume which it occupies at 0° 0., subject to the condition that the pressure remains the same during the rise of temperature. If vQ and v are the volumes occupied by a given mass of gas at 0° C. and t° C. respectively under equal pressures, and if a = represents the coefficient of expansion common to all gases, then Gay-Lussac’s law may be expressed algebraically by the equation v = v0( 1 + at).

From the foregoing, taken in conjunction with Boyle’s law, it is easy to show that the pressure exerted by a given mass of gas kept at constant volume must increase with rising temperature in the same proportion as the volume increases at constant pressure ; so that, if p0 and p represent the pressure at 0° O. and t° C. respectively, p=p0(l-i at), subject to the condition that the volume of the gas remains the same throughout. This formula is not only deducible from the equations pv — C and v = v0(l-\- at), but is also in harmony with the results of experimental work.

The formula pv—C is applicable only when the temperature is constant, and the formula v = v0(l -+ at) only when the pressure is constant ; but since the final condition of a gas may differ from its initial condition in respect both of temperature and of pressure, it is obvious that there must be also some one equation connecting the i initial and the final volumes in this case. This equation may be deduced easily in the following manner. We may suppose that a given quantity of a gas, occupying the volume v0 at the pressure p0 and the temperature 0° C., occupies the volume v at the pressure p and the temperature t° C. ; the problem, then, is to find the algebraic relationship between v and v0. If we start with the gas at 0° and raise its temperature to t°, the pressure being kept constant, the new volume v1 occupied by the gas can be easily calculated, for these simultaneous changes of volume and temperature are subject to Gay- Lussac’s law; that is, v1 — v0(l--'r at). If now, at the

temperature t°, we alter the pressure from p0 to p, the volume changes from vx, to v, which we have chosen to represent the final volume. To simultaneous changes of pressure and volume at constant temperature Boyle’s law is applicable, so that we have pv=p0v1=p0v0(l-\at). This equation, pv=p0v0(l + at), is the algebraical expression both of Boyle’s law and of Gay-Lussac’s law. Its validity is not absolute, inasmuch as gases exhibit deviations from strict obedience to Gay-Lussac’s law as well as Boyle’s law.

If the numerical value of the coefficient a is inserted in the equation it assumes the form pv =p v0—^„ ^ ; if,

further, it is agreed to reckon temperature, not from 0° C., but from a point 273 degrees lower, and to take T as the symbol of temperature on this new scale, then

the equation may be written pv=^J^T. Temperature

reckoned in this way is known as c absolute ’ temperature, and —273° 0., the starting point of the ‘absolute’ scale, is termed the ‘ absolute ’ zero.

The equation pv = ^T sums up the physical behaviour of gases so far as that is defined by the laws of Boyle and Gay-Lussac, but for certain purposes it is desirable to have the direct relationship between vv the volume which a quantity of gas occupies at pressure p1 and absolute temperature Tv and v2, the volume which it occupies at pressure p.2 and absolute temperature rJ\ A little consideration of the foregoing equation will show

that the relationship required is = ~1-2.

(c) Gay-Lussac's Law of Volumes. — This third experimental law, although associated with the same name as the second law, is purely chemical in its character, and deals with the relative proportions by volume in which chemical reaction between gases takes place. The law i states that when two gases combine with each other to form a third gas, the volumes of the reacting gases are in a simple ratio to one another and to the volume of the gaseous product (all volumes being measured at the same temperature and pressure). Special cases of this will doubtless occur to the reader ; it is, for instance, well known that 1 volume of hydrogen combines with 1 volume of chlorine to form 2 volumes of hydrogen chloride, and that 2 volumes of hydrogen combine with 1 volume of oxygen to form 2 volumes of water vapour.

No gas is absolutely ‘perfect,’ that is, no gas conforms rigidly to the first two laws, and hence it follows that the volume ratio of reacting gases found in the most accurate experimental work is less simple than the preceding paragraph would seem to indicate. At 0° C. and 760 mm., for instance, the ratio of the volumes of hydrogen and oxygen uniting to form water is 2’0028: 1, according to Scott’s accurate investigations.1 If, however, a correction is made for the slight extent to which hydrogen and oxygen deviate from Boyle’s law (see p. 2), the volume ratio is almost exactly 2: 1.

1 Phil. Trans., 1893, A, 184, 543. See also Morley, Zcit. physikal . Chcm., 1896. 20, 417.

Theories bearing on the Nature of Gases. — (a) The

Kinetic Theory of Gases. — A little consideration of the experimental laws which have just been enunciated shows that gases are characterised by simplicity and uniformity, both in their physical behaviour and in their chemical relationships. Various theories have been brought forward which offer an interpretation of this simple and uniform behaviour. According to one of these, the kinetic gas theory, the ultimate particles of a gas are rushing about at a high speed, the direction of their motion being altered only when they collide with one another or impinge on the walls of the containing vessel. The velocity of motion will vary somewhat from one particle to another, but so long as the temperature of a mass of gas remains the same, the average velocity of the constituent particles will be constant. The pressure exerted by the gas is due to the impacts delivered on the walls of the containing vessel by the moving particles. If it is further assumed that the volume of the particles themselves is negligible compared with the total volume of the gas, and that they are perfectly elastic, it follows by the principles of mechanics that at constant temperature pv = ^mnu2, in which equation m is the mass of an individual particle of the gas, n is the number of particles in volume v of the gas, and u is the average velocity of the molecules at the temperature considered. So long as the temperature is unchanged the product \mnu 2 has a constant value, hence pv = const., which is the algebraic expression of Boyle’s law. The assumptions of the kinetic gas theory, then, involve the relation between pressure and volume required by the first fundamental law of gases. If the temperature is changed, then the value of pv for a given mass of gas alters

according to the formula already discussed — pv = ^jr^T, or, in words, the product of pressure and volume is proportional to the absolute temperature. But, according to the kinetic theory, pv = ^mnu2, and, if we are dealing throughout with the same quantity of a given gas, the values of m and n are independent of temperature, so that u 2 must be proportional to the absolute temperature. The kinetic gas theory involves therefore a definite conception of what happens when the temperature of a gas is raised ; the kinetic energy of the molecules increases proportionally to the absolute temperature.

(b) Avogadro’s Hypothesis. — According to this hypothesis, which bears especially on the third experimental law, equal volumes of different gases, measured at the same temperature and pressure, contain the same number of ultimate particles or molecules. If it is supposed that when two gases combine chemically one ultimate particle of the first gas reacts with one, two, or three ultimate particles of the second gas, then Avogadro’s hypothesis is seen to offer a plausible and natural interpretation of Gay-Lussac’s Law of Volumes. But the essential point of the hypothesis, as it was enunciated by Avogadro, lay in the distinction which he drew between atoms and molecules. He suggested that the molecule of an element was not necessarily the same as the atom, and that the ultimate particle of a gaseous element might contain one, two, or more atoms of that element. Only when this suggestion is adopted is Avogadro’s hypothesis capable of interpreting all the special cases which are summarised in Gay-Lussac’s law.

Avogadro’s hypothesis was brought forward primarily as offering an explanation of the volume relationships of chemically reacting gases, but it obviously furnishes also a simple interpretation of the uniform behaviour of different gases when exposed to changes of pressure and temperature. It is noteworthy also that the hypothesis is found to be in harmony with the consequences of the kinetic gas theory.

The proposition advanced by Avogadro has been adopted as a working hypothesis, and as such has stood the test of time ; it is, in fact, a necessary supplement to the Atomic Theory. Since the hypothesis is closely connected with much that is to follow, it is essential to indicate at this stage the results that flow directly from its acceptance.

First of all, the acceptance of Avogadro’ s hypothesis leads to a definite conception of the relation between the atom and the molecule of the gaseous elements. The argument may be stated as follows. It is a recognised experimental result that 1 volume of hydrogen unites with 1 volume of chlorine to form 2 volumes of hydrogen chloride. If now we suppose that 1 volume of hydrogen contains n ultimate particles of hydrogen, then, according to Avogadro, the 1 volume of chlorine also contains n ultimate particles of chlorine, whilst the 2 volumes of the product contain 2 n ultimate particles of hydrogen chloride ; that is, n ultimate particles of hydrogen unite with n ultimate particles of chlorine to form 2 n ultimate particles of hydrogen chloride. Since we cannot conceive of an ultimate particle of hydrogen chloride which does not contain at least one atom of hydrogen, the n ultimate particles of hydrogen must have contained at least 2 n atoms. Hence each ultimate particle, or molecule, of hydrogen must contain at least two atoms. There are grounds, which cannot be discussed here, for supposing that the molecule of hydrogen does not contain more than two atoms ; hence we must conclude that the molecule of hydrogen contains two atoms.

The argument may be similarly stated iu the case of other gaseous elements.

Secondly, the acceptance of Avogadro’s hypothesis o leads to a definite relationship between density and molecular weight. Suppose that D is the density of a gas, and that M is the weight of one molecule : let Dh and Mu represent the corresponding quantities for hydrogen. Suppose also that in unit volume of the gas at N.T.P. (that is, at normal temperature and pressure— 0° 0. and 1 atmosphere) there are n molecules ; then, according to Avogadro, unit volume of hydrogen at N.T.P. also contains n molecules. Now the ratio of the densities of two gases is equal to the ratio of the weights of equal volumes of the two . gases, measured of course at the same temperature and pressure ; hence D _ Weight of unit volume of the gas at N.T.P. _ n.M _ M Ds~ Weight of unit volume of hydrogen at N.T.P. ~ n. MH~ MH'

As has been already shown, the molecule of hydrogen contains two atoms, and therefore the value of Mu is twice the atomic weight. On the basis of 0 = 16, the atomic weight of hydrogen is POOS, so that Mu — 2-016. If, further, it is agreed to refer the density of gases and vapours to that of hydrogen taken as unity, then Du = 1, and we have df=2‘016j9. In words, the molecular weight of a gas is approximately equal to twice its density (relatively to hydrogen).

Thirdly, the adoption of Avogadro’s hypothesis permits

us to cast the equation = into a more general

form, although it should be borne in mind that in so doing we are introducing a hypothetical element into what is otherwise an expression of purely experimental laws. It is obvious that if we take weights of two gases in the ratio of their molecular weights, we are taking an equal number of molecules in the two cases, which means, according to Avogadro’s hypothesis, that we are taking equal volumes (measured, naturally, at the same temperature and pressure). Hence, if we are dealing with the molecular weight in grams of any gas, a gram-molecule, or £ mol ’ as it is called, the volume occupied at 1 atmosphere and 0° C. should always be the same. This gram-molecular volume must be the volume occupied at 1 atmosphere and 0° C. by 2-016 grams of hydrogen or 32 grams of oxygen, and that has been found to be 22 -4 litres. If, then, it is agreed that in applying the equation

pv = T the quantity of gas considered is always 1 gram-

molecule, the value of v0 for y>0= 1 is the same in all cases.

Hence the equation may be written pv = Mr, where R—^-—^

is a constant for all gases. The actual numerical value of R depends on the units in which the pressure and volume are measured ; if, for instance, pressure is measured in atmospheres and volume in litres, then R— ^ —'082.

The equation pv — RT is termed the gas equation, and is of the utmost importance, not only in connection with gases, but also in relation to the behaviour of dissolved substances, as will appear later. Whenever the equation is applied, it is understood that 1 gram-molecule of the substance is being considered.

Determination of the Molecular Weight of Gases and Vapours. — As has already been pointed out, the acceptance of Avogadro’s proposition as a working hypothesis leads to a definite relationship between molecular weight and density, expressed by the equation M= 2-016H, D being the density of the gas relatively to hydrogen. The determination of molecular weight resolves itself therefore into a determination of density, and it is necessary to consider at least two of the practical methods available for this purpose.

RegnauWs Method. — Two spherical glass bulbs, each provided with narrow tube and stopcock, and of approximately equal volume, are required. The one is used merely as a counterpoise on the balance, the other is weighed (a) when completely evacuated, (b) when filled at. known temperature and pressure with the gas under examination. The volume of tlie second bulb having been deduced from the quantity of water or mercury

B

B which it contains, the difference of the weights (a) and (b) is the weight of a known volume of the gas at known temperature and pressure.

From these data it is easy to calculate the weight of 1 cub. cm. of the gas at N.T.P., and the result so obtained is compared with the corresponding figure for hydrogen.

Victor Meyers Method. — While Kegnault’s method is specially applicable to substances which are gases at the ordinary temperature, this second method is employed in the case of

Fig. 1.

I substances which are normally liquid, but can be vaporised without difficulty.

The necessary apparatus is sketched in the preceding diagram (Fig. 1). The glass tube A with cylindrical bulb B and the two side tubes C and D is suspended in the wide vessel E, so that the end of the bulb B is a. short distance above the surface of the liquid which occupies the bottom of E. The glass rod F, which is pushed through the side tube C, is kept in position by indiarubber tubing ; the elasticity of ' the latter allows F to be temporarily pulled clear of A without any disturbance of its permanent position. The end of the other side tube D is placed under a graduated tube full of water standing in the vessel G. When the apparatus has been set up the liquid in E is boiled and the rate of ebullition is adjusted, so that ultimately the greater part of the tube E is filled with vapour ; the liquid in E must have a boiling point at least 20° above that of the liquid the vapour density of which is being determined. The boiling of the liquid in E will obviously expel a certain amount of air from the bulb B and the tube A, but ultimately, when the ebullition is steady, the expulsion of air will cease, and there will be temperature equilibrium between the inner vessel and the surrounding vapour. This state of equilibrium has been reached when after the insertion of a stopper in the top of the tube A no bubbles of air are expelled through D.

A small bottle containing a weighed quantity of the liquid under examination is then dropped through the top of A on to the end of F, and the stopper is re-inserted. When the rod F is pulled back for a moment the bottle falls to the bottom of B, in which a little glass wool has previously been placed to prevent fracture. At the temperature which prevails in B the liquid is rapidly vaporised and a corresponding quantity of air is expelled in successive bubbles from the end of D. The air thus

collected in H is the exact equivalent of the vapour

produced in B, and when no more bubbles are expelled,

its volume is found by transferring H to a cylinder full

of water and measuring at known temperature and pressure

in the usual way. Since this volume of vapour has been

produced from the known weight of the liquid taken, the

weight of 1 cub. cm. of the vapour at N.T.P. may easily

be calculated ; the density is then obtained by comparing

this result with the corresponding figure for hydrogen.

An example may be taken to show how the data obtained

in an experiment with Victor Meyer’s apparatus are used

to calculate the density, and from that the molecular

weight. In a particular case OT gram of a substance was

weighed out and vaporised in a Victor Meyer apparatus.

The expelled air was collected over water and found to

measure 32 cub. cm. at 17° C. and 750 mm. pressure.

Now the tension of aqueous vapour at 17° is 14-4 mm.,

and the volume of air expelled, when allowance has been made lor this tension, becomes ->90 x 760

= 29T6 cub. cm. at N.T.P. This, then, would be the volume of vapour produced if OT gram of the substance were vaporised at N.T.P., and it follows that the weight

of 1 cnb. cm. of the vapour at N.T.P. would be gram.

The weight of 1 cub. cm. of hydrogen under these conditions is -00009 gram, and therefore the density of the

vapour (relatively to hydrogen) is 29-i6x 4)0009 5 the

molecular weight is then 38T X 2‘016 = 76*8.

Gaseous Diffusion. — One characteristic feature of a gas as compared with a liquid or a solid is its ability to occupy fully any space which is offered to it ; it is capable of infinite expansion, and more than that, the occupation of any vacant space by a gas is accomplished with great t rapidity. Again, when two vessels containing two different gases at the same pressure are put into communication with each other, a process of diffusion goes on until the composition of the gaseous mixture is the same at all points. Each gas moves from places where its concentration is high to places where its concentration is low, and equilibrium is not attained until the partial pressure of each gas is the same throughout. Such diffusion or mutual interpenetration is quite distinct from movement of the gas as a whole. A difference of gas pressure in two places may be equalised by mass movement— air currents, for example — but diffusion goes on where such movement is excluded ; it is a molecular process.

The kinetic gas theory, which has so far been discussed only in its bearing on Boyle’s law and Gay-Lussac’s law, supplies a plausible interpretation of these diffusion phenomena. If, as the theory supposes, each molecule is moving at a high speed (a mile per second, more or less, according to the density and the temperature of the gas), it is intelligible that a gas brought in contact with a vacuous space should occupy the latter practically instantaneously. On the other hand, when one gas is diffusing into another gas the rate of advance is naturally much slower, for the forward path of each molecule, on account of the frequent collisions with the molecules of the other gas, is of a zigzag character.

One of the conclusions which can be deduced from the assumptions of the kinetic gas theory is that the velocity with which a gaseous molecule is endowed is inversely proportional to the square root of the density of the gas. It follows from this, for instance, that the hydrogen molecule has a velocity four times as great as that of the oxygen molecule at the same temperature, for oxygen is sixteen times as heavy as hydrogen. If, then, we are correct in suggesting that diffusion pheno-

OASES mena are closely related to molecular velocity, we may expect to find a definite connection between the rate of diffusion and the density of a gas. In circumstances where the molecular movement alone comes into play, the rate of diffusion of a gas ought in fact to be inversely proportional to the square root of its density.

This important relationship was verified by Graham 1 in his experiments on the rate of passage of different gases through minute apertures into a vacuum. The experiments consisted in determining the times required for a given volume of various gases kept at steady pressure to pass through a minute perforation in a metal plate into a receiver which was being constantly evacuated. Graham found that the time required for the escape, or ‘ effusion ’ as he called it, of a given' volume of any gas was proportional to the square root of its density ; in otheT words, the velocity of effusion of a gas is inversely proportional to the square root of its density.

Some of Graham’s results are recorded in the accompanying table. The times necessary for the effusion of a certain volume of gas are given in the second column, while in the third column are the figures calculated on the assumption that the time of effusion is proportional to the square root of the density ; in both cases the time required for the effusion of air is taken as unity.

Time of Effusion.

Gas. Experiment. Theory.

Air 1 1

Nitrogen 0984 0986

Oxygen l-050 T052

Hydrogen 0276 0263

Carbon Dioxide .... 1 ’197 l-237

This relationship has been confirmed by Bunsen,2 who has further based on it a method for the approximate determination of the density of a gas.

1 Graham, Chemical and Physical Researches, p. 95. 2 Oasometry, p. 121, i

Tlie rate of passage of a gas through a capillary tube into a vacuum is not inversely proportional to the square root of the density ; the friction at the interior surface of the tube comes in as a disturbing factor. The velocity of diffusion of one gas into another through a porous diaphragm is inversely proportional to the square root of the density only when the diaphragm is extremely thin.