The New Physics and Its Evolution Part 8

We should not hesitate, however, to apply the Phase Law to solutions, and this law already gives us the key to a certain number of facts. It puts in evidence, for example, the part played by the eutectic point-- that is to say, the point at which (to keep to the simple case in which we have to do with two bodies only, the solvent and the solute) the solution is in equilibrium at once with the two possible solids, the dissolved body and the solvent solidified. The knowledge of this point explains the properties of refrigerating mixtures, and it is also one of the most useful for the theory of alloys. The scruples of physicists ought to have been removed on the memorable occasion when Professor Van t'Hoff demonstrated that solution can operate reversibly by reason of the phenomena of osmosis. But the experiment can only succeed in very rare cases; and, on the other hand, Professor Van t'Hoff was naturally led to another very bold conception. He regarded the molecule of the dissolved body as a gaseous one, and a.s.similated solution, not as had hitherto been the rule, to fusion, but to a kind of vaporization. Naturally his ideas were not immediately accepted by the scholars most closely identified with the cla.s.sic tradition. It may perhaps not be without use to examine here the principles of Professor Van t'Hoff's theory.

-- 2. OSMOSIS

Osmosis, or diffusion through a septum, is a phenomenon which has been known for some time. The discovery of it is attributed to the Abbe Nollet, who is supposed to have observed it in 1748, during some "researches on liquids in ebullition." A cla.s.sic experiment by Dutrochet, effected about 1830, makes this phenomenon clear. Into pure water is plunged the lower part of a vertical tube containing pure alcohol, open at the top and closed at the bottom by a membrane, such as a pig's bladder, without any visible perforation. In a very short time it will be found, by means of an areometer for instance, that the water outside contains alcohol, while the alcohol of the tube, pure at first, is now diluted. Two currents have therefore pa.s.sed through the membrane, one of water from the outside to the inside, and one of alcohol in the converse direction. It is also noted that a difference in the levels has occurred, and that the liquid in the tube now rises to a considerable height. It must therefore be admitted that the flow of the water has been more rapid than that of the alcohol. At the commencement, the water must have penetrated into the tube much more rapidly than the alcohol left it. Hence the difference in the levels, and, consequently, a difference of pressure on the two faces of the membrane. This difference goes on increasing, reaches a maximum, then diminishes, and vanishes when the diffusion is complete, final equilibrium being then attained.

The phenomenon is evidently connected with diffusion. If water is very carefully poured on to alcohol, the two layers, separate at first, mingle by degrees till a h.o.m.ogeneous substance is obtained. The bladder seems not to have prevented this diffusion from taking place, but it seems to have shown itself more permeable to water than to alcohol. May it not therefore be supposed that there must exist dividing walls in which this difference of permeability becomes greater and greater, which would be permeable to the solvent and absolutely impermeable to the solute? If this be so, the phenomena of these _semi-permeable_ walls, as they are termed, can be observed in particularly simple conditions.

The answer to this question has been furnished by biologists, at which we cannot be surprised. The phenomena of osmosis are naturally of the first importance in the action of organisms, and for a long time have attracted the attention of naturalists. De Vries imagined that the contractions noticed in the protoplasm of cells placed in saline solutions were due to a phenomenon of osmosis, and, upon examining more closely certain peculiarities of cell life, various scholars have demonstrated that living cells are enclosed in membranes permeable to certain substances and entirely impermeable to others. It was interesting to try to reproduce artificially semi-permeable walls a.n.a.logous to those thus met with in nature;[15] and Traube and Pfeffer seem to have succeeded in one particular case. Traube has pointed out that the very delicate membrane of ferrocyanide of pota.s.sium which is obtained with some difficulty by exposing it to the reaction of sulphate of copper, is permeable to water, but will not permit the pa.s.sage of the majority of salts. Pfeffer, by producing these walls in the interstices of a porous porcelain, has succeeded in giving them sufficient rigidity to allow measurements to be made. It must be allowed that, unfortunately, no physicist or chemist has been as lucky as these two botanists; and the attempts to reproduce semi-permeable walls completely answering to the definition, have never given but mediocre results. If, however, the experimental difficulty has not been overcome in an entirely satisfactory manner, it at least appears very probable that such walls may nevertheless exist.[16]

[Footnote 15: See next note.--ED.]

[Footnote 16: M. Stephane Leduc, Professor of Biology of Nantes, has made many experiments in this connection, and the artificial cells exhibited by him to the a.s.sociation francaise pour l'avancement des Sciences, at their meeting at Gren.o.ble in 1904 and reproduced in their "Actes," are particularly noteworthy.--ED.]

Nevertheless, in the case of gases, there exists an excellent example of a semi-permeable wall, and a part.i.tion of platinum brought to a higher than red heat is, as shown by M. Villard in some ingenious experiments, completely impermeable to air, and very permeable, on the contrary, to hydrogen. It can also be experimentally demonstrated that on taking two recipients separated by such a part.i.tion, and both containing nitrogen mixed with varying proportions of hydrogen, the last-named gas will pa.s.s through the part.i.tion in such a way that the concentration--that is to say, the ma.s.s of gas per unit of volume-- will become the same on both sides. Only then will equilibrium be established; and, at that moment, an excess of pressure will naturally be produced in that recipient which, at the commencement, contained the gas with the smallest quant.i.ty of hydrogen.

This experiment enables us to antic.i.p.ate what will happen in a liquid medium with semi-permeable part.i.tions. Between two recipients, one containing pure water, the other, say, water with sugar in solution, separated by one of these part.i.tions, there will be produced merely a movement of the pure towards the sugared water, and following this, an increase of pressure on the side of the last. But this increase will not be without limits. At a certain moment the pressure will cease to increase and will remain at a fixed value which now has a given direction. This is the osmotic pressure.

Pfeffer demonstrated that, for the same substance, the osmotic pressure is proportional to the concentration, and consequently in inverse ratio to the volume occupied by a similar ma.s.s of the solute.

He gave figures from which it was easy, as Professor Van t'Hoff found, to draw the conclusion that, in a constant volume, the osmotic pressure is proportional to the absolute temperature. De Vries, moreover, by his remarks on living cells, extended the results which Pfeffer had applied to one case only--that is, to the one that he had been able to examine experimentally.

Such are the essential facts of osmosis. We may seek to interpret them and to thoroughly examine the mechanism of the phenomenon; but it must be acknowledged that as regards this point, physicists are not entirely in accord. In the opinion of Professor Nernst, the permeability of semi-permeable membranes is simply due to differences of solubility in one of the substances of the membrane itself. Other physicists think it attributable, either to the difference in the dimensions of the molecules, of which some might pa.s.s through the pores of the membrane and others be stopped by their relative size, or to these molecules' greater or less mobility. For others, again, it is the capillary phenomena which here act a preponderating part.

This last idea is already an old one: Jager, More, and Professor Traube have all endeavoured to show that the direction and speed of osmosis are determined by differences in the surface-tensions; and recent experiments, especially those of Batelli, seem to prove that osmosis establishes itself in the way which best equalizes the surface-tensions of the liquids on both sides of the part.i.tion.

Solutions possessing the same surface-tension, though not in molecular equilibrium, would thus be always in osmotic equilibrium. We must not conceal from ourselves that this result would be in contradiction with the kinetic theory.

-- 3. APPLICATION TO THE THEORY OF SOLUTION

If there really exist part.i.tions permeable to one body and impermeable to another, it may be imagined that the h.o.m.ogeneous mixture of these two bodies might be effected in the converse way. It can be easily conceived, in fact, that by the aid of osmotic pressure it would be possible, for example, to dilute or concentrate a solution by driving through the part.i.tion in one direction or another a certain quant.i.ty of the solvent by means of a pressure kept equal to the osmotic pressure. This is the important fact which Professor Van t' Hoff perceived. The existence of such a wall in all possible cases evidently remains only a very legitimate hypothesis,--a fact which ought not to be concealed.

Relying solely on this postulate, Professor Van t' Hoff easily established, by the most correct method, certain properties of the solutions of gases in a volatile liquid, or of non-volatile bodies in a volatile liquid. To state precisely the other relations, we must admit, in addition, the experimental laws discovered by Pfeffer. But without any hypothesis it becomes possible to demonstrate the laws of Raoult on the lowering of the vapour-tension and of the freezing point of solutions, and also the ratio which connects the heat of fusion with this decrease.

These considerable results can evidently be invoked as _a posteriori_ proofs of the exact.i.tude of the experimental laws of osmosis. They are not, however, the only ones that Professor Van t' Hoff has obtained by the same method. This ill.u.s.trious scholar was thus able to find anew Guldberg and Waage's law on chemical equilibrium at a constant temperature, and to show how the position of the equilibrium changes when the temperature happens to change.

If now we state, in conformity with the laws of Pfeffer, that the product of the osmotic pressure by the volume of the solution is equal to the absolute temperature multiplied by a coefficient, and then look for the numerical figure of this latter in a solution of sugar, for instance, we find that this value is the same as that of the a.n.a.logous coefficient of the characteristic equation of a perfect gas. There is in this a coincidence which has also been utilized in the preceding thermodynamic calculations. It may be purely fortuitous, but we can hardly refrain from finding in it a physical meaning.

Professor Van t'Hoff has considered this coincidence a demonstration that there exists a strong a.n.a.logy between a body in solution and a gas; as a matter of fact, it may seem that, in a solution, the distance between the molecules becomes comparable to the molecular distances met with in gases, and that the molecule acquires the same degree of liberty and the same simplicity in both phenomena. In that case it seems probable that solutions will be subject to laws independent of the chemical nature of the dissolved molecule and comparable to the laws governing gases, while if we adopt the kinetic image for the gas, we shall be led to represent to ourselves in a similar way the phenomena which manifest themselves in a solution.

Osmotic pressure will then appear to be due to the shock of the dissolved molecules against the membrane. It will come from one side of this part.i.tion to superpose itself on the hydrostatic pressure, which latter must have the same value on both sides.

The a.n.a.logy with a perfect gas naturally becomes much greater as the solution becomes more diluted. It then imitates gas in some other properties; the internal work of the variation of volume is nil, and the specific heat is only a function of the temperature. A solution which is diluted by a reversible method is cooled like a gas which expands adiabatically.[17]

[Footnote 17: That is, without receiving or emitting any heat.--ED.]

It must, however, be acknowledged that, in other points, the a.n.a.logy is much less perfect. The opinion which sees in solution a phenomenon resembling fusion, and which has left an indelible trace in everyday language (we shall always say: to melt sugar in water) is certainly not without foundation. Certain of the reasons which might be invoked to uphold this opinion are too evident to be repeated here, though others more recondite might be quoted. The fact that the internal energy generally becomes independent of the concentration when the dilution reaches even a moderately high value is rather in favour of the hypothesis of fusion.

We must not forget, however, the continuity of the liquid and gaseous states; and we may consider it in an absolute way a question devoid of sense to ask whether in a solution the solute is in the liquid or the gaseous state. It is in the fluid state, and perhaps in conditions opposed to those of a body in the state of a perfect gas. It is known, of course, that in this case the manometrical pressure must be regarded as very great in relation to the internal pressure which, in the characteristic equation, is added to the other. May it not seem possible that in the solution it is, on the contrary, the internal pressure which is dominant, the manometric pressure becoming of no account? The coincidence of the formulas would thus be verified, for all the characteristic equations are symmetrical with regard to these two pressures. From this point of view the osmotic pressure would be considered as the result of an attraction between the solvent and the solute; and it would represent the difference between the internal pressures of the solution and of the pure solvent. These hypotheses are highly interesting, and very suggestive; but from the way in which the facts have been set forth, it will appear, no doubt, that there is no obligation to admit them in order to believe in the legitimacy of the application of thermodynamics to the phenomena of solution.

-- 4. ELECTROLYTIC DISSOCIATION

From the outset Professor Van t' Hoff was brought to acknowledge that a great number of solutions formed very notable exceptions which were very irregular in appearance. The a.n.a.logy with gases did not seem to be maintained, for the osmotic pressure had a very different value from that indicated by the theory. Everything, however, came right if one multiplied by a factor, determined according to each case, but greater than unity, the constant of the characteristic formula.

Similar divergences were manifested in the delays observed in congelation, and disappeared when subjected to an a.n.a.logous correction.

Thus the freezing-point of a normal solution, containing a molecule gramme (that is, the number of grammes equal to the figure representing the molecular ma.s.s) of alcohol or sugar in water, falls 1.85 C. If the laws of solution were identically the same for a solution of sea-salt, the same depression should be noticed in a saline solution also containing 1 molecule per litre. In fact, the fall reaches 3.26, and the solution behaves as if it contained, not 1, but 1.75 normal molecules per litre. The consideration of the osmotic pressures would lead to similar observations, but we know that the experiment would be more difficult and less precise.

We may wonder whether anything really a.n.a.logous to this can be met with in the case of a gas, and we are thus led to consider the phenomena of dissociation.[18] If we heat a body which, in a gaseous state, is capable of dissociation--hydriodic acid, for example--at a given temperature, an equilibrium is established between three gaseous bodies, the acid, the iodine, and the hydrogen. The total ma.s.s will follow with fair closeness Mariotte's law, but the characteristic constant will no longer be the same as in the case of a non-dissociated gas. We here no longer have to do with a single molecule, since each molecule is in part dissociated.

[Footnote 18: Dissociation must be distinguished from decomposition, which is what occurs when the whole of a particle (compound, molecule, atom, etc.) breaks up into its component parts. In dissociation the breaking up is only partial, and the resultant consists of a mixture of decomposed and undecomposed parts. See Ganot's Physics, 17th English edition, -- 395, for examples.--ED.]

The comparison of the two cases leads to the employment of a new image for representing the phenomenon which has been produced throughout the saline solution. We have introduced a single molecule of salt, and everything occurs as if there were 1.75 molecules. May it not really be said that the number is 1.75, because the sea-salt is partly dissociated, and a molecule has become transformed into 0.75 molecule of sodium, 0.75 of chlorium, and 0.25 of salt?

This is a way of speaking which seems, at first sight, strangely contradicted by experiment. Professor Van t' Hoff, like other chemists, would certainly have rejected--in fact, he did so at first-- such a conception, if, about the same time, an ill.u.s.trious Swedish scholar, M. Arrhenius, had not been brought to the same idea by another road, and, had not by stating it precisely and modifying it, presented it in an acceptable form.

A brief examination will easily show that all the substances which are exceptions to the laws of Van t'Hoff are precisely those which are capable of conducting electricity when undergoing decomposition--that is to say, are electrolytes. The coincidence is absolute, and cannot be simply due to chance.

Now, the phenomena of electrolysis have, for a long time, forced upon us an almost necessary image. The saline molecule is always decomposed, as we know, in the primary phenomenon of electrolysis into two elements which Faraday termed ions. Secondary reactions, no doubt, often come to complicate the question, but these are chemical reactions belonging to the general order of things, and have nothing to do with the electric action working on the solution. The simple phenomenon is always the same--decomposition into two ions, followed by the appearance of one of these ions at the positive and of the other at the negative electrode. But as the very slightest expenditure of energy is sufficient to produce the commencement of electrolysis, it is necessary to suppose that these two ions are not united by any force. Thus the two ions are, in a way, dissociated. Clausius, who was the first to represent the phenomena by this symbol, supposed, in order not to shock the feelings of chemists too much, that this dissociation only affected an infinitesimal fraction of the total number of the molecules of the salt, and thereby escaped all check.

This concession was unfortunate, and the hypothesis thus lost the greater part of its usefulness. M. Arrhenius was bolder, and frankly recognized that dissociation occurs at once in the case of a great number of molecules, and tends to increase more and more as the solution becomes more dilute. It follows the comparison with a gas which, while partially dissociated in an enclosed s.p.a.ce, becomes wholly so in an infinite one.

M. Arrhenius was led to adopt this hypothesis by the examination of experimental results relating to the conductivity of electrolytes. In order to interpret certain facts, it has to be recognized that a part only of the molecules in a saline solution can be considered as conductors of electricity, and that by adding water the number of molecular conductors is increased. This increase, too, though rapid at first, soon becomes slower, and approaches a certain limit which an infinite dilution would enable it to attain. If the conducting molecules are the dissociated molecules, then the dissociation (so long as it is a question of strong acids and salts) tends to become complete in the case of an unlimited dilution.

The opposition of a large number of chemists and physicists to the ideas of M. Arrhenius was at first very fierce. It must be noted with regret that, in France particularly, recourse was had to an arm which scholars often wield rather clumsily. They joked about these free ions in solution, and they asked to see this chlorine and this sodium which swam about the water in a state of liberty. But in science, as elsewhere, irony is not argument, and it soon had to be acknowledged that the hypothesis of M. Arrhenius showed itself singularly fertile and had to be regarded, at all events, as a very expressive image, if not, indeed, entirely in conformity with reality.

It would certainly be contrary to all experience, and even to common sense itself, to suppose that in dissolved chloride of sodium there is really free sodium, if we suppose these atoms of sodium to be absolutely identical with ordinary atoms. But there is a great difference. In the one case the atoms are electrified, and carry a relatively considerable positive charge, inseparable from their state as ions, while in the other they are in the neutral state. We may suppose that the presence of this charge brings about modifications as extensive as one pleases in the chemical properties of the atom. Thus the hypothesis will be removed from all discussion of a chemical order, since it will have been made plastic enough beforehand to adapt itself to all the known facts; and if we object that sodium cannot subsist in water because it instantaneously decomposes the latter, the answer is simply that the sodium ion does not decompose water as does ordinary sodium.

Still, other objections might be raised which could not be so easily refuted. One, to which chemists not unreasonably attached great importance, was this:--If a certain quant.i.ty of chloride of sodium is dissociated into chlorine and sodium, it should be possible, by diffusion, for example, which brings out plainly the phenomena of dissociation in gases, to extract from the solution a part either of the chlorine or of the sodium, while the corresponding part of the other compound would remain. This result would be in flagrant contradiction with the fact that, everywhere and always, a solution of salt contains strictly the same proportions of its component elements.

M. Arrhenius answers to this that the electrical forces in ordinary conditions prevent separation by diffusion or by any other process.

Professor Nernst goes further, and has shown that the concentration currents which are produced when two electrodes of the same substance are plunged into two unequally concentrated solutions may be interpreted by the hypothesis that, in these particular conditions, the diffusion does bring about a separation of the ions. Thus the argument is turned round, and the proof supposed to be given of the incorrectness of the theory becomes a further reason in its favour.

It is possible, no doubt, to adduce a few other experiments which are not very favourable to M. Arrhenius's point of view, but they are isolated cases; and, on the whole, his theory has enabled many isolated facts, till then scattered, to be co-ordinated, and has allowed very varied phenomena to be linked together. It has also suggested--and, moreover, still daily suggests--researches of the highest order.

In the first place, the theory of Arrhenius explains electrolysis very simply. The ions which, so to speak, wander about haphazard, and are uniformly distributed throughout the liquid, steer a regular course as soon as we dip in the trough containing the electrolyte the two electrodes connected with the poles of the dynamo or generator of electricity. Then the charged positive ions travel in the direction of the electromotive force and the negative ions in the opposite direction. On reaching the electrodes they yield up to them the charges they carry, and thus pa.s.s from the state of ion into that of ordinary atom. Moreover, for the solution to remain in equilibrium, the vanished ions must be immediately replaced by others, and thus the state of ionisation of the electrolyte remains constant and its conductivity persists.

All the peculiarities of electrolysis are capable of interpretation: the phenomena of the transport of ions, the fine experiments of M.

Bouty, those of Professor Kohlrausch and of Professor Ostwald on various points in electrolytic conduction, all support the theory. The verifications of it can even be quant.i.tative, and we can foresee numerical relations between conductivity and other phenomena. The measurement of the conductivity permits the number of molecules dissociated in a given solution to be calculated, and the number is thus found to be precisely the same as that arrived at if it is wished to remove the disagreement between reality and the antic.i.p.ations which result from the theory of Professor Van t' Hoff. The laws of cryoscopy, of tonometry, and of osmosis thus again become strict, and no exception to them remains.

If the dissociation of salts is a reality and is complete in a dilute solution, any of the properties of a saline solution whatever should be represented numerically as the sum of three values, of which one concerns the positive ion, a second the negative ion, and the third the solvent. The properties of the solutions would then be what are called additive properties. Numerous verifications may be attempted by very different roads. They generally succeed very well; and whether we measure the electric conductivity, the density, the specific heats, the index of refraction, the power of rotatory polarization, the colour, or the absorption spectrum, the additive property will everywhere be found in the solution.

The hypothesis, so contested at the outset by the chemists, is, moreover, a.s.suring its triumph by important conquests in the domain of chemistry itself. It permits us to give a vivid explanation of chemical reaction, and for the old motto of the chemists, "Corpora non agunt, nisi soluta," it subst.i.tutes a modern one, "It is especially the ions which react." Thus, for example, all salts of iron, which contain iron in the state of ions, give similar reactions; but salts such as ferrocyanide of pota.s.sium, in which iron does not play the part of an ion, never give the characteristic reactions of iron.

Professor Ostwald and his pupils have drawn from the hypothesis of Arrhenius manifold consequences which have been the cause of considerable progress in physical chemistry. Professor Ostwald has shown, in particular, how this hypothesis permits the quant.i.tative calculation of the conditions of equilibrium of electrolytes and solutions, and especially of the phenomena of neutralization. If a dissolved salt is partly dissociated into ions, this solution must be limited by an equilibrium between the non-dissociated molecule and the two ions resulting from the dissociation; and, a.s.similating the phenomenon to the case of gases, we may take for its study the laws of Gibbs and of Guldberg and Waage. The results are generally very satisfactory, and new researches daily furnish new checks.

Professor Nernst, who before gave, as has been said, a remarkable interpretation of the diffusion of electrolytes, has, in the direction pointed out by M. Arrhenius, developed a theory of the entire phenomena of electrolysis, which, in particular, furnishes a striking explanation of the mechanism of the production of electromotive force in galvanic batteries.

Extending the a.n.a.logy, already so happily invoked, between the phenomena met with in solutions and those produced in gases, Professor Nernst supposes that metals tend, as it were, to vaporize when in presence of a liquid. A piece of zinc introduced, for example, into pure water gives birth to a few metallic ions. These ions become positively charged, while the metal naturally takes an equal charge, but of contrary sign. Thus the solution and the metal are both electrified; but this sort of vaporization is hindered by electrostatic attraction, and as the charges borne by the ions are considerable, an equilibrium will be established, although the number of ions which enter the solution will be very small.

If the liquid, instead of being a solvent like pure water, contains an electrolyte, it already contains metallic ions, the osmotic pressure of which will be opposite to that of the solution. Three cases may then present themselves--either there will be equilibrium, or the electrostatic attraction will oppose itself to the pressure of solution and the metal will be negatively charged, or, finally, the attraction will act in the same direction as the pressure, and the metal will become positively and the solution negatively charged.