191. Dissociation appears as a particular instance of the application of Pfaundler's hypothesis of chemical equilibrium'. This subject has been treated by more purely mathematical methods by Hicks, who has arrived at results very similar to those obtained by Pfaundler. Hicks has, it is true, failed to deduce any simple relation between the mutual atomic actions of an elementary gas and the phenomena which attend the dissociation of the molecules of that gas, but he arrives at the same general conception of a gaseous system as Pfaundler had done before, the conception, namely, of equilibrium, even the equilibrium of an elementary gas, as the result of the continual interchange of atoms, or atomic groups, between the molecules of the constituents. Hicks also points out that it may be possible to treat mathematically the questions presented by the phenomenon of the passage of the same gaseous system through various states, or phases, of chemical and physical equilibrium, one of which phases is always considerably more stable, as regards temperature at any rate, than the others.

192. In 1873 Horstmann3 propounded a thermodynamical theory of dissociation which is also applicable, in its broad features, to other cases of chemical equilibrium. The fundamental position of Horstmann's theory is that the degree of dissociation of any system is conditioned by all the circumstances which determine the value of the entropy of that system. The system attains stable equilibrium when the entropy is as great as possible under the conditions. To determine the conditions under which the entropy of any dissociating system is at its maximum is therefore, according to Horstmann, to solve the problem of dissociation. The

1 I have devoted considerable space to an account of Pfaundler's papers, because they contain, so far as I know, the only attempt that has been made to develope a kinetical hypothesis of chemical action in terms of the molecular theory of gases. It is however questionable whether hypotheses such as this are of much scientific value. We have no exact knowledge of the forces acting between the parts of molecules; and we know almost nothing of the mechanism whereby the energy absorbed by this or that substance is employed.

2 Phil. Mag. (5) 4. 80 and 174.

3 Annalen 170. 192.

maximum entropy is attained when as many molecules as possible are decomposed with the minimum consumption of heat, and when the molecules of all the gases forming the system are as far as possible separated from one another, (i. e. when the disgregation [see chap. III. par. 239] of the system is at a maximum). But these conditions are fulfilled before complete decomposition occurs, therefore only a portion of the original substance is separated into its constituents'.

193. But the whole subject of chemical equilibrium has been treated in a masterly manner by Willard Gibbs*.

The fundamental principle on which the theory of Gibbs is founded is, that, when the entropy of any isolated material system has reached a maximum, the system will be in a state of equilibrium. The form in which Gibbs puts this statement is as follows:

'For the equilibrium of any isolated system it is necessary 'and sufficient that in all possible variations of the state of 'the system which do not alter its entropy, the variation of 'its energy shall either vanish or be positive.'

The stability of a system depends upon the 'magnitudes' of the system, which are

(1) the component masses of its constituents, m1

... Mng V1... V n Φι Pni

...

and upon the intensities' of the system, which are

(4) the pressure p,

(5) the temperature (reckoned on the absolute or thermodynamic scale), (6) the potentials of the components μ1

...

μπ

The potential of a component is thus defined by Gibbs :

'If to any homogeneous mass in a state of hydrostatic 'stress we suppose an infinitesimal quantity of any substance 'to be added, the mass remaining homogeneous, and its 'entropy and volume remaining unchanged, the increase of

1 Horstmann's treatment of this subject is not, I think, very happy. The thermodynamical conception of entropy can scarcely be applied to statistical questions regarding the motions of molecules.

Amer. Journ. of Sci. and Arts (3) 16. 441: 18. 277. See also Clerk Maxwell, South Kensington Science Conferences, [1876].

'the energy of the mass divided by the quantity of the sub'stance added is the potential for that substance in the mass 'considered.'

Clerk Maxwell defines the potential for any substance as 'the intensity with which the system tends to expel that 'component from its mass.'

The entropy of a body is a quantity such that without a change in its value no heat can enter or leave the body'; as the isothermal lines of a gas furnish a scale of temperature, so the adiabatics furnish a scale of entropy1.

Gibbs then attempts to determine the relations between the energy of homogeneous masses and the variables m1, m,,...m v, p, p, t, μ1, H2... Many different homogeneous bodies can be formed out of any set of component substances; any such body considered solely with regard to its composition and thermodynamic state is called by Gibbs a phase of the system considered. Two or more phases may coexist. If the stability of phase A is positive with regard to that of another phase, B, then phase A is stable; but if the stability of A is negative with regard to B, then phase A will tend to pass into phase B. Phase A may be stable in itself but may have its stability destroyed by contact with the smallest portion of matter in certain other phases'; certain changes may therefore be commenced by very small exciting causes. The possible existence of unstable phases in heterogeneous systems has of course been known to chemists, although such phases have been almost entirely overlooked in chemical investigations; but we are taught by the researches of Gibbs that the conditions of existence of such phases, and their relations to stable phases of the same systems, can be deduced from the principles of the conservation and degradation of energy.

Gibbs then proceeds to find the 'fundamental equations' for ideal gases and mixtures of gases; a fundamental equation being one between the energy, entropy, volume, and component masses of a system; 'all the thermal, mechanical

1 See on this subject Clerk Maxwell's Heat, p. 161: also 192-194 (6th ed.). 2 For a fuller treatment of the 'criterion of stability' of homogeneous fluids, see Gibbs's first paper (loc. cit.), p. 447.

and chemical properties of a compound, so far as active tendencies are concerned [depend on these relations], when the form of the mass does not require consideration.'

When the energy of a mixture of gases, some of the proximate components of which can be formed out of others, has the least value consistent with its entropy and volume, we have what is called by Gibbs 'a phase of dissipated energy'; for such a phase the potentials for the proximate components must satisfy an equation similar to that which expresses the relation between the units of weight of these components'. Thus if the components of the system are hydrogen, oxygen, and water-gas, the potentials for these substances must satisfy the relation

μ + 8μο=9μω,

inasmuch as 8 of oxygen + 1 of hydrogen = 9 of water.

Dissociable gases are called by Gibbs 'gas-mixtures with convertible components'. If the general laws of ideal gasmixtures apply to these gases, it may be shewn that the phases of dissipated energy are the only phases that can exist. An equation may be obtained for the relations of pressure, temperature, and density in such a mixture, and the results calculated by means of this equation may be compared with experimentally determined numbers. If the calculated agree with the experimentally determined results, then some of the general laws of chemical equilibrium may be deduced from the study of ideal gas-mixtures.

Take for instance the dissociation of N,O,; equilibrium is established at a given temperature for the system consisting of N2O, and NO,. The assumption made by Gibbs for this system is, that equilibrium is determined by the condition that its entropy has the greatest possible value consistent with the energy and the volume of the system; he thus obtains an equation between m,, m,,...m, t, and v1.

Gibbs compares the observed densities of the vapours of nitrogen peroxide, formic acid, acetic acid, and phosphorus

1 For the development of the formula in question into a form which admits of ready application to such cases as the dissociation of NO4, see Gibbs's second paper, loc. cit., pp. 280-281.

pentachloride at different temperatures and pressures with the densities calculated by his formula. The agreement is on the whole very satisfactory, although there are some discrepancies, especially in the case of phosphorus pentachloride.

As an example of a system existing under special conditions in a phase beyond the limits of absolute stability, and of the sudden overthrow of the equilibrium of such a system by small exciting causes, Clerk Maxwell (South Kensington Sci. Conferences, 1876) notices the case of water, freed from air, remaining in the liquid state at a temperature much above the boiling point normally corresponding to the existent pressure, but exploding instantly it comes in contact with any gas. He also cites the equilibrium of a 37 per cent. aqueous solution of calcium chloride cooled below 37°, as described by Guthrie in his study of cryohydrates.

Many of the examples already given of contact-actions and predisposing affinity (pars. 178, 179) may serve to illustrate the influence exerted by matter in one phase when brought into contact with material systems in other phases. If the latter systems are in indifférent equilibrium, a very small external action may suffice to produce a large result, because when the equilibrium has been overthrown the components of the system are free to act and react, and a considerable chemical change may occur.

It may be possible to convert a phase of absolute stability first into one of relative instability, and then into one of absolute instability, by contact with matter in another phase, i.e. in ordinary chemical language by the action of a reagent'.

If the kinetic theory of chemical action developed by Pfaundler and others is in the main accepted, then it would appear that many, if not indeed most, chemically heterogeneous systems, the average state of which remains constant (i.e. sys

1 A mixture of marsh gas and oxygen which undergoes slow combustion at a certain temperature will explode, according to Mallard and Le Chatelier, after the expiration of a variable time which is longer the lower the temperature [see Compt. rend. 91. 825]. We have here probably an example of the passage from a stable phase, through a relatively unstable, to an absolutely unstable phase.