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affinity-constant, and this number conveys much information regarding the substance when regarded from a kinetical stand-point. These affinity-constants are true equivalents; they express power of doing definite amounts of chemical work. It was for such numbers that Bergmann sought, but sought in vain ; they have at last been found, or, at any rate, we have been shewn how they are to be found, by following in the steps of Bergmann's great opponent, Claud Louis Berthollet.

SECTION 2. Thermal and other methods of studying affinity.

238. The subject of affinity has thus far been considered, for the most part, apart from any kinetic theory of chemical action. But it is scarcely possible to be satisfied with this treatment. We cannot but attempt to form some mental image of the molecular and atomic mechanism of the changes which are conditioned by the affinities of bodies exerting chemical action on each other. Is affinity, in the last analysis, to be ascribed to attractions between atoms; or is it due to the electrical conditions of different atoms? How far do measurements of the quantities of heat evolved, or absorbed, during chemical operations, afford an insight into the nature of these processes ? Questions of this kind cannot be overlooked, however difficult, or even impossible, it may be at present to answer them.

239. The attempts which have been made to apply the data of thermal chemistry to the problems of affinity have generally been based on the hypothesis, that affinity is an attraction between atoms which is dependent on variations in the potential energies of these atoms. On this hypothesis, the thermal changes which accompany definite chemical processes may be regarded as affording measurements of the change of potential into kinetic energy which proceeds along with the rearrangement of the atoms of the elements constituting the chemical systems.

i Compare Mills, Phil. Mag. (5) 1. 13. with Ostwald, Journal für prakt. Chemie (2) 29. 57.

But even if this is granted, it is at present impossible to make much use of this means of measuring the energy-change in question.

Take a simple case. Given the heat evolved during the change of 2 parts by weight of gaseous hydrogen and 16 parts of oxygen into 18 parts of liquid water, we have the difference between the energies of the two systems, (1) gaseous H, + O, and (2) liquid H,O, as measured by the amount of heat appearing in the calorimeter. But a part of the energy-difference, as thus determined, is due to the change of gaseous into liquid water, and another part to the contraction which occurs when two volumes of hydrogen and one of oxygen combine to produce two volumes of water-gas!.

In the majority of chemical operations, the physical changes are more complex than in this instance. Different fractions of the total quantities of heat measured by the calorimeter are connected with changes in the densities, the crystalline forms, the thermal capacities, or generally, with changes in the disgregation' of the substances taking part in the chemical processes for which thermal values are required. But we are not, generally speaking, able to measure the thermal change which accompanies a disgregation-change. Indeed we cannot always decide whether the value of this part of the total thermal change is equal to, greater, or less than, the value of that part which measures the affinities of the chemically reacting substances.

1 For methods of calculating these two parts of the total loss of energy see Naumann, Thermochemie 217—219; and also Lothar Meyer, loc. cit. 430—434.

? Clausius, Pogg. Ann. 116. 79, &c. Disgregation is a quantity depending on the arrangement in space of the molecules of a substance ; it expresses to what extent the separation of the molecules, which is brought about by the action of heat, has been accomplished. The disgregation of a body is greater in the gaseous than in the liquid, and greater in the liquid than in the solid state. The disgregation may change without an alteration of the chemical composition or the physical state of the body; thus, when a gas expands, its disgregation increases. As a rule, disgregation increases when the distance between the molecules of a substance is increased. Compare Horstmann, Annalen, 170. 195; also Naumann, ioc. cit. 209.

L. Meyer (loc. cit. 429) considers Disgregation as equivalent to degree of division (Vertheilungsgrad).

3 Favre and Valson's experiments shew that the thermal changes attending the contraction of solutions in which various salts are formed and dissolve, are very

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240. Even in cases of dissociation, brought about by the supply of energy in the form of heat, it is not at present possible to separate the energy used in effecting disgregationchanges from that entirely employed in separating the molecules into less complex molecules, or into atoms.

But even if this could be done, a difficulty would still remain.

Take the formation of gaseous hydriodic acid from gaseous hydrogen and iodine; the purely chemical reaction is not fully represented by the statement, H + I = HI, but rather by the equation, H, +1, = 2HI, which is divisible into two parts;

(1) H, +1,=H+H+I+I,

(2) H+H+1+1=2HI. The problem presented is, to measure the energy-change which accompanies the second part of this chemical change. But the calorimetric determinations hitherto made furnish no means for separating the total thermal value into its constituent parts. A number is obtained which is the sum of two quantities neither of which is known.

241. But there is a more far-reaching objection to many of the conclusions regarding affinity which have been drawn from thermal measurements. It is, to say the least, improbable, that affinity consists of an attraction between atoms, depending on the energy of position of these atoms. The atoms of which a molecule is composed must be regarded as in motion within the molecule ; but of the nature of this

large. See Watts's Dict. 2nd Supplt. 292 et seq.; and 3rd Supplt. 983. See also for more details Die modernen Theorien der Chemie, (4th ed.) p. 436.

Berthelot's law of maximum work' (see book 1. chap. IV. par. 133) is based on the assumption that affinity is a form of potential energy. Meyer shews that there are cases where this law cannot hold good, even when we assume that all actions, other than the attractions between atoms, are eliminated. For a fuller discussion of the connections between this law and affinity see L. Meyer, loc. cit. pp. 440—460. That a degradation of energy is an invariable accompaniment of a chemical action, occurring by itself, is certain, but it is not the case that an operation involving degradation of energy necessarily occurs.

A chemical change between gases, involving degradation of energy, may be rendered impossible by causing the gases to expand, and this although the total heat evolved during the operation is almost the same whether the gases are expanded or condensed. See Lord Rayleigh, Proc. R. 1. March 5, 1875.

motion we know little or nothing. A feasible hypothesis is that the motion is such as produces a constant change of potential into kinetic energy, and vice versa. But if this view is adopted, the same compound will be more or less ready to undergo chemical change, according to the phase (see ante, chap. II. par. 193, p. 395) in which it is. Let AB, a diatomic molecule of a gas, collide with C, a monatomic molecule of a gas; more than one change may occur; AC and B may be produced although the affinity of C for A is less than that of C for B. The motions of the atoms, and hence the relations between their potential and kinetic energies at any moment, will be conditioned by the temperature, among other causes. In cases more complex than that just considered, e.g, in the reactions between two diatomic gaseous molecules, AB and CD, it is not at present possible to separate the action of heat, in bringing the molecules into phases whereat chemical change occurs, from the action of affinity pure and simple.

242. Thus, we come back to the statement, already insisted on in book I., that there is no essential difference of kind between so-called endothermic and exothermic actions.

Until there is a more definite kinetic theory of affinity than has yet been proposed, it will not be possible to apply thermal methods, except in a general and broad way, to the questions suggested by the term affinity.

243. Every chemical change involves a degradation of energy, but chemical energy, of whatever form, cannot be entirely run down into heat.

This subject has been considered by Helmholtz?.

The action of chemical forces gives rise not only to heat, but also to other forms of energy, and, in the latter cases,

1 See L. Meyer, loc. cit. 447–448. Compare also book 1. chap. IV. pars. 119, and 133; also book 11. chap. II. section 2, especially par. 193. Thomsen's • Theoretische Betrachtungen über die Dynamik der chemischen Processe,' in Thermochemische Untersuchungen 2. 468—-474, should also be carefully studied. See also in connection with this, Rathke, über die Principien der Thermochemie, und ihre Anwendung (Halle, 1881). There is also an abstract of an interesting paper by Potilitzin in Ber. 14. 2044.

2 • Die Thermodynamik chemischer Vorgänge,' Sitzber. der Wiss. Akad. zu Berlin, 1882 ; see Wissenschaftliche Abhandlungen, 2. 958.

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sometimes without a change of temperature bearing any kind of relation to the magnitude of the actions between the changing substances; e.g. in the performance of work by the battery. Hence, we must distinguish, in chemical processes, between those parts of the chemical energy which are freely changeable into other forms, and those which can only be produced in the form of heat. The former is called, by Helmholtz, the free energy, the latter the bound energy (freie und gebundene Energie). The bound energy is the difference between the total internal energy and the free energy. Changes proceeding of themselves from a state of rest, and at a uniform temperature, without the help of energy from without the system, can only proceed in directions such that the free energy decreases. Assuming the universality of the second law of thermodynamics, it follows that the direction in which the chemical affinity of a substance can act depends . on the value of the free energy, and not on that of the total energies which make themselves known by the production of heat. The free energy can only be calculated in completely reversible changes. Electrolytic decompositions with unpolarised electrodes serve well for this purpose; indeed it was when examining the relations between the electromotive force of such cells and the chemical changes which proceed within them that Helmholtz was led to the conception of free chemi

cal energy.

In all isothermal changes work is done only at the cost of the free energy; in all adiabatic changes work is produced at the cost both of the free and the bound energy of the system. In all other cases, external work is carried on at the cost of the free energy, and loss of heat at the cost of the bound energy; and for every rise of temperature of the system, free is changed into bound energy. This last case may occur in irreversible processes, so that free energy is changed into kinetic energy which again may be converted, by friction, &c., either wholly or in part into heat. In such a case the heat evolved in the change from the initial to the final state of the system represents the difference between the total internal energies of the system. Now this difference is the quantity

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