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of heat. In other words the reverse operation, thermally considered, will be a negative change, and it must be accompanied by a compensating positive change.

Let heat pass from a hotter body to the mixture of AD and BC molecules, then this addition of heat (i.e. this positive change) may be accompanied by an equivalent, or less than an equivalent, negative change; the re-formation of AB and CD, or generally an action involving absorption of heat, may occur.

Suppose that in a given space there is a limited number of molecules AB, CD, AD, and BC, that no heat enters or leaves the system, and that the temperature of the space remains constant; then a series of molecules may be produced, represented by the formulæ AC, BD, AA, BB, CC,

BD' ) BB
BB' CC' CCDD, &c. But according to

) the hypothesis already made, the production of AA, BB...DD, must be accompanied by an absorption of heat. The formation of the elementary molecules, AA, &c. would require the greatest absorption of heat; on the other hand, the formation

(АВ of the complex molecules &c. will, as a rule, be attended

CD with evolution of heat. If molecules are formed with heatabsorption, such changes must be accompanied by others wherein equivalent quantities of heat are evolved.

Pfaundler then gives a rough classification of these positive and negative thermal changes'.

The relations between the distribution of the energy and the distribution of the molecular configurations in such a system are considered in Pfaundler's second paper,

The hypothesis asserts that exchange of atoms, or atomic groups, is constantly proceeding in chemical systems; but the consideration of this withdrawal and replacement of atoms, from and in the molecules of the reacting substances, can be approached only by statistical methods. There may be more withdrawals than replacements of individual atoms, but, when equilibrium is established, the mean number of each in a given time is equal.

1 See Posst. Ann. Jubelbd. 187--8.

But why do exchanges of parts of molecules occur? Pfaundler's hypothesis refers these atomic exchanges to momentary differences in the states of motion of individual molecules, which is a fundamental point in the kinetic theory

of gases.

Consider the motion of agitation of the molecules, and the motion of the parts of the molecules; the kinetic theory asserts that, at a constant temperature, the sum of the kinetic energies of these two motions is constant, and also the sum of each is constant, but the two motions may be very differently distributed among the individual molecules. Calling the energy of agitation of the molecules of a system (a), and the energy of rotation of the parts of the molecules (6), there are four limiting cases for the distribution of these two energies. Case 1: (a) and (6) are both at a maximum;

2: (a) and (6) are both at a minimum;
3: (a) is at a minimum, and (6) at a maximum ;

4: (a) is at a maximum, and (6) at a minimum.
Pfaundler illustrates these four cases as follows:

(1) Two molecules, AB and CD, collide, so that at the next instant (a) is wholly or almost wholly changed to (6); therefore (6) is greater than the maximum for stability in both molecules. The molecules AB and CD separate into A, B, C, and D.

(2) Two molecules, AB and CD, collide; it is possible that the resulting internal motion of the parts of the molecules is too small to separate AB and CD into their constituents; but is also too small to prevent the formation of the complex molecule ABCD, which is therefore produced.

(3) After collision the resulting internal motion is too small to separate AB and CD into their constituent parts, but is sufficient to prevent the formation of ABCD; the original molecules, AB and CD, therefore rebound unchanged.

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(4) The complex molecule ABCD is momentarily formed; but the blow of AB on CD being, according to the simplest hypothesis, direct and central, the whole system vibrates. Whether ABCD shall separate into AB and CD, or into AC and BD, depends on the magnitude of the affinities of A, B, C, and D for each other, and also on the previous internal motions of the parts of AB and CD; the greater this internal motion, the more readily will the change now proceed in the direction of AC and BD, because the further will the separation of A from B, and of C from D, have been already carried.

Hence, Pfaundler concludes, the nature (Art) of a decomposition depends on the mutual affinities of the constituents of the system, and also on the conditions of motion of these constituents; reactions may occur in directions apparently opposed to the affinities.

Cases (3) and (4) will probably occur more frequently than cases (1) and (2), because the former require smaller differences between the motions of the individual molecules than the latter.

Remembering that the kinetic energy of the atoms in the various molecules may be associated with many kinds of motion (swinging motions, rotations, &c.), one recognises how manifold may be the possible distributions of molecular configuration. The molecules may undergo many changes (the mean temperature of the system remaining constant) which we should regard as departures from a normal condition obtaining if all the molecules were simultaneously in the same state. The simplest of such departures from the average state is exhibited by the processes of dissociation, which is however only a special (although the simplest) case of simultaneous reciprocal reactions in consequence of varia* tions in the motions of individual molecules".'


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1 Pfaundler devotes some space to considering the best name to give to the general phenomenon of which he says dissociation is a special case ; he finally adopts the expression competition (concurrenz) of the molecules' (see Pogg. Ann. Jubelbd. 189). This theory of chemical change developed by Pfaundler is not opposed to the results of recent electrical investigations regarding chemical affinity; see post, chap. III. par. 252.


188. The hypothesis of Pfaundler indicates that there must be a temperature at which any given chemical change begins, and that for every temperature there is a limit beyond which the change does not proceed. Only a few determinations have as yet been made of the limiting conditions of chemical operations, and of the rates at which the operations proceed within these limits.

Menschutkin's experiments on the rates and limits of etherification', which have been partly considered in book I., and more especially Ostwald's studies of the velocities of various chemical changes", furnish examples of the kind of work that is required'. [For a few examples of such investigations see post, pars. 195–199.]

189. Pfaundler's treatment of chemical equilibrium throws some light on the questions of nascent actions discussed from the statical point of view in book I. (chap. II. section 1). These actions may I think be treated as special instances of equilibrium coming under Pfaundler's case (4) (see ante, p. 389). If we grant that when hydrogen, for in

p stance, is evolved by the action of zinc on dilute sulphuric acid, the gas consists for a short but appreciable time for the most part of atoms (or monatomic molecules), then we have a system wherein the motion of rotation of the parts of one kind of the molecules AA (or BB) is so great that most of these molecules are actually separated into their constituent parts A, A (or B, B); hence, if there be within the sphere of action another set of molecules, CD, the change will proceed in the direction indicated by the formation of the new molecules AC and AD. If however the energy due to the separation

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i See ante, book I. chap. iv. pars. 157–8; also post, par. 197. ? See post, chap. III. par. 222.

3 Hood's experiments (Phil. Mag. (5) 6. 371) on the oxidation of ferrous sulphate solution by potassium chlorate led to the probable conclusion that the amount of chemical change varied as the square of the temperature. Warder (Amer. Chem. Journal, 3. No. 5) has arrived at the same conclusion from his study of the influence of temperature, &c., on the rate of saponification of ethylic acetate. Mills and Mackey (Phil

. Mag. (5) 16. 429) have examined the relations between the strength of aqueous sulphuric acid and the line of ‘no chemical change', for given temperatures, in the reaction between that acid and metallic zinc.

of A A into A and A is not employed in bringing about the secondary change, namely, formation of AC and AD, then the separated atoms swing back into their previous configuration, and the whole system assumes a new condition of equilibrium.

Moreover, whether the molecules AA (or BB) shall, or shall not, be separated into the atoms A, A (or B, B) must to a great extent depend on the materials from which, and the conditions under which, these molecules have been produced. Again, whether these monatomic molecules (A, A), having been produced shall react with the molecules CD, to form AC and AD, or shall swing back to the configuration AA, must be conditioned, among other things, by the nature of the molecules CD. Finally the equilibrium of the entire system will vary with variations in the rate of production of A, A, and with variations of physical conditions, among which conditions temperature will be especially important.

190. Pfaundler shews that his hypothesis affords a fairly satisfactory explanation of many cases of contact-action and predisposing affinity', this explanation being based on the deduction from the hypothesis in question, that the number of molecules of one kind present at any time in a changing system must depend on the nature and number of all the molecules, of whatever kind, which comprise the system.

Thus let a gaseous system consist of the molecules AB, BC, A, and C. Let the temperature be constant, but let the mass of AB be increased; the number of free molecules of C decreases, more of BC forms, but at the same time more molecules of BC are decomposed in a given time than before the number of AB molecules was increased.

Decreasing the amount of A will decrease the decomposition of BC by A, and hence will decrease the number of C molecules. If AB increases, and A simultaneously decreases, C will soon disappear. On the other hand it is evident that if AB decreases, and A increases, the number of molecules of C will also increase?.

1 See ante, pars, 178, 179. ? See also Hicks, Phil. Mag. (5) 4. 82.

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