270 Mr. O. W. Richardson on the Solubility and 
sae akighs Va 1 p.Ve 
Now a Ra and = RG 
gas which are dissociated at volumes V, and V, respectively. 
By hypothesis is ¢1, «7. e. the gas does not contract in 
l PoVo 1 Pi*: V 1 
ssoclatine. c 7 = so = 
dissociating Hence, except when 7 ‘at Tee 1s 7 Re 
are the fractional aia of the 


if Vois > Vy. When n=1, the value of wb is independent 
of V. We see therefore that in both cases the only relation 
between Wa and V. which satisfies the above transcendental 
equation is V;=V>. Hence P;=P, and p,=p., from which 
we conclude that portions of a dissociating gas which are 
separately in equilibrium with either of the constituents of 
the mixture in the same solution, are in equilibrium with one 
another. 
We now come to the equation which is obtained when we 
equate to zero the sum of the quantities of heat given out 
in the various chemical and physical actions which take 
place during our cycle. We have seen already that owing to 
the modification in the “chemical potential”? of the dis- 
sociated molecules produced by the solvent, the dissociation 
constant is not necessarily the same in the solution as in 
the free gas. For precisely similar reasons the heat given 
out for a given amount of dissociation is not necessarily 
identical inside and outside the solution. Let go be the 
heat evolved when x gram-molecules of X unite to form 
X, outside the solution, and gq the corresponding quantity 
inside ; let Qx be the heat evolved when 1 gram-molecule of 
X gas dissolves in the solvent without recombination, and 
Qx,, the corresponding quantity for 1 gram-molecule of Xn. 
By following the course of the cycle we ae get 
q.+n2Qx— Qx,,— q=0 
This equation shows, as we should oe. that g, is only 
equal to g, in the special case when the heat of solution of 
n gram-molecules of X is equal to that of 1 gram-molecule 
at X,. 
For any reversible chemical action the variation with tem- 
perature of the reaction constant is given by the equation 
d(logk) Q 
dg Te 
where Q is the heat of reaction together with terms depending 
on the volume changes occurring. Applying this we obtain 
ad Yo, 
7 (log ky —log eee, j 

