
Solubility of Dissociated Gases. 267 
type X,=nX and takes place, to a greater or less extent, 
both in the solution and in the surrounding gas. In the 
investigation given by Van t’ Hoff (loc. cit.) certain relations 
are deduced by making the dissociated portion of the gas 
obey Henry’s Law. Tt is ev ident, however, that for a 
steady state not only must there be equilibrium between the 
free and dissolved parts of the dissociated gas, but the 
undissociated portion must also be governed by a similar 
relation. It is not sufficient for equilibrium merely to 
postulate equality between the total amount of gas entering 
and leaving the solvent in a given time. It is necessary 
that the amount entering and leaving should be the same for 
each constituent. The only alternative is to suppose the gas 
to enter the solution in one form, to dissociate or Seen 
there and leave in the other form. Such processes involve 
a continuous transfer of heat at a rate depending on the 
value of the heat of dissociation. It is thus necessary that 
there should be a separate relation between the concentrations 
of the free and dissolved portions of each constituent ; this 
reasoning is true whatever be the nature of the relation, 
quite apart from its assuming the special form of Henry’s 
Law. 
We have to take into account then four different equili- 
brium conditions. We have two equations which determine 
the relation between the undissociated and dissociated con- 
stituents of the dissolved, and undissolved, gas respectively, 
and two more equations which make the internal concentra- 
tion proportional to the external concentration of each con- 
stituent. If these relations do not hold it is easy to see that 
perpetual motion is obtained. 
Let the suffix 0 denote the gas outside, and «¢ inside the 
solution. Let C be the concentration of the undissociated, 
and ¢ of the dissociated portion. The equations which 
determine the equilibrium between the dissociated and undis- 
sociated portions of the gas inside and outside the solution 
respectively are then : 
Cy” ay d C n 
— =k, an Hh, 
ee Qi © Gis ] 
where &, and & are the dissociation constants of the free 
and dissolved gas respectively. In general kj will not be 
equal to &., as for instance in the case of an acid gas like 
HCl where electrolytic dissociation occurs in solution. 
Applying Henry’s Law to ae of the two constituents we get 
two further equations, viz. 
C= AG, and cy=aci, 
