Diffusion in Solution of Dissociated Gases. 271 
since the volume changes are the same for both internal and 
external dissociation. 
But we have seen that 
a = > 
whence 
Neon 
a (n log a —log A) = ee p) 
HN n : —nQx TQx, 
ot a (= =| == Cer) a ys 
where C is a constant. Thus the variation with temperature 
of the solubilities is determined entirely by the difference 
of the heats of solution of the dissociated and undissociated 
gas. 
§ 2. Calculation of the Rate of Diffusion. 
We now come to the problem, to which the preceding dis- 
cussion is to a large extent a necessary preliminary, of the 
distribution, in the steady state, of a dissociating gas inside 
an infinite slab of solution of finite thickness, when one side 
of the slab is in contact with the dissociating gas at a finite 
pressure and the other is maintained at pressure zero. 
Naturally the resulting equations also lead to the rate of 
diffusion of the gas bodily through the slab. 
In order to obtain the equations which determine the dis- 
tribution of the gas in the solution, let us consider the rate 
of increase of the concentration inside an infinitesimal cube 
whose angular points are given by the necessary combination 
of the coordinates 2, y, z, v+dz, y+dy,z+dz. Let C be 
the concentration and yu the coefficient of diffusion of the 
undissociated gas, c and wn being the corresponding quantities 
for the dissociated portion. Then the rate of flow of the 
undissociated gas in at the « face of the cube is ap dy dz. 
Similarly the rate of flow in of this part of the gas at the 
«z+dz face is 
i FC 
In this way we see that the rate of increase of the concentra- 
tion C in the element of volume due to diffusion is 
pao a CY 
‘ v dx? + dy” ae. dz bade dy dz. 
U2 
