272 Mr. O. W. Richardson on the Solubility and 
But diffusion is not the only cause tending to change the 
concentration at a given point ; the molecules are dissociating 
at a rate proportional to C and recombining at a rate pro- 
portional to c’. Hence the total rate of increase of CO is 
given by : 
dC _ 
ates 
where @ is the rate of recombination and £ that of dis- 
sociation, and B/a=k. Juike considerations give us a similar 
equation for c, viz.: 
V?C—BC + ae’, 
ze ge = PY 7c + BC —ace?®. 
n at l 
In the steady state 
= ide Se 
Tatar ‘ 
Returning to the one baa problem we started with 
let the faces of the slab be perpendicular to the axis of 2 and 
its thickness be d. Addition of the above equations gives 
2 }2 
pos + es =O (in the steady state), 
whence l 
se Ot t As. 
n 
When g= dd, C= ¢= 00, that 
ng Cae P C=A,(e—d). 
nr Bn 
When x=0, Henry’s Law gives C)=AC and q=ac. In 
addition to these we have the two following relations between 
Cy and co, viz. : | 
eg’ =k Co. and Pyp= Cy Area 
if Po is the total external concentration. The equation for cy 
in terms of P, is therefore 
Gy? + kek Pee 
Let Ao be a real root of this, then 
1 
Oe a 
ie) 8 
If we determine A, and replace a by (az): , we obtain 
wet eo eo 13 (.); oA ae *). 
