158 HYDROGEN ION CONCENTRATION 



In the one case we can calculate the electrical work and in the other 

 case the osmotic work performed. The electrical work is equal to 

 the product of the potential difference ir and the transported amount 

 of electricity, or 96,450 coulombs, wliich is attached to one gram- 

 ion of silver. This amount of 96,450 coulombs is designated as 

 1 F (faraday). The electric work W is, therefore, x F. If the 

 potential were increased to t + d tt, then the work would be in- 

 creased by the amount of d W = F d r. 



The osmotic work performed in the above cited case consists 

 entirely of the work of compression; the restoration to the original 

 volume does not demand nor ^deld any work, for no change of con- 

 centration is involved. This osmotic pressure depends upon the 

 osmotic pressure against which it is exerted, which means that it 

 depends upon the concentration of the Ag-ions already present in 

 the solution. Therefore it can not be defined without going into 

 further explanation. But this much can be said: if the osmotic 

 process consists of a dilution, and if the osmotic pressure is at first p 

 and then p — d tt, then the work to be obtained in the latter case is less 

 by v-dp than in the first case. Here v stands for the volume con- 

 taining one gram-ion in solution. When, on the other hand, the 

 osmotic process consists of compression (concentration), then the 

 sign is to be reversed and taken as negative. 



Thus the osmotic work must be equal to the electrical work, which 

 can be expressed in terms of differentials as 



F d TT = — V dp 



RT 



Since p v = RT and v = — , hence 



P 



Fd7r= dp 



P 



_ _ RT dp 

 F * p 



and integrating: 



RT , 1 ^ 



IT = -—- la — h Constant 

 F p 



