Theory of Solution Pressure. 421 



partment. Calling the osmotic pressure of the ions in B 

 necessary to produce this P, and <§ the excess of the potential 

 of the electrode in A over that of the solution, we have 





=£•*> (2) 



from which Nernst's formula (1) follows at once under the 

 application of the gas law pv = W\ 



In the above it has been assumed that the silver nitrate is 

 completely dissociated. When this is not the case it is usually 

 taken for granted that the only effective pressure in producing 

 the potential step is that of the metallic ions. The correctness 

 of this follows thermodynamically if the isotherm of disso- 

 ciation is taken to be that given by the law of mass-action, 

 viz.: — 



Kc' = c 2 , 



where d is the concentration of the undissociated, and c that 

 of the dissociated, molecules. The expression for the E.M.F. 

 of the cell considered above is general if it be written in the 

 form 



E= I VdF, 

 Jp, 



where V and P represent the molecular volume and pressure 

 of the whole salt, both the undissociated molecules and the 

 ions. Integrating this under the conditions 



c +c 



P=/4 2^ = RT(c / + 2c), 



Kc'=c 2 , 



(where the 's refer to the undissociated molecules, and the 

 unmarked letters to the ions), we get 



E=2^1og». 



716 P'J 



From this is to be subtracted the potential step (/> at Z, the 



1 C Pl 

 value of which is — j v dp for the negative ions only, or 



PT n ne Jt>2 



— log ~. Hence the difference in the potential steps at the 



electrodes is 



r ne ^ p 2 



