418 Dr. S. R. Milner on the 



1 f p 

 work of osmotic expansion — l p dv between the two 



*J Pi 



pressures of the ions in the metal and the solution, without 



further examination. The expression for the potential step 



1 C Pl 



given by a cycle is, however, —I v dp ; and although 



116 J ^ 



the difference between these two results vanishes so long as 

 the gas laws apply, it is of some importance theoretically, as for 

 example in the application to incompletely dissociated electro- 

 lytes. A further difficulty in them is that the case is treated 

 of a single electrode in a liquid, and it is impossible here to 

 imagine reversible electrolytic solution to take place without 

 charging up the solution, and the removal of this charge can 

 only be brought about by the introduction of negative ions 

 into the solution, from which process more osmotic work 

 might theoretically be obtained. The neglect of this effect 

 may be shown to give correct results, but the arbitrariness 

 resulting, from it makes it difficult to recognize the nature of 

 the real assumptions on which the formula depends for its 

 validity. For a thermodynamical proof to satisfactorily admit 

 of this, it seems essential that the operations should be re- 

 ducible to an exact cycle, in which also the possibility of 

 carrying out the individual processes should be evident. 



The importance of the theory is so great, in view of the 

 remarkable way in which it has shown itself applicable to so 

 many different phenomena in electrochemistry, that it seems 

 advisable that the exact nature of the assumptions which under- 

 lie the validity of Nernst's formula should be recognizable as 

 clearly as possible. The following simple derivation, by a 

 cyclical application of the second law, which allows this 

 recognition, may therefore not be without interest. 



Take for simplicity the special case of a cell composed of 

 silver electrodes in concentrations c 1? c 2 (c 1 >c 2 ) of silver, 

 nitrate, in the vessels A and B respectively in the figure. 

 We assume that the silver nitrate is completely dissociated, 

 and that the ions both exert osmotic pressures (p l in 

 A, p 2 in B) against semipermeable partitions X and Y, by 

 the motion of which work may be done on or obtained from 

 the cell reversibly. Electrical work may also be obtained by 

 allowing electricity to pass round the circuit formed by 

 balancing the cell against an accumulator D. 



In order, however, to make this operation reversible, the 

 two concentrations must be separated by some form of par- 

 tition which will prevent diffusion, and yet allow the reversible 

 passage of electricity through it. For this purpose we may 



