at the Electrodes in a Solution. 



59 



We thus find that if we pass a current of constant density i 

 through an acid solution of copper sulphate, until the con- 

 centration at the cathode has gone down to zero, the values 

 of F at the beginning and at the end of the experiment can 

 both be calculated, and we shall be justified in assuming that 

 the concentration actually attained at any time t could also 



71 % 



have been attained if a constant flow F' = uaKAti ly m g some- 

 where between the extreme values of F had taken place. 

 Thus, as far as variability of F is concerned, we can express 

 the concentration at the electrode at any time by the formula 



c = c — 



1\L284 

 96540 



Vi 



(13) 



n' being contained between 1 and the value of 1 — n c given 

 in equation (12). 



We now come to the consideration of the effect of the 

 passage of the current through the liquid on its con- 

 centration. As has already been stated, this is expressed 

 for a positive ion by the equation 



~dc _ i ~d (ac\ 

 ~dt ~~ 96540 cm */ 



In the case we are now considering the concentration c of 

 the copper will vary extremely rapidly as we approach the 

 cathode, the conductivity k of the solution on the other hand 

 will remain fairly constant, as the solution, while becoming 

 poorer in Cu and S0 4 ions, will at the same time become 

 richer in H ions, which are brought to the electrode without 

 being liberated there. As we only desire to obtain rough 

 values, we shall therefore be justified in assuming k constant 

 and equal to the conductivity at the beginning of the 

 experiment. The mobility of the copper we also assume 

 constant. We thus have 



3* 



ia ~dc 

 y6540 k §# 



3* ... 



As ^— is always positive, we can conclude that the passage 



of the current will have the general effect of raising the 

 concentration in parts of the liquid near and at the electrode 



where ^— is of appreciable magnitude. The value given by 



equation (13) must therefore be regarded as a lower limit. 



