54 Dr. H. J. S. Sand oh the Concentration 



Experimental application of equation (7). — (a) Application 

 to the Solution of a Single Salt. 



If we electrolyse the solution of a single salt, for example 

 that of pure copper sulphate, we know that the value o£ F at 



the cathode in — -;-- "is 

 cm/ sec. 



in a __ i(l — n c ) 



96540" 96540 ' 



i being the current-density in ^ , n u the transport value of 



the anion S0 4 , and n c that of the cation Cu in the solution. The 

 concentration at the electrode after electrolysing for t seconds 

 will therefore be 



1-1284 



c=c 



It 1-1284 V1 . It fQS 



96540 lna V K =C «- 96540 ?(1 -^ V K ' (b> 



This formula can be employed for the determination of K if 

 coordinate values of c and t are known. Before, however, 

 further attempting to apply it to electrolysis, it will be 

 necessary to consider to what extent ihe conditions on which 

 it is based can be fulfilled in electrolytic experiments. 



Let us suppose electrolysis of a pure copper-sulphate solu- 

 tion to take place in a cylindrical vessel of length /, bounded 

 at the top by a horizontal cathode, at the bottom by a 

 horizontal copper anode. In such a vessel, kept at constant 

 temperature, convection-currents will be reduced to a mini- 

 mum, as the lighter layers of less concentrated solution are 

 continually being produced at the top, and the more concen- 

 trated ones at the bottom. 



Our formula being based on the assumption of an infinitely 

 distant anode does not comprise the fact that the anode of 

 the real vessel we are now considering is causing a con- 

 tinuous flow of salt into the liquid at the distance / below 

 the cathode, which is equal to the flow out of it. It is, how- 

 ever, not difficult to see that the following statements are 

 correct : — (1) The real concentration at the anode and in the 

 solution is greater than that given by the formula. (2) The 

 difference between the real concentration and the calculated 

 value is a maximum at the anode, and decreases continually 

 as we approach the cathode. These first two statements can 

 be inferred from the principle of superposition. (3) The real 



concentration at the distance — below the cathode is (either 



according to Weber's formula (5) or from considerations of 



