56 Dr. H. J. S. Sand on the Concentration 



independent of concentration, no change of concentration is 

 ever brought about by the passage of the current. In the 

 case of copper sulphate, however, n c , the transport value of 

 the copper, is not independent of the concentration. It is 

 given according to Koblrausch by Hittorf and Kirmis as 



* n ° -0-047 Cm - 3 



~dc mg.-equiv.* 



We have, therefore, for differences of concentration brought 

 about by the passage of the current at every point of a copper- 

 sulphate solution: 



dc_ 0-047 ,3c 



~dt~ U 6540*3^ 



~- in our solutions being always positive, we can conclude 



that this effect will cause a general lowering of concentration, 

 and that the value given by equation (8) for c is slightly too 

 large and must be regarded as an upper limit. 



We can also find a lower limit for c by the following con- 

 siderations. The value of ~- £° r <# = is given bv equation (1), 



0* 



we therefore know that at the electrode, owing to the effect 

 we are considering alone 



~dc _ _ 0-047 i 2 n a 

 ~bt ~ 96540 2 K ' 



0-047 i 2 n a 



%540 2 K 



This value is, however, too large when taken to represent 

 the total lowering of concentration. We see this when we 

 remember that the gradient of concentration is always a 

 maximum at the electrode, decreasing continuously as we 

 depart from it, and that the lowering of concentration due only 

 to passage of the current will therefore, according to the 

 general equation (10), also be a maximum at the electrode, 

 decreasing with increasing distance from it ; this in its turn 

 will have the effect of increasing the gradient at all points of 

 the liquid and thus also increasing diffusion. We have 

 therefore as extreme limits for the concentration at the elec- 

 trodes of a copper-sulphate solution in which diffusion takes 

 place according to Fick's law, the values given by the equa- 

 tion 8 and by the equation 



1-128 4 . /— 0'047w a Pt f 



y0540 ?nj VK"TK3540 2 -K ' " (11 ^ 



C = Cn — 



