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



;Still more must 



1-1284. ft 



c>Co "woVk S u ) 



\ : We can also find an upper limit for c, by determining the 

 increase of concentration Ac at the electrode due only to 

 passage of the current through the solution, by a precisely 

 •similar method to that employed for finding the corresponding 

 decrease in the case of pure CuS0 4 on page 56. In the way 

 shown there, it can also be seen here that the value obtained 

 is too large when taken to represent the combined effect of 

 diffusion and passage of the current. As the final result, 

 we obtain 



1-1284 ,. fl an' r # 



C < C ° 96540 n *V K + 96540 2 * K ; 



id: l:ii 



* Note. — If we had made no assumption about a and k this inequality 

 •would be 



1-1284 ,. /T C* dti d iac\ 

 . , c < c ~ ^6540 ^ V K + J 96540 &* \k)' 



from which, in conjunction with inequality No. 14, can be concluded 



c . »' d ( ac ) 

 °6540^rU/' 



ftc_ _ 1-1284 rii 



H>i~ 2 x 9d540 V IS"" 1 "" 96£ 



.€ being a number contained between and 1. 



This formula enables us to obtain some further information about the 



ratio =^ 1 , in which two monovalent metals can be deposited, which is 



mentioned in the note on p. 49, if we suppose that in the mixture 

 assumed there the two salts diffuse independently of each other. The 

 equation 



& p 2 d> 



then leads to 



M28 4 w, 7 ^ W[ g /« lCl \ac 



Pi = 2 x 96-540 j/Kt x 9(3540 c{ k I fry 

 P 2 ._ 1-1 284 w 2 V 2 i 2 </f ^ , ae i ^ 



+ «2„-, 



\m. 



2 x 96540 V K 2 2 96540 dc \ k ) ^x 



from which for £=0 we obtain, remembering that for this value of t 



i F 



n' = l — n c ; and also that ~- = ~ : 

 :■■;■■■■' ^o F 



F 2 P 2 (l-We : 



j\/k; 



This equation for the limiting value of the ratio in which the two 

 metals separate out in the first differential of time is based on no other 

 assumption than that the two salts diffuse independently of each other, 

 according to Fick's law (besides those assumptions stated on p. 47. 



