at the Electrodes in a Solution. 



49 



According to Neumann *, when copper is deposited from 

 the normal solution of its sulphate on a copper electrode, 

 it produces an E.M.F. aiding the current of 0*515 volt 

 hydrogen; on the other hand, when it is reversibly deposited 

 on a platinized platinum hydrogen electrode an E.M.F. of 

 only 0*238 volt, i. e. a voltage higher by 0*277, is required to 

 liberate hydrogen reversibly from a normal solution of its 

 sulphate than is required to liberate copper under the same 

 conditions. 



Now according to Oaspari's experiments f, a 0*23 volt 

 higher electromotive force is required to set hydrogen free on 

 a copper than on a platinized platinum electrode; i. <?., in 

 order to deposit hydrogen on a copper electrode from a 

 normal solution of sulphuric acid 0*507 volt more is required 

 than to deposit copper on the same electrode from the normal 

 solution of its sulphate. If we employ Nernst's formula to 

 calculate the concentration of a copper solution, to deposit 



It is easy to see that from the two equations (A) and (B) the ratio y men- 

 tioned above can be calculated to be y= p-Tp. This is the formula 



given without explanation by Nernst. It should, however, be parti- 

 cularly noted that this ratio y is not the result of simultaneous, but of 

 successive deposition of the two metals, depending on the rate of stirring, 

 and that, as will be seen later (note, p. 60), the ratio of simultaneous 

 deposition, e. g. at the beginning of the experiment, has a different value, 

 irrespective of the fact whether the current employed be large or small. > 

 In order to obtain formulas referring to simultaneous deposition, when 

 no stirring takes place we assume the electrolysis to take place in a 

 cylindrical vessel bounded by its cathode, and indicate distances from it 

 by x, times by t, and name the quantity of each ion crossing any section 

 in the differential of time in the direction towards the electrode, i. e. from 

 greater values of x to less, F^lt and F 2 dt respectively ; then, assuming 

 complete dissociation, we have for simultaneous deposition of the two 

 (monovalent) metals as above, 



from which follows : 



c x = — l c^ for x=0; 



L 2 



^l = ?x^ for.r=0: 



' . 3F_dc . 



and as in every cross section =rz — -. ., tins gives : — 









~P 2 





for 



.r=0. 



(See also note on p. 60.) 



* Zeitschr. phys. Chem. xiv. p. 



t Ibid. xxx. p. 93. 



222. 







PkiL Mag. 



s. 



6. Vol. 1. 



No. 



1. 



Jan, 



1901 



E 



