6 54 
ionized into simple, anhydrous ions. Nernst’) and his pupils have 
derived an equation of the current potential line for this in the 
following way. 
On deposition of a metal the solution gets poorer in metal ions 
in the neighbourhood of the cathode; the concentration of the metal 
ions at the cathode would very soon have become 0, and then the 
deposition of metal would stop, when not continually metal ions 
were added to the cathode. This supply takes place in two ways. 
First in this way that metal ions migrate with the current to the 
cathode, secondly in this way that the ions go to the cathode by 
diffusion. : 
The migration of the metal ions with the current can be practic- 
ally excluded by addition of an excess of a second electrolyte. In 
this case the transmission of the current takes chiefly place through 
the ions of the added electrolyte, and only the diffusion of the ion 
that is discharged, is to be taken into account. If the added electro- 
lyte is chosen so that it has the same anion as the original one, 
the diffusion coefficient of the metal ion is proportional with its 
mobility, viz. for a binary electrolyte at 18° 0,0224 w, in which w 
is the electrolytic mobility, expressed in rec. ohms. 
If the solution is strongly stirred, it may be assumed that the 
liquid bas the same concentration throughout, except in a very thin 
layer on the electrode, which is not set in motion by the stirring. 
In this layer, the thickness of which is dependent on the velocity 
of the stirring, the movement of the ion only takes place by diffusion. 
When we electrolize with a constant current density, and all cir- 
cumstances remain the same for the rest, a stationary state will 
arise in this diffusion layer. An equal number of ions then pass 
per second through every section of the diffusion layer, and all the 
ions arriving per second at the cathode, are discharged per second 
there. This latter condition gives a connection between the current 
density and the diffusion velocity. 
If the concentration of the ions in the solution outside the diffusion 
layer is C and at the cathode c, and the thickness of the diffusion layer 
d, the gradient of concentration in the diffusion layer is nj and the 
quantity of ions passing per second through a section or 4 "ens 
Pie CI . voy: eee 
is ____ _—_, if D is the coefficient of diffusion per day. 
86400 Jd 
') Of. Nernst, Ber. 80 (1897) 1553. SALOMON, Z. phys. Chemie 24 (1897) 54, 
25 (1898) 365, CorrreLL ibid 42 (1903) 385, Grassi, ibid 44 (1905) 4,60 
BRUNNER, ibid 47 (1904) 56, Nernst and MERRIAM, ibid. 58 (1905) 235. 
