1494 
5. Introduction of the solubility product of the metal in the equation 
of the potential difference. 
It has been shown in chapter 3 that the solubility product of a 
noble metal must be smaller than that of a base one. from which 
it follows that the potential difference metal, solution must be a 
function of the solubility product, and that such a one that for a 
greater value of the solubility product the metal gets a more negative 
potential. 
In the following way the solubility product is easy to introduce 
into the equation for the potential difference. For: 
we may write: *) 
ul le mf Ui: 
A = M4 t 97 f M if TMM 7 
= Fr 
If we write u=u + RTlnc we get: 
Ws War, TU, — Wy, + RT In(Mz,) — RT In (Mr) (Or) 
N= F He Dn ET 
Fr 
A 2 ee 
= - = f ores rr LA : 
Fr Fae L) F (Mr) (Gz) 
The last term of this equation contains the’ above mentioned 
solubility product of the metal, which is indicated by Ly, hence: 
' 
AE (ae an) (34) 
= -— — n(Ly ini PI 
F F F 1 F L 
Besides the solubility product of the metal and the metal ion 
concentration, also the thermodynamic potential of the electrons in 
Ww, 
the metal and the term — FE oceur in this equation. 
The last is independent of the concentration of the electrons, and 
only dependent on the temperature and the nature of the solvent. 
Hence this term has the same value for all metals. 
Hos 
The term Ei has values for different metals which differ little 
H 
inter se. 
') Here for shortness’ sake we suppose the metal univalent, so 7=— 1. 
