702 



regard to a metal merged in this solution, which is thought to be 

 entirely built up of J/-molecules. 



The point b denotes the same thing for a solution of the same 

 metal-ion concentration as the just-mentioned solution, but containing 

 exclusively il/j'-'-ions, a metal being immersed in this solution which 

 consists exclusively of il^V^^olecules. The metal M is here supposed 

 to be a base state, and M^ to be a noble state of the same metal. 



Now it has been assumed in fig 1 that the metals M and M^ are 

 miscible to a limited degree in the solid state with the assumed T 

 and P. The two branches of the interrupted series of mixing are 

 indicated by the lines ad and eh, the solutions which can be in 

 electromotive equihbrium with these metal phases being indicated by 

 ac and cb. The line cde denotes the three-phase electromotive equili- 

 brium. In general this three-phase equilibrium can also lie above the 

 potential difference of the two metals, but this case is not considered 

 here, because we shall no doubt always have to do with association 

 in metals, in which it is to be expected that the metal phase will 

 contain more of the most composite pseudo-component than the coexist- 

 ing solution. 



The phases coexisting in case of electromotive equilibrium of 

 course lie on a horizontal line, which, the A,,r-figure being given, 

 and the potential difference being known, immediately enables us to 

 know the concentration of the coexisting phases. 



Now we may of course apply Van Laar's ') formula for the 

 potential difference between mixed crystals of two metals and electrolyte 

 also to the case supposed here. Considering that for electromotive 

 equilibrium 



+ 4- 



VMS VMS 



(1) 



in which hm and (im^ are the mol. -potentials of the 31" and M,'-'' 

 ions in the electrol} te, and hm and ^im^ those of the molecules 

 AI and M^ in the metal, v^ and rj/, representing the number of 

 charges of the different metal-ions, we arrive at the following relation 

 for the potential difference 



RT Km{1-^v) RT Km,x 

 A= In = "* "TT-T ^^> 



It follows from this formula, in which as I showed before, Km 



1) Chem. Weekbl. 41, 1905. 



Lehrbuch der Theoretischen Elektrochemie. 



