198 GUGGENHEIM art. e 



been applied only too often under conditions where it cannot 

 be even approximately correct. 



14. Electric Potential Difference between Two Identical Phases. 

 Up to this point we have tacitly assumed that all the species 

 present were electrically neutral. The fundamental difference 

 between the behavior of ions and of uncharged species is the 

 following. The potential of an uncharged species in a phase at 

 given temperature and pressure is completely determined by 

 the bulk composition of the phase, and is independent of the 

 presence of any impurity at the surface as long as its concen- 

 tration in the bulk is negligible. This, however, is not the case 

 for ions. Let us consider two phases identical with respect to 

 temperature, pressure, size, shape and bulk composition. Then 

 it may be that the first phase contains an excess of ions of one or 

 more kinds over the second phase, this excess being so small that 

 its effect on the size, shape and bulk concentration of the phase 

 is entirely negligible. If however the total excess of ions in the 

 first phase over those in the second has a net electric charge, 

 the corresponding excess charge will be distributed over the 

 surface of the first phase, and the potential of any ionic species 

 within the phase will be affected thereby. The difference 

 between the potential of a given ionic species in the first phase 

 and in the second will be determined entirely by the difference 

 in distribution of electric charge over the surfaces of the two 

 phases and independent of the chemical nature of the excess 

 ions. One might describe the situation roughly by saying that 

 the excess ions in the first phase over those in the second are too 

 few to show themselves in any manner except by their electrical 

 effect. It is usual and convenient to refer to two such phases 

 as "of identical composition but at different electric potentials." 

 To emphasize the peculiar property of the potential of an ionic 

 species, that it is not completely determined by the bulk com- 

 position of the phase, a slightly modified symbol will be used. 

 The potential of the ionic species Si will be denoted by [nil- 

 The difference between its value in the two phases of identical 

 composition will be of the form 



Wi]' -im]" = ZiF{V' -V") (70) 



