OSMOTIC AND MEMBRANE EQUILIBRIA 199 



where z » denotes the valency (positive or negative) of the ionic 

 species Si and F denotes the faraday, so that ZiF is the charge 

 of one mol of the ionic species. Finally V, Y" have values 

 independent of the type of ion being considered, and V — V" is 

 called the "electric potential difference" between the two 

 phases. 



This may at first sight appear a strange method of defining 

 electric potential difference between two phases of "identical" 

 composition, but it does not seem possible to give a simpler 

 definition that is not ambiguous. The usual definition of the 

 mathematical theory of electrostatics is not applicable to thermo- 

 dynamic systems, for the conditions of thermodynamic equihb- 

 rium of ions are by no means the same as the conditions of 

 equilibrium of "static electricity." 



15. Electric Potential Difference between Two Phases of 

 Different Composition. If we now consider the difference of the 

 potential of a given ionic species between two phases of different 

 bulk composition, this difference will be determined partly by 

 the difference in the chemical composition in the bulk and 

 partly by the distribution of electric charge at the surfaces. 

 This may be expressed formally as 



M' - W = W - m/0 + ZiFiV - 7"), (71) 



where [m] denotes the potential of the ionic species, m* denotes 

 the part of the potential due to the chemical composition of the 

 phase and z,- FV the part due to the distribution of electric charge 

 at its surface. The quantity [m,] may be called the "electro- 

 chemical potential" of the species Si, m may be called the 

 "chemical potential" of the species Si, and V may be called the 

 "electric potential." 



When, however, we come to ask ourselves exactly what would 

 be meant by the statement that the electric potential V had 

 the same value in two phases of different composition, w^e would 

 have to admit that the statement had in general no physical 

 significance. All equifibria and changes towards equihbrium 

 are completely determined by the electrochemical potentials 

 IJLti], and any decomposition of [m] into two terms m and ZiFV 

 is in general arbitrary. This attitude is in accordance with a 



