E 



OSMOTIC AND MEMBRANE EQUILIBRIA, IN- 

 CLUDING ELECTROCHEMICAL SYSTEMS 



[Gibbs, I, pp. 83-85; 4iS-417] 



E. A. GUGGENHEIM 



1. Introduction. The power and elegance of the methods of 

 Willard Gibbs in thermodynamics are nowhere better illustrated 

 than in their apphcation to membrane equilibria.* Owing to 

 the form in which he expressed the conditions for chemical 

 equilibria, the same conditions for the equilibrium between two 

 phases as regards a given species hold good whether the two 



* A list of the most important symbols used, in addition to those used 

 by Gibbs, is as follows: 



E Electromotive force of cell. 

 F Faraday. 



/, Activity coefficient of species St. 

 /± Mean activity coefficient of electrolyte. 



g Osmotic coefficient. 

 Ni Mol fraction of species St. 

 P Osmotic pressure. 

 q+, q- Number of cations and anions per mol of electrolyte. 



r Ratio of partial molar volume at infinite dilution of electrolyte to 

 that of solvent, both at a pressure equal to the mean of those 

 at either side of membrane. 

 Vi Partial molar volume of species Si at given temperature, pressure 



and composition. 

 Vi* Partial molar volume of species Si at given temperature, zero 



pressure and infinite dilution. 

 [vi] Partial molar volume of species Si at given temperature, infinite 

 dilution and at a pressure equal to the mean of those at either 

 side of the membrane. 

 Zi Valency, positive or negative, of ionic species Si. 

 Ki Coefficient of compressibility of species Si at infinite dilution, 

 [/i,] Potential of ionic species Si. 

 The suffix always refers to the solvent species, e.g., Vo* is the molar 

 volume of the pure solvent at zero pressure. 



