OSMOTIC AND MEMBRANE EQUILIBRIA 211 



More detailed discussion of electrochemical cells would be 

 outside our province, but the above example serves to show that 

 the electromotive force of any cell may be computed by regard- 

 ing the mechanism of the cell as a combination of several 

 membrane equilibria. The electromotive force E is equal to the 

 difference of potential of any univalent positive ion in the two 

 terminals of the same metal at the two ends of the cell. This 

 is the only electric potential difference that is measured, and is 

 the only one to which any reference is made in this treatment. 

 As already mentioned, this attitude towards the conception of 

 electric potential is in accordance with views expressed by 

 WiUard Gibbs. 



BIBLIOGRAPHY 



Laws of Ideal Solutions These were given in an exact form by G. N. 

 Lewis, J. Am. Chem. Soc, 30. 668 (1908) and by E. W. Washburn, 

 Z. physikal. Chem., 74, 537 (1910). 



Activity Coefficient. The definition of this useful function is due to 

 G. N. Lewis. See Thermodynamics and The Free Energy of Chemical 

 Substances, by G. N. Lewis and M. Randall (New York, 1923). 



Osmotic Coefficient. This was first used by N. Bjerrum at the Scandina- 

 vian Science Congress 1916. See German translation in Z. Elek- 

 trochem., 24, 325 (1918). 



Membrane Equilibrium. The theory of ionic membrane equilibrium was 

 first developed for extremely dilute ideal solutions by F. G. Donnan, 

 Z.Elektrochem., 17, 572 (1911). The exact thermodynamic treatment 

 of solutions neither ideal nor dilute was given by F. G. Donnan 

 and E. A. Guggenheim, Z. physikal. Chem., A 162, 346 (1932); F. G. 

 Donnan, ibid., A 168, 369 (1934). 



Electrochemical Systems. Gibbs' method of treatment of equilibrium 

 and stability was extended to electrochemical systems by E. A, 

 Milne, Proc. Camb. Phil. Soc, 22, 493 (1925) and by J. A. V. Butler, 

 Proc. Roy. Soc, 112, 129 (1926). 



Electrochemical Potentials. The use of these functions to replace the 

 conception of electric potential difference between phases of differ- 

 ent chemical composition is due to E. A. Guggenheim, /. Phya. 

 Chem.. 33, 842 (1929), 



