A unified approach to glass electrode theory.

A unified derivation of ion-exchange theories and "n-type" descriptions of glass-membrane potentials is presented. A review and comparison of the existing theories of glass electrodes given on this basis. Nearly all of the earlier approaches correspond to or follow from special cases of the present theory. For general practical applications the following simple equation is suggested, which incorporates the familiar Eisenman equation and Nikolskii's results for heterogeneous-site glasses: E = const - RT/F ln Sigma i beta(i)[(a'(H))(1 n(i)) + (K(i)a'(M))(1 n(i))](-n(i)) where E is the emf, a'(H) and a'(M) are the cation activities in the sample solution, and K(i), beta(i), and n(i) are the selectivity-determining parameters for sites i in the glass membrane. The published response of Na(2)OAl(2)O(3)SiO(2) glasses is used to test this equation; the results are compared with different extensions of glass-electrode theory.