DEVIATIONS OF H-BONDED AGGREGATES IN LIQUIDS FROM THE GULDBERG AND WAAGE EQUILIBRIUM EXPRESSION

The absorption peak of alcohols near 3650 cm-1 (and its harmonics) concerns not only the monomolecules but also all the bonded vibrators ...O-H at the end of the chains of H-bonds. However, its relative intensity gives the probability gamma in the time of an alcohol molecule escaping from H-bonding in the liquid. This non-ergodic character of these H-bonds makes the Guldberg and Waage equilibrium expression in terms of the concentrations of the various i-mers in the ensemble no longer valid, and leads to its replacement by an equation in functions of the time fractions: (1-gamma)/gamma = K(A)C(A). In a large concentration range, the insertion constant K(A) varies from the limiting value K(A)degrees at high dilution to the asymptotic value K(A)infinity characterizing long chains. Neglecting these differences, the fraction alpha(i) of the alcohol molecules belonging to an i-mer in the ensemble is given by almost-equal-to igamma2 (1-gamma)i-1, the average number of associations of one alcohol molecule n(w) almost-equal-to (2/gamma)-1 and the average number of molecules in a chain is given by n(N) = 1/gamma.