Publication costs assisted by Fonds der Chemie, Frankfurt these bonds as the bonds of cyclic dimers and linear higher polymers, as suggested by previous authors. However, due to the complications of the alcohol association as well as to the inherent simplifications of the model the calculated energies may not be related to the bonds in a simple manner. From K2 and K3 the activity coefficients and the excess free energy can be recalculated. The comparison of the obtained values with the conventionally calculated values proves that the amines and the short chain alcohols fit the two-constant model within a wide range of concentrations, while this is not the case with long chain alcohols.

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On rearranging, Equation (6) may be put into the form a = X,$ + 2 4 J , 4 2 ( % -% ) ( ? I -Y 2 ) / Y a . (7)From Equation (7) one may calculate the temperature dependence of the excess volume:V, and V2 designating the molar volumes of the unmixed liquid components. According to Equation (I), ( -yr*) is obtained from (g) by subtracting ('r,") __ that, in turn, is equal to VFH/T r,x P . X P.X 6n acLount of since = 0 for athermal mixtures. Once the temperature derivative of V* is known. we may use Equations (4) and (1) to calculate C: from Vb.