An upper bound on the theoretical activity coefficient of non-electrolytes.

Abstract

An upper bound on the activity coefficient, calculated from its theoretical definition, is formulated and discussed in detail for binary solutions of non-electrolytes. It is compared with a previous order-of-magnitude analysis that predicted it to be e. The existence of an upper bound points to a major discrepancy between theoretical and actual (experimentally measured) activity coefficients in highly nonideal solutions: The actual activity coefficient may be much higher than the theoretical upper bound. It is shown that the theoretical activity coefficient of the more volatile component must indeed be much smaller than e for slightly soluble components. For the less volatile component, the upper bound on the theoretical activity coefficient is shown to be approximately equal to the relative volatility. However, it is demonstrated that this upper bound may be grossly exaggerated when the relative volatility is high. In addition, as shown for aqueous solutions of n-alkanes that are less volatile than water, even when the upper bound is much higher than e, it may still be much smaller than the actual activity coefficient.