Two new methods are examined for computing liquid phase activity coefficients at low pressures. The first is the Modified Regular Solution Theory (MRST), the second is a new group contribution method. These two methods are based entirely on the mean density approximation (MDA) to evaluate pair distribution functions in mixtures. The mean density approximation assumes that a pair distribution function in a mixture is the same as for this pair in a pure component at a composition dependent average density which is different from the mixture density. The original Regular Solution Theory of Scatchard and Hildebrand made some assumptions. The first is that the probability of finding a particular pair having a specified center-to-center separation distance in a mixture is independent of composition and is the same as the probability for the pair in the pure component. The second assumption is that the entropy change is the same as the ideal solution entropy change. In this work,we incorporate the mean density approximation and the Flory-Huggins entropy change into the Regular Solution Theory of Scatchard and Hildebrand instead of the unrealistic assumptions about pair distribution functions and the entropy change made in the original theory. The result is called the Modified Regular Solution Theory (MRST). In 197, Funk and Prausnitz have proposed the incorporation of an unlike pair coefficient in the original Regular Solution Theory to derive the Funic version of the Regular Solution Theory(RST). The unlike pair coefficient is used to relate the interactions between unlike molecules to those between like molecules. This work likewise incorporates an unlike pair coefficient in the MRST. In Chapter II,we predict excess thermodynamic functions and activity coefficients from the MRST, the incorporation of the ideal solution entropy change to the RST, the incorporation of the Flory - Huggins entropy change to the RST respectively. Each of these are compared with experimental data. Prom the predicted values, we observe that the results from the MRST is the best and results using the ideal solution entropy change with the RST are poorer. Unlike pair coefficients are necessary in all the theories test. With unlike pair coefficients the MRST is better in predicting excess thermodynamic functions and activity coefficients in mixtures with large differences in molecular size and shape. We also calculate activity coefficients for the MRST by a new analytical differentiation developed in this work and compare with a numerical differentiation.We find the results from these two differentiation methods are almost same. The mean density approximation is also used in this work to develop a new theory of group contributions. This new theory was tested by studying the effect of different molecular species on the inter-group parameters. The group contribution method results from an expansion of a mixture property about this property of a pure reference component conformal with the constituents of the mixture. The expansion is developed in terms of the deviations of the interaction parameters for the individual molecules of the mixture from those of the reference. These deviations constitute effective group contributions for liquid phase activity coefficients. In Chapter III, we predict activity coefficients based on this group contribution method in binary mixtures of acetone-methanol, methanol-ethanol, acetone-ethanol and ternary mixtures of acetone-methanol-ethanol and compare with experimental data. The predicted values are generally good but the errors from the binary mixtures are usually smaller than those from the ternary mixtures.