In this paper we use the generic van der Waals equation of state to define the free volume of liquids along the liquid–vapor coexistence line (liquids curve) in the case of liquid argon and along three isotherms in the high-pressure regime in the case of liquid methane. With the free volume computed from the cavity function obtained by means of a Monte Carlo simulation method, we have calculated the self-diffusion coefficients of liquid argon and liquid methane. The Cohen–Turnbull free volume theory is used to calculate them. With the empirical parameter appearing in the Cohen–Turnbull theory suitably adjusted, the theoretical and experimental values of the self-diffusion coefficients agree very well with regard to the density and temperature dependence for the cases of available data compared. A pair of analytic formulas for density dependence of the self-diffusion coefficient is obtained by using the approximate cavity functions for hard spheres and tested against the experimental data on methane. A comparison of the analytic formulas with experiment is also very good.

A simple formula for the diffusion coefficient of liquid mixtures, expressed in terms of the work necessary to create a characteristic free volume in the liquid, is presented in the spirit of the Arrhenius activation theory and tested in comparison with available experimental data. If use is made of the generic van der Waals equation of state, the free volume appearing in the formula for the diffusion coefficient can be expressed in terms of the equilibrium pair correlation functions. The theoretical values for diffusion coefficients agree excellently with experimental values with regard to the density and temperature dependence of the diffusion coefficients of argon and krypton.

It is shown that the tracer diffusion and self-diffusion coefficients of liquids are in a simple linear relation with a constant coefficient, which depends on only the molecular size ratio and the mass ratio of the solute and the solvent molecule. With experimentally determined tracer diffusion and self-diffusion coefficients, the relation can be used for estimating the molecular sizes of polyatomic molecules. By estimation of the size ratio with the van der Waals radii of the constituent molecules, the relation is shown to account excellently for the experimental data on diffusion of various solutes, such as a series of benzene derivatives, ketones, alcohols, and so on, in organic solvents or water. The systems investigated include those in which the hydrogen bonding effects are expected to affect the diffusion of tracer molecules (e.g., alcohols in water and vice versa). The relation of diffusion coefficients presented is thus shown to be an excellent means to estimate molecular sizes from the data on diffusion coefficients measurable by various methods including NMR techniques.

A statistical mechanical formula is developed for the bulk viscosity of molecular liquids. It is expressed in terms of the self-diffusion coefficient of the liquid, intermolecular forces, and the site–site pair correlation functions. The density and temperature dependence of the bulk viscosity of carbon dioxide and nitrogen are calculated therewith and compared with experimental data wherever possible. In the case of liquid nitrogen for which experimental data are available the theoretical values of the bulk viscosity are well within the experimental error ranges in almost all cases. There are no experimental data to compare with the theoretical results for liquid carbon dioxide, but in the light of the comparison for nitrogen and the excellent shear viscosity results which were obtained in the same line of approach in the previous work the calculated bulk viscosity values of liquid carbon dioxide may be treated as theoretical predictions.