In the framework of the mean-field kinetic variational theory, a numerical study is presented to understand the concentration dependence of the mutual diffusion coefficient in terms of molecular sizes and interaction parameters for the van der Waals binary mixtures of types II, III, IV, and V, in the scheme of Scott and van Konynenburg. This work is an extension to the study for systems of type I presented by us quite recently. In addition, the behavior of the mutual diffusion coefficient of the van der Waals mixture is compared with that of the hard-sphere mixture and for the case of systems of type II, with experimental data of actual systems : water/n-propanol, n-hexane/acetone, and n-heptane/acetone. The mutual diffusion coefficients for the last two systems were determined by us with the Taylor dispersion technique. The mutual diffusion coefficients for the systems n-hexane/acetone and n-heptane/acetone are reported here at 298.15 and 303.15 K, respectively, along all the concentration range. The explicit model used here allows us to obtain an explanation about the role played by the variables that determine the concentration dependence of the mutual diffusion coefficient for actual systems.