The primary goal of this and a previous paper(1) is to determine whether molar volume makes significant contributions to the partitioning of solute molecules between different phases. The previous paper considered the entropies of mixing of chainlike solvent molecules where volume effects arising from chain connectivity were found to raise the chemical potential of dissolved solutes. In this paper we consider the case of spherical solvent molecules. An expression is derived for the entropy of mixing of hard spheres under additive volume conditions. In addition to suggesting how volume effects may be related to molecular shape, our results allow us to consider the relationship between various theories which have related mixing entropies to molar volume. It is shown that volume-dependent contributions to solvation entropies can be interpreted in terms of pressure-volume effects involving hard sphere or ideal pressure rather than ambient pressures. Entropic effects result directly from changes in free volume resulting from transfer of solute to solvents of different size and packing fraction. Moreover, the solvent size and packing fraction are interlinked, since from ambient pressure constraints, an increase in the solvent packing fraction usually accompanies increases in solvent size. in contrast to their significant contribution to mixing entropies, it is reasonable to expect, based again on ambient pressure arguments, that volume effects make only small contributions to the chemical potential of spherelike solutes due to compensating enthalpic effects, The results obtained here and previously(1) thus suggest that size effects on solvent density contribute significantly to the chemical potential for chainlike solvent molecules and contribute much less for spherical solvent molecules. Nevertheless, molar volume affects the mixing of spherical molecules as well, a result which appears to contradict the classical study of Shinoda and Hildebrand. However, the theory presented in this paper provides a direct explanation of the Shinoda-Hildebrand data. On the basis of these studies, one expects that molar volume makes only minor contributions to the aqueous solubility of molecules from the gas phase. However, for the partitioning of solutes between water and chainlike organic solvents, volume effects are to be expected. The latter conclusion implies, as suggested earlier, that the magnitude of the hydrophobic effect is larger than previously believed.