For the theoretical modeling of physical transformations such as boiling, freezing, glassification, or mixing, it is necessary to know how the partition function of a system depends on its density. Many current treatments rely either on low density expansions or they apply to very simple and symmetric molecular shapes, like spheres or rods. Here we develop an exact analytical lattice theory of materials and mixtures that applies to arbitrarily complex molecular shapes over the full range of densities from gas to crystal. The approach is to compute partition functions for small numbers of shapes and to explore the dependence on density by varying the volume of the system. Recently a question has been raised about whether entropies of dissolution are better treated using classical solvation theories or Flory-Huggins theory We explore this for a range of molecular sizes and shapes, from lattice squares and cubes, to rods, polymers, crosses, and other shapes. Beyond low densities, the entropic component of the chemical potential depends on shape due to the different degrees to which molecules "interfere" with each other. We find that neither Flory-Huggins nor classical solvation theories is correct for all shapes. Molecules that are "articulated" are remarkably well treated by Flory-Huggins theory, over all densities, but globular molecules are qualitatively and quantitatively different, and are better treated by the classical chemical potential, consistent with experiments of Shinoda and Hildebrand. These results confirm that the Flory-Huggins theory differs from classical theory not because of molecular size differences per se; it accounts for the coupling between translations and conformational steric interference.