A kinetic approach is used to examine the structure of the approximations that lead to the Flory-Huggins expression for the free energy of mixing of a polymer solution. The kinetic model that we study can be solved exactly in one dimension, and also on an infinite-dimensional lattice, in which case it reduces to the Flory-Huggins formula. An approximate solution that interpolates between these limits gives results for a three-dimensional lattice that differ rather little from those of the original Flory-Huggins theory.