We derived theoretical free energies and chemical potentials as a function of composition for intercalation systems with repulsive interaction (J) acting between neighbor guest ions, assuming some forms of the configuration entropy such as the one (S-beta) equivalent to the Bethe approximation and the form (S-alpha) analogous to the exact entropy of the 1-dimensional lattice. We found that, though the free energy based on S-beta is no longer a good approximation at a relatively small value of J, the free energy and the chemical potential on S-alpha would fit the true ones as J is increased, if an intercalation lattice has an ordered structure without adjacent occupation of the guests at the half-filled state. The potential-composition (phi-x) relationship based on the theory was compared to an experimental result observed for a spinel type intercalation system LixMn2O4. Satisfactory agreement was confirmed in the region 1/2 < x < 1, assuming J = 1.86 kT per A bond of lithium ions on the neighboring 8a sites.