Although enthalpies of mixing are straightforward to calculate using molecular simulations when the individual components are both pure liquids, substantial difficulties arise when one of the components is already itself a concentrated electrolytic medium, and for the dissolution of solids in liquids. Further complications arise when entropies must be calculated to determine free energies of mixing. Using a combination of theoretical and modeling results, we show how molecular dynamics can be used to estimate the mixing properties and energies of such thermodynamic systems, using dissolution of cellulose as a test case for demonstrating the effectiveness of the method. Comparison to experimental results show good agreement as a function of solution composition.