Chemical and Solubility Equilibria

Recall that solution formation is regulated by the entropy of mixing, ΔS_mixing. The associated free energy of mixing, ΔG_mixing, is expressed by substituting ΔS_mixing in the Gibbs free energy equation.

Since ΔS_mixing is independent of intermolecular interactions, the energy changes associated with these interactions are neglected, and the value of ΔH_mixing in the equation is 0. Thus, ΔG_mixing is equal to negative T times ΔS_mixing.

The free energy change associated with dissolving a solute in a liter of solvent is called the free energy of a solution, ΔG_solution. Mathematically, it is expressed as the sum of the free energy of mixing, ΔG_mixing, and the free energy of interaction, ΔG_interaction, between the component particles.

If the solvent–solute interactions cannot overcome the solute–solute and solvent–solvent interactions, ΔG_interaction is greater than 0.

If ΔG_interaction is large enough, the ΔG_solution is greater than zero. As ΔG_solution increases, the amount of solute that dissolves in a solvent decreases.

In contrast, if ΔG_interaction is negligible, the overall ΔG_solution equals ΔG_mixing, and the solute dissolves completely in the solvent.

Consider dissolving pentane in hexane. Hexane–pentane attractions in the solution replace some of the pentane–pentane and hexane–hexane attractions in the pure liquid. Since both the molecules are of the same type, ΔG_interaction is close to 0, ΔG_mixing dominates, and a solution is formed.

Solution formation depends on the balance between ΔG_interaction and ΔG_mixing. A solution can form even if ΔG_interaction is positive, provided it’s not too high.

In short, solution formation is favorable if the ΔG_solution is less than 0, whereas it is unfavorable if the ΔG_solution is greater than 0.