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The free energy of a solution, ΔGsolution, represents the total free energy change when a solute dissolves in a solvent. It combines the free energy of mixing, ΔGmixing, and the free energy of interaction, ΔGinteraction, between component particles. Solution formation is favorable when ΔGsolution is less than zero, allowing the solute to dissolve. When ΔGsolution is greater than zero, dissolution is unfavorable and the solute remains insoluble.

Solution formation depends on the balance between ΔGinteraction and ΔGmixing. If solvent-solute interactions cannot overcome solute-solute and solvent-solvent interactions, ΔGinteraction becomes positive and large, making ΔGsolution positive and preventing dissolution. However, if ΔGinteraction is negligible, the overall ΔGsolution equals ΔGmixing, and the solute dissolves completely in the solvent.

Nonpolar liquids are miscible because there is no appreciable difference in the strengths of solute-solute, solvent-solvent, and solute-solvent intermolecular attractions. Since the intermolecular forces are similar across all interactions, ΔGinteraction is negligible. The free energy of mixing dominates, making ΔGsolution negative and allowing complete dissolution and mixing.

Solution formation is regulated by the entropy of mixing, ΔSmixing, which is independent of intermolecular interactions. The free energy of mixing, ΔGmixing, equals negative T times ΔSmixing. Since ΔSmixing is always favorable, ΔGmixing is always negative and drives solution formation. This entropy effect can overcome positive ΔGinteraction values, provided they are not too large.

Polar substances that form hydrogen bonds mix easily because solute particles' dipole-dipole attractions with solvent particles are as strong as attractions between molecules in pure solute or solvent. Since the intermolecular forces are comparable, ΔGinteraction is negligible, and the two kinds of molecules readily combine. The free energy of mixing dominates, making solution formation favorable.

Yes, two significantly different substances can form a solution even if ΔGinteraction is positive, provided it is not too high. The always-favorable free energy of mixing, ΔGmixing, can offset a moderate positive ΔGinteraction. Solution formation depends on the overall balance between these two terms; if the combined ΔGsolution remains negative, dissolution occurs.

When pentane dissolves in hexane, hexane-pentane attractions in the solution replace some pentane-pentane and hexane-hexane attractions in pure liquids. Since both molecules are similar in type, ΔGinteraction is close to zero, and ΔGmixing dominates. The overall ΔGsolution becomes negative, making the solution formation favorable and resulting in complete miscibility.