2.6
Chemical and Solubility Equilibria
The free energy change associated with dissolving a solute in a liter of solvent is called the free energy of a solution, ΔGsolution. The overall ΔGso…
Recall that solution formation is regulated by the entropy of mixing, ΔSmixing. The associated free energy of mixing, ΔGmixing, is expressed by substituting ΔSmixing in the Gibbs free energy equation.
Since ΔSmixing is independent of intermolecular interactions, the energy changes associated with these interactions are neglected, and the value of ΔHmixing in the equation is 0. Thus, ΔGmixing is equal to negative T times ΔSmixing.
The free energy change associated with dissolving a solute in a liter of solvent is called the free energy of a solution, ΔGsolution. Mathematically, it is expressed as the sum of the free energy of mixing, ΔGmixing, and the free energy of interaction, ΔGinteraction, between the component particles.
If the solvent–solute interactions cannot overcome the solute–solute and solvent–solvent interactions, ΔGinteraction is greater than 0.
If ΔGinteraction is large enough, the ΔGsolution is greater than zero. As ΔGsolution increases, the amount of solute that dissolves in a solvent decreases.
In contrast, if ΔGinteraction is negligible, the overall ΔGsolution equals ΔGmixing, 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, ΔGinteraction is close to 0, ΔGmixing dominates, and a solution is formed.
Solution formation depends on the balance between ΔGinteraction and ΔGmixing. A solution can form even if ΔGinteraction is positive, provided it’s not too high.
In short, solution formation is favorable if the ΔGsolution is less than 0, whereas it is unfavorable if the ΔGsolution is greater than 0.
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Q1: What is the free energy of a solution and how does it determine whether a solute dissolves?
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.
Q2: How do intermolecular interactions affect whether two substances will mix to form a solution?
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.
Q3: Why do nonpolar liquids mix easily with each other?
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.
Q4: What role does entropy of mixing play in solution formation?
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.
Q5: How do polar substances with hydrogen bonding behave when mixed together?
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.
Q6: Can two significantly different substances form a solution even if their interaction free energy is positive?
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.
Q7: What happens when pentane dissolves in hexane, and why is this a favorable process?
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.