Solutions with positive excess volume: For a solution (excluding solids dissolving in liquids) where the total volume after mixing is greater than the sum of the pure-component volumes, how does the solubility change with increasing pressure?

Introduction / Context:
Many liquid–liquid and gas–liquid solutions exhibit a non-ideal volume change on mixing. When the total volume of the solution exceeds the sum of the pure-component volumes, the mixture displays a positive excess molar volume. Le Chatelier’s principle and fundamental thermodynamics allow us to predict how pressure affects solubility under such conditions.

Given Data / Assumptions:

• Solution shows positive excess volume (total volume after mixing > sum of component volumes).
• Temperature is fixed; only the effect of pressure on solubility is examined.
• System is not a solid–liquid dissolution case (excluded in the stem).
• Near-equilibrium, reversible considerations apply.

Concept / Approach:
For a process that increases volume (positive ΔV_mix > 0), an increase in pressure shifts equilibrium to reduce the total volume. According to dG = V dP − S dT and the pressure derivative of chemical potential, higher pressure penalizes states with larger partial molar volumes. Therefore, pressure opposes the extent of a mixing process that creates additional volume, decreasing the solubility of the solute in the solvent when ΔV_mix is positive.

Step-by-Step Solution:

Verification / Alternative check:
In partial molar terms, μ_i(P) increases with P roughly by ∫ V̄_i dP. A positive excess volume implies larger V̄_i upon mixing; increasing P raises μ_i of the mixed state more than that of unmixed components, reducing the driving force for dissolution and thus lowering solubility.

Why Other Options Are Wrong:

• Independent of temperature: Irrelevant to pressure dependence; the stem fixes temperature.
• Increased with the increase in pressure: Opposite to the expected shift for ΔV_mix > 0.
• Unchanged by pressure: Contradicts thermodynamic response to volume changes.
• None of these: Not correct because a definite trend exists.

Common Pitfalls:
Confusing this case with gas solubility following Henry’s law (often increases with pressure). Here the key is the sign of excess volume of mixing for the specific solution in question.

Final Answer:
decreased with the increase in pressure