Osmotic pressure control: which action will increase the osmotic pressure (π) of a solution, all else being equal?

Introduction / Context:
Osmotic pressure is critical in membrane separations, food preservation, and biological cells. It scales with solute particle concentration and absolute temperature.

Given Data / Assumptions:

• Dilute solution obeying van’t Hoff relation: π = i * C * R * T.
• i is the van’t Hoff factor; C is molar concentration; T is absolute temperature.
• Closed system with a semipermeable membrane conceptually present.

Concept / Approach:
From π = i C R T, increasing π requires increasing either i (more dissociation), C (more moles of solute per unit volume), or T (higher temperature). The listed actions either decrease T, decrease C, or effectively dilute the solution—none of which raise π.

Step-by-Step Solution:
Option (a): lowering temperature reduces T → π decreases.Option (b): increasing volume at fixed solute moles reduces C → π decreases.Option (c): dilution reduces C → π decreases.Thus, none of the listed actions increase π.

Verification / Alternative check:
To increase π in practice: add solute (increase C), choose a solute with higher dissociation i, or raise the solution temperature.

Why Other Options Are Wrong:
Each proposed action moves π in the opposite direction predicted by the van’t Hoff equation.

Common Pitfalls:
Assuming vessel expansion increases pressure (it lowers concentration instead); confusing osmotic pressure with hydrostatic pressure.

Final Answer:
none of these