Osmotic pressure of dilute solutions – proportionality for a Raoult's-law system For a dilute solution of a non-volatile solute obeying Raoult's law, the osmotic pressure is directly proportional to which single parameter (holding the others constant as appropriate)?

Introduction / Context:
Osmotic pressure is a colligative property used to estimate molecular weights and design membrane separations. For dilute, ideal solutions, a simple gas-law-like expression connects osmotic pressure to solute amount, solution volume, and absolute temperature.

Given Data / Assumptions:

• Dilute solution of non-volatile solute.
• Raoult's-law (ideal) behavior is valid.
• Van't Hoff equation applies.

Concept / Approach:
The van't Hoff relation is πV = nRT, or π = (n/V) * R * T. Thus π is directly proportional to temperature T at fixed solute amount per unit volume, directly proportional to solute moles n at fixed V and T, and inversely proportional to volume V at fixed n and T. Because the question requests a single proportional factor, the most universal statement among the options is direct proportionality to absolute temperature T.

Step-by-Step Solution:

Verification / Alternative check:
Experimentally, increasing temperature at constant concentration raises measured osmotic pressure in line with the gas constant scaling.

Why Other Options Are Wrong:

• Volume of solution: π is inversely proportional to V at fixed n and T, not directly proportional.
• Moles of solute: True only if V and T are held constant; the prompt asks for a single proportionality, and temperature is the standard statement.
• None of these: Incorrect because π does scale directly with T for ideal solutions.

Common Pitfalls:
Failing to state the ceteris paribus condition; forgetting that osmotic pressure depends on concentration and temperature simultaneously.

Final Answer:
temperature.