Osmosis calculation at 0°C: One gram-mole of a non-electrolyte is dissolved to make 22.4 litres of solution at 0°C. What is the osmotic pressure (in atm) of this solution?

Introduction / Context:Osmotic pressure is central to membrane separations, food science, and bioprocessing. For dilute solutions of non-electrolytes, it mirrors the ideal-gas law, enabling quick head calculations for reverse osmosis or dialysis design.

Given Data / Assumptions:

• Moles of solute n = 1 mol.
• Solution volume V = 22.4 L.
• Temperature T = 0°C = 273 K.
• R = 0.082057 L·atm·mol^-1·K^-1; ideal dilute solution.

Concept / Approach:For dilute, non-electrolyte solutions, osmotic pressure π follows πV = nRT, analogous to PV = nRT for gases.

Step-by-Step Solution:

Verification / Alternative check:This setup intentionally mirrors one mole of ideal gas at STP occupying about 22.4 L and exerting ~1 atm, hence the neat numerical result for π.

Why Other Options Are Wrong:

• 0.5, 1.5, 2: Do not match the direct calculation from π = nRT/V.

Common Pitfalls:For electrolytes, include van’t Hoff factor i. Also ensure volume is solution volume and temperature is in Kelvin for consistency.

Final Answer:1