Osmosis and colligative properties: The osmotic pressure of a solution increases when which variable is decreased (other factors constant)?

Introduction / Context:
Osmotic pressure is a colligative property proportional to the solute particle concentration in a solution. It matters in biological systems, membrane separations, and food processing. Understanding how manipulation of volume, concentration, and temperature affects osmotic pressure helps in designing desalination, dialysis, and concentration processes.

Given Data / Assumptions:

• For dilute solutions, van 't Hoff relation applies: π = i * M * R * T.
• M is molarity = moles of solute per litre of solution.
• i and R are taken as constants for the same solute and system; T is constant unless otherwise noted.

Concept / Approach:
Holding solute moles and temperature constant, decreasing the solution volume increases molarity M. Because π is directly proportional to M, osmotic pressure increases as volume decreases. Decreasing solute concentration would lower M and therefore lower π. Decreasing temperature would also lower π. Only a decrease in volume, with moles fixed, raises π in this list of options.

Step-by-Step Solution:
Write π = i * M * R * T for dilute solutions.Fix i, R, T and number of solute moles.Note that M = n / V; decreasing V increases M.Conclude that π increases when V decreases.

Verification / Alternative check:
Membrane operations observe higher osmotic back-pressure as solutions concentrate during water removal, consistent with π rising as volume falls at constant solute moles.

Why Other Options Are Wrong:
Solute concentration: decreasing it reduces π, not increases it.Temperature: lowering T reduces π in the van 't Hoff equation.None of these: incorrect because volume decrease clearly increases π under constant moles.

Common Pitfalls:
Confusing mass fraction with molarity; ignoring that π depends on particle concentration, not just mass of solute; forgetting the temperature factor in π for nonisothermal systems.

Final Answer:
Volume