A solution contains 0.010 moles of a nonvolatile solute in 1.00 kg water. Using π = MRT with T = 298 K, R = 0.0821 L atm mol−1 K−1, and M ≈ 0.010 M, what is the osmotic pressure?

• A. 0.210 atm
• B. 0.245 atm
• C. 0.302 atm
• D. 0.189 atm

Answer: (B)

Osmotic pressure is driven by the number of solute particles in solution and increases with temperature. For a dilute solution, the van't Hoff relation π = MRT gives a good estimate, where M is the molarity, R is the gas constant, and T is temperature in kelvin.

Here, 0.010 moles of solute are in about 1.00 kg of water. Since 1 L of water has a mass of roughly 1 kg, the solution’s volume is about 1.00 L, so the concentration is about 0.010 mol per liter, i.e., M ≈ 0.010 M.

Plug in the values: π = (0.010 mol/L)(0.0821 L atm mol−1 K−1)(298 K).

Calculate the product: 0.0821 × 298 ≈ 24.46, and multiplying by 0.010 gives π ≈ 0.2446 atm. Rounding, the osmotic pressure is about 0.245 atm.

This result reflects that a small amount of nonvolatile solute in water at room temperature produces a modest osmotic pressure, consistent with dilute-solution behavior.