The osmotic pressure of a solution of NaCl is 0.10 atm and that of a glucose solution is 0.20 atm. The osmotic pressure of a solution formed by mixing 1 L of the sodium chloride solution with 2 L of
the glucose solution is x × 10 –3 atm. x is _____. (nearest integer)

Solution

Chemistry ma’am · 3 steps

Osmotic pressure counts particles, so take the volume-weighted average of the two pressures.

1. Pressure tracks particles. Since π = iCRT, each pressure already measures the total concentration of dissolved particles. The factor i = 2 for NaCl is built into its 0.10 atm, so you do not need to apply it again.
2. Particles before mixing. At the same temperature, the moles of particles in each solution are proportional to π × V. That gives 0.10 × 1 = 0.10 from the NaCl solution and 0.20 × 2 = 0.40 from the glucose solution, in atm L.

   πₘᵢₓ = (π₁ V₁ + π₂ V₂)/(V₁ + V₂) = (0.10 × 1 + 0.20 × 2)/(1 + 2) = 0.50/3 atm

3. So. πₘᵢₓ = 0.1667 atm = 166.7 × 10⁻³ atm, so x rounds to 167.

The common slip: 150. Averaging 0.10 and 0.20 without weighting by volume gives 0.15 atm, that is 150. The glucose solution has twice the volume, so it counts twice.

The idea to keep. When you mix solutions at the same temperature, the particles are shared over the total volume. Weight each osmotic pressure by its volume, then divide by the total volume.

Answer from the NTA final answer key. Solution by PrepWiser.