Solution of 12 g of non-electrolyte (A) prepared by dissolving it in 1000 mL of water exerts the same osmotic pressure as that of 0.05 M glucose solution at the same temperature. The empirical formula of A is CH₂ O. The molecular mass of A is __________ g. (Nearest integer)

Solution

Chemistry ma’am · 4 steps

Same osmotic pressure at the same temperature means the same molarity, so A is also 0.05 M.

1. Isotonic means equal molarity. For a non-electrolyte, π = CRT. Both solutions are at the same T and have the same π, so their concentrations must match: C_A = 0.05 mol L⁻¹.
2. Moles of A. The volume is 1000 mL = 1 L, so the solution holds 0.05 mol of A.

   M_A = mass/moles = (12 g)/(0.05 mol) = 240 g mol⁻¹

3. Check with the formula. The mass of CH₂O is 12 + 2 + 16 = 30, and 240 / 30 = 8. A whole number fits, so A is C₈H₁₆O₈.
4. So. The molecular mass of A is 240 g.

The common slip: 30. Stopping at the empirical formula mass of CH₂O gives 30, not 240. The empirical formula only checks the answer. The osmotic pressure data gives the molecular mass.

The idea to keep. Equal osmotic pressure at the same temperature means equal particle concentration. For non-electrolytes, that is just equal molarity, so you never need R or T.

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