Calculate the molar mass of a nonvolatile solute if 6.4 g of it dissolved in 100 g water produces a relative lowering in vapour pressure of 0 016 at 300 K.

Step-by-step solution

The relative lowering in vapour pressure is given by Raoult's law: P P^0 = n₂ n₁ + n₂ For a dilute solution, n₂ n₁ , so n₁ + n₂ n₁ . The equation simplifies to: P P^0 n₂ n₁ = w₂ M₁ M₂ w₁ Given: Relative lowering in vapour pressure, P P^0 = 0.016 Mass of solute, w₂ = 6.4 g Mass of solvent (water), w₁ = 100 g Molar mass of water, M₁ = 18 g mol ⁻¹ Substituting the values into the formula: 0.016 = 6.4 18 M₂ 100 M₂ = 6.4 18 0.016 100 M₂ = 115.2 1.6 = 72 g mol ⁻¹ Answer: 72 gmol ⁻¹