2 g nonelectrolyte solute when dissolved in 50 g water increases its boiling point by 0.13 K. Calculate the molar mass of solute if molal elevation constant of water is 0.52 K kg mol ⁻¹

Step-by-step solution

The elevation in boiling point is given by the formula: T_b = K_b m where m is the molality of the solution, which can be expressed as: m = w₂ 1000 M₂ w₁ Substituting the expression for molality into the boiling point elevation formula gives: T_b = K_b w₂ 1000 M₂ w₁ Rearranging to solve for the molar mass of the solute, M₂ : M₂ = K_b w₂ 1000 T_b w₁ Substituting the given values ( K_b = 0.52 K kg mol ⁻¹ , w₂ = 2 g, T_b = 0.13 K, w₁ = 50 g): M₂ = 0.52 2 1000 0.13 50 M₂ = 4 40 = 160 g/mol