Two elements X and Y form two non-electrolyte compounds with the formulas XY ₂ and X ₂ Y ₃ . When 2.0 g of XY ₂ is dissolved in 50 g of a solvent, the depression in freezing point is 2.0 K. When 1.7 g of X ₂ Y ₃ is dissolved in 50 g of the same solvent, the depression in freezing point is 1.0 K. Given that the molal depression constant ( K_ f ) of the solvent is 5.0 K kg mol ⁻¹ , the atomic masses of elements X and Y

Step-by-step solution

Using the formula for depression in freezing point: T_ f = K_ f w M 1000 W For XY ₂ : 2.0 = 5.0 2.0 M_ XY ₂ 1000 50 2.0 = 200 M_ XY ₂ M_ XY ₂ = 100 g mol ⁻¹ For X ₂ Y ₃ : 1.0 = 5.0 1.7 M_ X ₂ Y ₃ 1000 50 1.0 = 170 M_ X ₂ Y ₃ M_ X ₂ Y ₃ = 170 g mol ⁻¹ Let the atomic masses of X and Y be x and y respectively. x + 2y = 100 ... (i) 2x + 3y = 170 ... (ii) Multiplying equation (i) by 2: 2x + 4y = 200 ... (iii) Subtracting equation (ii) from (iii): y = 30 g mol ⁻¹ Substituting the value of y in equation (i): x + 2(30) = 1