Elements A and B form two compounds, AB and A ₂ B . When 3.5 g of AB is dissolved in 50 g of water, the freezing point of the solution is depressed by 1.86 K. On the other hand, when 5.5 g of A ₂ B is dissolved in water to make 250 mL of solution, it exhibits an osmotic pressure of 4.92 atm at 300 K. Given K_ f for water is 1.86 K kg mol ⁻¹ and the universal gas constant R = 0.082 L atm K ⁻¹ mol ⁻¹ , the atomic masse

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For compound AB , using the depression in freezing point: T_ f = K_ f w M_ AB 1000 W 1.86 = 1.86 3.5 M_ AB 1000 50 1 = 3.5 M_ AB 20 M_ AB = 70 g mol ⁻¹ For compound A ₂ B , using osmotic pressure: = C R T = n V R T = w M_ A ₂ B V( in L ) R T 4.92 = 5.5 M_ A ₂ B 0.25 0.082 300 4.92 = 5.5 4 M_ A ₂ B 24.6 4.92 = 22 M_ A ₂ B 24.6 M_ A ₂ B = 22 24.6 4.92 = 22 5 = 110 g mol ⁻¹ Let the atomic masses of A and B be a and b respectively. a + b = 70 ... (i) 2a + b = 110 ... (ii) Subtracting equation (i) from (ii): a = 40 g mo