For a 1.0 molal solution containing the non-volatile solute Urea, the elevation in boiling point is 2.0 K while the depression in freezing point in a 3.0 molal solution having the same solvent is 4.0 K . If the ratio K_b K_f = 1 X , what is the value of X ?

Step-by-step solution

The elevation in boiling point is given by T_b = K_b m₁ , where m₁ = 1.0 molal and T_b = 2.0 K. Thus, 2.0 = K_b 1.0 , which implies K_b = 2.0 K kg mol ⁻¹ . The depression in freezing point is given by T_f = K_f m₂ , where m₂ = 3.0 molal and T_f = 4.0 K. Thus, 4.0 = K_f 3.0 , which implies K_f = 4.0 3.0 = 4 3 K kg mol ⁻¹ . The ratio K_b K_f is calculated as 2.0 4/3 = 2.0 3 4 = 6 4 = 3 2 . Given K_b K_f = 1 X , we have 3 2 = 1 X , which implies X = 2 3 . Answer: 2 3