A solute X is found to exist as a dimer in water. A 4 molal solution of X shows a boiling point of 101.04^ C . What is the percentage association of X ? ( K _ b for water =0.52 ~K / m ).

Step-by-step solution

The elevation in boiling point is given by T_b = T_b - T_b^ = 101.04^ C - 100^ C = 1.04 K . Using the formula T_b = i K_b m , where i is the van't Hoff factor, K_b = 0.52 K kg mol ⁻¹ , and m = 4 m : 1.04 = i 0.52 4 i = 1.04 2.08 = 0.5 . For the dimerization of solute X, the reaction is 2X X₂ . If is the degree of association, the van't Hoff factor is given by i = 1 - + n , where n=2 for a dimer. 0.5 = 1 - + 2 0.5 = 1 - 2 2 = 0.5 = 1 . The percentage association is 100 = 1 100 = 100 % . Answer: 100