When 0.4 ~g CH ₃ COOH is added to 40 g of Benzene to form a solution, the freezing point is depressed by 0.45^ C . If Acetic acid undergoes dimerisation in Benzene ( K _ f =5.12 ~K ~kg / mol ) what is the percentage association of the acid in Benzene?

Step-by-step solution

The molar mass of CH ₃ COOH is M = 12 + 3 + 12 + 16 + 16 + 1 = 60 g/mol . The molality m of the solution is calculated as m = mass of solute molar mass mass of solvent in kg = 0.4 60 0.040 = 0.4 2.4 = 1 6 mol/kg . The theoretical depression in freezing point is T_f = K_f m = 5.12 1 6 = 0.8533 K . The van't Hoff factor i is given by i = ( T_f)_ observed ( T_f)_ theoretical = 0.45 0.8533 0.5273 . For dimerization, 2 CH ₃ COOH ( CH ₃ COOH )₂ , the relation between i and degree of association is i = 1 - + 2 = 1 - 2 . S