The freezing point of a solution containing 0.2 ~g of acetic acid in 20.0 ~g benzene is lowered by 0.45^ C . The degree of association of acetic acid in benzene is (Assume acetic acid dimerises in benzene and K_f for benzene =5.12 ~K ~kg ~mol ⁻¹ ) M_ observed of acetic acid =113.78

Step-by-step solution

Given : w₂=0.2 ~g , w₁=20 ~g , T_f=0.45^ C T_f= 1000 K_f w₂ w₁ M 0.45= 1000 5.12 0.2 20 M M_ (observed) =113.78 (acetic acid) 2 CH ₃ COOH ( CH ₃ COOH )₂ Before association After association 1- / 2 (where is degree of association) Molecular weight of acetic acid =60 aligned & i= Normal molecular mass Observed molecular mass & M_ ( normal ) M_ ( observed) =1- + 2 & or, 60 113.78 =1- + 2 =0.945 or 94.5 % aligned