The freezing point of a solution containing 0.2g 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

$$\begin{gathered} {\mathrm{W}}_{{\mathrm{C}}_6{\mathrm{H}}_6}\left(\mathrm{solvent}\right)=20\mathrm{g} ; ∆{\mathrm{T}}_{\mathrm{f}}=0.45 ; {\mathrm{K}}_{\mathrm{f}}\left({\mathrm{C}}_6{\mathrm{H}}_6\right)=5.12\mathrm{K} \mathrm{Kg} {\mathrm{mol}}^{-1} \\ {\mathrm{W}}_{{\mathrm{CH}}_3\mathrm{COOH}}\left(\mathrm{solute}\right)=0.2\mathrm{g} \\ ∆{\mathrm{T}}_{\mathrm{f}}={\mathrm{K}}_{\mathrm{f}}\times \frac{{\mathrm{W}}_{\mathrm{s}}}{\mathrm{Molar} \mathrm{mass}}\times \frac{1000}{{\mathrm{W}}_{\mathrm{o}}} \\ 0.45=5.12\times \frac{0.2}{{\mathrm{M}}_{\mathrm{s}}}\times \frac{1000}{20} \\ \mathrm{observed} \mathrm{molar} \mathrm{mass}\left({\mathrm{M}}_{\mathrm{s}}\right)=113.78\mathrm{g} \\ \mathrm{i}=\frac{\mathrm{calculated} \mathrm{molar} \mathrm{mass}}{\mathrm{observed} \mathrm{molar} \mathrm{mass} }=\frac{60}{113.78}=0.527 \end{gathered}$$
 

i<1  ;  CH₃COOH associates(dimerizes)in Benzene

i=1-+/2

0.527 = 1-/2

/2 =0.473

= 0.946

% of association = 94.6%