The freezing point of a solution containing 0.2 g of acetic acid in 20.0 g benzene is lowered by 0.45°C. Calculate the degree of dimerization of acetic acid in benzene. K_f for benzene is 5.12 $\mathrm{K}{\mathrm{mol}}^{-1}\mathrm{kg}$, Round off the answer to the nearest integer value.

Given $w=0.2g, W=20\mathrm{g},\mathrm{\Delta T}=0.45$
${\mathrm{\Delta T}}_{\mathrm{f}}=\frac{1000\left({\mathrm{K}}_{\mathrm{f}}\right)\left(\mathrm{W}\right)}{\mathrm{M}\left(\mathrm{W}\right)}0.45=\frac{1000\times 5.12\times 0.2}{20\times \mathrm{M}}$ M(observed) = 113.78
Now for ${\mathrm{CH}}_3\mathrm{COOH}\rightleftharpoons {\left({\mathrm{CH}}_3\mathrm{COOH}\right)}_2$Before association                            
0                                                                 
After association     $1-\mathrm{\alpha }$                    $\frac{\mathrm{\alpha }}{2}$Where $\mathrm{\alpha }$ is the degree of association
$\frac{{\mathrm{M}}_{\text{nomal }}}{{\mathrm{M}}_{\text{observed }}}=1-\mathrm{\alpha }+\frac{\mathrm{\alpha }}{2}\text{ Or }\frac{60}{113.78}=1-\mathrm{\alpha }+\frac{\mathrm{\alpha }}{2}\Rightarrow \mathrm{\alpha }=0.945$