Question

What will be the percentage of dimerization of $ 61 \,g $ of benzoic acid in $ 1000\,g $ of a solvent and producing a depression in freezing point of $ 2 \,{}^{\circ}C $ ? Consider $ K_f $ to be $ 6 $ .

• A. $ 72\% $
• B. $ 67\% $
• C. $ 43\% $
• D. $ 28\% $

Answer 1

Answer: (B)

$W_{\text{benzoic acid}} =61\, g ;$
$W_{\text{solvent}}=1000\,g $
$\Delta T_{f} =2^{\circ}C ; K_{f} =6$
$\Delta T_{f} =iK_{f} m $
$m=\frac{61 /122}{1000}\times1000=0.5 ;$
$i=\frac{\Delta T_{f}}{k_{f} m}$
$=\frac{2}{6\times0.5}$
$=0.67$
$\alpha=\frac{1-i}{1-1/ n}$ $[\therefore n=2$ for benzoic acid]
$\alpha=\frac{1-0.67}{1-0.5}=0.66$
$=66\%$