Question

12.2 g of benzoic acid (Mw =122) in 100 g benzene has depression in freezing point ${2.6}^o$, $K_f=5.2{}^{o}Ckg{mol}^{-1}$. If there is 100% polymerization, the number of molecules of benzoic acid in associated state is:

• A. 1
• B. 2
• C. 3
• D. 4

Answer 1

The correct option is B 2

$\Delta T_f={2.6}^o$

$K_f=5.2{}^{o}Ckg{mol}^{-1}$

The molality $m=\frac{12.2g}{122g/mol\times 100g}\times 1000g/kg=1m$

$\Delta T_f=i{K}_{f}m$

${2.6}^{o}C=i\times 5.2{}^{o}Ckg{mol}^{-1}\times 1mol/kg$

$i=0.5$

Let n molecules of benzoic acid associate to form 1 mole of polymer.

$i=\frac{\text{observed molecules in solution}}{\text{theoretical molecules}}=0.5$

$i=\frac{\text{1}}{\text{n}}=0.5$

$n=\frac{1}{0.5}=2$

The number of molecules of benzoic acid in associated state is 2.