Question

$0.5$ molal solution of a solute in benzene shows a depression in freezing point equal to $2K$. Molal depression constant for benzene is $5Kkgmo{l}^{-1}$. If the solute forms dimer in benzene, what is the $\%$ association?

• A. 40
• B. 50
• C. 60
• D. 80

Answer 1

Answer: (A)

Given, molality of solution, $m=0.5m$
$\Delta T_f=2K$
$K_f=5Kkgmo{l}^{-1}$
of association, $\alpha =$ ?
Step I Calculation of van't Hoff factor (i)
$\Delta T_f=i{K}_{f}M$
$i=\frac{\Delta T_f}{K_{f}M}$
$i=\frac{2K}{5Kkgmo{l}^{-1}\times 0.5m}$
$i=\frac{4}{5}$
Step II Calculation of $\%$ association of acid $(\alpha )$.
As solute form dimer in benzene, i.e. $2A{A}_2$
Therefore, value of $x=2$
$\alpha =\frac{i-1}{1/x-1}$
$\alpha =\frac{4/5-1}{1/2-1}=0.4$
$\therefore \%$ of $\alpha =0.4\times 100=40\%$