Question

The freezing point of $0.02mol$ fraction solution of acetic acid $\left(A\right)$ in benzene $\left(B\right)$ is $277.4K$. Acetic acid exists partly as a dimer $2A=A_2$. Calculate equilibrium constant for the dimerisation. Freezing point of benzene is $278.4K$ and its heat of fusion $\Delta H_f$ is $10.042kJmo{l}^{-1}$.

Answer 1

$K_f=\frac{8.314\times (278.4{)}^2\times 78}{1000\times 10042}=5$

$m=\frac{0.02\times 1000}{0.98\times 78}=0.2614$
$\Delta T_f=i\times K_f\times m$

$i=1-\frac{\alpha }{2}=0.7643$

$\alpha =0.4713$

$2A\rightleftharpoons A_2$

$C-C\alpha C\alpha /2$
$K=\frac{C\alpha /2}{(C-C\alpha {)}^2}=\frac{\alpha }{2C(1-\alpha {)}^2}$

$K=\frac{0.4713}{2\times 0.2614(1-0.4713{)}^2}=3.225$