Question

For a reaction,

$nA\rightleftharpoons A_n$,

Find a relation between the degree of association, observed vapor density and theoretical vapor density when $A$ trimerizes.

$d=$ Observed vapour density,

$D=$ Theoretical vapour density,
$\alpha =$ degree of association

• A. $2\left(\frac{d-D}{d}\right)$
• B. $\frac{3}{2}\left(\frac{d-D}{d}\right)$
• C. $\frac{4}{3}\left(\frac{d-D}{d}\right)$
• D. $2\left(\frac{D-d}{d}\right)$

Answer 1

Answer: (B)

$\frac{3}{2}\left(\frac{d-D}{d}\right)$

According to Ostwald's law of dilution,

where $d=$ Observed vapour density
$D=$ Theoretical vapour density
$\alpha =$ degree of association
$n=$ number of molecules that undergo association.

For association of molecule,
$\alpha =\frac{d-D}{d(1-\frac{1}{n})}$

Substitute $n=3$

$\alpha =\frac{d-D}{d(1-\frac{1}{3})}$

$\alpha =\frac{d-D}{d\left(\frac{2}{3}\right)}$

$\alpha =\frac{3}{2}\left(\frac{d-D}{d}\right)$

Hence, option $\left(C\right)$ is the correct answer.