MCQ
The degree of dissociation $(\alpha )$ of $PCl_5$ obeying the equilibrium;  is $PC{l_5}\, \rightleftharpoons \,PC{l_3}\, + \,C{l_2}$ related to the pressure at equlibrium by
  • A
    $\alpha \, \propto \,P$
  • $\alpha \, \propto \,\frac{1}{{\sqrt P }}$
  • C
    $\alpha \, \propto \,\frac{1}{{{P^2}}}$
  • D
    $\alpha \, \propto \,\frac{1}{{{P^4}}}$

Answer

Correct option: B.
$\alpha \, \propto \,\frac{1}{{\sqrt P }}$
b
$\mathop {\mathop {PC{l_5}}\limits_1 }\limits_{1 - \alpha }  \rightleftharpoons \mathop {\mathop {PC{l_3}}\limits_0 }\limits_\alpha   + \mathop {\mathop {C{l_2}}\limits_0 }\limits_\alpha  $

$\mathrm{K}_{\mathrm{P}}=\frac{\alpha^{2}}{1-\alpha}\left(\frac{\mathrm{P}}{1+\alpha}\right)=\frac{\alpha^{2} \mathrm{P}}{1-\alpha^{2}}$

$\alpha=\sqrt{\frac{\mathrm{K}_{\mathrm{p}}}{\mathrm{P}}} ; \alpha \propto \frac{1}{\sqrt{\mathrm{p}}}$

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