$P C l_{5}$ in solid exists as $P C l_{4}^{+}$ and $P C l_{6}^{-}$ . Also in some solvents its undergoes dissociation $2 P C l_{5} ⇌ P C l_{4}^{+} + P C l_{6}^{-}$ . Find dissociation constant.

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Solution

$P C l_{5} ⇌ P C l_{4}^{+} + P C l_{6}^{-}$
At $t = 0 a_{0}$
At $t i m e t a - 2 α ⇌ α + α$
where $a_{0} =$ initial concentration, $α =$ degree of dissociation
$K_{c} = \frac{[P C l_{4}^{+}] [P C l_{6}^{-}]}{[P C l_{5}]^{2}} = \frac{α^{2}}{(a_{0} - 2 α)^{2}}$
$∴ \frac{α}{a_{0} - 2 α} = \sqrt{K_{c}}$
$\Rightarrow∴ α = \frac{a_{0} \sqrt{K_{c}}}{1 + 2 \sqrt{K_{c}}}$

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