A) \[{{K}_{a}}=\frac{C{{\alpha }^{2}}}{(1-\alpha )}\]
B) \[{{K}_{a}}=\frac{C\alpha }{(1-\alpha )}\]
C) \[{{K}_{a}}=\frac{1-\alpha }{C{{\alpha }^{2}}}\]
D) \[{{K}_{a}}=\frac{C\,(1-\alpha )}{{{\alpha }^{2}}}\]
Correct Answer: A
Solution :
Ostwald dilution law is applicable only in case of weak electrolyte. Consider 1 mole of a weak binary electrolyte AB, is present in V litre of solution and a is the degree of ionisation \[\underset{\begin{align} & \\ & 1 \\ & \\ & (1-\alpha ) \\ \end{align}}{\mathop{AB}}\,\,\,\,\,\,\,\,\,\,\underset{\begin{align} & \\ & 0 \\ & \\ & \alpha \\ \end{align}}{\mathop{{{A}^{+}}}}\,\,\,\,+\,\,\,\,\underset{\begin{align} & \\ & 0 \\ & \\ & \alpha \\ \end{align}}{\mathop{{{B}^{-}}}}\,\begin{matrix} initial\text{ }state \\ at\text{ }equilibrium \\ \end{matrix}\] Applying law of mass action \[K=\frac{[{{A}^{+}}]\,\,[{{B}^{-}}]}{[AB]}=\frac{\frac{\alpha }{V},\frac{\alpha }{V}}{\frac{(1-\alpha )}{V}}\] \[K=\frac{{{\alpha }^{2}}}{(1-\alpha )\,\,V}\] or \[K=\frac{{{\alpha }^{2}}C}{1-\alpha }\]\[\left( V=\frac{1}{C} \right)\] where, K = dissociation or ionisation constant C = concentration in mol/L a = degree of ionisation
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