At $30^{o} C$ , the degree of dissociation of $0.066 M$ $H A$ is $0.0145$ . What would be the degree of dissociation of $0.02 M$ solution of the acid at the same temperature?

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Solution

Let the ionisation constant of the acid be $K_{a}$ .
Degree of dissociation at $0.066 M$ concentration $= 0.0145$
Applying $α = \sqrt{\frac{K_{a}}{C}}$
$0.0145 = \sqrt{\frac{K_{a}}{0.066}} . . . (i)$
Let the degree of dissociation of the acid at $0.02 M$ concentration be $α_{1}$
$α_{1} = \sqrt{\frac{K_{a}}{0.02}} . . . (i i)$
Dividing eq (ii) by (i)
$\frac{α_{1}}{0.0145} = \sqrt{\frac{0.066}{0.02}} = 1.8166$
or $α_{1} = 0.0145 \times 1.8166 = 0.0263$

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