Question

$X\times 100$ mL water must be added to $300$ mL of $0.2M$ solution of ${CH}_{3}COOH$ for the degree of dissociation of the acid to double? The value of X is ____.

$[K_a$ for acetic acid $=1.8\times {10}^{-5}]$

Answer 1

$$K=c \times (\alpha) ^2 = c' \times (\alpha ') ^2$ .... (1)

The degree of dissociation doubles.

${\alpha }^{\prime }=2\alpha$ ....(2)

The new concentration is $c^{\prime }=\left(\frac{300\times 0.2}{300+100X}\right)$......(3)

From equations (1), (2) and (3)

$0.2\times (\alpha {)}^2=(\frac{300\times 0.2}{300+100X})\times (2\times \alpha {)}^2$.

Hence, the value of $X=9$