How much must a $0.2 M$ solution of sodium acetate be diluted at $25^{o} C$ in order to double the degree of hydrolysis?

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Solution

Let $h$ be the initial degree of hydrolysis.
$K_{h} = C h^{2} = 0.2 h^{2}$
Let the concentration be $C_{1}$ when degree of hydrolysis is $2 h$ .
$K_{h} = C_{1} {(2 h)}^{2}$
Dividing both the equations
$1 = \frac{0.2 \times h^{2}}{4 C_{1} h^{2}}$
$C_{1} = \frac{0.2}{4} = 0.05 M$
Applying $M_{1} V_{1} = M_{2} V_{2}$
$V_{2} = \frac{0.2}{0.05} V_{1} = 4 V_{1}$
The solution be diluted four times.

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