Question

At ${30}^{o}C$, the degree of dissociation of $0.066M$ $HA$ is $0.0145$. The degree of dissociation of $0.02M$ solution of acid at the same temperature is $x$, then find the value of $x\times 100$ to the nearest integer.

Answer 1

For a weak acid, the degree of dissociation is inversely proportional to the square root of concentration.
$\alpha =\sqrt{\frac{K_a}{c}}$
Hence, $\frac{{\alpha }_2}{{\alpha }_1}=\sqrt{\frac{c_1}{c_2}}$
Substitute values in the above expression.
$\frac{{\alpha }_2}{0.0145}=\sqrt{\frac{0.066}{0.02}}$
Hence, ${\alpha }_2=0.0265$.
Hence, the degree of dissociation of 0.02 M solution of acid is 0.0265.

Answer is 3.