Question

In $0.01M$ solution, $HCN$ is $0.01$% ionized. Its $K_a$ is __.

• A. ${10}^{-6}$
• B. ${10}^{-10}$
• C. ${10}^{-3}$
• D. $0.02$

Answer 1

The correct option is B ${10}^{-10}$

The weak acid $HCN$ is $0.01$% ionized. The degree of dissociation is $\alpha =\frac{0.01}{100}=0.0001$.
According to ostwald's dilution law equation, $\alpha =\sqrt{\frac{K_a}{C}}$.
Here, $C$ is the concentration.
$⟹0.0001=\sqrt{\frac{K_a}{0.01}}$ or $K_a={10}^{-10}$.