Question

The pH of $0.1M$ hydrocyanic acid solution is $5.2$. What is the value of $K_a$ for hydrocyanic acid?

Answer 1

$pH=-\log \left[H^{+}\right]$
or $\log \left[H^{+}\right]=-pH=-5.2$
$\left[H^{+}\right]={10}^{-5.2}=6.3\times {10}^{-6}M$
'$\alpha$' degree of dissociation$=\frac{\left[H^{+}\right]}{C}=\frac{6.3\times {10}^{-6}}{0.1}=6.3\times {10}^{-5}$
According to Ostwald's formula for weak electrolyte
$K_a={\alpha }^{2}C=6.3\times {10}^{-5}\times 6.3\times {10}^{-5}\times 0.1=3.69\times {10}^{-10}$