Chemistry - Ionic Equilibrium Question with Solution | TestHub

On mixing the given solutions, acidic buffer will be formed. Thus applying Henderson equation to find the pH-

$\mathrm{pH} = {\mathrm{pK}}_{\mathrm{a}} + {\log }_{10} \frac{\left[{\mathrm{CN}}^{-}\right]}{\left[\mathrm{HCN}\right]}$

$\text{pH}=-\text{log} 5\times 10^{-10}+\text{log }\frac{5\times \text{V}/\text{V}+10}{10\times 2/\text{V}+10}$

$9=-\text{log }5\times 10^{-10}+\text{log }\frac{\text{V}}{4}$

$9=10-0\text{.}7+\text{log }\frac{\text{V}}{4}$

$-0\text{.}3=\text{log }\frac{\text{V}}{4}$

$\therefore$$\text{log}\frac{\text{V}}{4}{=}^{-}0\text{.}3=\text{log}\frac{1}{2}$

$\frac{\text{V}}{4}=\frac{1}{2}$

$\therefore$V = 2 mL.