What is the concentration of ${\mathrm{CN}}^{-}$ ions in a solution with 0.1 M HCl and 0.01 M HCN where ${\mathrm{K}}_{\mathrm{a}}$ of HCN is ${10}^{-6}?$

HCl is a strong acid and completely dissociates in water. Therefore, the concentration of HCl, H⁺ and Cl^- is the same, 0.1 M.

HCN is a weak acid and partially dissociates.

$\mathrm{HCN}\rightleftharpoons {\mathrm{H}}^{+}+{\mathrm{CN}}^{-}$

K_a expression of HCN:

$$\begin{gathered} {\mathrm{K}}_{\mathrm{a}}=\frac{\left[{\mathrm{H}}^{+}\right]\left[{\mathrm{CN}}^{-}\right]}{\left[\mathrm{HCN}\right]} \\ {10}^{-6}=\frac{\left[0.1\right]\left[{\mathrm{CN}}^{-}\right]}{\left[0.01\right]} \\ \left[{\mathrm{CN}}^{-}\right]={10}^{-7} \end{gathered}$$