Problem: Find the percent ionization of a 0.250 M solution of HC2H3O2. Express your answer numerically to two significant figures.

Step 1. Calculate [H⁺]

HC₂H₃O₂  ⇌ H⁺   +  C₂H₃O₂^-

^{$$\begin{gathered} \boxed{{\mathbf{K}}_{\mathbf{a}}\mathbf{=}\frac{\mathbf{products}}{\mathbf{reactants}}} \\ {\mathbf{K}}_{\mathbf{a}}\mathbf{=}\frac{\left[H^{+}\right]\left[C_2{H}_3{O_2}^{-}\right]}{\left[{\mathrm{HC}}_2{H}_3{O}_2\right]}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}} \\ \frac{\mathbf{\left[}\mathbf{x}\mathbf{\right]}\mathbf{\left[}\mathbf{x}\mathbf{\right]}}{[0.250]}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{8}\mathbf{\times }{\mathbf{10}}^{\mathbf{-}\mathbf{5}} \\ \sqrt{{\mathbf{x}}^{\mathbf{2}}}\mathbf{ }\mathbf{=}\sqrt{\mathbf{ }(1.8\times {10}^{-5})(0.250)} \end{gathered}$$}

x = 2.12x10^-3 M = [H⁺]