5.5 Percent Ionization
The percent ionization of an acid can be determined using
\[\%~\mathrm{ionization} = \dfrac{[\mathrm{H_3O^+}]_{\mathrm {eq}}}{[\mathrm{HA}]_0} \times 100\%\]
This is a ratio of the hydronium ion concentration at equilibrium (can be directly determined from a pH measurement) and the original acid concentration before dissociation.
The plot below shows the percent ionization of various acids (strong and weak) in aqueous solution at varying molar concentrations.
Figure 5.1: Percent ionization of some acid solutions
Clearly, strong acids and bases will have (essentially) 100% ionization whereas weak acids and bases will have a smaller percent ionizations at increasing concentration. As the concentration of the acid decreases, percent ionization generally decreases as well as the resulting pH. The plot below presents the pH of the acidic solutions presented above.
Figure 5.2: pH of some acid solutions
Practice
A 0.1 M acetic acid solution (CH3COOH; Ka = 1.75 × 10–5) has a pH of 2.88. What is the percent ionization of the acid?
Solution
Determine the hydronium ion concentration at equilibrium.
\[\begin{align*} [\mathrm{H_3O^+}] &= 10^{-\mathrm{pH}} \\[1.5ex] &= 10^{-2.88} \\[1.5ex] &= 1.31\times 10^{-3}~M \end{align*}\]
Determine the percent ionization of the acid.
\[\begin{align*} \%~\mathrm{ionization} &= \dfrac{[\mathrm{H_3O^+}]_{\mathrm {eq}}}{[\mathrm{HA}]_0} \times 100\% \\[1.5ex] &= \dfrac{1.31\times 10^{-3}~M}{0.1} \times 100\% \\[1.5ex] &= 1.31\% \end{align*}\]