Here is a way to test the validity of the statement made on page 719 in
conjunction with the three key ideas governing the ionization of polyprotic
acids. Determine the \(\mathrm{pH}\) of \(0.100 \mathrm{M}\) succinic acid in two
ways: first by assuming that \(\mathrm{H}_{3} \mathrm{O}^{+}\) is produced only
in the first ionization step, and then by allowing for the possibility that
some \(\mathrm{H}_{3} \mathrm{O}^{+}\) is also produced in the second ionization
step. Compare the results, and discuss the significance of your finding.
$$\begin{array}{c}
\mathrm{H}_{2} \mathrm{C}_{4} \mathrm{H}_{4} \mathrm{O}_{4}+\mathrm{H}_{2}
\mathrm{O} \rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{HC}_{4}
\mathrm{H}_{4} \mathrm{O}_{4}^{-} \\
&K_{\mathrm{a}_{1}}=6.2 \times 10^{-5} \\
\mathrm{HC}_{4} \mathrm{H}_{4} \mathrm{O}_{4}^{-}+\mathrm{H}_{2} \mathrm{O}
\rightleftharpoons \mathrm{H}_{3} \mathrm{O}^{+}+\mathrm{C}_{4} \mathrm{H}_{4}
\mathrm{O}_{4}^{2-} \\
&K_{\mathrm{a}_{2}}=2.3 \times 10^{-6}
\end{array}$$