Quinine \(\left(\mathrm{C}_{20} \mathrm{H}_{24} \mathrm{N}_{2}
\mathrm{O}_{2}\right)\) is the most important alkaloid derived from cinchona
bark. It is used as an antimalarial drug. For quinine, \(\mathrm{p}
K_{\mathrm{b}_{1}}=5.1\) and \(\mathrm{p} K_{\mathrm{b}_{2}}=9.7\left(\mathrm{p}
K_{\mathrm{b}}=-\log K_{\mathrm{b}}\right) .\) Only 1 g quinine will dissolve
in 1900.0 \(\mathrm{mL}\) of solution. Calculate the pH of a saturated aqueous
solution of quinine. Consider only the reaction \(\mathrm{Q}+\mathrm{H}_{2}
\mathrm{O} \rightleftharpoons \mathrm{QH}^{+}+\mathrm{OH}^{-}\) described by
\(\mathrm{p} K_{\mathrm{b}_{1}},\) where \(\mathrm{Q}=\) quinine.