Malonic acid \(\left(\mathrm{HO}_{2} \mathrm{CCH}_{2} \mathrm{CO}_{2}
\mathrm{H}\right)\) is a diprotic acid. In the titration of malonic acid with
\(\mathrm{NaOH}\), stoichiometric points occur at \(\mathrm{pH}=3.9\) and \(8.8\). A
\(25.00-\mathrm{mL}\) sample of malonic acid of unknown concentration is
titrated with \(0.0984 \mathrm{M} \mathrm{NaOH}\), requiring \(31.50
\mathrm{~mL}\) of the \(\mathrm{NaOH}\) solution to reach the phenolphthalein end
point. Calculate the concentration of the initial malonic acid solution. (See
Exercise 113.)