A \(500.0 \mathrm{~mL}\) sample of an equilibrium mixture of gaseous
\(\mathrm{N}_{2} \mathrm{O}_{4}\) and \(\mathrm{NO}_{2}\) at \(25^{\circ}
\mathrm{C}\) and \(753 \mathrm{~mm} \mathrm{Hg}\) pressure was allowed to react
with enough water to make \(250.0 \mathrm{~mL}\) of solution at \(25^{\circ}
\mathrm{C}\). You may assume that all the dissolved \(\mathrm{N}_{2}
\mathrm{O}_{4}\) is converted to \(\mathrm{NO}_{2}\), which disproportionates in
water, yielding a solution of nitrous acid and nitric acid. Assume further
that the disproportionation reaction goes to completion and that none of the
nitrous acid disproportionates. The equilibrium constant \(K_{\mathrm{p}}\) for
the reaction \(\mathrm{N}_{2} \mathrm{O}_{4}(g) \rightleftharpoons 2
\mathrm{NO}_{2}(g)\) is \(0.113\) at \(25^{\circ} \mathrm{C} . K_{\mathrm{a}}\) for
\(\mathrm{HNO}_{2}\) is
\(4.5 \times 10^{-4}\) at \(25^{\circ} \mathrm{C}\)
(a) Write a balanced equation for the disproportionation reaction.
(b) What is the molar concentration of \(\mathrm{NO}_{2}^{-}\), and what is the
\(\mathrm{pH}\) of the solution?
(c) What is the osmotic pressure of the solution in atmospheres?
(d) How many grams of lime (CaO) would be needed to neutralize the solution?