Question

Citric acid, \(\mathrm{HOOC}-\mathrm{CH}_{2}-\mathrm{C}(\mathrm{OH})(\mathrm{COOH})-\mathrm{CH}_{2}-\mathrm{COOH},\) which we can

abbreviate as \(\mathrm{H}_{3} \mathrm{Cit},\) is a triprotic carboxylic acid with acidity constants \(\mathrm{p} K_{a 1}=3.13, \mathrm{p} K_{a 2}=4.72,\) and \(\mathrm{p} K_{a 3}=6.33\)

a. Consider a solution made by adding lemon juice to water until the \(\mathrm{pH}\) of the solution is 2.2. Assuming all the acidity is from dissociation of citric acid, find the total concentration of citrate species, i.e., TOTCit, and the concentration of \(\mathrm{HCit}^{2-}\)

b. The solution in part \((a)\) is diluted 1: 10 and partly neutralized by addition of sodium bicarbonate \(\left(\mathrm{NaHCO}_{3}\right)\). Designating the total concentration of carbonate species added as \(T O T \mathrm{CO}_{3},\) write out all the equations necessary to compute the new \(\mathrm{pH}\). You need not solve the equations.

c. If the final pH of the solution in part \(b\) is \(6.0,\) what is the ratio of \(\left\{\mathrm{HCO}_{3}^{-}\right\}\) to \(\left\{\mathrm{H}_{2} \mathrm{CO}_{3}\right\}\) in the solution? What is the ratio of \(\left\{\mathrm{CO}_{3}^{2-}\right\}\) to \(\left\{\mathrm{H}_{2} \mathrm{CO}_{3}\right\} ?\) Would these ratios change if the pH were still \(6.0,\) but \(T O T\) Cit were doubled?