(Solved): Phosphoric acid is used widely in fertilizers and is used in certain types of pop to make them more ...

Phosphoric acid is used widely in fertilizers and is used in certain types of pop to make them more tart. It is a triprotic acid with a chemical formula $${\mathrm{H}}_3{\mathrm{PO}}_4(\mathrm{aq})$$. Estimate the $$\mathrm{pH}$$ and the concentrations of all species at equilibrium in a $$0.370\mathrm{M}$$ solution of phosphoric acid. The three acid dissociation steps are as follows: $$\begin{array}{ll}{\mathrm{H}}_3{\mathrm{PO}}_4(\mathrm{aq})+{\mathrm{H}}_2\mathrm{O}(\mathrm{l})?{\mathrm{H}}_2{\mathrm{PO}}_4^{?}(\mathrm{aq})+{\mathrm{H}}_3{\mathrm{O}}^{+}(\mathrm{aq})& {\mathrm{K}}_{\mathrm{a}}=6.92\times 10^{?3}\\ {\mathrm{H}}_2{\mathrm{PO}}_4^{?}(\mathrm{aq})+{\mathrm{H}}_2\mathrm{O}(\mathrm{l})?{\mathrm{HPO}}_4^2(\mathrm{aq})+{\mathrm{H}}_3{\mathrm{O}}^{+}(\mathrm{aq})& {\mathrm{K}}_{\mathrm{ay}}=6.17\times 10^{?8}\\ {\mathrm{HPO}}_4^2(\mathrm{aq})+{\mathrm{H}}_2\mathrm{O}(1)?{\mathrm{PO}}_4^3(\mathrm{aq})+{\mathrm{H}}_3{\mathrm{O}}^{+}(\mathrm{aq})& {\mathrm{K}}_{\mathrm{ay}}=4.79\times 10^{?13}\end{array}$$