Consider a system where you want to add NaOH to a solution of $0\mathrm{.}01MN{a}_{2}HP{O}_4+0\mathrm{.}003M{H}_{3}P{O}_4$ to increase the $pH$ to $10\mathrm{.}0.$ Following the steps below, derive the equation needed to solve for the amount of NaOH to be added to the system. $K_w={10}^{-14},K_{Al}={10}^{-}{?}^{2\mathrm{.}2},K_{A2}={10}^{-7\mathrm{.}2},K_{A3}={10}^{-12\mathrm{.}2}$

a$.$ Write the disassociation reactions for $H_{2}O,$NaOH,$N{a}_{2}HP{O}_4,$ and $H_{3}P{O}_4$

b$.$ Identify the species in solution

c$.$ Write the equilibrium equations $K_w,K_{A1},K_{A2},K_{A3}$

d$.$ Write the mass balances for TOT ${?}_{PO4}$ and TOT ${?}_{Na}$

e$.$ Write the charge balance

f$.$ Simplify the charge balance

g$.$ Using the equations in a$-$d$,$ substitute into the charge balance to come up with a single equation with single unknown