Question 6.10: Write a mass balance and charge balance equations for a 0.10...

It is easier to keep track of what species are in solution if we write down the reactions that control the solution’s composition. These reactions are the dissolution of a soluble salt

$NaHCO_3(s) → Na^+(aq) + HCO_3  ^–(aq)$

and the acid–base dissociation reactions of $HCO_3  ^–   and   H_2O$

$HCO_3  ^–(aq) + H_2O(\ell) \rightleftharpoons H_3O+(aq) + CO_3   ^{2–}(aq)$
$HCO_3  ^–(aq) + H_2O(\ell) \rightleftharpoons OH^–(aq) + H_2CO_3(aq)$

$2H_2O(\ell)  \rightleftharpoons H_3O^+(aq) + OH^–(aq)$

The mass balance equations are

$0.10  M = [H_2CO_3] + [HCO_3  ^–] + [CO_3  ^{2–}]$

0.10 M = $[Na^+]$

The charge balance equation is

$[Na^+] + [H_3O^+] = [OH^–] + [HCO_3  ^–] + 2 × [CO_3  ^{2–}]$