Textbook Problem

a. The principal equilibrium in a solution of NaHCO₃ is

${\text{HCO}}_3{}^{-}\left(aq\right)+{\text{HCO}}_3{}^{-}\left(aq\right)\rightleftharpoons {\text{H}}_2{\text{CO}}_3\left(aq\right)+{\text{CO}}_3{}^{2-}\left(aq\right)$

Calculate the value of the equilibrium constant for this reaction.

b. At equilibrium, what is the relationship between [H₂CO₃] and [CO₃²⁻]?

c. Using the equilibrium

${\text{H}}_{\text{2}}{\text{CO}}_{\text{3}}\left(aq\right)\rightleftharpoons 2{\text{H}}^{+}\left(aq\right)+{\text{CO}}_{\text{3}}{}^{2-}\left(aq\right)$

derive an expression for the pH of the solution in terms of $K_{a_1}$ and $K_{a_2}$ using the result from part b.

d. What is the pH of a solution of NaHCO₃?