Chapter 17, Problem 89IAE

The pH of ocean water depends on the amount of atmospheric carbon dioxide. The dissolution of carbon dioxide in ocean water can be approximated by the following chemical reactions (Henry’s Law constant for ${\text{CO}}_{\text{2}}$ is $\begin{array}{l}{\text{K}}_M=\left[{\text{CO}}_{\text{2}}\left(\text{aq}\right)\right]/\left[{\text{CO}}_{\text{2}}\left(\text{g}\right)\right]=\mathrm{0.8317.}\\ \end{array}$ ) For reaction (2) $K=2.8\times {10}^{-2}$ .

${\text{CO}}_{\text{2}}\left(\text{g}\right)\rightleftharpoons {\text{CO}}_{\text{2}}\left(\text{aq}\right)(1)$

${\text{CaCO}}_{\text{3}}\left(\text{s}\right)\rightleftharpoons {\text{Ca}}^{+}\left(\text{aq}\right)+{\text{CO}}_3^{-}(\text{aq})(2)$

${\text{H}}_3{\text{O}}^{+}\left(\text{aq}\right)+{\text{CO}}_{\text{3}}^{\text{-}}\left(\text{aq}\right)\rightleftharpoons {\text{HCO}}_3^{-}\left(\text{aq}\right)+{\text{H}}_2\text{O}(\text{l})(3)$

${\text{H}}_3{\text{O}}^{+}\left(\text{aq}\right)+{\text{HCO}}_{\text{3}}^{\text{-}}\left(\text{aq}\right)\rightleftharpoons {\text{CO}}_2\left(\text{aq}\right)+{\text{H}}_2\text{O}(\text{l})(4)$

1. Use the equations above to determine the hydronium ion concentration as a function of $\left[{\text{CO}}_{\text{2}}\left(\text{g}\right)\right]$ and $\left[{\text{CO}}^{2+}\right]$ .
2. During preindustrial conditions, we will assume that the equilibrium concentration of $\left[{\text{CO}}_{\text{2}}\left(\text{g}\right)\right]=280\text{ppm}\text{and}\left[{\text{Ca}}^{2+}\right]=10.24\text{mM}$ Calculate the pH of a ocean water.