The \(\mathrm{pH}\) 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 \(\left.\mathrm{CO}_{2} \text { is } K_{\mathrm{H}}=\left[\mathrm{CO}_{2}(\mathrm{aq})\right] /\left[\mathrm{CO}_{2}(\mathrm{g})\right]=0.8317 .\right)\) \(\mathrm{CO}_{2}(\mathrm{g}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{aq})\) \(\mathrm{CaCO}_{3}(\mathrm{s}) \rightleftharpoons \mathrm{Ca}^{2+}(\mathrm{aq})+\mathrm{CO}_{3}^{-}(\mathrm{aq})\) \(\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{CO}_{3}^{-}(\mathrm{aq}) \rightleftharpoons \mathrm{HCO}_{3}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(\mathrm{l})\) \(\mathrm{H}_{3} \mathrm{O}^{+}(\mathrm{aq})+\mathrm{HCO}_{3}^{-}(\mathrm{aq}) \rightleftharpoons \mathrm{CO}_{2}(\mathrm{aq})+2 \mathrm{H}_{2} \mathrm{O}(1)\) (a) Use the equations above to determine the hydronium ion concentration as a function of \(\left[\mathrm{CO}_{2}(\mathrm{g})\right]\) and \(\left[\mathrm{Ca}^{2+}\right]\) (b) During preindustrial conditions, we will assume that the equilibrium concentration of \(\left[\mathrm{CO}_{2}(\mathrm{g})\right]=280\) ppm and \(\left[\mathrm{Ca}^{2+}\right]=10.24 \mathrm{mM} .\) Calculate the \(\mathrm{pH}\) of a sample of ocean water.

Step by step solution

01

Determine the concentration of hydronium ions

According to the provided chemical reactions, we can declare the equilibrium constant expression for each of them as follows: \(K_{c_{1}}=\left[\mathrm{CO}_{2}(\mathrm{aq})\right]/\left[\mathrm{CO}_{2}(\mathrm{g})\right]\) and \(K_{c_{2}}=\left[\mathrm{HCO}_{3}^{-}\right]\) / \(\left[\mathrm{H_{3}O^{+}}\right]\left[\mathrm{CO}_{3}^{2-}}\right]\) Thus, the equilibrium constant K_1 can be equal to KH (Henry's Law constant). So, after rearranging the Equation we can find \( \left[\mathrm{H_{3}O^{+}}\right]=\left(\left[\mathrm{HCO}_{3}^{-}\right]*\left[\mathrm{CO}_{2}(\mathrm{g})\right]\right) / EH\), which is the concentration of hydronium ions.

02

Calculating the pH of ocean water

Now, to calculate pH, one needs to know the concentration of hydronium ions, which represents the acidity of the solution. The formula to be used to calculate pH is given by; pH = -log(\( \left[\mathrm{H_{3}O^{+}}\right]\)). where log denotes logarithm to the base 10. Plug the values of concentration obtained from the previous step into this formula to estimate the pH. This provides the pH of a sample of ocean water based on the CO2(g) and Ca2+ concentrations.

03

Predicting the pH for preindustrial conditions

Next, to find the pH under different conditions, substitute the given values for CO2(g) and Ca2+ concentrations into the equation obtained from step 1 to get the hydronium ion concentration. Use this to calculate the pH in the same way as in step 2. This will give the pH of ocean water under the stated preindustrial conditions.

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