Question

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 ${\mathrm{CO}}_2\text{ is }{K}_{\mathrm{H}}=[{\mathrm{CO}}_2(\mathrm{aq})]/[{\mathrm{CO}}_2(\mathrm{g})]=0.8317.)$ ${\mathrm{CO}}_2(\mathrm{g})\rightleftharpoons {\mathrm{CO}}_2(\mathrm{aq})$ ${\mathrm{CaCO}}_3(\mathrm{s})\rightleftharpoons {\mathrm{Ca}}^{2+}(\mathrm{aq})+{\mathrm{CO}}_3^{-}(\mathrm{aq})$ ${\mathrm{H}}_3{\mathrm{O}}^{+}(\mathrm{aq})+{\mathrm{CO}}_3^{-}(\mathrm{aq})\rightleftharpoons {\mathrm{HCO}}_3^{-}(\mathrm{aq})+{\mathrm{H}}_2\mathrm{O}(\mathrm{l})$ ${\mathrm{H}}_3{\mathrm{O}}^{+}(\mathrm{aq})+{\mathrm{HCO}}_3^{-}(\mathrm{aq})\rightleftharpoons {\mathrm{CO}}_2(\mathrm{aq})+2{\mathrm{H}}_2\mathrm{O}(1)$ (a) Use the equations above to determine the hydronium ion concentration as a function of $[{\mathrm{CO}}_2(\mathrm{g})]$ and $\left[{\mathrm{Ca}}^{2+}\right]$ (b) During preindustrial conditions, we will assume that the equilibrium concentration of $[{\mathrm{CO}}_2(\mathrm{g})]=280$ ppm and $\left[{\mathrm{Ca}}^{2+}\right]=10.24\mathrm{mM}.$ Calculate the $\mathrm{pH}$ of a sample of ocean water.

Short answer

To calculate the hydronium ion concentration, an equilibrium expression derived from the given chemical equations is created. This concentration is used to calculate pH. For preindustrial conditions, given concentrations of CO2(g) and Ca2+ are substituted into the equilibrium expression to obtain the preindustrial hydronium ion concentration and consequent pH value.

Step-by-step solution

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: $K_{c_1}=[{\mathrm{CO}}_2(\mathrm{aq})]/[{\mathrm{CO}}_2(\mathrm{g})]$ and $K_{c_2}=\left[{\mathrm{HCO}}_3^{-}\right]$ / $\text{Extra close brace or missing open brace}$ Thus, the equilibrium constant K_1 can be equal to KH (Henry's Law constant). So, after rearranging the Equation we can find $\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]=(\left[{\mathrm{HCO}}_3^{-}\right]\ast [{\mathrm{CO}}_2(\mathrm{g})])/EH$, which is the concentration of hydronium ions.

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($\left[{\mathrm{H}}_3{\mathrm{O}}^{+}\right]$). 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.

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.

Key concepts

Carbon Dioxide Dissolution

When discussing the ocean water's pH, it's crucial to understand how carbon dioxide ( CO_2 ) dissolves in water. Carbon dioxide gas from the atmosphere interacts with ocean water, leading to several chemical reactions. When CO_2 gas enters the water, it converts to aqueous carbon dioxide, denoted as CO_2( aq). This process of gas dissolving into a liquid, especially involving carbon dioxide, plays a significant role in maintaining the ocean's chemical balance.

A few key reactions help balance the ocean's acidity: the formation of carbonic acid, bicarbonate, and carbonate ions. These chemical species work together to buffer the water's pH, preventing drastic changes that could harm marine life and ecosystems.

• Direct absorption of CO_2(g) leads to the formation of carbonic acid.
• Carbonic acid further dissociates into bicarbonate and hydrogen ions, influencing the pH levels directly.
• Calcium carbonate in rocks helps neutralize excess hydrogen ions, acting as a natural buffer.

Henry's Law Constant

Henry's Law is a fundamental principle in understanding how gases dissolve in liquids, such as how carbon dioxide interacts with ocean water. Henry’s Law constant (K_H) helps predict how much CO_2 will dissolve in the ocean from the atmosphere. It is defined by the ratio:

$$K_H=\frac{[{\mathrm{CO}}_2(\mathrm{aq})]}{[{\mathrm{CO}}_2(\mathrm{g})]}$$

This equation shows that the concentration of dissolved CO_2 in water depends directly on the gaseous CO_2 present. A higher K_H value means that more CO_2 will dissolve at equilibrium.

Understanding Henry’s Law helps students solve problems related to ocean water CO_2 levels and their influence on oceanic pH:

• It enables the calculation of dissolved gas concentrations when given the partial pressure of the gas.
• This principle explains why changes in atmospheric CO_2 levels can significantly affect marine chemistry over time.

Equilibrium Constant Expressions

Equilibrium constant expressions are integral to understanding the behavior of chemical reactions, especially in complex systems like the ocean. These expressions are used to predict the concentrations of reactants and products at equilibrium.

For the dissolution of carbon dioxide in ocean water, several equilibrium constants describe how CO_2(aq) interacts with other species, such as bicarbonate ions:

• The equilibrium constant for this conversion is essential for finding hydronium ( H_3O^+ ) ion concentration, which directly affects pH.
• These constants, usually derived from experiments, inform us how likely reactions are to proceed in a given direction under specific conditions.

Applying equilibrium constant expressions allows accurate calculations of pH in ocean water, especially when influenced by varying concentrations of CO_2 and Ca^{2+} . The interplay between these constants and environmental variables allows marine chemists to predict changes in ocean chemistry due to environmental or atmospheric changes.

Preindustrial Ocean Conditions

Before the industrial revolution, atmospheric CO_2 levels were significantly lower. Understanding these preindustrial conditions provides a baseline for how increased industrial activity affects ocean chemistry today. During preindustrial times, the equilibrium concentration of CO_2(g) was about 280 ppm, and Ca^{2+} in ocean water was relatively stable.

Studying preindustrial conditions helps us understand:

• How natural levels of atmospheric CO_2 influenced ocean pH.
• The natural buffering capacity of ocean water using minerals like calcium carbonate.
• Comparisons between historic and modern-day conditions highlight human impact on the environment.

By analyzing changes from preindustrial levels, scientists can model potential future changes and develop strategies to mitigate negative effects on marine environments, such as ocean acidification and loss of biodiversity.