by James R. Barrante, Ph.D.
Ocean chemistry essentially involves the chemistry of the carbonic acid buffer system to which is added the chemistry of insoluble carbonates such as calcite and aragonite, CaCO3. When the Earth formed, the atmosphere was approximately 95% carbon dioxide and water vapor. No free oxygen or nitrogen gas was present. As the planet cooled, however, the temperature dropped to below the boiling point of water, and the majority of the water vapor in the atmosphere along with outgassing vapors formed our oceans. Because of its high solubility in water, the CO2 in the atmosphere began to dissolve into the oceans. The high solubility of CO2 in water is mainly because CO2 reacts with water to form a weak acid, known as carbonic acid, H2CO3. Carbonic acid in turn slightly dissociates in water giving:
Here the K‘s are the dissociation constants for carbonic acid and the a‘s represent the activities (effective concentrations) of the subscripted ions.
If we multiply the two dissociation constant equations together, we obtain an expression for the activity of CO3= .
As the concentration of CO3= increased in the oceans, it began to react with soluble salts of magnesium and calcium that found its way into the ocean to form insoluble carbonates. These carbonates settled to the bottom of the oceans and became rock. For example, marble is calcium carbonate. The removal the carbonate ion from the ocean, allowed more CO2 to dissolve. Eventually, the level of CO2 dropped to parts per million range and has remained there for millions of years.
The solubility of calcium carbonate (calcite and aragonite are two crystalline forms) can be described by the equation
where Ksp is the solubility product for CaCO3. As a true equilibrium constant, it value is only a function of temperature. To obtain concentrations from activities, however, require a knowledge of activity coefficients, and these are a function of the ionic strength of the solution. In terms of concentrations, the above expression becomes
Here, γ ±2 represents the mean activity coefficient of calcium carbonate and () represent molar concentrations of the ions in solution.
Any solution of calcium carbonate in the presence of the carbonic acid buffer system must be electrically neutral.
Substituting the above equilibrium equations into this equation gives
The activity of dissolved CO2 (H2CO3) depends on the partial pressure of CO2 over the solution. This is known as Henry’s Law
Here, kH is the Henry’s Law constant and P is the partial pressure of CO2 in atmospheres. Multiplying the above equation by aH+2 and substituting Henry’s Law into the equation gives
We see this to be a quadric equation that can be solved numerically for pH as a function of CO2 pressure. Once the pH is known, values of the other species can be determined. The graph and Table below give values for pH, partial pressure of CO2, and activities of ionic species. To get the concentrations from the activities, the high ionic strength of the sea water must be taken into account. Concentrations could be significantly different from activities. Other values at 298.2 K are: K1 = 4.45 x 10-7, K2 = 4.69 x 10-11, kH = 29.41 atm/M, Ksp = 6 x 10-9 (an average for the minerals marble and aragonite), and pH = – log aH+ .
It appears, looking at the activities of Ca++ and CO3=, that as the partial pressure of CO2 in the atmosphere goes up, the activity of the Ca++ goes up, thus causing the activity of the CO3= to decrease. The activity of the calcium ion represents the solubility of the CaCO3. It is clear that the solubility of CaCO3 increases as the pH decreases. What is not intuitively obvious is that the process is not linear. Note that as the partial pressure of CO2 approaches 3000 ppm the concentrations of calcium and carbonate level off. This would explain how the coral reefs could have formed in the first place at CO2 levels of 3000 to 4000 ppm. The calculations producing the data in the graph were at 298.2K.