by James R. Barrante, Ph.D.
In OAI we showed the effect of increasing dissolved CO2 in seawater on ocean pH, and the carbonic acid buffer system including insoluble carbonate salts. The calculations performed in the study involved using thermodynamic equilibrium constants found in the literature at 298.2K. It is important to understand that a true thermodynamic equilibrium constant depends only on temperature and requires that activities (effective concentrations) be used in the calculations. If concentrations are used, then either activity coefficients must be known in order to substitute concentrations for activities, or apparent equilibrium constants must be used, found by correcting thermodynamic equilibrium constants for the ionic strength of the solutions.
Unfortunately, while the data presented in OAI is consistent with data presented by others performing similar calculations, it’s not consistent with reality. For example, the calculated ocean pH at a CO2 pressure of 276 ppm is found to be 8.41. According to published values for ocean pH experimentally determined in the mid-1800s at CO2 pressures of 280 ppm, the value was closer to 8.20. Today, at atmospheric pressures of CO2 close to 380 ppm, experimental values for ocean pH are approximately 8.13. The calculated value using numbers found in OAI is 8.29. It is apparent that the model used in OAI is not correct. One might think that perhaps the temperature is the problem. The temperature of the oceans is not 25˚C, but closer to 15˚C and even colder as depth is increased. Unfortunately, using values for the equilibrium constants at lower temperatures only make the discrepancies larger. As temperature goes down, calculated pH values go up.
We find that if we assume that the pH of our oceans is behaving more like a system where the calcium ion concentration is constant, we get calculated results that are closer to experimentally determined values. Consider another approach to the calculations performed in OAI. First, let us combine the two dissociation equations for carbonic acid. This gives
Rearranging and taking the logarithm (base 10),
which is a modified form of the Henderson-Hasselbalch equation. The activity of the dissolved carbon dioxide can be replaced with Henry’s Law and the activity of the carbonate ion can be replaced with the Ksp equation for CaCO3.
There are studies that show that the bulk calcium ion concentration in the surface layers of the ocean are relatively constant at approximately 0.0104M . The relationship between the activity of Ca++ and its concentration is
where γ+ is the activity coefficient of Ca++ . While it is impossible to measure the activity coefficient of an individual ion, we can approximate it using a modified form of the Debye-Hückel equation
where zi is the charge number on the ion and I is the ionic strength of the solution. The ionic strength of the oceans is approximately 0.7. Therefore, we have
= – 0.9274
γ+ = 0.1182
Substituting physical constants used in OAI for K1, K2, Ksp, and kH into the pH equation, we have
In the mid-1800s the partial pressure of CO2 in the atmosphere was approximately 0.000280 atm (280 ppm). Substituting this into the pH equation gives
pH = 6.418 – 0.5 log (0.000280) = 8.194
which is very close to the reported value. Today, atmospheric CO2 level is close to 0.000380 atm (380 ppm). Using this value in the equation gives pH = 8.128, again very close to the measured value. Using this equation to find the pH, we can calculate the data found in the following graph:
The most difficult part of this model to come to terms with is assuming that Ca+2 and CO3-2 concentrations are constant with changing pH. A possible explanation is that while it is assumed that atmospheric CO2 is in equilibrium with CaCO3 in our oceans, it is apparent that the calcium ion concentration far exceeds the total concentration of all carbonate components. That would indicate that the calcium ion concentration is so overwhelmingly large that the equilibrium between dissolved CO2 and CaCO3 is destroyed. This is the only way the acceptable values for ocean pH can be found. In OAIII we will look at the effect of temperature on the system.