by James R. Barrante, Ph.D.
In OA I and OA II we considered the ocean chemistry of the carbonic acid system at constant temperature. Under these circumstances, it is apparent that if the partial pressure of carbon dioxide in the atmosphere increases, the pH of a buffered ocean must drop. We were able to show in OAII that increasing the partial pressure from 280 ppmv to 380 ppmv will decrease ocean pH from a values of approximately 8.2 to 8.1. pH units. In OAIII we shall consider the effect of temperature on these equilibria. Since we are working with activities rather than concentrations, it is not necessary to consider ocean salinity here. A significant amount of research has been done concerning the temperature dependence of the equilibrium constants. This data can be found online. A typical set of equations are:
ln K1 = – 1596.1/T – 9.2597
ln K2 = – 2174.5/T – 16.467
ln kH = – 2400/T + 11.431
ln Ksp = 2388.9/T – 27.213
where K1 is the first dissociation constant of H2CO3, K2 is the second dissociation constant of H2CO3, kH is the Henry’s Law constant, and Ksp is the average solubility constant of CaCO3.
The equation relating the pH of ocean water to the partial pressure of atmospheric CO2 at temperature T is
This equation was derived in OAII. There are obviously a number of variables in this equation that could be changing at the same time. It might be interesting to approach the problem as one does with PVT data and look at a surface graph. First note that because the concentration of calcium ion in the oceans is so large, we can assume that the activity is constant at 0.00123.
It is well-known that pH is a sensitive function of temperature. Consequently, to assume that the pH of our oceans depends only on the concentration of dissolved CO2 is a sophomoric definition of the boundaries of the system. To express the data graphically, it is necessary to do so on a surface. Slices of the three-dimensional graph are easily seen by following isotherms or CO2 isobars. Note that the change in pH with temperature is not insignificant. It has been noted that the pH of the oceans has dropped about 0.1 pH units in 150 years. This normally is incorrectly attributed to the absorption of atmospheric CO2, and while atmospheric CO2 does come into play here, one should note that as little as a 2-degree C increase in ocean temperature can decrease ocean pH by as much as 0.05 pH units. Moreover, assuming that the concentration of dissolved CO2 increases in a solution in which its temperature increases is not consistent with Henry’s Law.
Below is the P-pH-T representation of ocean pH. Keep in mind that the system is highly buffered. For clarity, the pH at various intersections of the curves is given. Because of the three-dimensional nature of the graph, to find temperatures and pressures, be sure to follow the intersections along lines to their respective axes. The temperature range was taken to represent global SST in zones from the equator at 303K to Antarctica at 273K. Note the variation in ocean pH between these two temperatures on any isobar. At today’s value of 400 ppmv, the pH changes from 8.30 to 8.00. This would suggest that describing an average ocean pH has no physical meaning. I would imagine that a similar effect occurs going from surface temperature to deep-water temperature. It’s clear that using a secondary school chemistry course definition of pH in this complex system serves no useful purpose and leads one to the wrong conclusions about ocean acidification.
P-pH-T Data for Ocean pH.