Seawater Equilibria
The audience for whom this piece is intended consists of people who know some chemistry and are uncertain about how to consider the often made claim by deniers that the oceans contain so much dissolved carbon that human production is inconsequential. What the article points out is that the elementary chemical concepts of chemical equilibrium and charge balance put restraints on the ability of the ocean to release carbon dioxide to the air. Because of these restraints the oceans locally can release only a small part of the total dissolved carbon dioxide and, more importantly, when averaged over a year the amount released equals the amount dissolved, i.e. there is not net addition of carbon dioxide to the atmosphere from the oceans so long as the temperature averaged over a year remains constant from year to year.
This topic deals with the acid-base chemistry of the species important in the solubility of
. These are: (g), (aq), 
, 
, 
, 
, 
, 
and 
. The amount of each of the dissolved substances is described by its molality, 
which is the number of moles dissolved in a kilogram (kg) of water. In order to consider the chemistry it is necessary to propose a model system. A model for the average ocean is: A 3.5% sodium chloride solution in water at T=288K in equilibrium with 387 ppm 
in air 
at a pH of 8.00 and in addition 0.416 millimoles of dissolved boric acid per kg of water. The molalities of the seven solute species are fixed by seven independent equations . 
is known from the Keeling curve so 
is fixed by the Henry’s law constant for
The molality of hydrogen ion is fixed by the measured pH, and the observed quantity of dissolved boric acid yields
.
Thus there are three restraints placed on the solute molalities at 288K by the known properties of average seawater. There are four more relations (restraints) relating the molalities namely the equilibrium constants for the four independent net reactions among the solute species. These were obtained as functions of T using tabulated thermodynamic data. Algebra then yields the molalities of the remaining solute species at 288K, specifically the equilibrium molalities of 
, , and
, as well as the other species, are determined for the average ocean. The total carbon dioxide molallity
is thus fixed in the equilibrium average ocean (its value is 1.65 millimolal). Bicarbonate is 91.5% of this total molality. An essential requirement for the evolution of carbon dioxide from the equilibrium ocean into the atmosphere is a perturbing influence. The one property of the solution that can be altered so as to affect the total molality is the temperature of the system.
E.g. consider the effect of changing the temperature at constant partial pressure of . The pH will change with T so the pH=8.00 restraint is lost. On the other hand, by charge balance
is constant ( 
are not included in the sum because they are present at such low concentration that they can be neglected). Thus even when T differs from 288K there are as many restraints as there are molalities. Tabulated thermodynamic data were used to calculate the equilibrium constants (including the Henry’s Law constant) at each of eight temperatures between 276 and 304K and the molalities for all species were found algebraically at the eight temperatures. In particular the three molalities in 
were found at each T . The eight values for 
were fit to a straight line as a function of T with the result:
.
This means that the 
locally in the ocean decreases by only 13.5 micromoles per kg for each degree that T increases. The opposite is also true: the increases by 13.5 micromoles locally for each degree of decrease. Since 288K is the average T, when there is an increase in one place there is a decrease in another and thus the net exchange of between the ocean and the atmosphere is zero if there is no other source of carbon dioxide such as human combustion of fossil fuels. Considering this human production leads to the conclusion that there is necessarily a net increase in dissolved carbon dioxide (see Henry's Law above) and the calculations yield in this case a decreasing average pH in the oceans. Perhaps someone more knowledgeable than I could add a comment about the effect of increasing acidity on coral reefs, plankton, fish, etc.
In conclusion :
1: Thermodynamics and charge balance place serious restraints on the ability of dissolved carbon dioxide to pass into the gas phase as a result of local temperature changes. The significance of these restraints should be considered by the deniers when they assert that the amount of carbon dioxide dissolved in the oceans is so large that exchanges between the ocean and the atmosphere dwarf human production.
2. The nature of the average temperature and the thermodynamics of the reactions means that there is, on the average, no net exchange of carbon dioxide between the oceans and the atmosphere i.e. the notion that somehow carbon dioxide is belched into the atmosphere by the oceans ignores the basic fact that whatever carbon dioxide is released in one part is compensated by an equal quantity dissolved in another.
Posted by hfranzen on Monday, 10 January, 2011
