Partitioning of CO₂ between the atmosphere and ocean

In order to consider other states of the system it is necessary to consider charge conservation. The hydrogen ion concentration is far below the concentrations of the negative ions. There is no charge balance without additional cations. We therefore determine the molarity of cations required to balance the charges due to CO₃^2- (aq), HCO₃^- (aq) and H⁺ (aq):

[OH^-] + [HCO₃^-] + 2[CO₃^2-] – [H⁺] = 9.2x10^-4

The majority of these compensating ions are calcium. These ions enter the ocean through riverine fluxes (i.e. weathering).

The total mass of the earth’s oceans is, m^ocean = 1.3 x 10²¹ kg.

n^ocean_eq represents the number of moles of CO₂ from the atmosphere that have dissolved in the ocean based on the above calculation:

n^ocean_eq = (1.27 x 10^-5 molar)(1.3 x 10²¹ kg) = 1.65 x 10¹⁶ moles

From the total mass of the atmosphere, 5.28 x 10¹⁸ kg, we can calculate the total number of moles of gas in the atmosphere:

n^atm = (m^atm kg)/(MW kg/mol) = (5.28 x 10¹⁸ kg)/(0.029 kg/mol) = 1.81 x 10²⁰ moles

Based on the known partial pressure of CO2, we can calculate the mass of CO₂ in the atmosphere,

n^atm_CO2 = x_CO2n^atm = (3.8 x 10^-4)(1.81 x 10²⁰ moles) = 6.88 x 10¹⁶ moles

Comparing the two values for the moles of CO₂ in the atmosphere and the ocean we find that

n^ocean_aq/ n^atm_CO2 ~ 0.25

which means that 25% of the CO₂ that enters the atmosphere ends up the ocean. Putting it another way the partitioning of CO₂ is 75% atmosphere and 25% ocean. Next we consider the fate of the CO₂ that ends up in the ocean.

The fate of CaCO₃ in the ocean

There is a further dimension to the problem of CO₂ uptake since CO₃^2- is removed from the ocean by the precipitation of CaCO₃. When the species were listed CaCO₃(s) was not included. In order for it to form the system must be saturated with respect to its formation. The saturation is determined with respect to the equilibrium,

CaCO₃(s) à Ca²⁺(aq) + CO₃^2-(aq)

which is defined as the solubility product. In the equilibrium constant the concentration of the solid CaCO₃ is not counted since the concentration of the solid is not defined.

It is reported that the surface of the ocean is 2.32 x 10^-3 molar in Ca²⁺. The solubility product for calcium carbonate is:

The product of concentrations in the ocean is:

2.32 x 10^-3 x 8.0 x 10^{-6 =}1.85 X 10^-8,

which is greater than the solubility product. We conclude that the ocean is supersaturated in CaCO₃. The direction of spontaneous change may be considered from the point of view of the dissolution of the solid as written in the chemical equation above. The three possible cases are:

DG > 0, Q = [Ca²⁺][CO₃^2-] > K Equilibrium shifts left to CaCO₃

DG = 0, Q = [Ca²⁺][CO₃^2-] = K System is at equilibrium

DG < 0, Q = [Ca²⁺][CO₃^2-] < K Equilibrium shifts to the right

The concentration of the CaCO₃ is not necessarily in equilibrium. In other words, there can be an excess or deficit of Ca²⁺ and CO₃^2- in the solution above the CaCO₃ solid. If there is an excess of ions in solution the solution is supersaturated. If the system is not in equilibrium then there will be a driving force DG to attain equilibrium:

DG = DG^o + RTlnQ

Factors that slow CaCO₃ precipitation rates: the carbon compensation depth

So could CaCO₃(s) be a significant sink for anthropogenic carbon dioxide? It has been observed that there are no large deposits of CaCO₃(s) on the bottom of the deep ocean, so the answer is probably no. There are several possible explanations for this, and all possibly contribute to failure of the precipitate to form or its redissolution in the deep ocean:

1. CO₂ redissolves in the deep ocean
2. Ionic activities are reduced (high salt concentration)
3. Surface free energy presents a barrier to precipitation.

There are large pressures (up to nearly 1 kbar) in the deep ocean. One scenario is that calcium carbonate forms at the surface and sinks to depths where it redissolves because of effect of pressure on the dissolution reaction:

CaCO₃(s) à Ca²⁺(aq) + CO₃^2-(aq)

DV_m = -62 cm³/mol [molar volume of reaction]

The molar volume water of solvation is less around the ion that around the solid (or the bulk).

For example, at 8000 m (P ~ 800 atm). The determine the pressure dependence of the equilibrium constant we begin with the expression,

at constant temperature. The integrated form is

This expression can be combeind with

To give

And finally in exponentiated form,

Substituting in the values we have

Thus, the effect of increasing pressure is to increase the solubility product, leading to greater solubility of Ca²⁺ and CO₃^2- ions.

The formation of calcium carbonate as a sediment in the oceans has been occurring for billions of years. This process leads to the formation of limestone (sedimenary rock). One can imagine CaCO₃ forming white particles and settling to the bottom. This is like snow in the ocean since the particles build up a layer on the ocean floor. However, in the deep ocean the pressure shifts the equilibrium so that this snow “melts” before it reaches the bottom. Below about 5000 m there is no limestone on the ocean floor. This part of the deep ocean is known as the abyssal plain. The depth at which CaCO₃ no longer forms is called the carbon compensation depth.