CO₂ is a common but very minor atmospheric constituent, which plays a major role in planetary processes, including here on earth. In this lecture we will discuss 3 functions of CO₂ that influenced the course of earth history.

CO₂ is:

• A greenhouse gas
• Involved in biological processes - photosynthesis, respiration, metabolism…

• Involved in marine geochemistry through reactions involving calcite (CaCO₃)
• A naturally occurring acid (carbonic acid H₂CO₃) responsible for chemical weathering

CO₂ occurs as a free gas in the atmosphere, which can dissolve in water. Other carbon compounds such as methane (CH₄), carbon monoxide (CO) and solid carbon (graphite, amorphous carbon, and diamond) are of interest as well.

Redox forms of carbon in nature are

                                                                        Reduced oxidized

We will try to understand the concentrations of gases in the atmosphere from the point of view of CHEMICAL EQUILIBRIUM between the air and the oceans (or lakes, rivers etc). A fundamental chemical law is the Law of Mass Action, which states that the proportions of reaction products (C, D) and reactants(A, B) at a given pressure and temperature are fixed, and can be calculated from tabulated data (thermochemical data) according to:

The things in brackets denote "concentrations" and 'log' is the logarithm of the product ratio and the equilibrium constant K_eq can be calculated from so-called Gibbs Free Energy data. For gases the concentration units are usually partial pressures.

So we can calculate the equilibrium condition for a reaction like

which may give us the ratio of CO₂ to O₂ in the atmosphere if that airmass is in chemical equilibrium with solid carbon (dead trees, diamonds, graphite etc). We write that equilibrium statement as follows:

log {P(CO₂)/P(O₂)} = Keq (= 69) or P(CO₂) = 10⁶⁹ x P(O₂) - the value of 69 was obtained from thermochemical data. We know from measurements that O₂ occurs at about 20 (volume) % in the air (PO₂ = 0.2 bar) and CO₂ occurs at about 0.038 % (or PCO₂ = 3.8 10^-3 bar). The prediction is thus off approximately by a factor of 10 to the power 71 (10⁷¹), which is not a little bit. In essence, the prediction says that the whole atmosphere should consist of CO₂ and that almost no O₂ would be left in the case of equilibrium between the atmosphere and solid carbon. So clearly, the atmospheric gases are not in equilibrium with solid carbon, which occurs in copious quantities at the surface of the earth (dead trees, coal deposits, dark specks in rocks of fossilized leaves, etc). We can make a similar estimate for the proportion between CO₂ and CO in the atmosphere according to

CO + ¹/₂ O₂  => CO₂ and log {P(CO₂) / (PO₂)^0.5 . P(CO)} = 45.

Because the amount of oxygen is so large compared to the carbon gases, we can take the oxygen partial pressure roughly as a constant (P(O₂)=0.2 bar) and then we obtain

P(CO₂) = 10²⁰ P(CO). Again, this is way off from our observations, indicating that chemical equilibrium between carbon species and O₂ within the atmosphere is not established.

So the question then becomes: what determines the abundance of gaseous compounds in the atmosphere? We have to think in more dynamic terms: although the CO₂ concentration in a given month this year is about 380 ppm (vol), every day that we measure the atmospheric composition there are other CO₂ molecules floating around. There is a continuous exchange of gases into and out of the atmosphere. We thus have to search for gas fluxes into the atmosphere (sources of CO₂) and gas fluxes out of the atmosphere (sinks of CO₂). If we can quantify the sources and sinks, we get to the carbon dynamics, usually referred to as "the carbon cycles". The magnitude of these fluxes is such that the rates towards chemical equilibration can not keep up with the size of the ins and outs, and so we have no chemical equilibrium. "LIFE" is obviously an important source and sink of CO₂, and therefore, scientists looking for extraterrestrial life, try to determine if the atmospheres of other planets far away are in chemical equilibrium or not. Dis-equilibrium is seen as evidence for the existence of life!

Identifying the processes that use or produce CO₂ is step one and quantifying these sources and sinks is our ultimate goal.

COMMONLY USED UNITS:

Simple volume units (v)

% (v) 10^-2 liters of pure O₂ / (liter of air)

ppm (v) 380 10^-6 liters of pure CO₂ / (liter of air) = 380 10^-3 ml pure CO₂ / (liter of air)

A mole is defined as the number of grams of a substance equal to its molar weight; the number of atoms/molecules in a mole is equal to the Avogadro number. Vol % are thus identical to mole %.

Lecture 2 CO₂

We spoke about the pathways of atmospheric CO₂ and distinguished two fundamental "sink routes"

Photosynthesis with fixation of CO₂ into organic carbon, which could decay away in a short time, releasing its CO₂ back to the atmosphere. Burial of the C_org could lead to a much longer isolation of the C from the atmosphere.

Dissolution of CO₂ in water will extract the CO₂ from the atmosphere and the two dissociation reactions of carbonic acid lead to the formation of some carbonate (CO₃⁼). This ion can combine with Ca⁺⁺ and / or Mg⁺⁺ and form carbonate minerals (calcite, aragonite, Mg-calcite), in many cases through the intermediate action of a small beastie (such as foram, coral, mollusc). We distinguished the two dissociation reactions of carbonic acid which each released a little bit of H⁺ and resp. bicarbonate and carbonate ions. The carbon (or CO₂) storage in the oceans is substantial, but the turn-over time of the oceans is on the order of 800-1000 years, so it is not an eternal resting place for CO₂.

The carbon that is fixed into "beastie houses" becomes part of the sediment layer at the bottom of the ocean. Once the C is fixed into buried C_org or in CaCO₃, its dynamics are then determined by the "rock cycle" a very slow moving affair compared to movements in the biosphere, hydrosphere and atmosphere. We thus distinguish two carbon cycles:

The short carbon cycle, with exchanges of carbon between the atmosphere, hydrosphere and biosphere (characteristic time scales ~seasons to 1000 years), and the long carbon cycle where C is fixed into rocks as C_org or as a carbonate minerals (characteristic time scales of millions to 100 millions of years).

We discussed the Keeling (père) curve (atmospheric CO₂ concentrations versus time) which runs from 1958 on, and shows a rise from about 315 to 380 ppm CO₂ over this 50 year period. The rate of rise increases with time, and the curve is characterized by an oscillation that follows the seasonal pulse of the N-hemisphere (Remind yourself what we said about that oscillation: about 5-6 ppm amplitude, most of the terrestrial biosphere on N-hemisphere). We also mentioned in passing that the amount of emitted CO₂ from fossil fuel burning would have caused about a 40-50 % larger increase in atmospheric CO₂ then that observed, and so there must be an additional sink (dissolution in the oceans, greening of the earth by an increase in the terrestrial biosphere). When we account for these two sinks in a quantitative way, there still is a missing (unidentified) sink. We also looked at a curve that gave CO₂ contents over the last 1000 years, showing remarkable little variation over the first 800 years. The pre-industrial atmospheric CO₂ contents was about 280 ppm CO₂. The short carbon cycle was reasonably well balanced during the period from Middle Ages till the industrial revolution.

We then discussed the linkage between the terrestrial oxygen cycle and the short carbon cycle, invoking the Keeling (fils) curve, where son is out of phase with father. Relatively speaking, the Keeling (fils) curve has a very small relative amplitude (small variations in that giant O₂ reservoir of >20% in the atmosphere). We realized that the amount of O₂ in the atmosphere must have its counterpart in buried C_org in equal molar amounts. There is a large total amount of moles of O₂ in the atmosphere and we wondered if we could finish that all up by burning all fossil fuel reserves in one day (former president Reagans birth day bonfire): Are fossil fuels the reservoir of buried organic carbon? Our comparison showed that this was not the case by far ? we would only use close to 1% of the available atmospheric oxygen. When we calculate the total budget of buried C_org from little "brown specks" in old sedimentary rocks, we get a number which creates an apparent surplus of O₂ in the air - more C_org is buried (in molar terms) than can be accounted for by the amount of moles of O₂ in the air. Then there must be another O₂ sink, and we philosophized about those elements that can extract O₂ from the atmosphere: Iron (symbol=Fe, going from Fe²⁺ to Fe³⁺) and sulfur (S) going from FeS₂ (pyrite) to SO₄⁼ (in water) or gypsum (CaSO₄).

We already had our intro into chemistry by introducing the "reaction constant" K

CO₂ + H₂O  => H₂CO₃ We can restate this as follows that at equilibrium:

[H₂CO₃] / PCO₂ = K_H

where the reaction constant for this reaction is known as the Henry's Law constant (proportionality constant of gas dissolution). The value for this parameter depends among other things on the temperature and can be calculated from thermodynamic data. The concentration of H₂CO₃ in water is given as [H₂CO₃ ], which refers to moles H₂CO₃ / kg water. The amount of CO₂ in the air is expressed either as ppm (v) CO₂ or as partial pressures (atm. or bar). The reasoning for that is outlined below.

The ideal gas law states PV = n RT or the product of Volume and Pressure of a gas or mixture of gases is equal to the amount of moles present, multiplied by the (absolute) temperature and the gas constant (R). For pure gases, it follows that at a given temperature and pressure, equal amounts of moles have an equal volume, whatever gas that is. Or you may remember from your chemistry lectures, all pure gases have a molar volume at 1 atmosphere of 22.48 liter at 0 ^oC. Then we have Boyle's Law, stating P₁V₁ = P₂V₂ When we change for a given gas the pressure from P₁ to P₂ the volume changes from V₁ to V₂ so the volume changes proportionately with the pressure. This leads to some important insights: we can imagine that a mixture of gases consists of small volumes of the pure gases - we unmix the gas mixture in our mind. The sum of all these volumes of pure gases is the total volume. Inside each little volume, we have a partial pressure that is proportional to the amount of molecules present. So the analysis of a gas mixture like the atmosphere can be expressed in volume units (20 % O₂ = 200 ml pure O₂ / liter of air), or 20 molecules of O₂ in a mixture of a total of 100 molecules, or the partial pressure of O₂ is equal to 0.2 times the total pressure. We can thus always calculate the partial gas pressure in a gas mixture from the following expression

P_tot / V_tot = P_x / V_x , where P_tot = total pressure (usually 1 atm), V_tot = the amount of volume that we consider (usually 1 liter), P_x = the unknown partial pressure of gas x and V_x is the volume of pure gas within the 1 liter that we consider. So for 380 ppm CO₂, we calculate

1 / 1 = P_x / 380 10^-6. P_x = 380 10^-6 atm = 10^-3.42 atm.

Now we can calculate the amount of CO₂ that dissolves in pure water as a result of the atmospheric CO₂ gas pressure:

[H₂CO₃] = K_H x 10^-3.42 . The value of K_H = 10^-1.5 at 25 ^oC, so [H₂CO₃] =~ 10^-5 (moles/kg water). To go from molar units to weight ppm values we have to multiply by the molar weight (62) and divide by 1000, which gives about 0.6 ppm of carbonic acid (these are weight ppm units or 0.6 . 10^-6 grams H₂CO₃ / gram water). That is a small amount and we conclude that CO₂ is only a moderately soluble gas in water. As a result of the 2 carbonate dissociation reactions, a little bit more will dissolve as bicarbonate and carbonate, but the total remains a relatively small number.