### It is well known that as abundances of CO2 increase in the

```ATOC/CHEM 5151 – Problem 28
Oceanic Uptake of CO2
Answers: To be posted Thursday, November 17, 2016
It is well known that as abundances of CO2 increase in the atmosphere, the pH of the oceans
decreases (i.e., the ocean becomes more acidic). This has important consequences for the
survival of animals that build shells out of calcium carbonate, as the increased acid content
erodes those shells. The ‘chemistry’ of CO2 in the ocean begins with exchange between the
atmosphere and ocean, a process that can be written as the following equilibrium
CO2 (g) + H2O H2CO3 (aq)
K1’ = K1/[H2O] = [H2CO3] / pCO2 = 3.45 x 10-2 M atm-1
where pCO2 is the partial pressure of CO2 (in atmospheres), and [H2CO3] is measured in Moles
per liter of water (or “Molar”), and K1’ is the equilibrium constant for formation of carbonic acid
in water from exchange of CO2 from air.
(1) Calculate the concentration of H2CO3 in water for a partial pressure of CO2 of 0.000400 atm.
Note, this is equivalent to a mixing ratio of 400 parts per million, the present day atmospheric
abundance of CO2.
[H2CO3] = 3.45 x 10-2 M atm-1 x 0.0004 atm = 1.38 x 10-5 M (or moles per liter)
(2) Once in water, [H2CO3] dissolves to form acid (H+) and bicarbonate ion (HCO3), with an
equilibrium constant K2 = [H+][HCO3]/[H2CO3] = 4.45 x 10-7 M.
H2CO3 (aq)  H+ + HCO3
Using the concentration of H2CO3 from Part (1), calculate the pH = log10[H+]. Note that the
concentration of bicarbonate ion and H+ are equal due to mass balance (or stoichiometry).
[H+][HCO3] = [H+]2 = 4.45 x 10-7 M x [H2CO3]
So [H+] = root of (4.45 x 10-7 M x 1.38 x 10-5 M) = 2.48x10-6 M
pH = 
 Bicarbonate ion also acts as a weak acid in water, forming another H+ and carbonate ion
(CO32, with an equilibrium constant of K3 = [H+][CO32 HCO34.68 x 10-11 M
HCO3–  H+ + CO32
In freshwater (i.e., without other sources of acid, base, etc.), the amount of H+ produced by
dissociation of bicarbonate ion will be very small, not adding significantly to the H+ produced in
the first step above (Part (2)). Using the [H+] and [HCO3–] from Part (2), calculate the
concentration of carbonate ion ([CO32 in freshwater in contact with 400 ppm of CO2. (Note
that [H+] and [HCO3–] are equal to each other under these conditions, and this is a pretty trivial
calculation).
[CO32HCO3[H+]x 4.68 x 10-11 M = 4.68 x 10-11 M
Determine the relative abundances of [H2CO3] : [HCO3-] : [CO32-] in freshwater.
295,000 : 5.6 : 1
(4) The pH of ocean water is about 8.3. Under these conditions, there is a dramatic shift in the relative
abundances of these “inorganic carbon” reservoirs in water, such that HCO3 becomes the dominant
species. Using the same equilibrium constants above, determine the relative ratios of the three
inorganic carbon compounds for a pCO2 of 0.000400 atm and a pH of 8.3.
[H2CO3] = 1.38 x 10-5 M
[HCO3] = (4.45 x 10-7 M x 1.38 x 10-5 M) / 10-8.3 M = 1.23x10-3 M
[CO32xx 4.68 x 10-11 M) / 10-8.3 M = 1.15 x 10-5 M
1.2 : 106 : 1
The Figure 6.7 in Daniel Jacob’s book
(http://acmg.seas.harvard.edu/publications/jacobbook/bookchap6.pdf) gives a graphical representation of
the ratios of the three inorganic carbon species in water as a function of pH. Compare your answers.
The relative abundance of CO32- isn’t quite the same. But note that Jacob uses a different value for the
third equilibrium constant. This is interesting. Probably worth exploring…but I’ve run out of time! It may
have something to do with activity coefficients – how ions actually behave in environments where there
are many other ions (like sodium and chloride). I used the IUPAC value for the equilibrium constant, so I
think that got that right.
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