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 HCO34.68 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). [CO32HCO3[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 [CO32xx 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.
© Copyright 2021 Paperzz