Chemistry for Everyone
Climate Change and Its Effect on Coral Reefs Ralph E. Weston Jr. Chemistry Department, Brookhaven National Laboratory, Upton, NY 119793-5000;
[email protected] The discussion of acid–base equilibria in general chemistry and physical chemistry texts usually extends to the treatment of polyprotic acids, and a frequently used example is the carbonic acid equilibrium (1). This system plays an important role in the chemistry of the sea, and books on chemical oceanography typically devote a chapter to the discussion of the carbonic acid system and the determination of the concentrations of the various species involved. In addition, the concentration of the carbonate ion is important in determining the solubility of calcium carbonate, which in turn is related to the formation of coral in tropical seas. (The reactions involved in these equilibria are presented in eqs 1–11.) The intent of this article is to provide a specific example of the way in which several concepts of elementary physical chemistry encountered by students in their first chemistry course (Henry’s law of gas solubility, acid–base equilibria and dissociation constants, and solubility products) apply to a realworld situation. To emphasize the timeliness of this topic, recent concerns about the effect of projected climate change on the health of tropical coral deposits are examined in detail. The Dependence of Coral Health on Atmospheric Carbon Dioxide A worldwide, disastrous decline in the growth of coral is being observed by marine scientists. Coral bleaching, coral disease outbreaks, and algal overgrowth are all increasing in
frequency, intensity, and range (2). There are a number of causes, some of them only local in effect, such as dust from the fringe of the Sahara loading the coral with sediment. Others are global in their range, such as enhanced UV radiation caused by the decrease in stratospheric ozone, and a general increase in global mean temperature. The effect of temperature is demonstrated strikingly by coral bleaching in tropical areas where unusual seawater temperatures have led to a series of intense El Niño events since the mid-1970s. But one particular threat is the result of a change in the chemical composition of seawater—specifically an increase in dissolved carbon dioxide due to the increased carbon dioxide content of the atmosphere. As Figure 1 shows, the carbon dioxide concentration in the atmosphere measured at the Mauna Loa observatory in Hawaii has increased steadily since these measurements were started in 1958. These data connect smoothly with the record of atmosphere carbon dioxide concentrations derived from ice cores that are as much as 1000 years old. Since this increase is most marked in the last century, it is attributed chiefly to the increasing use of fossil fuel as an energy source. Coral reefs depend upon the formation of calcium carbonate for their growth, and this in turn is related to the saturation state, defined as Ω = [Ca2+][CO32᎑ ]/Ksp, where the brackets indicate concentrations and Ksp is the solubility product constant for either of the forms of calcium carbonate involved, calcite or aragonite. A value of Ω larger than unity indicates 400
Carbonic Acid Equilibria Equilibrium Constants: CO2(aq)
(1)
Hydration of carbon dioxide: CO2(aq) + H2O H2CO3 [H2CO3]/[CO2(aq)] = K0
(2)
CO2*, [CO2*]/[CO2(g)] = Kh
(3)
Henry’s law: CO2(g)
where CO2* = H2CO3 + CO2(aq)
(4)
pCO2 / µatm
Dissolution of carbon dioxide: CO2(g)
350
300
Dissociation of carbonic acid: CO2* + H2O H+ + HCO3᎑ (5) [H+][HCO3᎑]/[CO2*] = K1 Dissociation of bicarbonate ion: HCO3᎑ H+ + CO32᎑ [H+][CO32᎑]/[HCO3᎑] = K2 Ionic product of water: H2O
(6)
H+ + OH᎑, [H+][OH᎑] = Kw (7)
Solubility product of CaCO3: CaCO3(s) [Ca2+][CO32᎑] = Ksp
Ca2+ + CO32᎑
(8)
Conservation Equations: Charge balance: 2[Ca2+] + [H+] = 2[CO32᎑] + [HCO3᎑] + [OH᎑] (9) Total carbon species: TCO2 = [CO32᎑] + [HCO3᎑] + [CO2*] (10) Conservation of carbon species: [Ca2+] = TCO2
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(11)
250 1000
1200
1400
1600
1800
2000
Years Figure 1. Atmospheric concentration of carbon dioxide for the past millennium. Circles, from ice core samples at site DSS of the Law Dome in Antarctica. Squares, from atmospheric measurements at Mauna Loa, Hawaii. Ice core data from Etheridge, D. M.; Steele, L. P.; Langenfelds, R. L.; Francey, R. J.; Barnola, J.-M.; Morgan, V. I. In Trends: A Compendium of Data on Global Change; Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, Oak Ridge, TN, 1998. Atmospheric data from Keeling, C. D.; Whorf, T. P. Scripps Institution of Oceanography, University of California, La Jolla, CA, July 1999. Available on the Internet at http://cdiac.esd.ornl.gov/ ndps/ndp001.html.
Journal of Chemical Education • Vol. 77 No. 12 December 2000 • JChemEd.chem.wisc.edu
Chemistry for Everyone
supersaturation, while a value less than unity implies that the solid will dissolve in order to achieve equilibrium. In fact, the upper layers of the world’s oceans are saturated or supersaturated with respect to calcium carbonate (3). The rates controlling the ionic equilibria cited in eqs 1–11 are very rapid, and even the relatively slow hydration of carbon dioxide has a half-life of less than one minute (4 ). On the other hand, achievement of an equilibrium between a solid and ions in solution is expected to be very slow. Kleypas et al. (5) have combined physical chemical data with databases containing global distributions of carbon dioxide, sea surface temperature, and other relevant parameters in order to calculate the global distribution of Ω values with atmospheric CO2 concentrations since 1880 and projected to 2100. Although even the “worst case” projections of the carbon dioxide increase still give values of Ω that are larger than unity, there is a pronounced decrease. The authors cite several studies indicating that a decreased saturation state leads to lower rates of calcification and increased stress on the coral reef. Equilibria in the Carbonate–Bicarbonate–Carbon Dioxide System The statement “addition of fossil fuel CO2 decreases [CO32᎑ ]” (5 ) is at first glance counterintuitive, since one might expect the increase in carbon dioxide to lead to a concomitant increase in carbonate. So let’s look at the equilibria involved (eqs 1–11). When carbon dioxide dissolves in water, only a very small amount of carbonic acid is actually formed (K0 ≈ 2 × 10᎑3). Furthermore, since CO2(aq) and H2CO 3 are difficult to distinguish experimentally, their concentrations are lumped together as CO2*. The equilibrium constants tabulated in the box are based on this convention. The relative amounts of the three carbon-containing species are a sensitive function of the pH, as shown by Figure 2. Such a diagram is sometimes known as a Bjerrum plot, and it has the same form for any acid–base equilibrium but is shifted along the pH axis according to the value of the pK ’s
(pK = ᎑log10 K ). Note that [CO2] = [HCO3᎑ ] when the pH equals pK1, and [HCO3᎑] = [CO32᎑ ] when the pH equals pK2. Also indicated in this figure are the large shifts in the equilibria caused by the change in the equilibrium constants in seawater, which has an ionic strength of about 0.7 mol per kilogram of solution, principally due to sodium chloride. In the pH region pertinent to seawater (pH = 8.0–8.2) the relative amounts of dissolved CO2* and CO32᎑ are very sensitive to the pH, whereas the relative concentration of HCO3᎑, the major constituent in this pH region, does not change dramatically. For example, if the total amount of carbon-containing species is kept constant and the pH increases by 0.1 unit, the relative concentration changes are HCO3᎑, 3.3%; CO32᎑, 21.7%; CO2*, ᎑23.2%. It can also be seen from Figure 2 that an increase in dissolved carbon dioxide concentration, directly proportional to the atmospheric concentration, is commensurate with a decrease in carbonate, but the bicarbonate concentration changes only slightly. A very complete discussion of the calcium carbonate– water–carbon dioxide system is given elsewhere (4, 6–8). Let us first consider the case where calcium carbonate dissolves in pure water. In addition to the equilibria involving only carbon dioxide and water, there are the additional constraints of the solubility product, charge balance, and the fact that all carbon species are formed from the carbonate dissolving from the calcium carbonate (eqs 1–11). Since we know that calcium carbonate is slightly basic, we can guess that the concentrations of H+ and CO2* will be negligibly small, thus simplifying eqs 9–11, which can then be combined to yield [HCO3᎑ ] = [OH᎑ ] = K w /[H+]
(12)
Substituting this concentration of bicarbonate into eq 6, we obtain [CO32᎑ ] = K 2 K w /[H+]2
(13)
and from eq 8 this leads to [Ca2+] = (K sp/K 2 K w)[H+]2
(14)
Now we can express eq 10 entirely in terms of [H+] in the form (K sp/K 2 K w)[H+]2 = K 2 K w /[H+]2 + K w /[H+]
100
Percentage total carbon
CO2*
HCO3
᎑
CO3
80
[H+] = 1.10 × 10᎑10; pH = 9.96 [HCO3᎑ ] = [OH᎑ ] = 9.07 × 10᎑5 [CO32᎑ ] = 3.85 × 10᎑5 [Ca2+] = 1.29 × 10᎑4 [CO2*] = 2.24 × 10᎑8
60
pH = pK 1
pH = pK 2
40
20
0 4
6
8
10
(15)
The constants we need, for pure water at 25 °C, are K1, 4.47 × 10᎑7; K2, 4.67 × 10᎑11; Kw, 1.00 × 10᎑14; and Ksp (calcite), 4.96 × 10᎑9 (9). These can be substituted into eq 15 and it can be solved graphically to yield the following concentrations:
2᎑
12
pH Figure 2. The relative amounts of dissolved carbon dioxide, bicarbonate, and carbonate. Solid lines, pure water at 25 °C. Calculated with pK1 = 6.350, pK2 = 10.331. The dashed lines indicate the relative amounts of dissolved carbon dioxide and carbonate in sea water with a salinity of 36.5‰ at 26 °C with pK1 = 5.831, pK2 = 8.915.
We see that our approximations involving the neglect of [H+] and [CO2*] in eqs 9–11 were justified. Next question: Does adding an atmosphere of carbon dioxide above the solution increase the solubility of calcium carbonate, as asserted by Kleypas et al. (5)? We need the additional Henry’s law constant Kh, which is 3.40 × 10᎑2 mol/kg water–atmosphere (9). Equation 11 is no longer valid, because some of the carbon species are derived from the carbon dioxide atmosphere. However, eq 5 gives
JChemEd.chem.wisc.edu • Vol. 77 No. 12 December 2000 • Journal of Chemical Education
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Chemistry for Everyone
[HCO3᎑] = K1[CO2*]/[H+]
(16) +
Now we can express the quantities in eq 9 in terms of [H ], yielding (2Ksp/K1K2KhPCO2)[H+]2 + [H+] =
(17)
(2K1K2KhPCO2)/[H+]2 + (K1KhPCO2 + Kw)/[H+] This equation can then be solved as before, and once [H+] has been found, the other concentrations can be calculated. The resulting dependence of the CaCO3 solubility on the pressure of carbon dioxide is shown in Figure 3. For the specific case of the present atmospheric concentration of carbon dioxide, ≈3.5 × 10᎑4 atm, the concentration of dissolved carbon dioxide is 1.20 × 10᎑5 M, and the following results are obtained: [H+] = 5.13 × 10᎑9; pH = 8.29 [OH᎑] = 1.93 × 10᎑6 [HCO3᎑] = 1.03 × 10᎑3 [CO32᎑ ] = 9.34 × 10᎑6 [Ca2+] = 5.31 × 10᎑4 [CO2*] = 1.20 × 10᎑5 The fact that this solution is more acidic than the system without carbon dioxide makes sense; one of the more colorful lecture demonstrations consists of showing the change in the color of an acid–base indicator dissolved in neutral water as one either breathes into the solution or tosses in a chunk of dry ice. It is apparent that the solubility of calcium carbonate is about four times greater in water in equilibrium with the present atmospheric concentration of carbon dioxide than in pure water. The Carbonate–Bicarbonate–Carbon Dioxide System in Seawater For accurate calculations, a number of corrections to this simple picture are needed, which require a more detailed knowledge of the constituents of seawater. Oceanographers typically measure several relevant parameters in a seawater 6
[Ca+2] / (10᎑4 mol L᎑1)
5
4
3
sample: temperature, salinity, pH, total inorganic carbon (TCO2), total alkalinity (TA), and fugacity (f CO2) or partial pressure ( pCO2) of dissolved carbon dioxide. The temperature and salinity determine the relevant equilibrium constants, and once these are specified any two of the last four variables suffice to determine the concentrations of the inorganic carbon species. The total alkalinity is defined as the amount of hydrogen ion required to neutralize the anions of all the weak acids present (7). After the carbonate and bicarbonate ions, the most important contribution is that of borate, B(OH)4᎑, which is typically a few percent of the total alkalinity. The concentration of this ion is usually calculated from the boric acid dissociation constants and the total boron content, which is linearly dependent on the salinity (10). Equations relating these four parameters are given by Skirrow (7 ) and in a Department of Energy publication (11). In addition, a report by Lewis and Wallace (12) is available online (13) with a detailed discussion of the equilibrium constants needed for the determination of the concentrations of the inorganic carbon species. Also available is a computer program that can be downloaded. This program allows the choice of several sets of equilibrium constants and the choice of the two parameters to be used as input. The output contains the concentrations of carbonate and bicarbonate and the partial pressure of carbon dioxide, as well as the pH and the values of Ω for calcite and aragonite. As discussed above, surface ocean water is usually saturated or supersaturated. In calculating Ω, the calcium concentration is assumed to be linearly proportional to the salinity, as extensive measurements indicate (14 ). However, the carbonate concentration is obtained by solving the appropriate equilibrium equations. To be thermodynamically rigorous the equilibrium constants for the reactions of eq 1–11 should be given in terms of activities. Thus, the partial pressure of carbon dioxide should be replaced by its fugacity, which takes into account that carbon dioxide is not an ideal gas. However, this is a very small effect (0.3–0.4%) at the relevant pressures. The activities for the ionic species are usually taken into account by putting the necessary activity coefficients into the equilibrium constants. Both K1 and K2 involve more ions in the numerator than in the denominator, and since the activity coefficients of ionic species are less than unity, one would expect the equilibrium constants to be smaller in seawater than in pure water. The major ionic species in seawater are sodium and chloride ions, so the equilibrium constants are often tabulated as a function of the salinity in parts per thousand (‰). This is not a trivial correction, as Figure 2 indicates, since pK1 decreases by about 0.5 units in going from pure water to water of 36.5‰ salinity and pK2 decreases by 1.4 units. To add a further complication, different conventions have been adopted by different authors in defining pH.
2
The Effect of Increased Carbon Dioxide on Coral Formation
1
0 0
50
100
150
200
250
300
350
pCO2 / µatm Figure 3. The solubility of calcite as a function of carbon dioxide partial pressure. The constants used in the calculation are given in the text.
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Several studies, cited by Kleypas et al. (5), indicate that the health of coral reefs shows a strong dependence on the saturation state, defined by Ω. Thus, it is interesting to see what a typical value of this quantity is in tropical waters, where such coral deposits exist. The necessary data can be found in the paper by Lee et al. (15), which describes measurements made
Journal of Chemical Education • Vol. 77 No. 12 December 2000 • JChemEd.chem.wisc.edu
Chemistry for Everyone
during a cruise closely following the 20° W meridian and ranging from 63° N to 5° S. The authors combine these data with similar data from an earlier NOAA-sponsored cruise, to obtain data appropriate to the tropical latitudes. For latitudes of 20° S and 20° N, the following values are appropriate: TCO2, 2050 µmol/kg; pCO2, 3.6 × 10᎑4 atm; salinity, 36.5‰; temperature 26 °C. These parameters are used as input for the CO2SYS program,1 with the following output: TA [HCO3᎑] [CO32᎑] [CO2*] pH pK1 pK2 Ωarag Ωcalcite
2435 µmol/kg 1761 µmol/kg 279 µmol/kg 9.9 µmol/kg 8.10 5.843 8.895 4.4 6.6
The value of the total alkalinity thus obtained is in good agreement with values measured in situ (15). Kleypas et al. calculated a value of 4.0 for Ωarag in the tropics, and they illustrated that no reefs are found in waters where the aragonite saturation factor is lower than this. Now we can look ahead to predict the consequences of increased atmospheric carbon dioxide. In their calculations, Kleypas et al. (5) assume a doubling to about 7.0 × 10᎑4 atmospheres, which has been predicted by some climate modelers (16 ). We now repeat the calculation just described, but with pCO2 and TCO2 as the input parameters, assuming that the latter quantity includes the additional carbon dioxide in solution corresponding to the increased atmospheric partial pressure, since this gas–solution equilibrium is maintained. The output of this new calculation is: [HCO3᎑] 2᎑
[CO3 ] [CO2*] pH Ωarag Ωcalcite
1877 µmol/kg 163 µmol/kg 19.2 µmol/kg 7.83 2.4 3.9
We see that the saturation value for aragonite has dropped below the value of 4 that is considered a minimum for coral reef health. Kleypas et al. obtained a value of 2.8 in their 2100 C.E. projection, and it is clear that the projected value of the saturation constant is dangerously low, compared with present values. Coral reefs are biologically diverse ecosystems that are important to fisheries and for coastal protection, as well as major tourist attractions in some areas. These simple acid–base calculations indicate the threat to these complicated systems posed by continued increases in anthropogenic carbon dioxide emissions. Acknowledgments This work was carried out at Brookhaven National Laboratory under Contract DE-AC02-98CH10886 with the U.S. Department of Energy and supported by its Division of
Chemical Sciences, Office of Basic Energy Sciences. I thank Ernie Lewis, Joan Kleypas, and an anonymous reviewer for helpful comments on this paper. Note 1. For those who want to use the CO2SYS program to check these calculations, the following options were chosen: constants, option 1, Roy et al. (17 ); sulfate, Dickson (18); pH scale, total.
Literature Cited 1. See, for example, Atkins, P. W. Physical Chemistry, 4th ed.; Oxford University Press: Oxford, 1990; p 231. 2. Hileman, B. Chem. Eng. News 1999, 77 (32), 16. 3. Skirrow, G. In Chemical Oceanography, Vol. 2, 2nd ed.; Riley, J. P.; Skirrow, G., Eds.; Academic: New York, 1975; pp 84, 95. 4. Millero, F. J.; Sohn, M. L. Chemical Oceanography; CRC Press: Boca Raton, FL, 1992. 5. Kleypas, J. A.; Buddemeir, R. W.; Archer, D.; Gattuso, J.-P.; Langdon, C.; Opdyke, B. N. Science 1999, 284, 118. 6. Garrels, R. M.; Christ, C. L. Solutions, Minerals, and Equilibria; Harper and Row, New York, 1965, p 74. 7. Skirrow, G. In Chemical Oceanography, Vol. 2, 2nd ed.; Op. cit.; Chapter 9. 8. Pilson, M. E. Q. An Introduction to the Chemistry of the Sea; Prentice-Hall: Englewood Cliffs, NJ, 1998; pp 102–155. 9. CRC Handbook of Chemistry and Physics, Lide, D. R., Ed.; CRC Press: Boca Raton, FL, 1994. 10. Skirrow, G. In Chemical Oceanography, Vol. 2, 2nd ed.; Op. cit.; p 29. 11. Handbook of Methods for the Analysis of the Various Parameters of the Carbon Dioxide System in Sea Water, version 2; Dickson, A. G.; Goyet, C., Eds.; ORNL/CDIAC-74; Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy: Oak Ridge, TN, 1994. Available online at http://www-mpl.ucsd.edu/people/adickson/CO2_QC/ (accessed Oct 2000). 12. Lewis, E.; Wallace, D. Program Developed for CO2 System Calculations; ORNL/CDIAC-105; Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy: Oak Ridge, TN, 1998. 13. Lewis, E.; Wallace, D. Program Developed for CO2 System Calculations; ORNL/CDIAC-105; Carbon Dioxide Information Analysis Center, Oak Ridge National Laboratory, U.S. Department of Energy: Oak Ridge, TN, 1998; http://cdiac.ESD. ORNL.GOV/oceans/co2rprt.html (accessed Oct 2000). 14. Chemical Oceanography, Vol. 2, 2nd ed.; Op. cit.; Appendix, Table 2. 15. Lee, K.; Millero, F. J.; Wanninkhof, R. J. Geophys. Res. 1997, 102, 15693. 16. Climate Change 1995: The Science of Climate Change; Houghton, J. T.; Meira Filho, L. G.; Callander, B. A.; Harris, N.; Kattenberg, A.; Maskell, K., Eds.; Cambridge University Press: Cambridge, 1995, p 83. 17. Roy, R. N.; Roy, L. N.; Vogel, K. M.; Porter-Moore, C.; Pearson, T.; Good, C. E.; Millero, F. J.; Campbell, D. M. Marine Chem. 1993, 44, 249. Erratum, Marine Chem. 1994, 45, 337. Erratum, Marine Chem. 1996, 52, 183. 18. Dickson, A. G. J. Chem. Thermo. 1990, 22, 113.
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