Chemistry for Everyone
A Simplified Model To Predict the Effect of Increasing
Atmospheric CO2 on Carbonate Chemistry in the Ocean
Brian J. Bozlee* and Maria Janebo
Department of Chemistry, Hawaii Pacific University, Kaneohe, HI 96744-5297; *[email protected]
Ginger Jahn
Department of Chemistry, University of Maryland, College Park, MD 20742
Textbooks in environmental chemistry apply chemical and
physical principles to numerous topics of current environmental
concern such as ozone depletion, acid rain, chemical wastes,
urban smog, and global warming. When the impact of rising
levels of CO2 in the atmosphere is treated in these texts it is
usually emphasized that CO2 is a greenhouse gas that can lead
to global warming (1–3). In that context, the role of the ocean in
dissolving atmospheric CO2 is considered a “good thing” since
it removes a greenhouse gas from the atmosphere. What is often
neglected is the likelihood that increasing levels of CO2 in the
ocean will significantly lower the pH of surface water and lead to
the dissolution of calcium carbonate in coral and other calcifying
organisms. Thus, while acidification of terrestrial waters (and the
related carbonate chemistry) is typically treated in the context
of “acid rain” (1–3) the acidification of surface seawater is often
not emphasized. Over the last few decades, however, this topic
has risen to the fore as a serious environmental concern and has
been reviewed recently in widely read scientific journals such as
Nature (4) and Scientific American (5).
It should be emphasized here that acid–base carbonate
chemistry in seawater is not entirely the same as in freshwater.
The presence of electrolytes in the ocean affects the activities of
solution species significantly, and the temperature of seawater
also varies over a wide range. Thus “apparent” acid ionization
constants (Ka) and the autoionization constant of water (Kw) in
seawater must be written as functions of both salinity (S) and
temperature (T). In addition a complete treatment of the topic
may necessitate the inclusion of multiple weak acids—such as
phosphoric, silicic, and boric acids—although these can be neglected to first-order approximation. It is also important to note
that the ocean is not a system at equilibrium. In particular, we
may not assume that calcium carbonate (in the form of aragonite
or calcite) is in equilibrium with calcium and carbonate ions in
the surrounding water. In fact, the Earth’s oceans are currently
supersaturated with respect to these ions and may become unsaturated in the future.
In a previous article published in this Journal (6), Weston
treats the topic of ocean acidification and its effects on coral
reefs, in the following manner. First, he outlines a detailed
treatment of “carbonic acid equilibria” in pure water. Then, after
establishing the basic concepts, he refers the reader to more ad-
vanced treatments in seawater without elaborating many details.
Readers are referred to a publicly available program (CO2SYS;
ref 7) to carry out more advanced calculations.
In this article, we attempt to fill in the pedagogical gap
between Weston’s elementary and advanced treatments. The
seawater carbonate calculations we present lie between those
two approaches. We treat the effects of seawater salinity and
temperature, and we drop the assumption of solubility equilibrium for CaCO3, in contrast to Weston (6, eq 8). The equations
we present are amenable to simple spreadsheet applications and
are thus less likely to be treated as “black box” calculations by
students.
The essential chemistry is as follows: Dissolved CO2 lowers
the pH of water by dissociating into protons and bicarbonate.
Protons can then react with dissolved carbonate to form more
bicarbonate ion:
H2O CO2 H HCO3
(acidification due to CO2)
H CO32 HCO3
The net effect of CO2 acidification is the sum of the above two
reactions (4):
H2O CO2 CO32
2HCO3
(1)
Thus the level of carbonate ion decreases when dissolved carbon
dioxide increases. At a sufficiently low pH (or high CO2 concentration) the carbonate concentration will drop below the
saturation level of aragonite (CaCO3) and thus cause dissolving
of coral structures. This scenario is most likely to be realized first
in cold arctic surface waters where CO2 is most soluble (4, 5).
As noted by Weston (6), the chemistry of ocean acidification can be used to illustrate the practical utility of many
chemical topics, such as polyprotic acid ionization, buffers
(the Henderson–Hasselbalch equation), effect of pressure on
gas solubility (Henry’s law), and the effect of temperature on
equilibrium constants (Le Châtelier’s principle).
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Chemistry for Everyone
Overview of Relevant Ocean Chemistry
Table 1 lists the concentrations of some of the major chemical species in seawater and is modified from Dickson and Goyet
(8). It should be noted that the pKa values are given for 25 °C
and a salinity of 35‰ (parts per thousand). The pH of ocean
water is near 8.1, and CO2* represents the sum of aqueous CO2
and H2CO3, which are difficult to distinguish experimentally
(6, 8). There are many other chemical species in the ocean as
well, including Na+ and Cl− ions, that do not influence the pH
except through the effects of ionic strength.
The surface of the ocean is expected to drop in pH by at
least 0.1 units in the next 100 years owing to acidification by
CO2 (1). We will assume here that the concentrations of metal
ions will not change appreciably over that pH range. Similarly,
the concentrations of anions from strong acids (Cl−, Br−, etc.)
will be unaffected by pH. What may change are the ratios of
weak acids (HA) to their conjugate bases (A−) according to the
Henderson–Hasselbalch equation,
A
pH pKa log
HA
which can be rearranged to
A
HA 10 pH pK a (2)
Table 1. Concentration of Conjugate Acid–Base Pairs in the Ocean
Acid
Form
(HA)
Conc/
M
Base
Form
(A–)
Conc/
M
Ratio
[A–]/[HA]
pKa
of HA
HSO4–
~0
SO42–
0.02824
∞
0.9989
HF
~0
F–
0.00007
∞
2.519
B(OH)3 0.00032 B(OH)4– 0.00010
0.31
8.597
CO2*
0.00177
177
5.856
0.00026
0.15
8.925
0.00001 HCO3–
Fraction of Conjugate Acid
HCO3– 0.00177 CO32–
HA
mole
fraction HA
HA A
HA
HA HA 10 pH pKa The predicted fraction of the acid form from eq 3 can be plotted,
for different pH, as a function of pKa (Figure 1).
This graph shows that the fraction of HA (and thus the
fraction of A−) will not change much for a 0.1 unit drop in pH,
except for species with pKa values between about 7 and 9. Referring
to Table 1, it therefore appears that only carbonate and borate
species will be affected by a pH lowering of 0.1. Since the total
concentration of borate is lower than the total concentration of
carbonate, we will treat only the latter in what follows. Similarly,
since the concentrations of phosphate and silicate are low in
most of the ocean we will neglect these as well, although they
could be significant in the near-shore environment.
A Simplified Model To Treat Carbonate Chemistry
in the Ocean
We will assume that surface waters reach equilibrium with
atmospheric CO2 (CO2* represents the sum of aqueous CO2
and H2CO3).
CO2(g)
CO2*(aq)
The equilibrium constant for the dissolution of CO2 is called
the Henry’s law constant and is given by
K0 HCO3
0.8
leading to
K1 pH = 8.1
0.4
change in
fraction
of HA
0.2
K2 0.0
6
8
10
12
pK a of Conjugate Acid
Figure 1. Effect of pKa value on conjugate acid–base ratios at pH
8.1 and 8.0.
(4)
PCO2
HCO3 H 1.0
pH = 8.0
CO 2*
where PCO2 is the pressure of CO2 in atmospheres.
The dissolved carbon dioxide in turn undergoes a first and
second acid ionization,
CO2*
0.6
(3)
1
pH pK a 1 10 4
214
Combining eq 2 with [HA] + [A−] = total concentration of A
species results in
Autoionization of water
H2O
CO32 H
H HCO3
CO 2*
H CO32 HCO3
(5)
(6)
H OH
Journal of Chemical Education • Vol. 85 No. 2 February 2008 • www.JCE.DivCHED.org • © Division of Chemical Education Chemistry for Everyone
gives
H OH Kw (7)
And charge balance (i.e., molarity of positive charge equals
molarity of negative charge) may be written as
H cation
ns
HCO3 2 CO32 OH anions
Here, [cations] is the sum of all positive ions whose concentrations do not change with pH. Similarly [anions] is the sum of
all negative ions whose concentrations do not change with pH.
Subtracting [anions] from both sides results in
H
HCO3
net cations where [net cations] is the residual positive charge concentration
after subtracting [anions]. Since both [H+] and [OH−] are small,
we may make the approximation
net caations ¾
HCO3 2 CO32 Using the concentrations in Table 1, the value of [net cations]
is therefore approximately 0.00229 M. This concentration is
assumed to be pH independent so that charge balance may be
finally written as
mol
H 0. 00229
L
(8)
HCO3
2 CO32 OH Equations 4–8 represent a system of five equations with six
unknowns. From these it should be possible to write [CO32−]
as a function of PCO2. However, since this proves to be mathematically difficult, we have chosen instead to express PCO2 as a
function of [CO32−] according to the equations
(9)
PCO2 x 2
where
x b b 2 4 ac
2a
a K 0 K1 K 2
CO32 K0 K1
mol K 0 K1 K 2
b 0. 00229
L
CO32 (11)
1
2
2 K 0 K 1 K 2 CO32 c Kw
1
CO 2*
HCO3
K0 x2
x
H x
(14)
K 0 K1 CO32 (15)
K2
K0 K1 K 2
(16)
CO32 Relationship to Oceanographic Parameters
Oceanographers express inorganic carbon chemistry in
terms of four measurable parameters. These are the pressure of
carbon dioxide (PCO2), pH, total inorganic carbon (CT ), and
alkalinity (A). The measurement of any two can be used to
calculate the remaining two (6, 7). In more careful work the
pressure of CO2 is replaced by the fugacity of CO2, but this is
only a small correction that we disregard (6, 7). Three of the four
oceanographic parameters may also be expressed as functions of
x and [CO32−]:
2
P
CO 2 x
pH log H log x
(9)
K 0 K1 K 2
(17)
CO32 CT (10)
and
2 CO32 OH The effective values of the equilibrium constants (K0, K1, K2
and Kw) are given as functions of temperature (T) and salinity
(S) in the online supplement and are taken from Dickson and
Goyet (8). By using these, it is possible to predict the pressure
of CO2 that corresponds to any chosen carbonate concentration
in seawater at any temperature and salinity.
It is worth noting that other concentrations of interest may
also be expressed as functions of x, as defined in eq 10. Although
these are not directly related to the saturation of calcium carbonate, we list them here for the sake of completeness.
CO 2*
2
K0 x x
HCO3
CO32 K 0 K1 CO32 K2
(18)
CO3
2
The alkalinity (A) may be defined as “the number of moles
of hydrogen ion equivalent to the excess of proton acceptors
(bases formed from weak acids with a dissociation constant K ≤
10‒4.5 at 25 °C and zero ionic strength) over proton donors (acids
with K > 10‒4.5) in one kilogram of sample”(8). In the context of
this model, the alkalinity is essentially the carbon alkalinity:
A HCO3 2 CO32 (12)
(13)
According to eq 1 when 1 mole of CO32− is lost, 2 moles of
HCO3− are gained. This results in no net gain or loss of alkalinity
as a result of acidification of seawater by CO2. Thus we expect A
to remain nearly constant at the current value of 2290 μM.
2
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215
Chemistry for Everyone
Predictions of Carbonate Levels in Seawater
and Other Calculated Results
Carbonate concentrations ranging from zero to 1000 μM
were entered into a spreadsheet column as the independent
variable and the corresponding values of x were determined,
using eqs 10–13. The values of x, in turn, were squared to find
the values of PCO2 (eq 9). Plots were made with concentration of
CO2 in ppm on the horizontal axis and [CO32‒] on the vertical
axis. Figure 2 shows such plots for two different temperatures,
assuming a salinity of 35‰. It is interesting to note that the
concentration of carbonate drops off dramatically in cold
water as the pressure of atmospheric CO2 increases, owing to
the enhanced solubility of CO2 at low temperature (in accord
with Le Châtelier’s principle for an exothermic process). At low
temperatures and high CO2 levels the concentration of carbonate in surface seawater is predicted to fall below the saturation
limit of aragonite (approximately 70 μM carbonate; ref 4)
resulting in the destruction of certain marine organisms (4–6).
Even in tropical regions, where the calcium carbonate remains
supersaturated, the health of coral may still be compromised by
lowered carbonate levels (6).
Further calculations are displayed in Figure 3. The predicted concentrations of carbonate in seawater are plotted versus
latitude for CO2 levels that correspond to pre-industrial (270
ppm), current (370 ppm), and modeled levels for the year 2100
C.E. (563 ppm from S650 model; 788 ppm from IS92a model;
ref 4). Reference 9 was used to estimate the average temperatures
and salinities at latitudes ranging from 60° S to 60° N. Our calculated carbonate concentrations are lower than those predicted
by Orr et al. (4, Figure 1) at polar latitudes (as much as 33%),
and higher near the equator (as much as 23%). Nevertheless we
show the same trends and are in qualitative agreement (average
percent difference of ‒3%). Similar to Orr et al. we find that aragonite (CaCO3) may become unsaturated in the surface waters
of polar regions by the year 2100 AD.
We have also compared our calculations to the Oak Ridge
National Laboratory’s program CO2SYS (7) using the input
parameters summarized in List 1. The output results compare
favorably with our own calculations (eqs 14–18; Table 2). The
Oak Ridge calculations include the effect of borate, while our
calculations do not. In spite of this, the agreement is quite heartening. This helps to justify our original assumption that borate
may be neglected, to a first degree of approximation.
[CO32ź] / (μmol/L)
1000
List 1. Input Options Used in CO2SYS
800
Type of Input
Single Input
600
Choice of constants
Mehrbach et al.
400
Choice of KSO4[sic]
Dickson
Choice of pH scale
Total scale
Total carbon
2030 μM (from Table 1)
Pressure of CO2
360 ppm
Input temperature
20 oC
Salinity
35‰
pre-industrial
(270 ppm)
Input pressure (i.e., depth)
0 (for surface waters)
current
(370 ppm)
[Phosphate]
zero
[Silicate]
zero
298 K
200
0
273 K
0
200
400
600
800
1000
Concentration CO2 / ppm
Figure 2. Effect of temperature (or latitude) on carbonate levels in
seawater.
350
[CO32ź] / (μmol/L)
300
2100 C.E.
(563 ppm)*
250
200
2100 C.E.
(788 ppm)*
150
100
Table 2. Comparison of Results CO2SYS and This Work
50
0
80
60
40
20
0
20
40
60
Latitude / deg
Figure 3. Calculated seawater carbonate concentrations as a function
of latitude for pre-industrial, current, and future scenarios. (The CO2
concentrations are shown in parentheses; the data marked with an
asterisk are from ref 4. Reference 9 was used to associate latitudes with
o
approximate surface temperatures and salinities: 60 = 278 K, 32.5‰;
o
o
o
o
40 = 285 K, 34.3‰; 20 = 298 K, 35.3‰; 0 = 300 K, 35.0‰; –20
o
o
–
–
= 296 K, 35.8‰; 40 = 287 K, 34.8‰; 60 = 274 K, 34.0‰.
216
Parameter
CO2SYS
This Work
[HCO3–]/mM
1819
1836
[CO32–]/mM
199
224
[CO2*]/mM
12
12
Alkalinity (‰)
2310
2290
pH (total scale)
8.085
8.100
Journal of Chemical Education • Vol. 85 No. 2 February 2008 • www.JCE.DivCHED.org • © Division of Chemical Education Chemistry for Everyone
Summary
We have presented a simplified model for dissolved inorganic carbon chemistry in seawater that is adaptable to the classroom and to spreadsheet calculations. The primary application
of this model has been the acidification of surface seawater by
rising CO2 levels. In agreement with oceanographic researchers
we predict that CaCO3 will become less oversaturated or even
unsaturated in the future, resulting in the probable destruction
of calcifying organisms, especially in the Earth’s polar regions.
Literature Cited
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Company: New York, 1999.
2. Langmuir, D. Aqueous Environmental Chemistry; Prentice Hall:
Upper Saddle River, NJ, 1997.
3. Eby, G. N. Principles of Environmental Geochemistry; Thomson
Brooks/Cole: Pacific Grove, CA, 2004.
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R. A.; Gnanadesikan, A.; Gruber, N.; Ishida, A.; Joos, F.; Key,
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Mouchet, A.; Najjar, R. G.; Plattner, G.-K.; Rodgers, K. B.; Sabine, C. L.; Sarmiento, J. L.; Schlitzer, R.; Slater, R. D.; Totterdell,
I. J.; Weirig, M.-F.; Yamanaka, Y.; Yool, A. Nature 2005, 437,
681–686.
5. Doney, Scott C. Scientific American 2006, 58–65.
6. Weston, Ralph E. J. Chem. Educ. 2000, 77, 1574–1577.
7. Lewis, E.; Wallace, D. Program Developed for CO2 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 Nov 2007).
8. 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 Ceter, Oak Ridge National Laboratory, U.S.
Department of Energy: Oak Ridge, TN, 1994.
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An Introduction, 2nd ed.; Daya Publishing House: Delhi, 2003;
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Supporting JCE Online Material
http://www.jce.divched.org/Journal/Issues/2008/Feb/abs213.html
Abstract and keywords
Full text (PDF) with links to cited URLs and JCE articles
Supplement
The effective values of the equilibrium constants (K0, K1, K2, and
Kw), given as functions of temperature (T) and salinity (S)
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