2 Solubility of CO2 and Carbonate Equilibrium KHK1K2CO2(g) ↔ CO2(aq) ↔ H2CO3 ↔ HCO3- ↔ CO32-1. KH = [H2CO3]/PCO2 = 3 x 10-2 M atm-1 = M atm-12. K1 = [HCO3-][H+]/[H2CO3] = 9 x 10-7 M = M3. K2 = [CO32-][H+]/[HCO3-] = 4.5 x M = M4. Kw = [H+][OH-] = M2Note: Values of these equil. constants are sensitive to temperature and ionic strength of the solution; these values are appropriate to seawater.
3 CO2 Partitioning Atmosphere - Ocean pH of Natural WatersSo we want to understand what controls pH…KKC Box Fig. 8-2
4 pH of Natural Waters General concept… At least six unknowns:H+, OH-PCO2H2CO3, HCO3-, CO32-\ Need at least six equations:Equilibrium expressions 1 - 4Typically, constraint on either PCO2 (“open system”) or total moles carbon (“closed system”)Charge balance; Sn[in+] = Sm[jm-]
5 pH of Natural Waters Pure water in contact with atmosphere Six unknownsEquilibrium expressions (4 equations)PCO2 = 3.5 x 10-4 atm (1 more equation)Charge balance (6th equation):[H+] = [HCO3-] + 2[CO32-] + [OH-]Strategy: Rewrite charge balance equation in terms of [H+] and known quantities…
6 pH of Natural Waters Example: Pure water in contact with atmosphere [H+] = K1KHPCO2/[H+] + 2K1K2KHPCO2/[H+]2 + Kw/[H+]Can solve rigorously for [H+]. Alternatively, make a simplifying assumption:[CO32-] << [HCO3-]In this case:[H+] = K1KHPCO2/[H+] + Kw/[H+]or[H+]2 = K1KHPCO2 + KwThis is easily solved:For pure K1 = 4.45 x 10-7 M; KH = 3.39 x 10-2 M/atm\ [H+] = 2.4 x 10-6 MpH = 5.62\ “Acid rain” is a term applied to pH < 5
7 pH of Natural Waters Assess simplifying assumption… Is it fair to assume [CO32-] << [HCO3-]?K2 = [CO32-][H+]/[HCO3-] = (pure water, 25°C)So: [CO32-]/[HCO3-] = /[H+]Clearly, [CO32-]/[HCO3-] << 1 as long as [H+] >>i.e., as long as pH << 10.33This is true in most natural waters
8 pH of Natural Waters Alkalinity Consider charge balance:[H+] = [HCO3-] + 2[CO32-] + [OH-]By definition, at pH = 7, [H+] = [OH-]So, if [HCO3-] or [CO32-] are at all comparable to [OH], [OH-] must be less than [H+].This would imply pH < 7, not pH > 7.So how does this work… How do we get pH > 7???Must add cations…
9 pH of Natural Waters Alkalinity Imagine we dissolve some CaCO3 in the systemNow: 2[Ca2+] + [H+] = [HCO3-] + 2[CO32-] + [OH-]In this case, [H+] is free to have lower values (pH > 7) as long as [Ca2+] is present
11 CO2 Dissolution, HCO3- and CO32- PCO2 = K3[HCO3-]2/[CO32-]This is the equilibrium expression for the reaction:CO2 + CO32- + H2O ↔ 2HCO3-i.e., dissolution of CO2 consumes CO32-, produces HCO3-;Note that dissolution of CO2 itself does not affect Alkalinity(gain 2 moles HCO3- for every CO32-)Note also that capacity for CO2 uptake determined by [CO32-]
12 CO2 Dissolution, HCO3- and CO32- Another perspectiveCO2 + H2O ↔ H2CO3H2CO3 H+ + HCO3- Net direction if pH >~ 6H+ + CO32- HCO3- Net direction if pH <~ 10CO2 + CO32- + H2O 2HCO3-
13 CO2 Dissolution, HCO3- and CO32- Alk ~ [HCO3-] + 2[CO32-]ΣCO2 = [H2CO3] + [HCO3-] + [CO32-]~ [HCO3-] + [CO32-]PCO2 = K3[HCO3-]2/[CO32-]Algebra…[CO32-] = Alk - ΣCO2[HCO3-] = 2 ΣCO2 - AlkPCO = K3(2 ΣCO2 - Alk)2/(Alk - ΣCO2)i.e., PCO2 is controlled by Alk and ΣCO2
14 CO32- in Ocean Today: [CO32-] ~ 1/50 [HCO3-] Didn’t we say [HCO3-] >> [CO32-]?Yes, but that doesn’t mean CO32- is irrelevant:Figure 11-3 Distribution of dissolved carbon species in seawater as a function of pH. Average oceanic pH is about The distribution is calculated for temperature of 15oC and a salinity of 35‰. The equilibrium constants are from Mehrbach et al. (1973).Today: [CO32-] ~ 1/50 [HCO3-]As long as there is excess CO32-, ocean can take up CO2 without change in alkalinity (or pH).
15 2CaCO3 + 2H+ + SO4= 2Ca + + + SO4= + 2HCO3- * Reactions are quite congruent, structure not attacked; simple reactions.* Acid Precipitation:2CaCO3 + 2H+ + SO4= 2Ca SO4= + 2HCO3-* There are natural acidsie. In rain CO2 in the atmosphere (pH = 5.6)CO2 + H2O H2CO3 H + + HCO3-PCO2 ~ 350 ppm pH = 5.6* Rate of carbonate weathering is about 100 times the rate of silicate weathering.ie. Florida- formation of karst due to the dissolving of calcite- wouldn't see that with silica.
16 pH of Natural Waters Alkalinity Not all cation sources will work this way…Imagine we dissolve some NaCl into the systemNow: [Na+] + [H+] = [HCO3-] + 2[CO32-] + [Cl-] + [OH-]But: [Na+] = [Cl-], right?So, no effect on charge balance equationTo cope: Distinguish between “conservative” and “nonconservative” ions…
17 pH of Natural Waters Alkalinity Conservative ions: Ions whose concentrations are not affected by pH (or pressure or temperature; not important variables here)Examples: Ca2+, Na+, NO3-, K+, Cl-, etc.Nonconservative ions: Ions whose concentrations are affected by pHExamples: CO32-, HCO3-, NH4+, B(OH)4-, H+, OH-“Alkalinity” ≡ Sn[in+] - Sm[jm-] where i and j are only conservative ions; alkalinity is what’s left over after these are accounted for.Units: equiv./liter
18 pH of Natural Waters Alkalinity If we consider only HCO3-, CO32-, OH- and H+ and conservative ions, then we may write:Sn[in+] + [H+] = [HCO3-] + 2[CO32-] + [OH-] + Sm[jm-]Sn[in+] - Sm[jm-] = [HCO3-] + 2[CO32-] + [OH-] - [H+]Alkalinity = [HCO3-] + 2[CO32-] + [OH-] - [H+]Typically, Alkalinity ~ [HCO3-] + 2[CO32-] ≡ AlkcarbFor seawater, Alkalinity ~ 2.3 x 10-3 equiv/liter
19 pH of Natural Waters Alkalinity Alkalinity of seawater allows it to dissolve more CO2Higher alkalinity leads to lower [H+] and higher pHAny reaction that introduces [H+] lowers alkalinitye.g., NH4+ + 2O2 → NO3- + H2O + 2H+Any reaction that raises [CO32-] or [HCO3-] raises alkalinity– e.g., CaCO3 + H2O + CO2 → Ca2+ + 2HCO3-
20 Distribution of major species of dissolved inorganic carbon at 20oC Figure 9.1 Fetter, Applied Hydrogeology 4th Edition
21 Organic acids (e.g.. Oxalic acid) * Organic material breaks down and releases acids ( pH ~ 5 ). These natural acids play an important role in weathering in absence of human activity; behaves very much like carbonic acid4H2C2O4 (oxalic acid) + 2O2 8CO2 + 4H2OH2CO3- -
22 Calcite reacting to acid Carbonate Weatheringlarge amounts of calcite is the reason, in general, why places such as Rochester and the Mid-Eastern states don't have problems with acid rain.Problem of acid rain: Determined basically by the presence of absence of calcite- Tells how sensitive an area will be to acid.Calcite reacting to acidSimplified reactions (removes H+ ions)CaCO3 + H2CO3 Ca++ + 2HCO3- pH ~ of water with bicarbonate; about neutral(Calcite) (Carbonic acid) (bicarbonate)
23 Distribution of major species of dissolved inorganic carbon at 20oC Figure 9.1 Fetter, Applied Hydrogeology 4th Edition
24 Concentration of calcium in equilibrium with calcite as a function of PC02 in the system of CaCO3-CO2-H20 at 25oC and 1 atm total pressure.Figure 3-4. Drever, The Geochemistry of Natural Waters
25 Concentration of calcium in equilibrium with calcite as a function PC02 and Na+ concentration in the system of CaCO3- Na2CO3-CO2-H20 at 25oC and 1 atm total pressure.Concentration of calcium in equilibrium with calcite as a function PC02 and Cl- concentration in the system of CaCO3- CaCl2-CO2-H20 at 25oC and 1 atm total pressure.Figure 3-5,6. Drever, The Geochemistry of Natural Waters
26 Changes in composition of carbonated water as it equilibrates with calcite when the system is either open or closed to exchange of CO2 gas. Initial PC02 values of 10-2 and 10-1 atm.Figure 3-8. Drever, The Geochemistry of Natural Waters