Soil Chemistry 5-1 CARBONATE EQUILIBRIA Carbonates are arguably the most important dissolved component of soil solutions and in alkaline soils this statement is even less disputable. Implicit in this statement is the relationship among dissolved carbonate species whether or not they are in equilibrium with solid phase metal carbonates. The simplest example of carbonates is the control which dissolved carbon dioxide has on water pH and buffering. In this section of the course we will consider the effect of carbon dioxide on water pH, the influence of solid phase calcium carbonate on solution composition and the implications of these reactions. Several systems including carbon dioxide, solution and solid phase carbonates can be envisioned. Some of these include (after Garrels and Christ, 1967). 1. The solution pH of water in equilibrium with carbon dioxide and essentially devoid of other controlling species. 2. The reaction of calcium carbonate saturated solutions with free access to carbon dioxide. In essence this is the equilibrium of lime with air or soil air. Also referred to as an open system with solid phase present. This case is of considerable interest as it represents the relationship of dilute natural waters in contact with the atmosphere and system control only by the carbonate equilibria. 3. The reactions of calcium carbonate with water where the gas phase is restricted or negligible. This condition is not common, but in situations were the equilibrium system has little head space and the mixing of air is restricted the attendant pH and slow rate of return to equilibrium is of interest. This is the famous "Turner Effect". Such as system is also referred to as a closed system since mass is not transferred or exchanged with the surroundings. 4. Equilibrium in systems with a fixed quantity of added alkalinity such as the addition of strong base to a system open to the atmosphere. Other cases can be considered, however these serve to illustrate the great utility of being able to understand the equilbrium behavior of carbonate species in soils and sediments. Section 5- Carbonate Chemistry Soil Chemistry 5-2 CASE 1 CO2 - H2O open system Aqueous carbon dioxide reacts to form carbonic acid via the following reaction: CO2 (aq)3 + H2O ® H 2CO H 2CO 3 = 10 -2.8 = 0.00159 CO 2 (aq) The hydration of carbon dioxide is slow to attain equilibrium below pH 8 in pure systems. However, above pH 11, the hydration reaction is relatively rapid as carbon dioxide reacts directly with hydroxide to form bicarbonate. - - CO2 (aq) + OH = HCO3 (1) In biological systems the hydration of carbon dioxide is catalyzed by carbonic anhydrase a Zn-containing * enzyme. Only a small portion of the aqueous carbon dioxide exists as carbonic acid. However, in most H2CO3 (as defined below) is used to represent solution carbonates. * H 2 CO3 = H 2CO3 + CO2(aq) (2) * Where H2CO3 is the total dissolved cabon including aqueous carbon dioxide. Carbonic acid dissociates into bicarbonate and carbonate according to the following equations: + - ( H ) (HCO3 ) o - 6.4 = K H 2CO3 = 10 (3) ( H 2CO3 ) * where H2CO3 = H2CO3 + CO2 (aq) = H2CO3 o -4 Note that K H2CO3 = 2*10 or pK = 3.69 if corrected for CO2(aq) Section 5- Carbonate Chemistry Soil Chemistry 5-3 + 2- ( H ) (CO3 ) o - 10.3 = - = (4) - K HCO 3 10 ( HCO3 ) As for every aqueous reaction the acid base relationship between the proton and hydroxide is an important relationship. + - (H ) ()OH o - 14 = KW = 10 (5) ( H2O ) Starting with the electrical neutrality expression: + -- 2- [ H ] = [ OH ] + [ HCO3 ] + 2 [ CO 3 ] (6) The system is manipulated to collect terms in the variables of interest - hydrogen ion concentration and carbon dioxide partial pressure. Note that the electrical neutrality expression is defined in terms of concentrations (mol/L). Therefore, in order to utilize values from the thermodynamic equilibrium expressions, the conditional equilibrium constants must be used which relate concentrations rather than activities to the ionic distributions at equilibrium. Defining OH - in terms of H + yields: c KW [OH - ] = (7) [ H + ] - Solving for HCO3 gives: c [ ] - KHH 2CO 3 2 CO3 [HCO 3 ] = (8) []H + Finding carbonate via bicarbonate: c - K - [HCO 3 ] 2 - HCO3 [CO 3 ] = []H + (9) Section 5- Carbonate Chemistry Soil Chemistry 5-4 cc [] KH 2CO3 KH- 2 CO 3 - 2 - HCO3 Substituting for HCO33 : [CO ] = (10) [ H + ] 2 + The rewritten electrical neutrality expression in terms of H and H2CO3 is: c c cc æö - [2 3 ] æöK W æöKHH 2CO33 []2CO 3 KKHH 2CO3 HCO CO [ + ] = + + 2 (11) H ç÷++ç÷ç÷+ 2 èø[HH]èø[] èø[ H ] + 2 Rearranging, multiplying by (H ) and substituting kH * PCO2 for H2CO3 yields: + 3 c+c+cc [] - W [ ] - [] HH - 2 - = 0 HKHKHH22CO3HkkPCO2KCO32KPHCO3 CO (12) + 3 +cccc [] - [] w + HH - 2 - = 0 HHK( KHH22CO3kkPCO2) KCO32KPHCO3 CO We are left with a polynomial equation in [H+]. In this formulation the only variables are (H+) and PCO2. If a known and constant value for the partial pressure of carbon dioxide is inserted into the above equation, (H+) can be found by a variety of numerical techniques. Henry's Law Constant for this reaction is strongly influenced by temperature and slightly affected by ionic strength. o Salt Level kH@ 298K Log kK 0.2 M NaCl 0.0328 -1.48 0.5 M NaCl 0.0304 -1.57 1.0 M NaCl 0.0273 -1.56 o Temp K kH @ 0.2 M NaCl Log kH @ 0.2 M NaCl 273 Ko 0.073 -1.13 278 Ko 0.061 -1.21 283 Ko 0.051 -1.29 288 Ko 0.043 -1.36 293 Ko 0.037 -1.47 298 Ko 0.033 -1.48 308 Ko 0.026 -1.58 Section 5- Carbonate Chemistry Soil Chemistry 5-5 Dissolved carbon is distributed among three species H2CO3, HCO3 and CO3 as a function of pH. In soil systems where there may be an external (to the carbonate system) control on pH it would be handy to know the distribution of the carbonate species given pH. This distribution of carbonate species can be derived from the Henderson-Hasslebach relationship knowing pH and pK’s. A slightly different approach is shown next. Assume : CT = the sum of all carbonate species concentration activity coefficients are neglected or equal to one. + 2 + define z as: z = (H ) + (H ) KH2CO3 + KH2CO3 KHCO3 or more generally as: + 2 + z = (H ) + (H ) K1 + K1 K2 where K1 and K2 are the first and second dissociation constants for the acid. then: +2 [ H2CO 3 ][ H ] = (13) CZT - + [HCO3 ][HK ] 1 = (14) CZT []HCOKK 23= 12 (15) CZT Figure 5.1. The distribution of carbonate species as a fraction of total dissolved carbonate in relation to solution pH. 1.00 ) T 0.75 / C 3 2- CO CO3 0.50 H2CO3 - 2-n HCO3 0.25 = ( H n a pK pK 0.00 1 2 2 4 6 8 10 12 14 Solution pH Section 5- Carbonate Chemistry Soil Chemistry 5-6 Figure 5.2. The activity of carbonate species in relation to pH for a carbon dioxide level of 10-3.5 atmospheres. 2 P = 10-3.5 0 co2 - HCO3 -2 o H2CO3 -4 -6 2- CO3 -8 Log activity of carbonate species -10 4 6 8 10 12 pH Section 5- Carbonate Chemistry Soil Chemistry 5-7 Figure 5.3 . The activity of carbonate species in relation to pH for a carbon dioxide level of 1 atmosphere. 2 Pco2 = 1 atm 0 -2 o -4 H2CO3 - HCO3 -6 2- -8 CO3 Log activity of carbonate species -10 4 6 8 10 12 pH Equilibrium Reactions in the CO2-H2O system. Reaction No. Equilibrium Reaction Log Ko o 1. CO2(g) + H2O W H2CO3 - 1.46 o + - 2. H2CO3 W H + HCO3 - 6.36 - + 2- 3. HCO3 W H + CO3 - 10.33 + - 4. CO2(g) + H2O W H + HCO3 - 7.82 + 2- 5. CO2(g) + H2O W 2 H + CO3 - 18.15 Section 5- Carbonate Chemistry Soil Chemistry 5-8 Figure 5.4 Effect of carbon dioxide partial pressure on the solution concentration of carbonate species in the CO2-water system. 0 H CO -2 2 3 -4 H+ -6 - + - HCO3 & H -8 HCO3 - Log C -10 -12 2- CO3 -14 -16 10 8 6 4 2 0 - Log P CO2 ALKALINITY Examination of Figure 5.4 indicates that as the carbon dioxide partial pressure goes to zero, the solution pH approaches 7 and increasing pressures of carbon dioxide cause the system to be acidic. Therefore, in the CO2- water system there is never a net excess of base. The system can neutralize added base, but can not neutralize added acid. Another way of saying the same thing is to state that the system do not contain any alkalinity. Alkalinity is an important concept in solution chemistry and relates to the acid neutralization capacity of solutions. The definition of alkalinity for the CO2-water system is: --2-+ Alkalinity=[OH]+[HCO33]+-2[]COH[] (16) In the CO2 -water system the electrical neutrality condition for the system is: +---2 [H]=[OH]++[]HCO332[]CO (17) Substituting the electrical neutrality equation into the alkalinity definition : Section 5- Carbonate Chemistry Soil Chemistry 5-9 --22---- Alkalinity=[OH]+[HCO3]+2[CO3]-[OH]--[HCO33]2[]CO (18) Therefore, there is no alkalinity in a CO2-water system, unless other sources of base are added. Case 2. CaCO3 -CO2-H2O system Calcium carbonate in water with a fixed partial pressure of carbon dioxide. For the case of a fixed partial pressure of carbon dioxide and calcium carbonate dissolved in the aqueous phase one more equation is need to describe the system.