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Open vs. Closed Carbonate System

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Equilibrium thermodynamics and speciation calculations of an open and closed H2O-CO2 system.

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Open vs. Closed Carbonate System

  1. 1. H2O + CO2 Open vs. Closed System aqion.de
  2. 2. Prelude1 Pure CO2 System2 Pure CO2 System + Acid/Base3
  3. 3. Prelude (Concepts & Notation) Part 1
  4. 4. CO2(g) closed system open system H2CO3 * HCO3 - CO3 -2 OH- H+ H2CO3 * HCO3 - CO3 -2 OH- H+
  5. 5. H2CO3 * HCO3 - CO3 -2 OH- H+ CO2(g) Open System 6Species H2CO3 * Composite Carbonic Acid = + = CO2CO2(aq) H2CO3 dissolved CO2 True Carbonic Acid KH abbreviation (used in PhreeqC)
  6. 6. Open System Composite Carbonic Acid {H2CO3 *} = KH ∙ PCO2 Henry’s Law CO2 Partial Pressure KH = 10-1.47 Matm-1 (at 25°C) H2CO3 * HCO3 - CO3 -2 OH- H+ CO2(g) 6Species KH
  7. 7. Three Uncharged Species (Notation !) {CO2} = {H2CO3 *} = KH ∙ 10-pCO2 Henry’s Law CO2 partial pressure CO2(g) CO2 in gas phase CO2(aq) dissolved CO2 (part of H2CO3 *) CO2 composite carbonic acid (H2CO3 *) log {CO2} = log KH – pCO2 PCO2 = 10-pCO2 curly braces {...} denote activities (i.e. effective concentrations)
  8. 8. Pure Water in Contact with Atmosphere Henry’s Law composite carbonic acid: (at 25°C) log {CO2} = log KH – pCO2 {CO2} = {H2CO3 *} = 0.013 mM CO2 Partial pressure PCO2 = 10-pCO2 = 0.00039 atm log {CO2} = – 1.47 – 3.408 = – 4.878 [ N.B. In this dilute system: activities = molar concentrations ]
  9. 9. The Pure CO2 System (Equilibrium Speciation) Part 2
  10. 10. Equilibrium Thermodynamics CO2(g) H2CO3 * KH K1 H2O K2 Kw Kw H+ HCO3 - H+ CO3 -2 CO2(g)  H2CO3 * log KH = -1.47 H2CO3 *  H+ + HCO3 - log K1 = -6.35 HCO3 -  H+ + CO3 -2 log K2 = -10.33 H2O  H+ + OH- log Kw = -14.0 equilibrium constants (at 25°C) Law of Mass Action 4 equations
  11. 11. Equilibrium Thermodynamics KH = {H2CO3 *} / PCO2 = 10-1.47 K1 = {H+} {HCO3 -} / {H2CO3 *} = 10-6.35 K2 = {H+} {CO3 -2} / {HCO3 -} = 10-10.33 Kw = {H+} {OH-} = 10-14.0 CT = [CO3 -2] + [HCO3 -] + [CO2] (Mass Balance) 0 = [H+] – [HCO3 -] – 2 [CO3 -2] – [OH-] (Charge Balance) Law of Mass Action closedsystem opensystem CO2(g) H2CO3 * KH K1 H2O K2 Kw Kw H+ HCO3 - H+ CO3 -2 6 unknowns  6 equations
  12. 12. KH = {H2CO3 *} / PCO2 = 10-1.47 K1 = {H+} {HCO3 -} / {H2CO3 *} = 10-6.35 K2 = {H+} {CO3 -2} / {HCO3 -} = 10-10.33 Kw = {H+} {OH-} = 10-14.0 CT = [CO3 -2] + [HCO3 -] + [CO2] Mass Balance 0 = [H+] – [HCO3 -] – 2 [CO3 -2] – [OH-] Charge Balance Law of Mass Action Equilibrium Thermodynamics ion activities {i} molar concentrations [i]
  13. 13. Open CO2 System Closed CO2 System Given (Input) pCO2 DIC Calculate (Output)  pH  carb. speciation  DIC  pH  carb. speciation  pCO2 DIC = [CO2] + [HCO3 -] + [CO3 -2] pCO2 = – log KH – log {CO2} In an open system you set pCO2; in a closed system you set DIC. You cannot set both values independently.
  14. 14. Equilibrium Speciation Example Calculations (with PhreeqC)
  15. 15. Equilibrium Speciation at 25 °C H2O + 1 mM DIC open system closed system input pCO2 = 3.408 DIC = 1 mM pH 5.61 4.68 CO2 mM 0.0133 0.979 HCO3 - mM 0.0024 0.021 CO3 -2 mM 4.7·10-8 4.8·10-8 DIC mM 0.0157 1.000 pCO2 3.408 1.54 CO2 abbreviates the composite carbonic acid: H2CO3 * = CO2(aq) + H2CO3 = CO2 + HCO3 - + CO3 -2 H2O in contact with atmosphere (PCO2 = 0.00039 atm = 10-pCO2) = H2CO3 * = – 1.47 – log CO2 (in M)
  16. 16. A closed system with 0.0157 mM DIC mimics an open CO2 system in contact with atmosphere. An open CO2 system with pCO2 = 1.54 mimics an closed system with 1 mM DIC. typical for groundwater (enhanced CO2 emerges from degradation of organic matter) In an open system you set pCO2; in a closed system you set DIC. You cannot set both values independently. However, you can outmaneuver this concept:
  17. 17. But this is only half the story, and the less important half. The concept of open/closed systems becomes especially relevant when the solution is attacked by acids or bases: In a open system the CO2 (or pCO2 value) remains constant, while in a closed system DIC remains constant (and CO2 changes).
  18. 18. CO2 System + Acid/Base (Titration Calculations) Part 3
  19. 19. For a given value of DIC, say 1 mM, the pH is fixed to 4.68. There is no chance to alter pH unless the pure CO2 system is attacked by HCl (to decrease pH) or NaOH (to increase pH). H2O + 1 mM DIC HCl pH  1 H2O + 1 mM DIC NaOH pH  14
  20. 20. pH Dependence Titration Calculations (with PhreeqC)
  21. 21. NaOH HCl Closed CO2-System + HCl or NaOH Note: Na forms aqueous complexes H2O + 1 mM DIC
  22. 22. Closed CO2-System + HCl or NaOH H2O + 1 mM DIC (pure system) pH HCl NaOH DIC CO2 HCO3- CO3-2 NaHCO3 NaCO3- I Alk mM mM mM mM mM mM mM mM mM mM 1 122.38 1 1 5.9E-06 5.9E-15 122.38 -122.38 2 10.99 1 1 4.8E-05 2.9E-13 10.99 -10.99 3 1.035 1 0.999 4.6E-04 2.4E-11 1.035 -1.035 4 0.097 1 0.996 4.5E-03 2.2E-09 0.101 -0.10 4.5 0.018 1 0.986 0.014 2.1E-08 0.032 -0.02 4.68 0 0 1 0.979 0.021 7.8E-08 0.021 0 5 0.033 1 0.957 0.043 2.1E-07 7.8E-07 1.2E-11 0.033 0.03 6 0.311 1 0.688 0.312 1.6E-05 5.3E-05 8.3E-08 0.31 0.31 7 0.822 1 0.172 0.821 4.3E-04 3.6E-04 5.7E-06 0.82 0.82 8 0.985 1 0.021 0.973 5.1E-03 5.0E-04 8.1E-05 0.99 0.99 9 1.059 1 2.10E-03 0.947 0.050 5.2E-04 8.4E-04 1.06 1.06 10 1.46 1 1.40E-04 0.644 0.347 4.8E-04 7.8E-03 1.46 1.46 11 2.93 1 3.00E-06 0.144 0.821 2.1E-04 0.034 2.93 2.93 12 13.2 1 2.60E-08 0.013 0.855 7.6E-04 0.132 13.2 13.2 13 137.2 1 8.70E-11 5.1E-04 0.530 2.3E-05 0.469 137.2 137.2 14 1745 1 7.40E-14 7.4E-06 0.139 2.3E-06 0.861 1745 1745 ionic strength
  23. 23. There are several types of graphical display (linear or log scale, XY plots, stacked-area charts, etc.)
  24. 24. linear scale logarithmic scale ClosedCO2-System(1mMDIC)
  25. 25. Closed CO2-System: Speciation = f(pH) In this (symmetric) form it enters a lot of textbooks. add together both curves
  26. 26. linear scale logarithmic scale ClosedCO2-System(1mMDIC)
  27. 27. XY chart stacked- area chart ClosedCO2-System(1mMDIC)
  28. 28. 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 mM pH HCO3- CO3-2 CO2 NaHCO3 NaCO3- Closed CO2-System: Mass Balance DIC = CO2 + HCO3 - + CO3 -2 + NaHCO3 + NaCO3 - = 1 mM stacked-areachart
  29. 29. Equivalence Points[H+] = [HCO3 -] Species Distribution CT = 10-4 M CT = 10-3 M
  30. 30. ... and now the Open System (which is quite different)
  31. 31. pH NaOH HCl Open CO2-System + HCl or NaOH pure H2O-CO2 system
  32. 32. Open CO2-System + HCl or NaOH pure CO2-H2O system pH HCl NaOH DIC CO2 HCO3- CO3-2 I Alk mM mM mM mM mM mM mM mM 1 122.38 0.0129 0.0129 7.6E-08 7.6E-17 122.4 -122.38 2 10.99 0.0133 0.0133 6.5E-07 4.2E-15 10.99 -10.99 3 1.035 0.0133 0.0133 6.1E-06 3.2E-13 1.035 -1.035 4 0.101 0.0134 0.0133 6.0E-05 2.9E-11 0.101 -0.10 5 0.009 0.0139 0.0133 0.001 2.9E-09 0.010 -0.01 5.3 0.0037 0.0145 0.0133 0.001 1.2E-08 0.005 -0.001 5.61 0 0 0.0157 0.0133 0.002 4.7E-08 0.002 0 5.7 0.001 0.0162 0.0133 0.003 6.8E-08 0.003 0.001 6 0.004 0.0183 0.0133 0.005 2.0E-07 0.005 0.005 6.5 0.009 0.0228 0.0133 0.010 7.3E-07 0.010 0.01 7 0.013 0.0266 0.0133 0.013 0 0.013 0.01 8 0.017 0.0301 0.0133 0.017 0 0.017 0.02 9 0.027 0.0400 0.0133 0.027 0 0.027 0.03 9.5 0.050 0.0631 0.0133 0.050 0 0.050 0.05 10 0.122 0.1353 0.0133 0.122 0 0.123 0.12 ionic strength There is no DIC conservation ! DIC grows exponentially for pH > 5.6
  33. 33. linear scale logarithmic scale OpenCO2-System(pCO2=3.408)
  34. 34. CO2 System Conserved quantity Open CO2 (or pCO2) Closed DIC Titration Calculations:
  35. 35. www.aqion.de/site/161 (EN) www.aqion.de/site/156 (DE) Ref

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