Slide 1SPECIATION IN OPEN CO2-H2O SYSTEMS - ISPECIATION IN OPEN CO2-H2O SYSTEMS - IISPECIATION IN OPEN CO2-H2O SYSTEMS - IIISPECIATION IN OPEN CO2-H2O SYSTEMS - IVSlide 6Slide 7Methods of solving equations that are ‘linked’Calcite SolubilityCharge BalanceUsing Keq to define equilibrium concentrationsSpeciationHow do we know about all those species??Aqueous ComplexesDefining ComplexesMass Action & Mass BalanceMineral dissolution/precipitationINCONGRUENT DISSOLUTIONACTIVITY DIAGRAMS: THE K2O-Al2O3-SiO2-H2O SYSTEMSlide 20Slide 21pH0 2 4 6 8 10 12 14log ai-8-7-6-5-4-3-26.3510.33H2CO3* HCO3-CO32-H+OH-Common pHrange in natureBjerrum plot showing the activities of inorganic carbon species as a function of pH for a value of total inorganic carbon of 10-3 mol L-1.In most natural waters, bicarbonate is the dominant carbonate species!SPECIATION IN OPEN CO2-H2O SYSTEMS - I•In an open system, the system is in contact with its surroundings and components such as CO2 can migrate in and out of the system. Therefore, the total carbonate concentration will not be constant.•Let us consider a natural water open to the atmosphere, for which pCO2 = 10-3.5 atm. We can calculate the concentration of H2CO3* directly from KCO2:Note that M H2CO3* is independent of pH!2322*COCOHCOpMK 2232* COCOCOHKpM 2232logloglog* COCOCOHKpM SPECIATION IN OPEN CO2-H2O SYSTEMS - II•The concentration of HCO3- as a function of pH is next calculated from K1: but we have already calculated M H2CO3*:so2232* COCOCOHKpM *1323COHHHCOMaMKHCOHHCOaMKM*1323HCOCOHCOapKKM2231 pHpKKMCOCOHCO2231loglogSPECIATION IN OPEN CO2-H2O SYSTEMS - III•The concentration of CO32- as a function of pH is next calculated from K2: but we have already calculated M HCO3- so:andHCOCOHCOapKKM22313232HCOHCOMaMKHHCOCOaMKM32322122223HCOCOCOapKKKM pHpKKKMCOCOCO2loglog222312SPECIATION IN OPEN CO2-H2O SYSTEMS - IV•The total concentration of carbonate CT is obtained by summing:23332*COHCOCOHTMMMC2211222222HCOCOHCOCOCOCOTaKpKKaKpKKpC22111loglog22HHCOCOTaKKaKKpCpH2 3 4 5 6 7 8 9 10 11 12log concentration (molar)-8-6-4-20CTH+OH-H2CO3*HCO3-CO32-pK1pK2Plot of log concentrations of inorganic carbon species H+ and OH-, for open-system conditions with a fixed pCO2 = 10-3.5 atm.pH2 3 4 5 6 7 8 9 10 11 12log concentration (molar)-8-6-4-20CTH+OH-H2CO3*HCO3-CO32-pK1pK2Plot of log concentrations of inorganic carbon species H+ and OH-, for open-system conditions with a fixed pCO2 = 10-2.0 atm.Methods of solving equations that are ‘linked’•Sequential (stepwise) or simultaneous methods•Sequential – assume rxns reach equilibrium in sequence:•0.1 moles H3PO4 in water:–H3PO4 = H+ + H2PO42-pK=2.1–[H3PO4]=0.1-x , [H+]=[HPO42-]=x–Apply mass action: K=10-2.1=[H+][HPO42-] / [H3PO4]–Substitute x  x2 / (0.1 – x) = 0.0079  x2+0.0079x-0.00079 = 0, solve via quadratic equation–x=0.024  pH would be 1.61•Next solve for H2PO42-=H+ + HPO4-…Calcite Solubility•CaCO3 -> Ca2+ + CO32- log K=8.48•We consider minerals to dissolve so that 1 Ca2+ dissolves with 1 CO32-•If dissolving into dilute water (effectively no Ca2+ or CO32- present): x2=10-8.48, x= aCa2+ = aCO32-•If controlled by atmospheric CO2, substitute CO32- for expression •What happens in real natural waters?? pHpKKKMCOCOCO2loglog222312Charge Balance•Principle of electroneutrality  For any solution, the total charge of positively charged ions will equal the total charge of negatively charged ions.–Net charge for any solution must = 0•Charge Balance Error (CBE)–Tells you how far off the analyses are (greater than 5% is not good, greater than 10% is terrible…)•Models adjust concentration of an anion or cation to make the charges balance before each iteration!  aaccaacczmzmzmzmCBEUsing Keq to define equilibrium concentrationsG0R = -RT ln Keq•Keq sets the amount of ions present relative to one another for any equilibrium conditioninineqreactantsproductsQK][][AT EquilibriuminineqreactantsproductsK][][Speciation•Any element exists in a solution, solid, or gas as 1 to n ions, molecules, or solids•Example: Ca2+ can exist in solution as: Ca++ CaCl+ CaNO3+ Ca(H3SiO4)2 CaF+ CaOH+ Ca(O-phth) CaH2SiO4 CaPO4- CaB(OH)4+ CaH3SiO4+ CaSO4 CaCH3COO+ CaHCO3+ CaHPO40 CaCO30•Plus more species  gases and minerals!!How do we know about all those species??•Based on complexation  how any ion interacts with another ion to form a molecule, or complex (many of these are still in solution)•Yet we do not measure how much CaNO3+, CaF+, or CaPO4- there is in a particular water sample•We measure Ca2+  But is that Ca2+ really how the Ca exists in a water??Aqueous Complexes•Why do we care??1. Complexation of an ion also occuring in a mineral increases solubility2. Some elements occur as complexes more commonly than as free ions3. Adsorption of elements greatly determined by the complex it resides in4. Toxicity/ bioavailability of elements depends on the complexationDefining Complexes•Use equilibrium expressions:G0R = -RT ln Keq•cC + lHL  CL + lH+•Where B is just like Keq!)reactants()(000iiiiiiRGnproductsGnGlcnciHLCHCL][][][][Mass Action & Mass Balance•mCa2+=mCa2++MCaCl+ + mCaCl20 + CaCL3- + CaHCO3+ + CaCO30 + CaF+ + CaSO40 + CaHSO4+ + CaOH+ +…•Final equation to solve the problem sees the mass action for each complex substituted into the mass balance equationlcnciHLCHCL][][][][nxLmCamCa22Mineral dissolution/precipitation•To determine whether or not a water is saturated with an aluminosilicate such as K-feldspar, we could write a dissolution reaction such as:•KAlSi3O8 + 4H+ + 4H2O  K+ + Al3+ + 3H4SiO40•We could then determine the equilibrium constant:•from Gibbs free energies of formation. The IAP could then be determined from a water analysis, and the saturation index calculated.43443HSiOHAlKaaaaKINCONGRUENT DISSOLUTION•Aluminosilicate minerals usually dissolve incongruently, e.g., 2KAlSi3O8 + 2H+ + 9H2O  Al2Si2O5(OH)4 + 2K+ + 4H4SiO40•As a result of these factors, relations among solutions and aluminosilicate minerals are often depicted graphically on a type of mineral stability diagram called