Bjerrum 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 2 Common pH range in nature 6 35 H2CO3 3 HCO3 10 33 2 CO3 log ai 4 OH 5 H 6 7 8 0 2 4 6 8 10 12 14 pH 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 CO 2 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 KCO2 M H 2CO3 pCO2 M H 2CO3 pCO2 KCO2 log M H 2CO3 log pCO2 log KCO2 Note that M H2CO3 is independent of pH SPECIATION IN OPEN CO2H2O SYSTEMS II The concentration of HCO3 as a function of pH is next calculated from K1 K1 M HCO aH M HCO 3 M H 2CO3 K1M H 2CO3 3 aH but we have already calculated M H2CO3 so M H 2CO3 pCO2 KCO2 M HCO aH log K1KCO2 pCO2 pH 3 log M HCO 3 K1KCO2 pCO2 SPECIATION IN OPEN CO2H2O SYSTEMS III The concentration of CO32 as a function of pH is next calculated from K2 K2 M CO 2 aH M CO 2 3 M HCO K 2 M HCO 3 3 3 aH but we have already calculated M HCO3 so M HCO 3 K1KCO2 pCO2 aH and M CO 2 3 K 2 K1KCO2 pCO2 a H2 log M CO 2 log K 2 K1KCO2 pCO2 2 pH 3 SPECIATION IN OPEN CO2H2O SYSTEMS IV The total concentration of carbonate CT is obtained by summing CT M H 2CO3 M HCO M CO 2 3 CT pCO2 KCO2 K1 pCO2 KCO2 aH 3 K1K 2 pCO2 KCO2 aH2 K K K log CT log pCO2 KCO2 1 1 12 2 a a H H Plot of log concentrations of inorganic carbon species H and OH for open system conditions with a fixed pCO2 10 3 5 atm pK1 log concentration molar 0 pK2 CO32 2 CT H OH 4 H2CO3 6 HCO3 8 2 3 4 5 6 7 pH 8 9 10 11 12 Plot of log concentrations of inorganic carbon species H and OH for open system conditions with a fixed pCO2 10 2 0 atm pK1 log concentration molar 0 4 CO32 H 2 pK2 CT H2CO3 OH 6 HCO3 8 2 3 4 5 6 7 pH 8 9 10 11 12 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 H2PO42pK 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 Ca 2 dissolves with 1 CO32 If dissolving into dilute water effectively no Ca 2 or CO32 present x2 10 8 48 x aCa2 aCO32 If controlled by atmospheric CO2 substitute CO32for expression log M CO 2 log K 2 K1KCO2 pCO2 2 pH 3 What happens in real natural waters 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 m z m CBE m z m c c a za c c a za 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 Using Keq to define equilibrium concentrations G0R RT ln Keq K eq n products i n reactants i Keq sets the amount of ions present relative to one another for any equilibrium condition AT Equilibrium K eq Q n products i n reactants i 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 Ca H3SiO4 2 Ca O phth CaB OH 4 CaCH3COO CaCO30 CaCl CaF CaH2SiO4 CaH3SiO4 CaHCO3 CaNO3 CaOH CaPO4CaSO4 CaHPO40 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 solubility 2 Some elements occur as complexes more commonly than as free ions 3 Adsorption of elements greatly determined by the complex it resides in 4 Toxicity bioavailability of elements depends on the complexation Defining Complexes Use equilibrium expressions 0 0 0 0 G n G products n G G R RT ln Keq i i i i reactants R i cC lHL CL lH c n CL H i c l C HL Where B is just like Keq i Mass Action Mass Balance c n CL H i c l C HL mCa 2 mCa L 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 equation 2 n x Mineral 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 aK a Al 3 a H3 4 SiO4 K aH4 from Gibbs free energies of formation The IAP could then be determined from a water analysis and the saturation index calculated INCONGRUENT 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 an activity diagram ACTIVITY DIAGRAMS THE K2O Al2O3 SiO2 H2O SYSTEM We will now calculate an activity diagram for the following phases gibbsite Al OH 3 kaolinite Al2Si2O5 OH 4 pyrophyllite Al2Si4O10 OH 2 muscovite KAl3Si3O10 OH 2 and K feldspar KAlSi3O8 The axes will be a K a H vs a H4SiO40 The diagram is divided up into fields where only one of the above phases is stable separated by straight line boundaries 6 Muscovite Quartz 7 Amorphous silica Activity diagram showing the stability relationships among some …