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Unit 08a : Advanced Hydrogeology Aqueous Geochemistry Aqueous Systems • In addition to water, mass exists in the subsurface as: – Separate gas phases (eg soil CO2) – Separate non-aqueous liquid phases (eg crude oil) – Separate solid phases (eg minerals forming the pm) – Mass dissolved in water (solutes eg Na+, Cl-) Chemical System in Groundwater • Ions, molecules and solid particles in water are not only transported. • Reactions can occur that redistribute mass among various ion species or between the solid, liquid and gas phases. • The chemical system in groundwater comprises a gas phase, an aqueous phase and a (large) number of solid phases Solutions • A solution is a homogeneous mixture where all particles exist as individual molecules or ions. This is the definition of a solution. • There are homogeneous mixtures where the particle size is much larger than individual molecules and the particle size is so small that the mixture never settles out. • Terms such as colloid, sol, and gel are used to identify these mixtures. Concentration Scales • Mass per unit volume (g/L, mg/L, mg/L) is the most commonly used scale for concentration • Mass per unit mass (ppm, ppb, mg/kg, mg/kg) is also widely used • For dilute solutions, the numbers are the same but in general: mg/kg = mg/L / solution density (kg/L) Molarity • Molar concentration (M) defines the number of moles of a species per litre of solution (mol.L-1) • One mole is the formula weight of a substance expressed in grams. Molarity Example • Na2SO4 has a formula weight of 142 g • A one litre solution containing 14.2 g of Na2SO4 has a molarity of 0.1 M (mol.L-1) • Na2SO4 dissociates in water: Na2SO4 = 2Na+ + SO42- • The molar concentrations of Na+ and SO42- are 0.2 M and 0.1 M respectively Seawater Molarity • Seawater contains roughly 31,000 ppm of NaCl and has a density of 1028 kg.m-3. What is the molarity of sodium chloride in sea water? • M = (mc/FW) * r where mc is mass concentration in g/kg; r is in kg/m3; and FW is in g. • Formula weight of NaCl is 58.45 • 31 g is about 0.530 moles • Seawater molarity = 0.530 * 1.028 = 0.545 M (mol.L-1) Molality • Molality (m) defines the number of moles of solute in a kilogram of solvent (mol.kg-1) • For dilute aqueous solutions at temperatures from around 0 to 40oC, molarity and molality are similar because one litre of water has a mass of approximately one kilogram. Molality Example • Na2SO4 has a formula weight of 142 g • One kilogram of solution containing 0.0142 kg of Na2SO4 contains 0.9858 kg of water. • The solution has a molality of 0.101 m (mol.kg-1) • Na2SO4 dissociates in water: Na2SO4 = 2Na+ + SO42- • The molal concentrations of Na+ and SO42- are 0.202 m and 0.101 m respectively Seawater Molality • Seawater contains roughly 3.1% of NaCl. What is the molality of sodium chloride in sea water? m = (mc/FW)/(1 – TDS) where mc is mass concentration in g/kg; TDS is in kg/kg and FW is in g. • Formula weight of NaCl is 58.45 • 31 g is about 0.530 moles • Average seawater TDS is 35,500 mg/kg (ppm) • m = (31/58.45)/ (1- 0.0355) = 0.550 mol.kg-1 Molar and Molal • The molarity definition is based on the volume of the solution. This makes molarity a temperature-dependent definition. • The molality definition does not have a volume in it and so is independent of any temperature changes. • The difference is IMPORTANT for concentrated solutions such as brines. Brine Example • Saturated brine has a TDS of about 319 g/L • Saturated brine has an average density of 1.203 at 15oC • The concentration of saturated brine is therefore 265 g/kg or 319 g/L • The molality m = (265/58.45)/(1-0.319)) is about 6.7 m (mol.kg-1) • The molarity M = (265/58.45)*1.203 is about 5.5 M (mol.L-1) Equivalents • Concentrations can be expressed in equivalent units to incorporate ionic charge meq/L = mg/L / (FW / charge) • Expressed in equivalent units, the number of cations and anions in dilute aqueous solutions should approximately balance Partial Pressures • Concentrations of gases are expressed as partial pressures. • The partial pressure of a gas in a mixture is the pressure that would be exerted by the gas if it occupied the volume alone. • Atmospheric CO2 has a partial pressure of 10-3.5atm or about 32 Pa. Mole Fractions • In solutions, the fundamental concentration unit in is the mole fraction Xi; in which for j components, the ith mole fraction is • Xi = ni/(n1 + n2 + ...nj), • where the number of moles n of a component is equal to the mass of the component divided by its molecular weight. Mole Fractions of Unity • In an aqueous solution, the mole fraction of water, the solvent, is always near unity. • In solids that are nearly pure phases, e.g., limestone, the mole fraction of the dominant component, e.g., calcite, will be near unity. • In general, only the solutes in a liquid solution and gas components in a gas phase will have mole fractions that are significantly different from unity. Structure of Water • Covalent bonds between H and O • 105o angle H-O-H + - • Water molecule is polar 105o • Hydrogen bonds join molecules – tetrahedral structure + • Polar molecules bind to charged species to “hydrate” ions in solution Chemical Equilibrium • The state of chemical equilibrium for a closed system is that of maximum thermodynamic stability • No chemical energy is available to redistribute mass between reactants and products • Away from equilibrium, chemical energy drives the system towards equilibrium through reactions Kinetic Concepts • Compositions of solutions in equilibrium with solid phase minerals and gases are readily calculated. • Equilibrium calculations provide no information about either the time to reach equilibrium or the reaction pathway. • Kinetic concepts introduce rates and reaction paths into the analysis of aqueous solutions. Reaction Rates Solute-Solute Solute-Water Gas-Water Hydrolysis of multivalent ions (polymerization) Adsorption-Desorption Mineral-Water Equilibria Mineral Recrystallization Secs Mins Hrs Days Months Years Centuries My Reaction Rate Half-Life After Langmuir and Mahoney, 1984 Relative Reaction Rates • An equilibrium reaction is “fast” if it takes place at a significantly greater rate than the transport processes that redistribute mass. • An equilibrium reaction is “slow” if it takes place at a significantly smaller rate than the transport processes that redistribute mass. • “Slow” reactions in groundwater require a kinetic description because the flow system can remove products and reactants before reactions can proceed to equilibrium. Partial Equilibrium • Reaction rates for most important reactions are relatively fast. Redox reactions are often relatively slow because they are mediated by micro-organisms. Radioactive decay reactions and isotopic fractionation are extremely variable. • This explains the success of equilibrium methods in modelling many aspects of groundwater chemistry. • Groundwater is best thought of as a partial equilibrium system with only a few reactions requiring a kinetic approach. Equilibrium Model • Consider a reaction where reactants A and B react to produce products C and D with a,b,c and d being the respective number of moles involved. aA + bB = cC + dD • For dilute solutions the law of mass action describes the equilibrium mass distribution K = (C)c(D)d (A)a(B)b where K is the equilibrium constant and (A),(B),(C), and (D) are the molal (or molar) concentrations Activity • In non-dilute solutions, ions interact electrostatically with each other. These interactions are modelled by using activity coefficients (g) to adjust molal (or molar) concentrations to effective concentrations [A] = ga(A) • Activities are usually smaller for multivalent ions than for those with a single charge • The law of mass action can now be written: K = gc(C)c gd(D)d = [C]c[D]d ga(A)a gb(B)b [A]a[B]b Debye-Hückel Equation • The simplest model to predict ion ion activity coefficients is the Debye-Hückel equation: log gi = - Azi2(I)0.5 where A is a constant, zi is the ion charge, and I is the ionic strength of the solution given by: I = 0.5 SMizi2 where (Mi) is the molar concentration of the ith species • The equation is valid and useful for dilute solutions where I < 0.005 M (TDS < 250 mg/L) Extended Debye-Hückel Equation • The extended Debye-Hückel equation is used to increase the solution strength for which estimates of g can be made: log gi = - Azi2(I)0.5 1 + Bai(I)0.5 where B is a further constant, ai is the ionic radius • This equation extends the estimates to solutions where I < 0.1 M (or TDS of about 5000 mg/L) More Activity Coefficient Models • The Davis equation further extends the ionic strength range to about 1 M (roughly 50,000 mg/L) using empirical curve fitting techniques • The Pitzer equation is a much more sophisticated ion interaction model that has been used in very high strength solutions up to 20 M Monovalent Ions 1 0.9 0.8 Activity Coefficient 0.7 0.6 0.5 Debye-Huckel 0.4 0.3 Extended 0.2 Davis 0.1 Pitzer 0 0.001 0.01 0.1 1 10 Ionic Strength Divalent Ions 1 0.9 0.8 Activity Coefficient 0.7 0.6 0.5 Debye-Huckel 0.4 0.3 Extended 0.2 Davis 0.1 Pitzer 0 0.001 0.01 0.1 1 10 Ionic Strength Activity and Ionic Charge 1 Monovalent 0.9 0.8 Activity Coefficient 0.7 0.6 Divalent 0.5 Debye-Huckel 0.4 0.3 Extended 0.2 Davis 0.1 Pitzer 0 0.001 0.01 0.1 1 10 Ionic Strength Non-Equilibrium • Viewing groundwater as a partial equilibrium system implies that some reactions may not be equilibrated. • Dissolution-precipitation reactions are certainly in the non-equilibrium category. • Departures from equilibrium can be detected by observing the ion activity product (IAP) relative to the equilibrium constant (K) where IAP = [C]c[D]d = products [A]a[B]b reactants Dissolution-Precipitation aA + bB = cC + dD • If IAP<K (IAP/K<1) then the reaction is proceeding from left to right. • If IAP>K (IAP/K>1) then the reaction is proceeding from right to left. • If the reaction is one of mineral dissolution and precipitation – IAP/K<1 the system in undersaturated and is moving towards saturation by dissolution – IAP/K>1 the system is supersaturated and is moving towards saturation by precipitation Saturation Index • Saturation index is defined as: SI = log(IAP/K) • When a mineral is in equilibrium with the aqueous solution SI = 0 • For undersaturation, SI < 0 • For supersaturation, SI > 0 Calcite • The equilibrium constant for the calcite dissolution reaction is K = 4.90 x 10-9 log(K) = -8.31 • Given the activity coefficients of 0.57 for Ca2+ and 0.56 for CO32- and molar concentrations of 3.74 x 10-4 and 5.50 x 10-5 respectively, calculate IAP/K. • Reaction: CaCO3 = Ca2+ + CO32- IAP = [Ca2+][CO32-] = 0.57x3.37x10-4x0.56x5.50x10-5 [CaCO3] 1.0 = 6.56 x 10-9 and log(IAP) = -8.18 {IAP/K}calcite = 6.56/4.90 = 1.34 log{IAP/K}calcite = 8.31 - 8.18 = 0.13 • The solution is slightly oversaturated wrt calcite. Dolomite • The equilibrium constant for the calcite dissolution reaction is K = 2.70 x 10-17 and log(K) = -16.57 • Given activity coefficients of 0.57, 0.59 and 0.56 for Ca2+, Mg2+ and CO32- and molar concentrations of 3.74 x 10-4, 8.11 x 10-5 and 5.50 x 10-5 respectively, calculate IAP/K. • Reaction: CaMg(CO3)2 = Ca2+ + Mg2+ + 2 CO32- • Assume the effective concentration of the solid dolomite phase is unity log[Ca2+] = -3.67 log[Mg2+] = -4.32 log[CO32-] = -4.51 log(IAP)=log([Ca2+][Mg2+][CO32-]2)= -3.67-4.32-9.02= -16.31 log{IAP/K}dolomite = 16.57 – 17.01 = -0.44 • The solution is undersaturated wrt dolomite. Kinetic Reactions • Reactions that are “slow” by comparison with groundwater transport rates require a kinetic model k1 aA + bB = cC + dD k2 where k1 and k2 are the rate constants for the forward (L to R) and reverse (R to L) reactions • Each constituent has a reaction rate: rA = dA/dt; rB = dB/dt; rc = dC/dt; rD = dD/dt; • Stoichiometry requires that: -rA/a = -rB/b = rC/c = rD/d Rate Laws • Each consituent has a rate law of the form: rA = -k1(A)n1(B)n2 + k2(C)m1(D)m2 where n1, n2, m1 and m2 are empirical or stoichiometric constants • If the original reaction is a single step (elementary) reaction then n1=a, n2=b, m1=c and m2=d Irreversible Decay 14C = 14N + e d(14C)/dt = -k1(14C) + k2(14N)(e) • Here there is only a forward reaction and k2 for the reverse reaction is effectively zero d(14C)/dt = -k1(14C) • k1 is the decay constant for radiocarbon Elementary Reactions Fe3+ + SO42- = FeSO4+ d(Fe3+)/dt = -k1(Fe3+)(SO42-) + k2(FeSO4+) • The reaction rate depends not only on how fast ferric iron and sulphate are being consumed in the forward reaction but also on the rate of dissociation of the FeSO4+ ion.