Read: Ch. 3, sections 1, 2, 3, 5, 7, 9; Ch. 7, sections 2, 3 PART 14 Groundwater chemistry Introduction Matter present in water can be divided into three categories: (1) Suspended solids (finest among them are colloids, <10-6 m) Most inorganic particles have density higher than the density of water. These will eventually settle down by gravity. The density of organic solids may be close to that of water. These will remain in suspension longer. Examples: clay particles, bacteria, products of bacteria activity. (2) Dissolved ionic species Charged molecules: major ions (cations Na +, K +, Ca 2+, Mg 2+ and anions Cl -, HCO3 -, SO 4 2 ) and minor ions (e.g., trace metals). (3) Dissolved neutral species Molecules with zero charge. They include noble gases (He, Ne, Ar, Kr, Xe, Rn), and organic chemicals (benzene, toluene). Some neutral species (especially noble gases) are good for tracers. Methods of expressing solute concentration (read Chapter 7.2) (1) Trilinear diagram (2) Bar graph (3) Pie diagram (4) Stiff diagram (5) Schoeller diagram
Groundwater chemistry 106 Controls on groundwater chemistry (1) Shift of dissolved species distribution Suppose ph=3, then a H+ =10-3 and a OH- =10-11 (2) Precipitation-dissolution (solubility) (3) Adsorption on solids Example: cation exchange (4) Change of phase Equilibria and disequilibria Equilibrium reactions Consider the chemical reaction where a, b, c, d are # of moles of A, B, C, D aa + bb cc + dd Law of mass action expresses the relationship between the constituents (reactants and products) at equilibrium: a C c ad d [ C] c [ D] d K = ---------------------- = ----------- [ A] a [ B] b a a b A a B where: [] (or a) denotes activity (i.e., effective concentration) K is thermodynamic equilibrium constant (or stability constant) Activity (a) is related to concentration (m) through the activity coefficient (γ): a = γm
Activity coefficient Activity coefficient Groundwater chemistry 107 The activity coefficient depends on the ionic strength I of water: I = 1 -- mz 2 2 where m is the molar concentration and z is the charge. Activity coefficients γ are calculated differently for different ionic strengths: For small I (<0.005M) logγ = Az 2 I For larger I (<0.1M) logγ = Az 2 I ---------------------- 1 + Ba I where A, B and a are specific constants for different ions (e.g., Appendix IV in Freeze and Cherry, 1979, Groundwater). Examples of activity coefficients calculated with these two equations are shown in the figures below. 1.0 0.8 logγ = Az 2 I 0.6 0.4 0.2 SO 4 2- and K + 0.0 0.0 0.2 0.4 0.6 0.8 1.0 1.0 0.8 0.6 Az 2 I logγ = ---------------------- 1 + Ba I 0.4 0.2 0.0 2- SO 4 K + 0.0 0.2 0.4 0.6 0.8 1.0 Ionic strength
Groundwater chemistry 108 Disequilibria Many reactions take a long time to reach an equilibrium. This leads to the concept of disequilibrium. The departure from equilibrium is manifested by the ion activity product (IAP; also called reaction quotient) that is not equal to the equilibrium constant, i.e., IAP = a D a ----------- C K a A a B The disequilibrium may favor reaction in either direction, depending on the value of IAP: when IAP<K, the reaction goes from left to right: aa + bb cc + dd when IAP>K, the reaction goes from right to left: aa + bb cc + dd At equilibrium, IAP=K The same relationships can be expressed using saturation index (S): IAP S = --------- K If S>1 (or logs>0), the solution is oversaturated If S<1 (or logs<0), the solution is undersaturated
Groundwater chemistry 109 Kinetic reactions Many environmental fate processes, such as degradation of chemicals, are not usefully modeled with equilibrium chemistry because the rate of the reaction is more important to quantify than the final composition of the system. For example, even if we know that certain chemical will be degraded eventually, it is crucial to know whether degradation will take seconds, years or centuries. Examples of reactions are in Table 5 (from Langmuir, 1997), and half-times of some reaction types (t 1/2 ) and residence times (t R ) of some waters in the hydrosphere are shown in the figure following the table (also from Langmuir, 1997). Table 5. Reactions at low temperatures and pressures and their approximate half-times (from Langmuir 1997) Reaction type and example Solute-solute H 2 CO 0 3 = H + - + HCO 3 Solute-water 0 CO 2 (aq) + H 2 O = H 2 CO 3 Cu 2 + + H 2 O = CuOH + + H + Fe(H 2 O) 6 2+ = Fe(H 2 O) 5 2+ + H 2 O acid-base hydration-hydrolysis hydrolysis-complexation hydrolysis-complexation Half-times ~10-6 s ~0.1 s ~10-10 s ~10-7 s Adsorption-desorption Cd 2+ + CaX = Ca 2+ + CdX X 2- is the surface site ~s - hr Gas-water or gas solution-exsolution CO 2 (g) = CO 2 (aq) ~min Oxidation-reduction Fe 2+ + (1/4)O 2 (g) + (5/2)H 2 O = Fe(OH) 3 (ppt) + 2H + min - hr Hydrolysis of multivalent ions Al n+m (OH) m+ 3n+2m + mh2o (n+m)al(oh) 3 (s) + mh + hr - y Mineral-water equilibria Ca 2+ + HCO - 3 = CaCO 3 + H + week - y Isotopic exchange SO 2-4 + H 32 S = H 34 S - + 32 2- SO 4 y Mineral recrystallization Fe(OH) 3 nh 2 O(am) α-feooh(goethite) + (n+1)h 2 O y Radioactive decay C 14 N + e - 5570 y
Groundwater chemistry 110 Precipitation Ocean Streams Soil moisture Lakes Groundwaters Residence time, t R Solute - solute Solute - water Adsorption - desorption Gas - water Hydrolysis of multivalent ions (polymerization) Mineral-water equilibria Mineral recrystallization Seconds Minutes Hours Days Months Years 10 6 years Reaction rate, t 1/2 Reaction order The rate of a reaction is limited by the frequency of collisions between the reacting molecules and the probability that any particular collision will cause the reaction to proceed. Depending on the number of molecules involved in reaction, we have different orders of reactions. For example, A + 2B C can be written dc --------- = KAB 2 The reaction is first-order with respect to A and C, second-order with respect to B, and third-order overall. Another example: radioactive decay of isotope C. Equation dc ------ = kc describes first-order reaction, whose rate depends on the number of molecules present. Note: the units for the rate constant k are different for different order reactions. Question: What are the units for k?
Groundwater chemistry 111 Rate laws (1) Zeroth-order Reaction rates are independent of the concentration of reactants and products. A as reactant: da ------ = k A A 0 kt t 1 2 0.5 A 0 = = ----- k A rate log rate slope = k k log k t A log A (2) First-order Rates are proportional to the concentrations of reactants or products. Examples: radioactive decay (see previous section for details). oxidation of organic matter sulfate reduction gypsum dissolution oxidation of pyrite A rate log rate t k A log k (slope = 1) log k + log A log A (3) Second-order
Groundwater chemistry 112 Rates depend on the concentration of two reactants or products, and are therefore bimolecular reactions. Example: oxidation of Fe 2+ under ph<2.2: Fe 2+ + (1/2)O 2 + H+ Fe 3+ + (1/2)H 2 O dfe 2+ -------------- = k Fe 2+ P O2 A t rate A log rate log k log k + log A (slope = 2) log A
Groundwater chemistry 113 Table 6. Simple rate laws, their integrated forms, and reaction half-times (t1/2) (from Langmuir, 1997). Reaction and equation Integrated rate equation Half-time Zeroth-order (A as reactant) da ------ = k A = A 0 -kt +0.5 A 0 /k (A as product) da ------ = k First-order (A B) da ------ = ka A = A 0 + kt ln A = ln A 0 - kt -0.5 A 0 /k (ln 2)/k B A da ------ = ka ( s A) A s A ln---------------- A s A 0 = kt Second-order (2A B) da ------ = ka 2 (A + B C) da ------ = ka ( )( B) 1 -- A = 1 ----- kt A 0 A 0 B ln--------- = ( B B 0 A 0 A 0 )kt 1 -------- ka 0 Note: The rate constant k is always positive. In the integrated rate expressions the concentration of A = A 0 at t = 0, and A = A 0 /2 at half-time (t 1/2 ). A s denotes the equilibrium, mineral saturation or steady state concentration of A.
Groundwater chemistry 114 Carbonate system CO 2 aquifer ;; yy CaCO 3 Carbonate species: H 2 CO 3 HCO - 3 CO 2-3 Carbonate reactions: CO 2 (atm) CO 2 (g) K H = 10-1.5 CO 2 (g) + H 2 O H 2 CO 3 K 1 = 10-2.8 H 2 CO 3 H + + HCO 3 - K 2 = 10-3.5 HCO 3 - H + + CO 3 2- K 3 = 10-10.3 CO 3 2- + Ca 2+ CaCO 3 (s) K so = 10-8.3
log(a) Groundwater chemistry 115 0-1 -2 H 2 CO 3 HCO 3 - CO 3 2- -3-4 -5 0 2 4 6 8 10 12 14 ph Things to note: (1) At low ph, all carbonate species CO 2 ( atm.). Lower CO 3 2- concentration leads to dissolution of CaCO 3. (2) At high ph, CO 2 from the atmosphere is dissolved and calcite precipitates. (3) At ph between 7 and 9, HCO - 3 dominates. We can rise ph by adding NaOH: - HCO 3 + OH - H 2 O + CO 2-3 All HCO - 3 must be used (buffering) before we can rise ph above 10.3. We can lower ph by adding HCl: HCO 3 - + H + H 2 CO 3 Again, all HCO 3 - must be used first before we can lower ph below 6.3. (4) Carbonate species in solution are important control on Ca 2+ and Mg 2+, and vice versa.
Groundwater chemistry 116 Adsorption Particles less than 1 µm have a significant percentage of their atoms at particle surface. These particles have important surface properties, which has the following important consequences: (1) They cause increase in solubilities of particles. (2) Particles can remain in suspension for long time. (3) Particles have unbalanced surface charge,which attracts ions, which in turn makes these particles active adsorption sites. Table 7. Surface charge and surface-site density for cubical particles of different sizes. Cube diameter Number of cubes Area (m 2 g -1 ) Mol % on surface 1 cm 1 0.00011 0.00012 1 µm 10 12 1.1 0.12 0.01 µm 10 18 110 12 Note: Total surface area of 1 cm3 of hematite subdivided into smaller and smaller cubes. Source: Langmuir, 1997, Aqueous Environmental Geochemistry, Prentice Hall, 600 pp. Depending on particle size, cation exchange capacity (in meq/100 g) is different. Figure to the right shows the cation exchange capacity of five clay minerals as a function of particle size. 10 Particle size (10-6 m) 1.0 Kaolinite Illite Attapulgite Saponite Nontronite 0.1 1 10 100 Cation exchange capacity (meq (100 g) -1 )
Groundwater chemistry 117 Adsorption isotherms Adsorption is often described in terms of isotherms, which show the relationship between the activity of ion in solution and amount adsorbed. Generally, as the concentration in solution increases, the amount sorbed also increases. Isotherm is a plot (or function) that describes the amount sorbed as a function of concentration. Freundlich isotherm x --- = KC n m x/m = sorbate/sorbent (mg g -1 ) K = constant distribution coefficient C = concentration in water (g l -1 ) Adsorbed concentration, C ads 0.1 0.01 0.001 Freundlich C ads = KC n log C ads = log K + n log C 0.01 0.1 1 10 n = constant, usually between 0.9 and 1.4 Alternative form of Freundlich isotherm: C adsorbed = KC n K and n = empirical constants Adsorbed concentration, C ads 0.100 0.075 0.050 0.025 0.000 Linear C ads = KC 0 2 4 6 8 10 Linear isotherm C adsorbed = KC Langmuir isotherm x --- m ac = ---------------- 1 + bc a and b = constants Adsorbed concentration, C ads 0.06 0.04 0.02 0.00 Langmuir C ads = ac/(1+bc) 0 2 4 6 8 10 Dissolved concentration, C
Groundwater chemistry 118