I. Recap of activities and equilibria from the last lecture
For solid phase in a dissolution/precipitation reaction, the activity is 1. The equilibrium constant for this type of reaction is a "solubility product" Ksp.
For redox reactions we defined a hypothetical electron activity, [e-]. Equilibrium constants for reduction half reactions are tabulated in terms of the log of the equilibrium constant, peo.
II. Classes of equations used in solved groundwater chemistry problems
A. Equilibrium relations employing activities
B. Mole balance equations employing molar (or molal) concentrations
C. Charge balance equations employing molar (or molal) concentrations or employing equivalent concentrations (moles of charge).
To solve a given problem, you need one independent equation for each unknown. (Sometimes you can reduce the number of unknows by making the assumption that one or more species has a negligible concentration.)
III. Sorption/Ion exchange
Like precipitation-dissolution reactions, sorption or ion-exchange reactions involve transfer of mass between aquifer solids and groundwater. However, sorption reactions differ significantly in the way these reactions respond to the effective concentration (or activity) of the solid phase. In the case of these "surface" reactions, the activity of the solid depends on how much of a given ion is held at the surface of the solid phase.
A. Sources of surface charge
Many of the interactions between solutes and solid surfaces are driven by attraction of oppositely charged ions and solids. This raises the question of how a solid can carry a charge. Some of the solid charge is due to attachment of H3O+ or OH- to the broken Si-O bonds on the surfaces of silcate minerals or O bonds in oxide minerals. This magnitude and sign (+ or -) of surface charge varies as a function of the pH of the water. At a certain pH (the isoelectric point or "point of zero charge") the mineral will have no net charge. Other sources of charge include isomorphous substitution in the crystal lattice of minerals such as clays. Substitution of cations with a lower charge for Si+4 or Al+3 gives these minerals a fixed negative charge.
B. Conceptual models of surface interactions
Cations in solution can interact with a negatively charged surface by increasing their concentrations in a diffuse layer near the mineral surface, as hydrated outer sphere complexes that approach the surface as closely as they can without shedding their associated water molecules, and as inner sphere complexes that can approach the surface more closely by shedding their associated water. Ions in the diffuse layer are relatively readily exchanged for other ions of similar charge, while outer sphere and inner sphere complexes interact more strongly and specifically with the surface.
C. Ion-exchange equilibria
Based on the conceptual models described above, particularly for interactions that are not strongly specific, as would be the case for ions in the diffuse layer, the surface reaction can be represented as an "exchange" of ions between solution and the solid surface. For example, A+ in solution could replace B+ attached to the surface as
A+ + B-clay Û B+ + A-clay
with the equilibrium relation
The activities of the solutes in this case can be computed in the standard manner. While there is no precise theoretical basis for determining activities of the sorbed species, A-clay and B-clay, these activities can be approximated in several ways. One approach to estimating an activity of the sorbed phase is to quantify it as the "mole fraction" of the sorbed solute. The "equilibrium constant" used in conjunction with a "mole fraction" estimate of sorbed activities is often referred to as the selectivity coefficient, Ks. (This is not a true equilbrium constant since the mole fractions are not true estimates of activity, but this approach works reasonably well in some cases.)
D. Isotherm models of sorption
If one of the exchanging ions is present only in trace concentrations in solution and on the solid surface, while the other is present in great abundance, a simplified version of the exchange equation can be derived by assuming that for the abundant species the ratio of solution activity to sorbed phase activity is approximately constant. This assumption leads to the "linear isotherm" model
S = Kd C where S is the sorbed phase concentration of the trace species, C is the solution concentration of the trace species, and Kd is an equilibrium "distribution coefficient". Note that since the sorbed and solute phases are the same element, the molar concentrations can be replaced by mass concentrations. The usual concentrations used for isotherms are S in ug/g and C in mg/L. (These are not the units shown in the figures in S&Z.)
Isotopes of a given element differ in the number of neutrons contained in the nucleus. Some important isotopes for groundwater studies are listed in Table 20.2 of S*Z. Among these, the isotopes of hydrogen and oxygen, the elements that make up the water molecule, are of particular interest. Isotopes can be stable or radioactive.
Fractionation of stable isotopes of hydrogen and oxygen during processes such as evaporation, condensation, freezing and melting leads to variations in the isotopic signature (see Figures 20.1 and 20.2). These variations in isotopic signature can in occur groundwater that has recently entered the saturated zone and can be interpreted to identify distinct sources of recharge such as summer rainfall or melted winter snow. Evaporation of lake water can generate "plumes" of heavy water in aquifers downgradient of a flow through lake. Because of temperature effects on isotopic fractionation, isotopes can also be used to infer the elevation at which recharge occurred for water in aquifers located in mountainous areas. Over geologic time, climate variations can lead to changes in isotopic signatures of groundwater. For example, the ice sheets covering much of north America during the last ice age resulted in recharge with a lighter isotope signature in midwest than is typical of current recharge. An example of using isotopic signatures in water to identify recharge from the last glacial period is illustrated in Figure 20.5. Isotopes in minerals precipitated from water will also reflect the isotopic signature of the water. Figure 20.6 illustrates variations in oxygen isotopes in calcite precipitated in a cave in Nevada and these have been interpreted to reflect climate changes over hundreds of thousands of years.
Radioactive isotopes can be used for age dating of groundwater because they have known rates of decay. For short, recent time scales, tritium has been a useful age dating isotope. High concentrations of tritium in atmospheric water vapor were created as the result of nuclear weapons testing in the 1950's-70s. The peak tritium concentrations from recharge in the mid-60s can still be identified in some aquifers. However, due to the relatively short half life of tritium (12.3 years) it has become difficult to use tritium concentrations alone to date more recent recharge. In such cases, using tritium and its daughter 3He together provides a quantitative dating tool - see equation 20.5 in S&Z. CFCs are another anthropegenic tracer that can be used to date recent water. Other isotopes are useful for longer time scales - e.g 14C.