The FREZCHEM Model

The current mantra of astrobiology is follow the water. Where there is water, there may be life. The FREZCHEM model can determine the presence or absence of water down to the eutectic temperature, below which only solid phases are thermodynamically stable. Salinity, the desiccation potential, and acidity are other potentially life-limiting factors that are calculated by FREZCHEM. In Chap. 4, we discuss potential life-limiting factors such as temperature, salinity, acidity, desiccation, radiation, pressure, and time. 

And finally, appendices provide a user s guide for the FREZCHEM model and tables of model parameters. Version 9.2 of this model includes the precipitation-dissolution of chloride, nitrate, sulfate, and bicarbonate-carbonate salts of calcium, magnesium, sodium, potassium, and ferrous iron. This version also contains strong acid chemistries (hydrochloric, nitric, and sulfuric), gas hydrate chemistries (carbon dioxide and methane), and tem-perature/pressure dependencies. Electronic copies of the FORTRAN code are available from the senior author (giles.marion dri.edu). 

The FREZCHEM model is based on molalities [moles/kg (water)] as the unit for solute concentrations. Other units that could have been used include mole fractions (rq/ where n is the number of moles of constituent i),... 

When Pitzer developed these equations, the ultimate form for describing the interaction terms was based on both theoretical models and experimental data. On the other hand, the number of terms to include in the equations is left to the user s discretion. For example, are neutral-neutral species interaction terms needed In some applications, yes in other applications, no. See Harvie et al. (1984), He and Morse (1993), and Pitzer (1995) for examples where different terms were selected. In what follows, we will specify the exact form of the Pitzer equations used in the FREZCHEM model. For a discussion of the connection between these equations (2.39 to 2.42) and Eq. 2.38, see Pitzer (1991, 1995). 

Table 3.1. A listing of chemical species in the FREZCHEM model (version 9.2) A. Solution and atmospheric species...

The FREZCHEM model is a chemical equilibrium model. For a reaction such as gypsum dissolution... 

Several reaction pathways are built into the FREZCHEM model including (1) temperature change, (2) evaporation, (3) pressure change, (4) equilibrium or fractional crystallization and, for gas hydrates, (5) open or closed carbon systems, and (6) pure or mixed gas hydrates. Under the temperature change option, the user can specify the upper and lower temperature range and a decremental temperature interval (AT) at which equilibrium at a fixed pressure is calculated (e.g., 298.15 to 253.15K with AT = 5 would result in... 

Incorporation of strong acids into the FREZCHEM model extended the model lower temperature range from 219 K (the eutectic of seawater) to 195 K [the eutectic of HCl-6H20(cr)[. As fpd data were used to define water activities at these low temperatures, it became apparent that the original equation defining the equilibrium of ice and liquid water at temperatures below 228 K (Spencer et al. 1990) did not fit the fpd data well. This necessitated a reevaluation of the relationship. 

In the FREZCHEM model, the density of pure water at T > 273 K and P — 1.01 bars is calculated with the Kell (1975) equation, which is given by... 

Table 3.2. The temperature range, maximum concentrations (or pressure), solid phases, and primary references for chemical systems in the FREZCHEM model...

Figure 3.4 exemplifies the type of chemical equilibria that are at the core of the FREZCHEM model. Both equilibria with ice and minerals are considered. Model calculations for NaCl solutions place the peritectic, where NaCl(cr) and NaCl-2H20(cr) are in equilibrium, at 0.1 °C and 6.096 m, in excellent agreement with experimental measurements of 0.1 °C and 6.096 m (Linke 1965). Similarly, model calculations of the eutectic are —21.3°C and 5.175 m, in excellent agreement with experimental measurements of —21.2 °C and 5.168 m (Hall et al. 1988). A different type of chemical system is exemplified by H2SO4 (Fig. 3.5), where the only solid-phase chemical equilibria are at subzero temperatures. In this case, the model predicts a eutectic at —62.0°C and 5.68 m, which is in excellent agreement with experimental measurements of —62.0°C and 5.68 (Linke 1965). 

Introducing pressure into the FREZCHEM model necessitates quantifying volumetric properties of ions in solution and solids in order to calculate the pressure dependence of K (Eq. 2.29), 7 (Eq. 2.87), and aw (Eq. 2.90). Figures 3.6 and 3.7 depict the molar volumes and compressibilities of ions... 

In applications of the FREZCHEM model to pressure, the assumption is made that solid phases (Table 3.1), other than ice, are incompressible therefore, in applying Eq. 2.29, only a constant molar volume for solids is used... 

In addition to equilibria for solid phases (Table 3.2) in the FREZCHEM model, there are also critical equilibria that control interactions among gas and aqueous phases (Table 3.3). 

Incorporating carbonate chemistry into the FREZCHEM model necessitates an explicit recognition of pH. In the pH range from 4 to 12, the following charge balance exists for the cations and anions in solution ... 

Only a few of the reactions summarized in Table 3.3 are actually based on data at subzero temperatures. In most cases, the lower temperature for data is 0°C. This could potentially be a serious limitation for the FREZCHEM model. For example, quantifying carbonate chemistry requires specification of Ah,co2 -ftcb - 2 and Kw all of these reactions are only quantified for temperatures > 0 °C (Table 3.3). Figure 3.9 demonstrates how six of the most important relationships of Table 3.3 extrapolate to subzero temperatures. We were able, based on these extrapolations, to quantify the solubility product of nahcolite (NaHCOa) and natron (Na2CO3 10H2O) to temperatures as low as — 22°C (251 K) (Marion 2001). Even for highly soluble bicarbonate and carbonate minerals such as nahcolite and natron, their solubilities decrease rapidly with temperature (Marion 2001). For example, for a hypothetical saline, alkaline brine that initially was 4.5 m alkalinity at 25 °C, the final alkalinity at the eutectic at —23.6°C was 0.3m (Marion 2001). At least for carbonate systems it is not necessary to extrapolate much beyond about —25 °C to quantify this chemistry, which we believe can reasonably be done using existing equation extrapolations (Fig. 3.9). 

In pressure applications of the FREZCHEM model, the molar volumes of the neutral species CC>2(aq), 02(aq), and CH aq) are constants independent of temperature and pressure (Appendix B). This is similar to how solids are handled in the FREZCHEM model (see previous section). Of the gas-phase gases, only C02(g) and CHi(g) at high pressures in gas hydrate equilibria are assumed to be compressible (see the following section on gas hydrate chemistry). That means that other gas constituents such as H2O, O2, HC1, HNO3, and H2SO4 are only validly parameterized for low pressures (a few bars). 

Two gas hydrates are now part of the FREZCHEM model C02-6H2 0 and CH46H2O (Table 3.2). Gas hydrate equilibrium for C02-6H20 is described by the reaction... 

To estimate a gas hydrate solubility product requires knowing g, Pg, and aw (Eq. 3.36). The gas partial pressure, Pg, is experimentally measured. The activity of water, aw, is calculated by the FREZCHEM model (Eq. 2.37), as is the gas fugacity coefficient (g) using a model developed by Duan et al. (1992b). The equation used to calculate gas fugacity coefficients is given by... 

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