Pitzer-Equation Parameterization Limitations

Earlier, when discussing historical development, we mentioned that different workers have used different equations to describe the Debye-Hiickel constant (A, Eq. 2.35) as a function of temperature. For example, at 0°C, the value of this constant is 0.3781, 0.3764, and 0.3767 kg1/2 mol-1/2 for the FREZCHEM, Archer and Wang (1990), and Pitzer (1991) models, respectively. At NaCl = 5 m and 0 °C, the calculated mean activity coefficients using these three parameters evaluated with the FREZCHEM model are 0.7957, 0.7995, and 0.7988, respectively. The largest discrepancy is 0.48%, which is within the range of model errors for activity coefficients (Table 3.5). 

One of the major limitations of the FREZCHEM model is the lack of key parameters and equilibrium relationships at subzero temperatures. Several 

An example not previously discussed is the Pitzer-Debye-Hiickel slope for apparent molar volume (Av) that is required in Eqs. 2.76, 2.80, and 2.81. A numerical equation for Ay as a function of temperature and pressure was derived from the database of Ananthaswamy and Atkinson (1984) over a temperature range of 273 to 298 K and over a pressure range of 1 to 1000 bars  

One of the inherent limitations of the Pitzer approach is the necessity that all significant interactions among ions and neutral species must be quantified. In appendix Tables B.4 to B.6, we quantify 291 binary and ternary interaction 

The pressure dependence of equilibrium constants in this work are estimated with Eq. 2.29, which requires knowledge of the partial molar volumes and compressibilities for ions, water, and solid phases. For ions and water, molar volumes and compressibilities are known as a function of temperature (Table B.8 Eqs. 3.14 to 3.19). Molar volumes for solid phases are also known (Table B.9) unfortunately, the isothermal compressibilities for many solid phases are lacking (Millero 1983 Krumgalz et al. 1999). 

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A number of limitations of the FREZCHEM model can be broadly grouped under Pitzer-equation parameterization, modeling (mathematics, convergence, and coding), and applications. The first two limitations are discussed in this chapter. Application limitations are discussed in Chap. 5 after presentation of multiple applications. 

In Chap. 3 (Sect. 3.6), we discussed limitations of the FREZCHEM model that were broadly grouped under Pitzer-equation parameterization and mathematical modeling. There exists another limitation related to equilibrium principles. The foundations of the FREZCHEM model rest on chemical thermodynamic equilibrium principles (Chap. 2). Thermodynamic equilibrium refers to a state of absolute rest from which a system has no tendency to depart. These stable states are what the FREZCHEM model predicts. But in the real world, unstable (also known as disequilibrium or metastable) states may persist indefinitely. Life depends on disequilibrium processes (Gaidos et al. 1999 Schulze-Makuch and Irwin 2004). As we point out in Chap. 6, if the Universe were ever to reach a state of chemical thermodynamic equilibrium, entropic death would terminate life. These nonequilibrium states are related to reaction kinetics that may be fast or slow or driven by either or both abiotic and biotic factors. Below are four examples of nonequilibrium thermodynamics and how we can cope, in some cases, with these unstable chemistries using existing equilibrium models. 

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