Equilibrium and reaction modelling

Parker, D.R., W. A. Norvell and R. L. Chaney, 1995, GEOCHEM-PC, a chemical speciation program for IBM and compatible personal computers. In R. H. Loep-pert, A. P. Schwab and S. Goldberg (eds.), Chemical Equilibrium and Reaction Models. Soil Science Society of America Special Publication 42,253-269. 

Santore, R.C. and Driscoll, C.T. (1995). The CHESS Model for Calculating Chemical Equilibria in Soils and Solutions, Chemical Equilibrium and Reaction Models. The Soil Society of America, American Society of Agronomy... 

Loeppert, R.H., Schwab, A.P., and Goldberg, S., Eds., 1993. Chemical Equilibrium and Reaction Models, Special Publication 42, Soil Science Society of America, Madison, WI. 

Parker, D. R., Chaney, R. L., and Norvell, W. A. (1995a). Chemical equilibrium models applications to plant nutrition. In Soil Chemical Equilibrium and Reaction Models, ed. Loeppert, R. H., Schwab, A. P., and Goldberg, S., Spec. Publ. 42, American Society of Agronomy, Soil Science Society of America, Madison, WI, 163-200. 

Mathematical approaches used to describe micelle-facilitated dissolution include film equilibrium and reaction plane models. The film equilibrium model assumes simultaneous diffusive transport of the drug and micelle in equilibrium within a common stagnant film at the surface of the solid as shown in Figure 7. The reaction plane approach has also been applied to micelle-facilitated dissolution and has the advantage of including a convective component in the transport analysis. While both models adequately predict micelle-facilitated dissolution, the scientific community perceives the film equilibrium model to be more mathematically tractable, so this model has found greater use. 

Beginning in the late 1980s, a number of groups have worked to develop reactive transport models of geochemical reaction in systems open to groundwater flow. As models of this class have become more sophisticated, reliable, and accessible, they have assumed increased importance in the geosciences (e.g., Steefel et al., 2005). The models are a natural marriage (Rubin, 1983 Bahr and Rubin, 1987) of the local equilibrium and kinetic models already discussed with the mass transport... 

This paper discusses the oxidation of Mn(II) in the presence of lepidocrocite, y-FeOOH. This solid was chosen because earlier work (18, 26) had shown that it significantly enhanced the rate of Mn(II) oxidation. The influence of Ca2+, Mg2+, Cl", SO,2-, phosphate, silicate, salicylate, and phthalate on the kinetics of this reaction is also considered. These ions are either important constituents in natural waters or simple models for naturally occurring organics. To try to identify the factors that influence the rate of Mn(II) oxidation in natural waters the surface equilibrium and kinetic models developed using the laboratory results have been used to predict the... 

Fig. 22 shows the residence times tR of waters in the hydrosphere and the half-life ti/2 of various reactions. If ti/2 tR then it can be assumed that the system is roughly in equilibrium and thermodynamic models can be used. If, on the other hand, tR ti/2 kinetic models must be applied. 

We have learned from previous chapters that equilibrium and reaction constants are affected by temperature. The length of time that a disinfection process proceeds is a function of the constants of the underlying reaction between the microorganism and the disinfectant thus, it must also be a function of temperature. The variation of the contact time to effect a given percentage kill with respect to temperature can therefore be modeled by means of the Van t Hoff equation. This equation was derived for the equilibrium constants in Chapter 11, which is reproduced next ... 

Process development has progressed from initial measurements of overall reaction rates under expected commercial conditions to the development of equilibrium and kinetic models for all process steps. The most... 

The computer program PHREEQE (3) was used for chemical equilibrium and reaction path modeling. PHREEQE does speciation and mass transfer calculations to find the distribution of aqueous complexes and the saturation indices of potential mineral phases present. 

Figure 6.5 shows the relative concentrations across a 1-m treatment wall for the migration of the parent product TCE and its reaction products cl2DCE and VC. The simulation is achieved with the equilibrium sorption reaction model. The results are identical to that analytically calculated by Khandelwal and Rabideau (1999). 

Modelling plasma chemical systems is a complex task, because these system are far from thennodynamical equilibrium. A complete model includes the external electric circuit, the various physical volume and surface reactions, the space charges and the internal electric fields, the electron kinetics, the homogeneous chemical reactions in the plasma volume as well as the heterogeneous reactions at the walls or electrodes. These reactions are initiated primarily by the electrons. In most cases, plasma chemical reactors work with a flowing gas so that the flow conditions, laminar or turbulent, must be taken into account. As discussed before, the electron gas is not in thennodynamic equilibrium... 

Decades of work have led to a profusion of LEERs for a variety of reactions, for both equilibrium constants and reaction rates. LEERs were also established for other observations such as spectral data. Furthermore, various different scales of substituent constants have been proposed to model these different chemical systems. Attempts were then made to come up with a few fundamental substituent constants, such as those for the inductive, resonance, steric, or field effects. These fundamental constants have then to be combined linearly to different extents to model the various real-world systems. However, for each chemical system investigated, it had to be established which effects are operative and with which weighting factors the frmdamental constants would have to be combined. Much of this work has been summarized in two books and has also been outlined in a more recent review [9-11]. 

In a recent paper [11] this approach has been generalized to deal with reactions at surfaces, notably dissociation of molecules. A lattice gas model is employed for homonuclear molecules with both atoms and molecules present on the surface, also accounting for lateral interactions between all species. In a series of model calculations equilibrium properties, such as heats of adsorption, are discussed, and the role of dissociation disequilibrium on the time evolution of an adsorbate during temperature-programmed desorption is examined. This approach is adaptable to more complicated systems, provided the individual species remain in local equilibrium, allowing of course for dissociation and reaction disequilibria. 

A detailed description of AA, BB, CC step-growth copolymerization with phase separation is an involved task. Generally, the system we are attempting to model is a polymerization which proceeds homogeneously until some critical point when phase separation occurs into what we will call hard and soft domains. Each chemical species present is assumed to distribute itself between the two phases at the instant of phase separation as dictated by equilibrium thermodynamics. The polymerization proceeds now in the separate domains, perhaps at differen-rates. The monomers continue to distribute themselves between the phases, according to thermodynamic dictates, insofar as the time scales of diffusion and reaction will allow. Newly-formed polymer goes to one or the other phase, also dictated by the thermodynamic preference of its built-in chain micro — architecture. 

Lindberg, R. D. and Runnells, D. D. (1984). Ground-water redox reactions An analysis of equilibrium state applied to Eh measurements and geochemical modeling. Science 225,925-927. 

---