Multireaction Equilibria

Equilibrium in multiphase and/or multireaction systems. If more than one phase is present in the system, a criterion of phase equilibria has to be satisfied together with the chemical equilibrium criterion. For instance, in a gas-liquid system components are in chemical equilibrium in the phase where the reaction occurs, but vapour-liquid equilibria between the gas and the liquid phases must also be taken into account. To determine the equilibrium composition of a reacting mixture in both phases, chemical equilibrium constants as well as data concerning vapour-liquid equilibria for all components of the reaction mixture should be known. In the equilibrium state ... 

Methods discussed for a one-reaction system can easily be extended to multireaction systems. For all independent reactions, a separate equilibrium constant is defined as ... 

In this section, the application of equilibrium theory is illustrated for a fairly complex multireaction system. The problem to be considered is that of the separation of binaphthol enantiomers through using achiral chromatography. This problem was studied by Baciocchi et al. [1] among others, who in particular made the following experimental observations. When a pulse with a racemic composition of enantiomers was injected on to the column, no separation occurred. However in all cases... 

Calculation of equilibrium conversions is based on the fundamental equations of chemical-reaction equilibrium, which in application require data for the standard Gibbs energy of reaction. The basic equations are developed in Secs. 15.1 through 15.4. These provide the relationship between the standard Gibbs energy change of reaction and the equilibrium constant. Evaluation of the equilibrium constant from thermodynamic data is considered in Sec. 15.5. Application of this information to the calculation of equilibrium conversions for single reactions is taken up in Sec. 15.7. In Sec. 15.8, the phase role is reconsidered finally, multireaction equilibrium is treated in Sec. I5.9.t... 

The calculations of the preceding example illustrate the complexity of equations that must be solved simultaneously (even for simple reactions) w the equilibrium-constant method is applied to multireaction equilibria. Mor the method does not lend itself to standardization so as to allow a general ] to be written for computer solution. The alternative method, mentioned in 15.2, is based on the fact that at equilibrium the total Gibbs energy of the s> has its minimum value. This is illustrated for a single reaction in Fig. 15.1. 

In order to avoid the restrictions to complicated adsorptive reactions in the MOC3D, Selim et al. (1990) developed a simulation system based on the multireaction model (MRM) and multireaction transport model (MRTM). The MRM model includes concurrent and concurrent-consecutive retention processes of the nonlinear kinetic type. It accounts for equilibrium (Freundlich) sorption and irreversible reactions. The processes considered are based on linear (first order) and nonlinear kinetic reactions. The MRM model assumes that the solute in the soil environment is present in the soil solution and in several phases representing retention by various soil... 

In this chapter we present a general-purpose transport model of the multireaction type. The model was successfully used to predict the adsorption as well as transport of several heavy metals in soils (Selim, 1992 Hinz and Selim, 1994 Selim and Amacher, 2001). Multireaction models are empirical and include linear and nonlinear equilibrium and reversible and irreversible retention reactions. A major feature of... 

The multireaction approach, often referred to as the multisite model, acknowledges that the soil solid phase is made up of different constituents (clay minerals, organic matter, iron, and aluminum oxides). Moreover, a heavy metal species is likely to react with various constituents (sites) via different mechanisms (Amacher et al 1988). As reported by Hinz et al. (1994), heavy metals are assumed to react at different rates with different sites on matrix surfaces. Therefore, a multireaction kinetic approach is used to describe heavy metal retention kinetics in soils. The multireaction model used here considers several interactions of one reactive solute species with soil matrix surfaces. Specifically, the model assumes that a fraction of the total sites reacts rapidly or instantaneously with solute in the soil solution, whereas the remaining fraction reacts more slowly with the solute. As shown in Figure 12.1, the model includes reversible as well as irreversible retention reactions that occur concurrently and consecutively. We assumed that a heavy metal species is present in the soil solution phase, C (mg/L), and in several phases representing metal species retained by the soil matrix designated as Se, S, S2, Ss, and Sirr (mg/kg of soil). We further considered that the sorbed phases Se, S, and S2 are in direct contact with the solution phase (C) and are governed by concurrent reactions. Specifically, C is assumed to react rapidly and reversibly with the equilibrium phase (Se) such that... 

Multireaction systems often have some quasi-equilibrium steps whose forward and reverse rates greatly exceed the net rate TZj at all conditions of interest. For such a reaction, the approximation... 

To describe the state of a reaction in a phase, we need to know the stoichiometric coefficients, j, and the chemical potential, pi, for each species in the reaction. For reaction equilibrium, the quantity AG = E Vi pi = 0 (as is T diS). For a possible, or spontaneous, reaction, AG < 0. For multireaction systems, complete equilibrium corresponds to dG = 0 for the system, that is, the Gibbs energy of the phase is a minimum. The total internal entropy production must vanish for the entire system. Similar consideration apply to multiphase systems. An expression analogous to equation 39 for dE, but for fixed T and p conditions, is ... 

At complete multiphase, multireaction equilibrium, is zero, and the Gibbs energy of the total system is a minimum. 

In the following analysis we followed similar overall structure for the second-order formulation to that described for the multireaction approach where three types of retention sites are considered with one equilibrium type sites (Se) and two kinetic type sites, namely S and S2. Therefore, we have <)) now related to the sorption capacity (Smax) by... 

The condition for chemical equilibrium in this multireaction system is G = minimum or dG = 0 for all variations consistent with the stoichiometry at constant temperature, pressure, and total mass. For the present case this implies... 

The dissolution and ionization of a mixture of electrolytes provides another example of equilibrium in a multireaction system. To be specific, suppose two electrolytes A aBv3 and GuqH ionize in solution as follows ... 

Nonlinear waves in RD have been studied by Balasubramhanya and Doyle III [4] who treat an idealized esterification system, and by Griiner et al. [33] who study a fairly complex, industrial multireaction process. An experimental study of methyl formate synthesis has been carried out by Reder [25, 87] using the lab-scale column introduced above (Fig. 10.2). In all cases the columns are close to chemical equilibrium and therefore behave similar to non-reactive separations. 

Coupled phase-reaction equilibrium problems not only raise no new thermodynamic issues, but they also raise few new computational issues. By building on the phase and reaction-equilibrium algorithms presented earlier in this chapter, we can devise an elementary algorithm. Reaction-equilibrium problems typically start with known values for T, P, and initial mole numbers N° in a phase-equilibrium context, these variables identify an T problem, such as an isothermal flash calculation. Therefore we can combine the Rachford-Rice method with the reaction-equilibrium calculation given in 11.2 an example is provided in Figure 11.8 for a vapor-liquid situation. This is a traditional way for attacking multiphase-multireaction problems [21, 22] ... 

Use the one-phase multireaction algorithm in Figure 11.6 to determine the extent to which formation of tetramers of acetic acid affect the fractional conversion during esterification of ethanol. That is, repeat the vapor-phase calculation at 358 K, 1.0133 bar illustrated in the last part of 11.3.3, but now include not only dimers but also tetramers. (Spectroscopic evidence suggests that formation of trimers is unfavored [32].) Sebastiani and Lacquaniti give the equilibrium constant for formation of tetramers as [32]... 

The Basis for Multiphase/Multireaction Equilibrium Calculations at Constant Temperature and Pressure... 

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