Chemical reaction equilibrium simultaneous

When liquid and gas phases are both present in an equilibrium mixture of reacting species, Eq. (11.30), a criterion of vapor/liquid equilibrium, must be satisfied along with the equation of chemical-reaction equilibrium. There is considerable choice in the method of treatment of such cases. For example, consider a reaction of gas A and water B to form an aqueous solution C. The reaction may be assumed to occur entirely in the gas phase with simultaneous transfer of material between phases to maintain phase equilibrium. In this case, the equilibrium constant is evaluated from AG° data based on standard states for the species as gases, i.e., the ideal-gas states at 1 bar and the reaction temperature. On the other hand, the reaction may be assumed to occur in the liquid phase, in which case AG° is based on standard states for the species as liquids. Alternatively, the reaction may be written... 

This chapter shows how to solve problems involving chemical reaction equihbrium. The chemical reaction equilibrium gives the upper limit for the conversion, so knowing the equilibrium conversion is the first step in analyzing a process. The second question, what the rate of reaction is, can then be answered to decide the volume of the reactor. This second question, using kinetics, is treated in Chapter 8. Chemical reaction equilibrium leads to one or more nonlinear algebraic equations which must be solved simultaneously, and such problems are described in this chapter. 

Unfortunately, few of the published studies of extraction equilibria heve provided complete quantitative models that are useful for extrapolation of data or for predicting multiple metal distribution equilibria from single metal data. The chemical-reaction equilibrium formulation provides a framework for constructing such models. One of the drawbacks of purely empirical correlations of distribution coefficients is that pH has often been chosen as an independent variable. Such a choice is suggested by the form of Pigs. 8-3-5 and 8.3-8. Although pH is readily measured and contmlled on a laboratory scale, it is really a dependent variable, which is detenmined by mass belances and simultaneous reaction equilibria. An appropriate phare-equilibrium model should be able to predict equilibrium pH, at least within a moderate activity coefficient correction, concurrently with other species concemrations. 

The mechanochemical treatment by ball milling is a very complex process, wherein a number of phenomena (such as plastic deformation, fracture and coalescence of particles, local heating, phase transformation, and chemical reaction) arise simultaneously influencing each other. The mechanochemical treatment is a non-equilibrium solid-state process whereby, the final product retains a very fine, typically nanocrystalline or amorphous structure. At the moment of ball impact, dissipation of mechanical energy is almost instant. Highly excited state of the short lifetime decays rapidly, hence a frozen disordered, metastable strucmre remains. Quantitative description of the mechanochemical processes is extremely difficult, herewith a mechanochemical reaction still lacks clear interpretations and adequate paradigm. 

Chemical reaction with simultaneous pervaporation has also been used in non-equilibrium systems, such as in the works of D. Fritsch and co-workers on the hydrodehalogenation of chlorophenol and chlorobenzene. - ... 

Say we have a system in which the species undergo chemical reaction by rearranging their bonds to minimize the total Gibbs energy and obtain equilibrium. While we have identified the significant species at play and their phases, we do not know what the reaction mechanism is. In fact, there may be many simultaneous reactions that describe these molecular rearrangements. We may be concerned with questions about how to set up the chemical reaction equilibrium problem, such as What equations should I use to describe the reactions and How do I know if I have included enough reactions ... 

Chemical reactions that are reversible are said to be in dynamic equilibrium because opposite reactions take place simultaneously at the same rate. A system that is at equilibrium can be shifted toward either reactants or products if the system is subjected to a stress. Changes in concentration, temperature, or pressure are examples of stresses. 

DR Olander. Simultaneous mass transfer and equilibrium chemical reaction. AIChE J 6 233-239, 1960. 

The treatment of chemical reaction equilibria outlined above can be generalized to cover the situation where multiple reactions occur simultaneously. In theory one can take all conceivable reactions into account in computing the composition of a gas mixture at equilibrium. However, because of kinetic limitations on the rate of approach to equilibrium of certain reactions, one can treat many systems as if equilibrium is achieved in some reactions, but not in others. In many cases reactions that are thermodynamically possible do not, in fact, occur at appreciable rates. 

Processes in which chemical reaction and phase equilibria are simultaneously of significance present a considerable challenge to the thermodynamicist. The challenge is both to develop models which are suitable to describe the mixtures and to find computational procedures which permit analysis of equilibrium behavior. 

In Unit 3, you learned that the rate of any reaction depends on the concentration of the reacting chemicals. As a reaction proceeds, the concentrations of the product chemicals increases, and the reverse reaction may re-form reactants. Under certain conditions, the rate of the reverse reaction increases as the rate of the forward reaction decreases. Eventually, the rate of the forward reaction equals the rate of the reverse reaction. Equilibrium occurs when opposing changes, such as those just described, are occurring simultaneously at the same rate. 

Many industrial processes involve mass transfer processes between a gas/vapour and a liquid. Usually, these transfer processes are described on the basis of Pick s law, but the Maxwell-Stefan theory finds increasing application. Especially for reactive distillation it can be anticipated that the Maxwell-Stefan theory should be used for describing the mass transfer processes. Moreover, with reactive distillation there is a need to take heat transfer and chemical reaction into account. The model developed in this study will be formulated on a generalized basis and as a consequence it can be used for many other gas-liquid and vapour-liquid transfer processes. However, reactive distillation has recently received considerable attention in literature. With reactive distillation reaction and separation are carried out simultaneously in one apparatus, usually a distillation column. This kind of processing can be advantageous for equilibrium reactions. By removing one of the products from the reactive zone by evaporation, the equilibrium is shifted to the product side and consequently higher conversions can be obtained. Commercial applications of reactive distillation are the production of methyl-... 

The variation of efficiencies is due to interaction phenomena caused by the simultaneous diffusional transport of several components. From a fundamental point of view one should therefore take these interaction phenomena explicitly into account in the description of the elementary processes (i.e. mass and heat transfer with chemical reaction). In literature this approach has been used within the non-equilibrium stage model (Sivasubramanian and Boston, 1990). Sawistowski (1983) and Sawistowski and Pilavakis (1979) have developed a model describing reactive distillation in a packed column. Their model incorporates a simple representation of the prevailing mass and heat transfer processes supplemented with a rate equation for chemical reaction, allowing chemical enhancement of mass transfer. They assumed elementary reaction kinetics, equal binary diffusion coefficients and equal molar latent heat of evaporation for each component. 

We first examine the final state of the reaction, i.e. the chemical equilibrium composition. This is not of great relevance to oscillatory behaviour but is an important first check that the model is chemically reasonable . Equilibrium arises when all three rates of change become zero simultaneously. Equations (2.1)—(2.3) have a unique point satisfying this condition, as required chemically, given by... 

It may occur that an electroactive species is present in the system in equilibrium with some electroinactive form. Then, in addition to diffusion, so-called coupled chemical reactions will occur delivering or consuming the electroactive component. If the rate of such a reaction is sufficiently fast, it will appear that all of the species concerned are diffusing simultaneously to take part in the heterogeneous process. If the reaction rate is much lower than that of the diffusion, only the free ... 

The above arguments for a single chemical reaction are readily extended to the case of several simultaneous reactions in the same system. In the equilibrium state, for several reactions, I, II,. . . , n the affinities of all reactions are zero ... 

As long as one has to consider no more than a single chemical reaction, one need compute only a single equilibrium constant from which the equilibrium compns are readily obtained. When, however, chemical processes take place at extreme temps and pressures, a large number of simultaneous equilibria may exist. For example, to calculate the flame temp for the combustion of a hydrocarbon in air it may be necessary to consider as many as 20 chemical reactions. As the number of reactions increases, so does the mathematical difficulty because no... 

For any pure chemical species, there exists a critical temperature (Tc) and pressure (Pc) immediately below which an equilibrium exists between the liquid and vapor phases (1). Above these critical points a two-phase system coalesces into a single phase referred to as a supercritical fluid. Supercritical fluids have received a great deal of attention in a number of important scientific fields. Interest is primarily a result of the ease with which the chemical potential of a supercritical fluid can be varied simply by adjustment of the system pressure. That is, one can cover an enormous range of, for example, diffusivities, viscosities, and dielectric constants while maintaining simultaneously the inherent chemical structure of the solvent (1-6). As a consequence of their unique solvating character, supercritical fluids have been used extensively for extractions, chromatographic separations, chemical reaction processes, and enhanced oil recovery (2-6). 

If a fast reaction system is considered, the RSP can be satisfactory described assuming a reaction equilibrium. Here, a proper modeling approach is based on the nonreactive equilibrium-stage model, extended by simultaneously using the chemical equilibrium relationship. 

The characteristic features of parameter estimation in a molecular model of adsorption are illustrated in Table 9.9, taking the simple example of the constant-capacitance model as applied to the acid-base reactions on a hydroxylated mineral surface. (It is instructive to work out the correspondence between equation (9.2) and the two reactions in Table 9.9.) Given the assumption of an average surface hydroxyl, there are just two chemical reactions involved (the background electrolyte is not considered). The constraint equations prescribe mass and charge balance (in terms of mole fractions, x) and two complex stability constants. Parameter estimation then requires the determination of the two equilibrium constants and the capacitance density simultaneously from experimental data on the species mole fractions as functions of pH. 

In this chapter, unifying concepts for analyzing and understanding the dynamics of integrated reaction separation processes with rapid chemical reactions are introduced. The text is based on some recent studies [11-13], and extends the concepts introduced earlier for reactive distillation processes [23] to other integrated reaction separation processes. The class of processes to be considered is rather broad. It includes reaction processes where simultaneous separation is used to enhance a reaction, for example, by shifting inherent equilibrium limitations. Various process examples of this kind are provided in this book. The chapter also includes separation processes with potentially reactive mixtures. In this case, a chemical reaction can be either an unwanted side effect or it can be used directly to achieve a certain separation, which is not possible under nonreactive conditions (see e.g. Ref. [10]). The latter represents a reaction-enhanced separation. 

Again, these structural results do not depend on specific values of the equilibrium constant K and the parameters of the Langmuir isotherm a , hi, as was shown in the appendix of Ref. [11]. Further, it was shown that the same patterns of behavior will arise if the chemical reaction is taking place in the solid phase instead of the fluid phase. The latter is of particular interest in applications where the adsorbent acts simultaneously as a catalyst. Practical examples will be discussed in the next section the interested reader is also referred to Chapter 6 of this book. In this context it is worth noting that the structural properties in Fig. 5.9 depend crucially on the stoichiometry of the system, which will be also discussed in the next section. 

With simultaneous phase and reaction equilibrium the system has only two dynamic degrees of freedom (five solutes - three chemical equilibria) and therefore corresponds again to a nonreactive system with two solutes. If the dimers are taken as reference components the following definition of the transformed concentration variables is found from Eq. (6)... 

In 1834 Faraday proposed that the reactants have to adsorb simultaneously at the surface, but he did not really explain the catalytic action. Of course, neither did Berzelius give an explanation, but he nicely generalized many results in a simple description. Later, Ostwald gave the definition that a catalyst does not influence the thermodynamic equilibrium of reactants and products but affects the rates of the chemical reactions. The conclusions of Berzelius and Faraday proved to be correct. 

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