Heterogeneous chemical equilibria equilibrium conditions

Fugacity. Accdg to Hackh s (Ref 1), it is the escaping tendency in a heterogeneous mixture, by which. a chemical equilibrium responds to altered conditions. In a dilute soln obeying the gas laws, the fugacity equals the osmotic pressure. In other solns it is the value of the pressure for which these equations are still valid... 

The oxidation of sulphur dioxide to trioxide is one of the oldest heterogeneous catalytic processes. The classic catalyst based on V2Os has therefore been the subject of numerous investigations which are amply reviewed by Weychert and Urbaneck [346]. These authors conclude that none of the 34 rate equations reported is applicable over a wide range of process conditions. Generally, these equations have the form of a power expression, in which the reverse reaction is taken into account within the limits imposed by chemical equilibrium, viz. 

The calculation of the equilibrium conversion of heterogeneous reactions is in most cases much more complicated then in the case of homogeneous reactions, because the calculations involve in general the solution of the conditions for chemical equilibrium and the conditions for phase equilibrium. In the following a relatively simple example is given. 

A cell may be considered as a heterogenous system at equilibrium with restrictions. In most cells the pressure on each phase is the same and a change of pressure of the system would cause the same change of pressure on all phases. However, it is possible to construct a cell so that the various phases may have different pressures. Then the pressures of some phases may be held constant while the pressures of other phases are changed. In such cases some of the derivatives of the chemical potentials in Equation (12.86) would be zero unless matter would have to be transported across the boundary between phases in order to maintain the equilibrium conditions with a change of pressure. 

In spite of the above justification for the kinetic approach to the estimate of l, this has a number of drawbacks. First of all, there is no point in using a kinetic approach to determine a thermodynamic equilibrium quantity such as l. The justification of the validity ofEqs. (42) and (45) by the resulting equilibrium condition of Eq. (46) is far from rigorous, just as is the justification of the empirical Butler-Volmer equation by the thermodynamic Nernst equation. Moreover, the kinetic expressions of Eq. (41) involve a number of arbitrary assumptions. Thus, considering the adsorption step of Eq. (38a) in quasi-equilibrium under kinetic conditions cannot be taken for granted a heterogeneous chemical step, such as a deformation of the solvation shell of the... 

It is of course well known that in nature heterogeneous chemical equilibria are possible systems in which chemical reactions may take place, and which at equilibrium will exist in mote than one phase. The question that arises is the analysis of the conditions under which heterogeneous chemical equilibria are possible in multicomponent mixtures. In this section, we follow closely the analysis that was recently presented by Astarita and Ocone (1989) earlier work on the subject is due to Caram and Scriven (1976) and Astarita (1976). 

In systems where heterogeneous chemical equilibria prevail, both chemical and phase equilibrium conditions must be simultaneously satisfied. In practice, this means that the chemical equilibrium condition—Eq. (51) in the discrete description, and Eq. (60) in the continuous one—must be satisfied in one phase, and the phase equilibrium condition [/( or fi(x) to be the same in all phases] must be satisfied this clearly guarantees that the chemical equilibrium condition is automatically satisfied in all phases. 

A homogeneous reaction is one that involves only one phase. A heterogeneous reaction involves more than one phase, and reaction usually occurs at, or very near the interface between the phases. An irreversible reaction is one that proceeds in only one direction and continues in that direction until the reactants Types of reactions are exhausted. A reversible reaction, on the other hand, can proceed in either direction, depending on the concentrations of reactants and products relative to the corresponding equilibrium concentrations. An irreversible reaction behaves as if no equilibrium condition exists. StrictW speaking, no chemical reaction is completely irreversible, but in very many reactions the equilibrium point lies so far to the right that they are treated as irreversible reactions. 

In theoretical studies on diamond nucleation, thermodynamic theory, homogeneous and heterogeneous chemical kinetics, classical nucleation theory, adsorption-desorption kinetics and equilibrium have been considered to predict preferential conditions for diamond nucleation and growth. A narrow range of conditions, such as pressure (supersaturation), temperature,... 

The total number of ways of distributing the species is independent of the order in which the species are attached. In transition state theory applied to heterogeneous catalysis the coverage of activated complexes is neglected. Consequently, interactions between a particular type of adsorbed species and activated complexe are also neglected. Equilibrium condition for adsorption again implies equality of the chemical potential in the gas-phase and the adsorbed phase ... 

If a mixture consisting of one or more components possesses uniform physical and chemical properties throughout, it is said to be a single-phase, homogeneous system. If, however, a system consists of one or more parts that have different properties and are set apart from each other by bounding surfaces, so that the phases are mechanically separable, the system is heterogeneous. When equilibrium exists between the distinct parts of the system, this condition is known as heterogeneous equilibrium. 

In this chapter we apply the general criteria for equilibrium developed in Chap. 6 to systems in which chemical reactions may occur. In Sec. 8-1, we present a general discussion of chemical equilibrium in homogeneous and heterogeneous systems. The concept of a progress variable is introduced, and the conditions for chemical equilibrium are derived. The equilibrium constant is defined, and some of its properties are developed. A discussion of the Le Chatelier-Braun principle applied to chemical reactions is presented. In Sec. 8-2, the results of Sec. 8-1 are applied to chemical reactions in mixtures of real gases. 

Equation (13-25) is a necessary condition for equilibrium in a galvanic cell for the process in which n moles of electrons are transported from phase V to phase 1 and in which the heterogeneous chemical reaction... 

Conditional equilibrium constants for reactions in heterogeneous chemical system.s are discu.ssed fully in Chap. 5 of G. Sposito. op, cit. ... 

If heterogeneous electrochemical steps are reversible (that is, the Nemst equa-ti(Mi obeyed), then the conditions of chemical equilibrium for any IVR are also obeyed. Certainly, the IVRs could be irreversible as well. However, this would not reveal itself in the shape of stationary voltage-current curves bringing about only the distortions in crmcentration profiles of the diffusion layers near the electrode. Then, conversely to the above, no electrochemical kinetics—no chemical kinetics should be trae as weU. ... 

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