Simultaneous reactions equilibrium treatment

Complex Clieinical-Reaction Equilibria When the composition of an equilibrium mixture is determined by a number of simultaneous reactions, calculations based on equilibrium constants become complex and tedious. A more direct procedure (and one suitable for general computer solution) is based on minimization of the total Gibbs energy G in accord with Eq. (4-271). The treatment here is... 

It is important to note that catalysts for alkoxysilane hydrolysis are usually catalysts for condensation. In typical silane surface treatment applications, alkoxysilane reaction products are removed from equilibrium by phase separation and deposition of condensation products. The overall complexity of hydrolysis and condensation has not allowed simultaneous determination of the kinetics of silanol formation and reaction. Equilibrium data for silanol formation and condensation, until now, have not been reported. 

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... 

The carbon dioxide reforming of methane has attracted academic and industrial interest, since it produces synthesis gas with a H2/CO ratio closed to 1, which is more suitable for methanol and Fischer-Tropsch synthesis compared to the steam reforming of methane providing synthesis gas with a H2/CO ratio = 3. This reaction is of particular importance for the valorization of C02-rich fossil natural gas but also for the transformation of biogas extensively produced by various anaerobic waste treatments [1]. The production of synthesis gas from CH4 and CO2 is highly endothermic (Eq. (22.1)), the reaction equilibrium is influenced by the simultaneous occurrence of the reverse water-gas shift reaction (RWGS) (Eq. (22.2)). 

We have considered thermodynamic equilibrium in homogeneous systems. When two or more phases exist, it is necessary that the requirements for reaction equilibria (i.e., Equations (7.46)) be satisfied simultaneously with the requirements for phase equilibria (i.e., that the component fugacities be equal in each phase). We leave the treatment of chemical equilibria in multiphase systems to the specialized literature, but note that the method of false transients normally works quite well for multiphase systems. The simulation includes reaction—typically confined to one phase—and mass transfer between the phases. The governing equations are given in Chapter 11. 

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. 

When buffer solutions were not used and the pH was not reported, we calculated the pH using the solution concentration and pK values for all dissociation reactions and assuming that the pH was 7.0 prior to solute addition. A general treatment of simultaneous equilibrium involving equations for all linearly independent reactions, the water dissociation reaction (K = 1.0 x lO" " ), a molecular balance on the active species, and an equation requiring solution electroneutrafity is required to calculate the natural pH (Brescia et al., 1975). A more detailed discussion of the adjustment for ionization and associated calculations is presented in Vecchia and Bimge (2002b). 

A simple and direct method of determining the equilibrium composition of a complex reaction is to solve simultaneously all of the equations comprising the complex network. The actual number of equations to be solved is equal to the number of independent reactions of the network. Chapter 5 deals formally with the treatment of complex reactions, and the method outlined therein can be applied to this problem. Where the number of reactions is relatively small, say 2 or 3, simple, less formal methods can be used as illustrated in the following example. 

The basis of the treatment discussed here is (1) postulation of an apparent or effective equilibrium constant for the reaction that occurs simultaneously and interactively in both phases and (2) finding a relationship between this and the true equilibrium constants in the individual phases. Such an approach (Martinek et al., 1977, 1980, 1981a,b Martinek and Semenov, 1981a,b Semenov et al.. 

The problems of simultaneously treating spatial distributions of both temperature and concentration are currently the concern of the chemical engineer in his treatment of catalyst particles, catalyst beds, and tubular reactors. These treatments are still concerned with systems that are kineticaliy simple. The need for a unified theory of ignition has been highlighted by contemporary studies of gas-phase oxidations, many features being revealed that neither thermal theory, nor branched-chain theory for that matter, can resolve alone. A successful theoretical basis for such reactions necessarily involves the treatment of both the enorgy balance and mass balance equations. Such equations are invariably coupled and cannot be solved independently of each other. However, much information is offered by the phase-plane analj s of the syst (e.g. stability of equilibrium solutions, existence of oscillations) without the need for a formal solution of the balance equations. 

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. 

The most successful of the later statistical treatments has been transition-state theory, first formulated simultaneously and independently in 1935 by H. Eyring (1901-1981) and by M. G. Evans (1904-1952) and M. Polanyi (1891-1976). Transition-state theory treats the rates of elementary reactions as if there were a special type of equilibrium, having an equilibrium constant K between reactants and activated complexes. The rate constant is then given by... 

The treatment of incomplete reaction kinetics via Equations 3.61 and 3.62 is a rough approximation. A more exact treatment of incomplete/equilibrium reaction kinetics requires simultaneous consideration of the rates for both the forward and reverse reaction processes. For a simple first-order reaction of the form... 

As distinct from almost all polymer materials, the kinetics of IPN formation is a governing factor in development of the system morphology. For traditional polymeric materials their structure and morphology depend on the ways of processing, heat treatment, and other physical, not chemical, factors, while for IPNs all depends on the kinetic conditions. One may say that thermodynamics gives the general rules of the equiUbrium state and determines the path to equilibrium, whereas the kinetics allows the reahzation of the path and predetermines the real structure far from equilibrium. This specific feature of the IPN formation is connected with the fact that in the reaction system two processes proceed simultaneously the chemical process of network formation and the physical process of phase separation. As will be shown below, these processes are interconnected. 

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