Equilibrium multiple reaction

Most processes are catalyzed where catalysts for the reaction are known. The choice of catalyst is crucially important. Catalysts increase the rate of reaction but are unchanged in quantity and chemical composition at the end of the reaction. If the catalyst is used to accelerate a reversible reaction, it does not by itself alter the position of the equilibrium. When systems of multiple reactions are involved, the catalyst may have different effects on the rates of the different reactions. This allows catalysts to be developed which increase the rate of the desired reactions relative to the undesired reactions. Hence the choice of catalyst can have a major influence on selectivity. 

For multiple reactions in which the byproduct is formed in series, the selectivity decreases as conversion increases. In this case, lower conversion than that for single reactions is expected to be appropriate. Again, the best guess at this stage is to set the conversion to 50 percent for irreversible reactions or to 50 percent of the equilibrium conversion for reversible reactions. 

The hydrogen concentration contours for 50 atm and 700°K (Figure 8) indicate that there is appreciable unreacted hydrogen after equilibrium is reached. It is clear that multiple reaction stages are required to approach pure methane. 

Equilibrium Compositions for Multiple Reactions. When there are two or more independent reactions. Equation (7.29) is written for each reaction ... 

In the preceding chapter, the choice of reactor type was made on the basis of the most appropriate concentration profile as the reaction progressed, in order to minimize reactor volume for single reactions or maximize selectivity (or yield) for multiple reactions for a given conversion. However, there are still important effects regarding reaction conditions to be considered. Before considering reaction conditions, some basic principles of chemical equilibrium need to be reviewed. 

The selection of reactor pressure for vapor-phase reversible reactions depends on whether there is a decrease or an increase in the number of moles. The value of AN in Equation 6.25 dictates whether the equilibrium conversion will increase or decrease with increasing pressure. If AN is negative, the equilibrium conversion will increase with increasing pressure. If AN is positive, it will decrease. The choice of pressure must also take account of whether the system involves multiple reactions. 

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. 

Although we have indicated some applications of thermodynamics to biological systems, more extensive discussions are available [6]. The study of equilibrium involving multiple reactions in multiphase systems and the estimation of their thermodynamic properties are now easier as a result of the development of computers and appropriate algorithms [7]. 

Students may have seen the acetaldehyde decomposition reaction system described as an example of the application of the pseudo steady state (PSS), which is usually covered in courses in chemical kinetics. We dealt with this assumption in Chapter 4 (along with the equilibrium step assumption) in the section on approximate methods for handling multiple reaction systems. In this approximation one tries to approximate a set of reactions by a simpler single reaction by invoking the pseudo steady state on suitable intermediate species. 

In catalytic distillation the temperature also varies with position in the column, and this will change the reaction rates and selectivities as well as the equilibrium compositions. Temperature variations between stages and vapor pressures of reactants and products can be exploited in designing for multiple-reaction processes to achieve a high selectivity to a desired product with essentially no unwanted products. 

Equation (2.38) has a first-order sink and a zero-order source, which meets our criteria for an analytical solution to the diffusion equation. Ce is the concentration of C at equilibrium for the reaction. This technique of assuming that multiple reactions are zero-order and first-order reactions will be utilized in Example 2.9. 

S. Ung and M. F. Doherty, Calculation of residue curve maps for mixtures with multiple equilibrium chemical reactions. Ind. Engng. Chem. Res.,... 

This chapter, after introducing the equilibrium constant, discusses briefly the rate of entropy production in chemical reactions and coupling aspects of multiple reactions. Enzyme kinetics is also summarized. 

This model represents the most frequently used description of chemical reaction equilibrium and should be familiar to most chemical engineering students. However, for multicomponent mixtures in which multiple reactions may take place, this type of non-linear problems may be cumbersome to solve numerically. One important obstacle is that the non-linear equilibrium constant definitions may give rise to multiple solutions, hence we have to identify which of them are the physical solutions. The stoichiometric formulation might thus be inconvenient for mixtures containing just a few species for which only a few reactions are taking place. 

In addition to using membrane reactors lo remove a reaction product in order to shift the equilibrium toward completion, we can use membrane reactors to increase selectivity in multiple reactions. This increase can be achieved by injecting one of the reactants along the length of the reactor. It is particularly effective in panial oxidation of hydrocarbons, chlorination, ethoxylation. hydrogenation, nitration, and sulfunation reactions to name a few. ... 

Nonequilibrium transport of solutes through porous media occurs when ground-water velocities are sufficiently fast to prevent attainment of chemical and physical equilibrium. Chemical reactions in porous media often require days or weeks to reach equilibrium. For example. Fuller and Davis Q) reported that cadmium sorption by a calcareous sand was characterized by multiple reactions, including a recrystallization reaction that continued for a period of days. Sorption of oxyanions by metal oxyhydroxides often occurs at an initially rapid rate the rate then decreases until steady-state is achieved (2-4). Unless ground-water velocity in such a situation is extremely slow, nonequilibrium transport will occur. 

This problem concerns thcrmod Tiamic equilibrium and multiple reactions. It is usually assigned at th.e graduate level. The heat of isomerization must be calculated at temperature below lOO C where no other reactions are dominate alternate to F6-5. 

An alternative method of obtaining a solution to the multiple-reaction, single-phase equilibrium problem is to use the method of Lagrange multipliers. Here one first rewrites the constraints as... 

These equations establish that one of the equilibrium conditions in a multiple-reaction, multiphase system is that phase equilibrium be established for each of the species among the phases in which the species is present. 

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