Reactions with Variable Density

It is evident that for multiple reactions with variable density, we rapidly arrive at rather complex expressions that require considerable manipulation even to formulate the expressions, which can be used to calculate numerical values of the reactor volume required for a given conversion and selectivity to a desired product. 

P3.05. 10. HALF TIME. REACTION WITH VARIABLE DENSITY... 

Adesina [14] considered the four main types of reactions for variable density conditions. It was shown that if the sums of the orders of the reactants and products are the same, then the OTP path is independent of the density parameter, implying that the ideal reactor size would be the same as no change in density. The optimal rate behavior with respect to T and the optimal temperature progression (T p ) have important roles in the design and operation of reactors performing reversible, exothermic reactions. Examples include the oxidation of SO2 to SO3 and the synthesis of NH3 and methanol CH3OH. 

Example 4.3 represents the simplest possible example of a variable-density CSTR. The reaction is isothermal, first-order, irreversible, and the density is a linear function of reactant concentration. This simplest system is about the most complicated one for which an analytical solution is possible. Realistic variable-density problems, whether in liquid or gas systems, require numerical solutions. These numerical solutions use the method of false transients and involve sets of first-order ODEs with various auxiliary functions. The solution methodology is similar to but simpler than that used for piston flow reactors in Chapter 3. Temperature is known and constant in the reactors described in this chapter. An ODE for temperature wiU be added in Chapter 5. Its addition does not change the basic methodology. 

We define the rate of reaction verbally for a species involved in a reacting system either as a reactant or as a product. The system may be single-phase or multiphase, may have fixed density or variable density as reaction proceeds, and may have uniform or varying properties (e.g., p, CA, T, P) with respect to position at any given time. The extensive rate of reaction with respect to a species A, RA, is the observed rate of formation of A ... 

The general characteristics of a batch reactor (BR) are introduced in Chapter 2, in connection with its use in measuring rate of reaction. The essential picture (Figure 2.1) in a BR is that of a well-stirred, closed system that may undergo heat transfer, and be of constant or variable density. The operation is inherently unsteady-state, but at any given instant, the system is uniform in all its properties. 

If the system is not of constant density, we must use the more general form of the equation for reaction time (12.3-2) to determine t for a specified conversion, together with a rate law, equation 12.3-3, and an equation of state, equation 2.2-9. Variable density implies that the volume of the reactor or reacting system is not constant. This may be visualized as a vessel equipped with a piston V changes with the position of the piston. Systems of variable density usually involve a gas phase. The density may vary if any one of T, P or n, (total number of moles) changes (so as to alter the position of the piston). 

The additional potential required to cause some electrode reactions to proceed at an appreciable rate. The result of an energy barrier to the electrode reaction concerned, it is substantial for gas evolution and for electrodes made of soft metals, e.g. Hg, Pb, Sn and Zn. It increases with current density and decreases with increasing temperature, but its magnitude is variable and indeterminate. It is negligible for the deposition of metals and for changes in oxidation state. 

In the reactors studied so far, we have shown the effects of variable holdups, variable densities, and higher-order kinetics on the total and component continuity equations. Energy equations were not needed because we assumed isothermal operations. Let us now consider a system in which temperature can change with time. An irreversible, exothermic reaction is carried out in a single perfectly mixed CSTR as shown in Fig. 3.3. 

When the density varies, we need to find another variable to express the progress of a reaction. Earlier we defined the fractional conversion X for a single reaction, and in this chapter we defined the conversion of a reactant species for reactant A and Xj for reaction j. For the conversion in a reaction we need a different variable, and we shall use Xj (bold type), with the index i describing the reaction. We will first work our series and parallel reactions with these variables and then consider a variable-density problem. 

The kinetics of the addition of aniline (PI1NH2) to ethyl propiolate (HC CCChEt) in DMSO as solvent has been studied by spectrophotometry at 399 nm using the variable time method. The initial rate method was employed to determine the order of the reaction with respect to the reactants, and a pseudo-first-order method was used to calculate the rate constant. The Arrhenius equation log k = 6.07 - (12.96/2.303RT) was obtained the activation parameters, Ea, AH, AG, and Aat 300 K were found to be 12.96, 13.55, 23.31 kcalmol-1 and -32.76 cal mol-1 K-1, respectively. The results revealed a first-order reaction with respect to both aniline and ethyl propiolate. In addition, combination of the experimental results and calculations using density functional theory (DFT) at the B3LYP/6-31G level, a mechanism for this reaction was proposed.181... 

A variety of parameters must be evaluated in any surface complexation model. Common to all surface reactions are the density of SOH sites, N, the specific surface area, A, the solid/liquid ratio, and the near-surface capacities, Ci inside the OHP, and C2 outside the OHP. Nj is a property of the solid for both quartz and corundum, Ng was taken as 5 sites/nm (11.28). A and solid/liquid ratio are experimental variables values reported with published adsorption data were used in each case. The value, 0.20 F/m (Farads per m ) (27), was adopted for C2 throughout this work. Every surface... 

The general case of variable density reactions is applicable mostly to gas-phase reactions and seldom to liquid-phase reactions. Because the gas law gives the precise relationship between P, V, T, and N, we start with that equation. Based... 

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