Effect of reaction order

The kinetic equations for systems at constant volume have a generic order, i.e. TR = kl- Q 

The number of moles of A transformed into R per unit of volume and time represents the formation rate of R, while the total number of moles of A reacted, under the same conditions, represents the consumption rate of A or formation rate of all products, then the local yield can be written as follows  

The overall yield in the CSTR is equal to the local yield, Equation 16.27, while in the PER the yield should be integrated, substituting Equation 16.27 into Equation 16.23, 

High yield is naturally desired and as the above equations show, they depend on the kinetics of each reaction, particularly the reaction order and kinetic constants for each step. 

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Effect Of Reaction Order All the designs up to this point have assumed that the reaction is first-order in the concentration of the reactant CA. Many reactions have reaction rates that depend on the reactant concentration to a power other than 1 ... 

Effect of reaction order on diffusion factor y. Calculation of the characteristic function of y applicable to the case of an n order reaction yields similar functional relationships, in which the modulus

concentration term. For example, the case of second-order reaction involves the modulus... 

Figure 7.9 shows the effect of reaction order for n > 1 in a spherical pellet. As the reaction order increases, the effectiveness factor decreases. Notice that the definition of Thiele modulus in Equation 7.47 has achieved the desired goal of giving all reaction orders a common asymptote at high values of Figure 7.10 shows the effectiveness factor versus Thiele modulus for reaction orders less than unity. Notice the discontinuity in slope of the effectiveness factor versus Thiele modulus that occurs when the order is less than unity. Recall from... 

Includes the effect of reaction order n for simple th-order chemical kinetics on optimum residence times and outlet reactant conversions in each CSTR. k T ) = k Ti) = 0.1 (L/mol)" Vmin ri - -T2 50 min Ca, inlet = 1 mol/L. 

When n = 1, Equation 13,12 reduces identically to the perfectly mixed CSTR equation [A]I[A]q =1/(1 + kt), that is, micromixing has no effect. Thus, as a general rule, conversion in a first-order reaction is uniquely detennined by the residence time distribution. This is true for both premixed and unpremixed feeds. We examine the effect of reaction order more fully in the following section. 

Effect of reaction order Choice of reactor becomes relatively easy if the orders of the two reactions of Scheme R19 are known. If reaction RI is first order and R2 second order in A, then the concentration environment of the reaction will have a major effect on the selectivity of R. Recall that conversion in an MFR occurs at the greatly reduced outlet concentration, while that in a PFR is the cumulative value determined by the changing concentration environment of the reactor starting from a high initial value. Thus, the selectivity for R will be higher in the MFR. On the other hand, if the order of reaction Rl is R2 and of R2 is Rl, then the selectivity for R will be lower in the MFR. 

Parallel reactions (nonreacting products) The general case Effect of reaction order One of the reactants undergoes a second reaction Parallel-consecutive reactions Plug-flow reactor with recycle The basic design equation Optimal design of RPR Use of RPR to resolve a selectivity dilemma Semibatch reactors... 

We show that physical conditions may be found under which this exothermic standard reaction may self-organize through the DMCI [20]. The analysis applies however to the large class of exothermic reactions in general, since the exponential temperature dependence of the rate constants dominates effects of reaction order. 

In the previous analyses of the combined effects of chemical reaction and diffusion, we have used first-order kinetics for the interfacial reaction. In this section we will examine the effect of reaction order with respect to the concentration of gaseous reactant ( , henceforth to be called simply, the reaction order ). We shall do this for the shrinking unreacted-core system without external-mass-transport resistance, and for irreversible reactions K oo). 

FIG. 3.13. The effect of reaction order n on the rate of regression of the reaction interface for various values of the reaction modulus CTs [44]. 

Fig. 15. Temperature vs heat generation or removal in estabHshing stationary states. The heavy line (—) shows the effect of reaction temperature on heat-generation rates for an exothermic first-order reaction. Curve A represents a high rate of heat removal resulting in the reactor operating at a low temperature with low conversion, ie, stationary state at a B represents a low rate of heat removal and consequently both a high temperature and high conversion at its stationary state, b and at intermediate heat removal rates, ie, C, multiple stationary states are attainable, c and The stationary state at c ...

FIG. 23-19 Effectiveness of first-order reactions in spheres under adiabatic conditions (Weisz and Hicks, Chem. Eng. Sci., 17, 26.5 [1962]). 

In order to understand the effect of reaction on membrane diffusion, we use the membrane without reaction as a reference. The corresponding flux [Eq. (39), where c2 is equal to zero] is... 

A related methodology that makes use of the calculated surface charges at the cavity surface to estimate the interaction with the solvent has been described in Ref. [54] in addition, the reaction field model can be extended to include the effects of higher order multipoles [55], In the present implementation, only dipole effects are considered. 

If the previous example is modified slightly to permit the volumes in each reactor to vary with time, both total and component continuity equations are required for each reactor. To show the effects of higher-order kinetics, assume the reaction is now nth-order in reactant A. 

Figure 8. The effect of FT on the reaction order after zero order behavior. Figure 9. The effect of zero order behavior on the % mannitol.

Figure 8. The effect of reaction temperature on ethyl stearate conversion as a function of time-on-stream and Arrhenius plot (based on zero order kinetics) Reaction conditions 5 mol% ethyl stearate in hexadecane, mcat=0.4 g, p27o-c=l bar, P3oo"c=3 bar, p33ox=5 bar, p36o-c=7 bar and V =0.1 ml/min.

Quayum, M. E., Kondo, T., Nihonyanagi, S., Miyamoto, D. and Uosaki, K. Formation of organic monolayer on a hydrogen terminated Si(l 11) surface via silicon-carbon bond monitored by ATR FT-IR and SFG spectroscopy Effect of orientational order on the reaction rate. Chemistry Letters, 208 (2002). 

FIG. 28. Kinetic in-cell investigation of the anode reaction of the MCFC establishing an effective H2-reaction order of close to one. 

Considerably fewer kinetic studies were performed with reactants in the vapour phase than in the liquid phase. The second-order rate equation was only used for acetic acid—ethanol esterification at 130°C and 175° C on a KU-2 standard ion exchanger [444,445]. A semiempirical second-order rate equation with slight inhibiting effect of reaction products, viz. 

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