Page 267 - Introduction to chemical reaction engineering and kinetics

248 Chapter 9: Multiphase Reacting Systems

For B, similarly, we have

d2CB - (-t-f& = 0
DBeJy (9.2-29)

The intrinsic rate of reaction is a function of cA, cn, and T

ter~hnt = rA(cAj CBpT) (9.2-30)

and ( -rA)inr and (-rn)& are related by

(9.1-8)
(-rB)inr = b(-r,4jint
The boundary conditions for the two simultaneous second-order ordinary differential
equations, 9.2-28 and -29, may be chosen as:

at x = 0, CA = CAi (9.2-31)

(9.2-32)

(consistent with no transport of B through the interface, since B is nonvolatile)

at x = a,, CA = cA(in bulk liquid) = C/Q, (9.2-33)

cn = cn(in bulk liquid) = Crib (9.2-34)

Equations 9.2-28 and -29, in general, are coupled through equation 9.2-30, and an-
alytical solutions may not exist (numerical solution may be required). The equations
can be uncoupled only if the reaction is first-order or pseudo-first-order with respect to
A, and exact analytical solutions are possible for reaction occurring in bulk liquid and
liquid film together and in the liquid film only. For second-order kinetics with reaction
occurring only in the liquid film, an approximate analytical solution is available. We
develop these three cases in the rest of this section.

9.2.3.4.1. First-order or pseudo-jr&order isothermal, irreversible reaction with re-
spect to A; reaction in liquidjlm and bulk liquid For a reaction that is first-order or
pseudo-first-order with respect to A, we have

(-rAL = kACA
or

(9.2-35a)

where kJ$ = kACB, which is of the same form as 9.2-35.
Use of either one of these for (-?-A& has the effect of uncoupling equation 9.2-
28 from -29, and we need only solve the former in terms of A. Thus, equation 9.2-28
becomes:

- kACA = 0 (9.2-36)