Page 265 - Introduction to chemical reaction engineering and kinetics

246 Chapter 9: Multiphase Reacting Systems

The value of cn in the bulk liquid is the largest value of cn that can influence the rate of
reaction, and may be designated $irnax. From equation (A), with 6 = 0, and S, = D,elk,e,
equation 9.2-7,

KAgDAtbpA
CB,max = (9.2-23)
DBt kA, -KA~HA 1
(
= k&‘PdkBe
if we use the condition for gas-film control, from equation 9.2-13, l/k,, >> HA/k,, or
kA, > > HA kAg, SO that KAg = kAg, together with equation 9.2-21 to eliminate DA, D,,,
and k,, in favor of k,,.
To obtain (-rA) for gas-film control, we may substitute cn,max from equation 9.2-23
into equation 9.2-22, and again use k,, >> HAkAg, together with equation 9.2-21:

(9.2-24)
(-rA) = kAgPA; CB z CB,max
Thus, when cn 2 crsrnax, the rate (-TA) depends only on PA.

This result also has implications for (-?-A) given by equation 9.2-22. This equation
applies as it stands only if cB I c~,~~. For higher values of cn, equation 9.2-24 governs.

What is the form of equation 9.2-22 for liquid-film control?

SOLUTION
For liquid-film control, there is no gas-phase resistance to mass transfer of A. Thus, in
eqUEitiOU 9.2-14, IlkA, >> l/HAkAg, and KAe = kAe, so that equation 9.2-22b may be
written

(-rA) = (9.2-25)

9.2.3.3.2. Fast reaction. If chemical reaction is sufficiently fast, even though not instan-
taneous, it is possible for it to occur entirely within the liquid-film, but not at a point or
plane. This case is considered as a special case of reaction in both bulk liquid and liquid
film in Section 9.2.3.4. In this situation, NA = (-TA).

9.2.3.3.3. Enhancement factor E. For reaction occurring only in the liquid film,
whether instantaneous or fast, the rate law may be put in an alternative form by means
of a factor that measures the enhancement of the rate relative to the rate of physical
absorption of A in the liquid without reaction. Reaction occurring only in the liquid
film is characterized by cA + 0 somewhere in the liquid film, and the enhancement
factor E is defined by

rate of reaction or flux of A
E =
maximum rate of mass transfer of A through the liquid film
= (-rdlkAt(CAi - cA) = (-rA)/kA&Ai
(9.2-26) /