Page 264 - Introduction to chemical reaction engineering and kinetics

9.2 Gas-Liquid Systems 245

These six governing equations may be solved for NA with elimination of pAI, CAi, Nn, kBe
and S,/S to result in the rate law, in terms of (- TA) = NA,

DEeHA
PA+-C B
DA@ (9.2-22)
NA = (-rA) =

or

(--A) = KAY

(9.2-22b)
= KAe
The last two forms come from the definitions of KAg and KAe in equations 9.2-13 and
-14, respectively.
Two extreme cases of equation 9.2-22 or -22a or -22b arise, corresponding to gas-
film control and liquid-film control, similar to those for mass transfer without chemical
reaction (Section 9.2.2). The former has implications for the location of the reaction
plane (at distance 6 from the interface in Figure 9.6) and the corresponding value of cn.
These points are developed further in the following two examples.

What is the form of equation 9.2-22 for gas-film control, and what are the implications
for the location Of the reaction plane (Vahe Of 6) and cs (and hence for (-t-A) in eCptiOn
9.2-22)?

SOLUTION

In Figure 9.6, the position of the reaction plane at distance 6 from the gas-liquid interface
is shown for a particular value of es. If cn changes (as a parameter), the position of the
reaction plane changes, 6 decreasing as cn increases. This may be realized intuitively from
Figure 9.6, or can be shown from equations 9.2-20, -2Oa, and -22a. Elimination of NA and
Nn from these three equations provides a relation between 6 and cB:

from which
as D~eDB&P.t
dCg=- <o (B)
KA,(DAebPA + DB~*ACBP
That is, 6 decreases as c, increases. 6 can only decrease to zero, since the reaction plane
cannot occur in the gas film (species B is nonvolatile). At this condition, the reaction plane
coincides with the gas-liquid interface, and PAi, cAi, and cs (at the interface) are all zero.
This corresponds to gas-film control, since species A does not penetrate the liquid film.