Page 262 - Introduction to chemical reaction engineering and kinetics

9.2 Gas-Liquid Systems 243

Figure 9.5 Two-film model (profiles) for rela-
tively slow reaction A(g) + bB(9 -+ products
g-e interface (nonvolatile B)

Since the system is Usdly specified in terms of pA and cu, rather than CA and cu, we
transform equation 9.2-17 into a more useful form by elimination of CA in favor of PA;
cA then becomes a dependent variable.
Since the three rate processes
Mass transfer of A through gas film
Mass transfer of A through liquid film
Reaction of A and B in bulk liquid
are in series, the steady-state rate of transport or reaction, NA or (- TA), is given inde-
pendently by equations 9.2-3, -6, and -17; a fourth relation is the equilibrium connection
between P& and cAi given by Henry’s law, equation 9.2-8. These four equations may
be solved simultaneously to eliminate c Ai, pAi, and cA (in favor of PA to represent the
concentration of A) to obtain the following result for (-IA):

(9.2-18)

k Ag ’ k,, ’ k&

The summation in the denominator represents the additivity of “resistances” for the
three series processes. From 9.2-17 and -18, we obtain cA in terms of pA and cu:

(9.2-Ma)

Three special cases of equation 9.2-18 arise, depending on the relative magnitudes of
the two mass-transfer terms in comparison with each other and with the reaction term
(which is always present for reaction in bulk liquid only). In the extreme, if all mass-
transfer resistance is negligible, the situation is the same as that for a homogeneous
liquid-phase reaction, (-rA)& = kACACB.
If the liquid-phase reaction is pseudo-first-order with respect to A (cu constant and
>’ cA),

(-rA) = (-rA)int/ai = (k&&A = k&

where kx = kacB = kAcBlai. Equations 9.2-18 and -18a apply with kAcB replaced
by k;.