Page 272 - Introduction to chemical reaction engineering and kinetics

9.2 Gas-Liquid Systems 253

film, and as such is analogous to the Thiele modulus 4 in catalytic reactions (Chap-
ter 8).
This interpretation of Ha may be deduced from its definition. For example, for a first-
order reaction, from equation 9.2-40,

~~2 = 62 kA _ 6 _ Vf kACAi
kAaicAi

e DA, e=- ai kAe cAi (9.2-55)
e maximum rate of reaction or flux in liquid film
= maximum rate of transport through liquid film

In equation 9.2-55, ai is the interfacial area, for example, in m2 me3 (liquid), and vf
is the volume of the liquid film. The rates are maximum rates because c,& is the high-
est value of CA in the film (for numerator), and the form of the denominator is con-
sistent with CA (bulk liquid) = 0, giving the largest possible driving force for mass
transfer.
Thus, if Ha (strictly, Ha2) >> 1, reaction occurs in the liquid film only, and if Ha or
Ha2 ==K 1, reaction occurs in bulk liquid. Numerically, these values for Ha may be set
at about 3 and 0.1, respectively.

Suppose pure CO, (A) at 1 bar is absorbed into an aqueous solution of NaOH (B) at 20” C.
Based on the data given below and the two-film model, how should the rate of absorption
be characterized (instantaneous, fast pseudo-first-order, fast second-order), if cu = (a) 0.1
and (b) 6 mol L- 1 ?
Data (Danckwerts, 1970, p. 118, in part): kA = 10,000 L mol-’ s-l; DA, = 1.8 X
lo-’ cm2 S-‘; kAe = 0.04 cm S-‘; D,e = 3.1 X 10-5cm2s-1;HA = 36barLmoll’.

SOLUTION

The chemical reaction (in the liquid phase) is

CO,(g) + 2NaOH(e) --r Na,CO, + H,O

Hence, b = 2.
Since a finite value of the rate constant kA is specified, the reaction is not instantaneous.
The units given for kA indicate that the reaction is second-order, presumably of the form in
equation 9.2-50. To obtain further insight, we calculate values of Ha and Ej, from equations
9.2-54 and 9.2-53, respectively. For Ej, since the gas phase is pure CO,, there is no gas-
phase resistance, and CAM = PA/HA, from equation 9.2-8, with pAi = pA( = 1 bar). The
results for the two cases are given in the following table (together with values of E, as
discussed below)