Page 274 - Introduction to chemical reaction engineering and kinetics

9.3 Intrinsic Kinetics of Heterogeneous Reactions Involving Solids 255

(approximate) value of E (24.3) calculated from equation 9.2-51 is 94% of the (exact)
value (26) calculated from equation 9.2-49 for pseudo-first-order. The simpler form of the
latter could be used with relatively little error.

9.2.3.6 Summary of Rate Expressions
Application of the two-film model to a particular type of gas-liquid reaction, repre-
sented by equation 9.2-1, results in a proliferation of rate expressions for the vari-
ous possible cases for which analytical solutions of the continuity equations are ob-
tained here. These are summarized in Figure 9.9, as a branching chart, for conve-
nient reference and to show the structure of their relationship to each other. The
chart is divided at the top into three main branches according to the supposed lo-
cation of chemical reaction, and progresses in individual cases from “slow” reaction
on the left to instantaneous reaction on the right. The equation number from the
text is given along with the rate expression or other relevant quantity such as E
or Ha. The first expression in the chart for E for an instantaneous reaction is not
given in the text, but is developed in problem 9-11, along with E given by equation
9.2-53.
Note that the enhancement factor E is relevant only for reaction occurring in the
liquid film. For an instantaneous reaction, the expressions may or may not involve E,
except that for liquid-film control, it is convenient, and for gas-film control, its use is
not practicable (see problem 9-12(a)). The Hatta number Ha, on the other hand, is not
relevant for the extremes of slow reaction (occurring in bulk liquid only) and instan-
taneous reaction. The two quantities are both involved in rate expressions for “fast”
reactions (occurring in the liquid film only).

9.3 INTRINSIC KINETICS OF HETEROGENEOUS REACTIONS
INVOLVING SOLIDS
The mechanisms, and hence theoretically derived rate laws, for noncatalytic heteroge-
neous reactions involving solids are even less well understood than those for surface-
catalyzed reactions. This arises because the solid surface changes as the reaction
proceeds, unlike catalytic surfaces which usually reach a steady-state behavior. The
examples discussed here are illustrative.
Gasification reactions of solids: The reactions of solids with gas-phase reactants to
form gaseous products are generally described in the same manner as are surface-
catalyzed reactions. The reaction of carbon with water vapor is an example:

C(s) + H,O + H, + CO (9.3-1)

This reaction is important in such processes as the decoking of catalysts, the manufac-
ture of activated carbon for adsorption, and the gasification of carbonaceous materials
for production of hydrogen or fuel gas.
A two-step mechanism and resulting rate law can be developed as follows. Reactive
carbon sites, C* (total number NC.), are assumed to exist on the surface of the solid.
These can be oxidized reversibly by water vapor:

C* + H,O f C*O + H, (1)
1