Page 275 - Introduction to chemical reaction engineering and kinetics

256 Chapter 9: Multiphase Reacting Systems
where C*O is an oxidized carbon site. The oxidized site can then “decompose” to pro-
duce CO(g):

co 4 O(g) (2)
C
In addition to CO(g) formation, step (2) exposes a variable number, it, of previously
inactive carbon atoms, C, thus producing c* to continue the reaction. The average value
of n is close to unity, so that N,. varies slowly as reaction proceeds.
If elementary rate laws are assumed for each step, and if NC* is essentially constant
over a short time, a (pseudo-) steady-state rate law can be developed:

NC kl k2cH20 (9.3-2)
’ = N, klcHzO + k-$H2 + 4
(Note the similarity to Langmuir-Hinshelwood kinetics.) The rate is expressed on the
basis of the instantaneous number of solid carbon atoms, Nc. The rate r (measured at
one gas composition) typically goes through a maximum as the carbon is converted. This
is the result of a maximum in the intrinsic activity (related to the fraction of reactive
carbon atoms, N&NC) because of both a change in Nc. and a decrease in Nc.
Since both Nc. and Nc change as the reaction proceeds, r can be expressed as a func-
tion of fractional conversion of carbon, fc, or of time, t:

keff h-ipo
r(t) = (9.3-3)
hCH20 + k-lCHz + k2

where keff(t) is a time-dependent rate constant given by

Other models allow for a distribution of site reactivities. Similar considerations apply
for reactions of solids in liquid solution.
Solid deposition from gas- or liquid-phase reactants: Solid-deposition reactions are
important in the formation of coatings and films from reactive vapors (called chemical
vapor deposition or CVD) and of pure powders of various solids. Examples are:

Si,H, + Si(S) i- 3H2 (9.34)
3TiC1, + 4NH, --, T&N,(s) + 12HCl (9.3-6)

These are the reverse of gasification reactions and proceed through initial adsorption
of intermediates on an existing solid surface. The kinetics of the deposition and decom-
position of the surface intermediates are often treated in Langmuir-Hinshelwood-type
models, where a dynamic balance of deposition sites is maintained, just as in surface-
catalyzed reactions. Further rearrangements or motion on the surface are often usually
necessary to form the desired solid (such as in silicon hlms where sufficient crystallinity
is required for semiconductor properties), and the kinetics of these arrangements can be
rate controlling. It is thought that decomposition of SiH, surface-intermediate species
to form hydrogen is the rate-limiting step during growth of silicon from disilane in re-
action 9.3-5. Problem 9-18 deals with the kinetics of a CVD reaction.
Solid-solid reactions: Most reactions of one solid with another require the existence
of mobile intermediates, because mixtures of solid particles have very few points of