Page 179 - Introduction to chemical reaction engineering and kinetics

7.1 Simple Homogeneous Reactions 161

is propagated first by reaction between Br’ and H, and second by reaction of Ho (released
in the previous step) with Br,. The chain is inhibited by reaction of HBr with Ho (i.e., HBr
competes with Br, for Ho). Chain termination occurs by recombination of Br’ atoms.
(a) Write the steps for a chain-reaction mechanism based on the above description.
(b) Derive the rate law (for rnnr) for the mechanism in (a), stating any assumption
made.

SOLUTION

(a) The overall reaction is

H, + Br, + 2HBr

The reaction steps are:
initiation: Br, 5 2Br’ (1)
propagation: Br’ + H, -%HBr + H’ (2)
Ho + Br, 2 HBr + Bf (3)
inhibition (reversal of (2)): Ho + HBr%H2 + Br* (4)
termination (reversal of (1)): 2 Br’ 3 Br, (5)
(b) By constructing the expression for rnnr from steps (2), (3), and (4), and then elimi-
nating cn,.. and cn. from this by means of the SSH (rBr. = rn. = 0), we obtain the rate
law (see problem 7-5):

2k3(qk-,xk,lk-,)
(k&Z) + hB&3r2)
rHBr = (7.1-3)

This has the same form as that obtained experimentally by Bodenstein and Lind earlier.

This rate law illustrates several complexities:
(1) The effects on the rate of temperature (through the rate constants) and concen-
tration are not separable, as they are in the power-law form of equation 6.1-1.
(2) Product inhibition of the rate is shown by the presence of cHBr in the denomi-
nator.
(3) At a given temperature, although the rate is first-order with respect to H2 at all
conditions, the order with respect to Br, and HBr varies from low conversion
(kslk-, > cHnrlcnrJ, (1/2) order for Br, and zero order for HBr, to high conver-
f
d
or
sion (k3/k2 =K cnnr/cnrz), (3/2) er or Br2 and negative first-order for HBr. It
was such experimental observations that led Bodenstein and Lind to deduce the
form of equation 7.1-3 (with empirical constants replacing the groupings of rate
constants).
7.1.3.2 Branched-Chain Mechanisms; Runaway Reactions (Explosions)
In a branched-chain mechanism, there are elementary reactions which produce more
than one chain carrier for each chain carrier reacted. An example of such an elementary
reaction is involved in the hydrogen-oxygen reaction:

0’ + H, --$ OH’ + Ho