Page 178 - Introduction to chemical reaction engineering and kinetics

160 Chapter 7: Homogeneous Reaction Mechanisms and Rate Laws
We eliminate ~~.u,~. by applying the stationary-state hypothesis to C,HsO’, ~C2u5@ = 0,
and also to the other chain carrier, CHj.

rCzHsO’ = kc, - hCC2H50* + hcAcCH; - 2k4c&2Hs0a = o
‘Cl-I; = k2Cc2H5v - k3CACCH; = o
Addition of these last two equations results in

112 112
CC2H50* = (WW cA
and substitution for cc2n500 in the equation for ru gives

rB = k2(k1/2k,)“2c~2

which is the rate law predicted by the mechanism. According to this, the reaction is half-
order.
(b) If we calculate the vah.te of kobs = (-rA)/cA1’2 for each of the five experiments, we
obtain an approximately constant value of 0.044 (mol m-3)1’2 s-t. Testing other reaction
orders in similar fashion results in values of kobs that are not constant. We conclude that
the experimental results support the proposed mechanism.
(c) From (b), we also conclude that

k obs = k2(k1/2k4) 112
from which

dlnkobs _ dlnk2 1 dln k, - 1 dln k4 -
-
-
- c - - dT +z dT 2 dT
or, from the Arrhenius equation, 3.1-6,

EA = EA, + $A, - EAI)

(d) From equation 7.1-2, the chain length is

CL = k2(k1/2k4) 1’2ca/2/kl cA
= k2(2kl k4cA)-“2

The rate law obtained from a chain-reaction mechanism is not necessarily of the
power-law form obtained in Example 7-2. The following example for the reaction of
H, and Br, illustrates how a more complex form (with respect to concentrations of
reactants and products) can result. This reaction is of historical importance because it
helped to establish the reality of the free-radical chain mechanism. Following the ex-
perimental determination of the rate law by Bodenstein and Lind (1907), the task was
to construct a mechanism consistent with their results. This was solved independently
by Christiansen, Herzfeld, and Polanyi in 1919-1920, as indicated in the example.

The gas-phase reaction between H, and Br, to form HBr is considered to be a chain reac-
tion in which the chain is initiated by the thermal dissociation of Brz molecules. The chain