Page 207 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 177

reactor design. This is because knowledge of the mechanism will make
if possible to fit the experimental data to a theoretical rate expression,
which will be more reliable than an empirical fit. Also, the mechanism
may require some modifications and optimization for the final design.

Example 3-1
−
(
(
−
2−
4
3
The oxidation of Fe CN) to Fe CN) by peroxidisulfate, SO ,
6 6 2 8
can be monitored spectrophotometrically by observing the increase in
absorbance at 420 nm, D 420 in a well-mixed batch system. Assume
that the kinetic scheme is:
Fe CN) 4 − + 1 S O 2 −  → ( 3 − + SO 2 −
(
Fe CN)

k 2
6 2 8 6 4
2
[
− d [ Fe (CN ) 4 − ] = k Fe (CN ) 4 − ][ S O 2 8 − ]
2
2
dt 6 6
×
Using pseudo-first order conditions with [SO 2− ] = . 18 10 − 2 M and
8
2
4−
×
[Fe (CN ) ] = . 65 10 − 4 M, the following absorbances were recorded
6
at 25°C:
t/s 0 900 1,800 2,700 3,600 4,500 ∞
D 0.120 0.290 0.420 0.510 0.581 0.632 0.781
420
2−
Calculate the pseudo-first order rate constant k = k S O ] and,
[
8
2
2
1
hence, k .
2
Solution
Table 3-6 gives D – D with time t. For a first order rate law, the
∞
rate equation is expressed by
( D − D)
ln ∞ =− kt
( D − D ) 1 (3-246)
∞
O
Equation 3-246 is further expressed by
ln (D – D) = ln (D – D ) – k t (3-247)
∞
∞
O
1