Page 266 - Elements of Chemical Reaction Engineering 3rd Edition

238 Collection and Analysis of Rate Data Chap. 5

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time
Figure 5-6 Plot of reciprocal concentfation as a function of time.

Example 5-2 Integral Method of Analysis of Pressure-Time Data
Use the integral method to confirm that the reaction order for the di-tert-butyl per-
oxide decomposition described in Example 5-1 is first order.

Solution
Recalling Example 5-1, the combined mole balance and rate law for a constant-vol-
ume batch reactor can be expressed in the form
dP -- - k'(3P0 - P)" (E5- 1.7)
dt
For a = 1,
-_
dP - k'(3P0 - P) (E5-2.1)
dt
Integrating with limits P = Po when t = 0 yields

Assuming a first- (E5-2.2)
order reaction
If the reaction is first order, a plot of In [2P0/(3P0 - P)] versus t should be linear.
-
TABLE E5-2.1. PROCESSED DATA
t P 2P01(3P0 - P)
(min) (mmHg) (-)
0.0 1.5 1 .oo
2.5 10.5 1.25
50 12.5 1.50
10.0 15.8 2.24
15.0 17.9 3.26
20.0 19.4 4.84

After completing Table ES-2.1, using the raw data, a plot of 2P,/(3P0 - P) as
\a function of time was made using semilog paper as shown in Figure E5-2.1. From