Page 238 - Modeling of Chemical Kinetics and Reactor Design

208 Modeling of Chemical Kinetics and Reactor Design

at a concentration C AO . Write a differential balance on A and integrate
it to obtain an expression for C (t) in terms of C AO and k.
A
(2) Let P (atm) be the initial reactor pressure. Prove that t , the
O
1/2
time required to achieve 50% conversion of A in the reactor, equals
RT/kp . Assume an ideal gas behavior.
O
(3) The decomposition of nitrous oxide (N O) to nitrogen and
2
oxygen is preformed in a 5.0 l batch reactor at a constant tem-
perature of 1,015 K, beginning with pure N O at several initial pres-
2
sures. The reactor pressure P(t) is monitored, and the times (t )
1/2
required to achieve 50% conversion of N O are noted in Table 3-19.
2
Use these results to verify that the N O decomposition reaction is
2
second order and determine the value of k at T = 1,015 K.
(4) The same experiment is performed at several other temperatures
at a single initial pressure of 1.0 atm. The results are shown in
Table 3-20. Determine the Arrhenius law parameters (k and E) for
O
the reaction.
Solution

(1) Since the reaction is carried out in a batch system of constant
volume, the rate expression for a second order rate law is

− ( r A ) =− 1 dn A = − dC A = kC 2 A (3-317)
V dt dt

where k = k exp(–E/RT).
O

Table 3-19
P (atm) 0.135 0.286 0.416 0.683
O
t 1/2 (sec) 1,060 500 344 209

Table 3-20
T(K) 900 950 1,000 1,050
t (sec) 5,464 1,004 219 55
1/2