# Exam 1 (FL2004)

```Fall 2004
ChE 471
Exam 1
(Closed book, closed notes)
1.The observed catalytic decomposition of ozone in the presence of nitrogen pentoxide
exhibits the following rate form:
RO3  k(O3 ) 2 / 3 (N 2O5 ) 2 / 3
The overall stoichiometry is:

2O 5
20 3 N
3O2
The following two mechanisms are proposed:
 Mechanism A:
N 2O5
k1



NO  NO3 ;K1  k1 /k1

 2
k 1
k2
NO2  O3 

NO3  O2



k3
NO3  O3 

2O2  NO2
Mechanism B:
k1



N 2O5
NO  NO3 ;K1  k1 /k1


 2
k1
k2
NO2  O3 

NO3  O2

k4
NO3  NO2 

O3  2NO2

The first step, common to both mechanisms, can be considered to be in equilibrium
compared to other steps. Each elementary step rate constant has an activation energy

associated with it, i.e., ki  k ioeE i / RT . The equilibrium constant for the first step is the
following function of temperature, K1  K1oeH r 1 / RT .
a) Which mechanism is consistent with the observed rate form? Please, fully

b) If we represent theobserved rate constant, k, in terms of the usual Arrhenius
form, i.e., k  koeE / RT , show what is ko in terms of k20,k30,k40,K1o and what is the
apparent activation energy E in terms of E1, E2, E3, E4 ,Hr1.



2. For a liquid phase reaction A  products you have measured reactant concentration as
a function of time in an isothermal, batch reactor and the data are given below:
t(min)
mol  0 5 10 20 40 60 100 
CA   10 7.31 6.30 4.81 3.42 2.73 2.00 0
 lit 
mol A
at CAo = 10
min
 (mol/lit) and to achieve conversion of 80%. What should the volume of the plug flow
reactor be? The PFR operates at the same temperature for which batch data are given.
[Hint: Consider the relation between reaction time in the batch and space time in PFR].

You want to design a plug flow reactor to process the feed rate of 100
3. Gas-phase reaction A  4P was studied in a batch autoclave at constant volume and at
constant temperature of 200˚C. The information obtained for the rate of disappearance of
reactant A is presented in a tabular form below:
PA (atm) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
kmolA  0 0.08 0.25 0.32 0.41 0.48 0.52 0.55 0.6 0.6 0.6
RA  3

m min 

You are to operate continually a jet-stirred reactor for this reaction, which you can
assume behaves as a continuous flow stirred tank reactor CSTR. The feed consists of
50% (molar) A and 50% inerts and is at a total pressure of 10 atm and 200˚C. We want
to achieve 90% conversion of A. Find the reactor volume necessary for a production rate
of 4 kmol P/min. The reactor operates isothermally at 200˚C .
4. A substrate inhibited enzyme catalyzed reaction, A  P , exhibits a peculiar rate form
and –1!
RA  0.05 CA /(0.1 CA ) 2 (mol /L min) as its apparent order can vary between 1

We want to make FP = 100 (mol/min) of P at 99% conversion of A of the feed that
 contains C = 1 (mol/L).
Ao
You want to minimize the reactor volume needed to achieve the above production rate at
the above specified conversion. To gain insight plot the rate (or its reciprocal) as a
function of conversion in the conversion range from 0 to 0.99.
a) What reactor type or reactor combinations do you recommend and why?
b) What is the needed total reactor(s) size?
Hint: This is a constant density system so CA = CAo (1-xA) and production rate FP =
FAoxAf by stoichiometry and xAf = 0.99. FAo=Q CAo where Q (L/min) is the volumetric
flow rate through the system.
```