Chemical Reaction Engineering (CBE 40445)
Homework 7
Due October 28, 2011
Problem 1. Which of the following reactions can be assumed to be elementary? Briefly justify
your answers.
1.
O3 −−→ O2 + O·
H2 +
1
2
O2 −−→ H2 O
C4 H8 + H2 S −−→ C4 H4 S + 3 H2
H· + I2 −−→ HI + I·
Problem 2. At high temperature ethylene can be hydrogenated to ethane. The proposed
mechanism has four steps, all of which are presumed to be elementary and essentially
irreversible under realistic conditions.
k
C2 H4 + H2 →1 C2 H5 · +H ·
k
H · +C2 H4 →2 C2 H5 ·
k
C2 H5 · +H2 →3 C2 H6 + H ·
k
C2 H5 · +H· →4 C2 H6
2. Identify the reactants, products, and intermediates, and state whether the mechanism is open
or closed.
3. Why is it reasonable to assume that the first reaction is irreversible (that is, that the forward
reaction rate is much greater than the reverse)? What about the second reaction?
4. Based on the mechanism above, write an expression for the rate of disappearance of ethylene.
5. Apply the pseudo-steady-state approximation separately to H atoms and ethyl radicals. Use
the results to derive expressions for the concentrations of each in terms of only reactants and
products. (Hint: After writing down the PSSA expressions for H atoms and ethyl radicals,
you will find that you can greatly simplify the two equations by adding and subtracting
them.)
6. Combine your answers to Questions 4 and 5 to obtain an expression for the rate of
disappearance of ethylene that involves only reactants and products. What is the apparent
reaction order with respect to H2? To C2H4?
7. What is the apparent rate constant? Do you expect it to exhibit Arrhenius behavior in
general?
CONTINUED NEXT PAGE
Chemical Reaction Engineering (CBE 40445)
Homework 7
Due October 28, 2011
Problem 3. Phosgene (COCl2) is a poisonous gas that can be prepared by chlorination of carbon
monoxide (if CO wasn’t already poisonous enough for you). The overall kinetics are observed to
be first order in CO and 3/2 order in Cl2. The following set of elementary step reactions have
been proposed for the reaction:
hν
−−
�
Cl2 �
−
− 2 Cl·
−
�
CO + Cl· −
�
−
− ClCO·
−
�
ClCO· + Cl2 −
�
−
− COCl2 + Cl·
8. The observed kinetics can be accounted for by assuming one of the steps is rate determining
and irreversible while the others are in quasi-equilibrium. Identify the rate-determining step
and demonstrate that it gives the desired kinetics.
9. Sketch a vector representation of the reaction rates given your assumption.