Chemical Engineering CHE 332H1F Applied Reaction Kinetics
University of Toronto
Fall 2015
Problem Set 2
Due at the dropbox located in the hallway outside of WB 25
by Monday Nov. 9, at 7 pm
Problem 1. The gas phase reaction of chlorine with chloroform is described by the reaction
Cl 2  CHCl 3 
 HCl  CCl 4
A proposed mechanism involves the following elementary steps:
k1

Cl 2 
2Cl 

k 1
Step 1.1
k2
Cl  CHCl 3 
HCl  CCl 3
Step 1.2
k3
Cl    CCl 3 
CCl 4
Step 1.3
a) Using the pseudo steady-state hypothesis for all reactive intermediates, derive the rate of CCl 4 production, described
in terms of the reaction rate constants and concentrations of reactants and products.
b) The rate of Cl2 decomposition (Step 1.1) is significantlly faster than the rate of hydrogen abstraction step (Step 2).
The Cl2 decomposition step can therefore be assumed to be quasi-equilibrated. Derive the rate of CCl4 production in
terms of reaction rate constants and concentrations of reactants and products.
c) When do the rate expressions derived from part a and part b become identical? What does this mean physically?
Draw an arrow diagram showing the net rate and the rate of each forward and reverse reaction when Cl2
decomposition is quasi-equilibrated.
Problem 2. W. H. Rodebush and W. C. Klingelhoefer [J. Am. Chem. Soc., 55, 130 (1933)] studied the reaction of atomic
chlorine with molecular hydrogen. Chlorine atoms were formed by partial dissociation of molecular chlorine in an
electrodeless discharge.
A stream of this gas was then mixed with a hydrogen stream and passed through a thermostatted reaction vessel. At the far
end of the vessel the reaction was effectively quenched by using a piece of silver foil to catalyze the recombination of
chlorine atoms. The products of the reaction were determined by freezing out the Cl2 and HCI in liquid air traps and titrating
samples with standard thiosulfate and alkali, respectively. On the basis of the data and assumptions listed below, determine:
(a) The average number of collisions that a chlorine atom undergoes with hydrogen molecules in the reaction vessel.
(b) The average number of HCI molecules formed per entering chlorine atom.
(c) The probability that a collision between a chlorine atom and a hydrogen molecule leads to reaction. It may be assumed
that each reaction of the type
Cl + H2 → HCl + H
is followed immediately by a much faster reaction:
H + Cl2 → HCl + Cl
The data are as follows, where σ represents the hardsphere diameter.
σ(H2) = 2.39 Å
σ(Cl) = 2.97 Å
Hydrogen flow rate= 6.3 cm3(STP)/min
Chlorine flow rate (as Cl2)=9.1 cm3(STP)/min
Fraction Cl2 dissociated= 11%
Volume of reaction vessel= 10 cm3
Pressure in vessel =0.340 torr
Temperature in vessel= 0 0C
Length of run= 10 min
Thiosulfate titer of products 36.5 cm3 of 0.2N solution
Alkali titer of products 9.1 cm3 of 0.1N solution
Problem 3. The kinetics of the liquid-phase, enzyme-catalyzed reaction
A→P+Q
Have been studied in an ideal, isothermal batch reactor. The rate equation is believed to be:
-rA = kCA/(1+KPCP)
[mol (L s)-1]
In one particular experiment, the concentrations of A, P, and Q were measured as a function of time. The initial concentration
of A in this experiment was CA0. There was no P or Q present initially, i.e., CP0 = CQ0 = 0.
a) Demonstrate how you would use the integral method of data analysis to test (graphically) this rate equation against
the experimental data. Carry out any mathematical operations that are required. Sketch the graph that you would
make, showing what you would plot against what.
b) Assuming that this rate equation did fit the data, how would you obtain estimates of k and KP from the graph that you
constructed?
Problem 4. Answer the following question based on the given figure.
Equilibrium constant based on pressure (with units based on atm), K eqp , versus temperature, the reference pressure is 1 atm.
4a. Circle the correct answer.
The reaction 0.5
i.
is
Exothermic
ii.
Endothermic
4b. Determine the equilibrium constant based on concentration, K eqc , at 2000 K for following reaction.
0.5
4c. The rate of the forward reaction is first order with respect to SO2. Propose a plausible rate equation for the reverse
reaction that is thermodynamically consistent.
4d. Figure below shows the Levenspiel plot generated based on the assumption that the reaction is irreversible (labeled Case
1) at 2000 K.
Case 1:
; irreversible reaction, reactor operating at 2000 K
You figure out that the reaction is indeed reversible and the rate of the forward reaction is first order with respect to SO2.
Given:
, where = 0.1 min-1 at 2000 K
= 1 min-1 at 5000 K.
If the same feed mixture was introduced to the same well-mixed reactor as described in Problem 1, sketch on the Levenspiel
plot (Figure 3) the following cases, indicating all limiting behaviours (qualitatively to show the trend and differences
among different cases but not the actual values):
Case 2:
Case 3:
reversible reaction, reactor operating at 2000 K
reversible reaction, reactor operating at 5000 K
Levenspiel Plot of the irreversible reaction