CHEM 341. Fall 2000. Problem Set #9.
Note: Please note that due to technical difficulties in creating the accepted notation for an
equilibrium reaction, this problem set uses  to indicate that equilibrium is established.
Rate Law
1. At 25C and at a constant pH of 5, the inversion of sucrose proceeds with a constant
half-life of 500 min. At this same temperature, but at a pH of 4, the half-life is constant at 50
b
d sucrose 
 k sucrose a H  . What are the values of a and b?
min. The rate law is
dt
2. The rate of acid catalyzed hydrolysis of ethyl acetate in hydrochloric acid solution
obeys the following rate law
d ester 
rate  
 k ester HCl 
dt
where k = 0.1 M1 h1 at 25C. Neglecting any back reaction, calculate the time required
for half of the ester to be hydrolyzed if the initial concentrations of ester and of HCl catalyst are
0.02 M and 0.01 M, respectively.
 
3. In the study of a first-order reaction
AB
it is found that A/Ao is 0.125 after 1 hour. The system initially consisted of 0.20 mole of
gaseous A at STP. Calculate the initial rate of reaction in moles of A reacting per minute.
4. For the following mechanism:
N 2 O5  NO2  NO3
(Reaction #1, fast)
NO  NO3  2 NO2
(Reaction #2, slow)
where k1 = rate of forward Reaction #1; k1 = rate of reverse reaction for Reaction #1; k2 = rate
of forward Reaction #2.
dPN 2O5
Using the steady-state assumption, find the expression for
in terms of PN2O5, PNO,
dt
PNO2, k2, k1, and/or k1.
k2
5. Consider the reaction
A B  C
(Reaction 1, fast)
C A P
(Reaction 2, slow)
where k1 = rate of forward Reaction #1; k1 = rate of reverse reaction for Reaction #1; k2 = rate
of forward Reaction #2.
Find the rate law of this reaction in terms of [A], [B], [P], k2, k1, and/or k1. Now suppose
that we set [B] = [A]. Under these conditions, what is the overall order of the reaction if k1 >>
k2[A]? What is the overall order of the reaction if k1 << k2[A]?
6. The reaction
CH 3CH 2 NO2  OH   H 2 O  CH 3CHNO2
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CHEM 341. Fall 2000. Problem Set #9.
d CH 3CH 2 NO2 
 k CH 3 CH 2 NO2  OH  . It takes 0.5 min for one
dt
percent of CH3CH2NO2 to react at 25C, in the case of a solution 0.002 M in CH3CH2NO2 and
0.3 M in NaOH. Calculate k. Calculate also how long it would take for half of CH3CH2NO2 to
react.

obeys the rate law: rate  

7. Complete the following statements:
Plot of ln [A]t or ln
At
Ao
vs. time yields a straight line of slope  for a first-order
reaction.
Plot of
1
vs. time gives a straight line of slope ________ for a second-order reaction.
At
8. Consider the following reaction
A B
where k1 = rate of forward reaction and k1 = rate of reverse reaction.
This reaction is first order in both the forward and the reverse direction.
(a) Calculate k1 if the initial velocity (i.e. while [B] is still insignificant) is 5.1  104 M
s1 and the initial concentration of A, [A]o is 4.7  102 M.
(b) A plot of ln  At  Aeq vs. time has a slope equal to 0.01795 s1. Find k1. Hint:
The information from part (a) is also true for part (b).
(c) Calculate the equilibrium constant and the half-life for this reaction.


9. Sketch approximate plots of the concentration of [A], [B], and [C] vs. time for
A  B  C (on the same graph) if both reactions are first order, and A  B is the rate-limiting
step (i.e. k1 << k2). Repeat these plots on a separate graph for the same reaction but if B  C is
the rate limiting step (i.e. k1 >> k2).
10. For the following reaction
Bt
A plot of ln
At
2 A  3B  P
vs. time has a slope of 5.0 s1. Calculate the rate constant, k, of the
forward reaction if the rate of the reverse reaction is insignificant and if [A]o = 3.1 M and [B]o =
4.7 M.
Simple Arrhenius Analysis
11. Suppose a reaction has a rate constant of 1.23 x 103 s1 at 300 K and of 6.45 x 103 s1
at 400 K. Calculate the Arrhenius activation energy and the pre-exponential factor A. Then use
these values to predict the rate constant at 500 K.
Eyring Analysis
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CHEM 341. Fall 2000. Problem Set #9.
12. Explain how a plot of ln (k/T) vs. 1/T can be used to determine Htransition state and
Stransition state if the values of kB, , and h are known. (kB is Boltzman's constant,  is the
tunneling factor, and h is Planck's constant).
Chain Reactions
13. The chlorination of an organic molecule (M)
M  Cl2  P
with initiation by thermal dissociation of chlorine, may proceed by the following mechanism (in
the absence of light).
Initiation
Cl 2  2Cl
v1  k1 Cl 2 
Propagatio n
Cl  M  R
Propagatio n
R  Cl 2  P  Cl
Terminatio n
Cl  Cl  Cl 2
v 2  k 2 M Cl 
v 3  k 3 R Cl 2 
v 4  k 4 Cl 2
Find the rate law for the overall reaction in terms of [M], [Cl2], and various constants (i.e.
k1 and/or k2 and/or k3 and/or k4).
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