Physical Chemistry Third Edition

554 12 Chemical Reaction Mechanisms I: Rate Laws and Mechanisms

PROBLEMS

Section 12.4: Reaction Mechanisms and Rate Laws

12.17The formation of phosgene

CO+Cl 2 
COCl 2

is thought to proceed by the mechanism^15

(1) Cl 2 
2Cl

(2) Cl+CO
COCl

(3) COCl+Cl 2 
COCl 2 +Cl

a. Find the forward rate law, assuming step (3) to be

rate-limiting.

b. Find the reverse rate law, assuming step (3) to be

rate-limiting.

c.Show that these expressions are consistent with the

equilibrium constant expression.

d.Find the forward rate law, assuming the steady-state

approximation.

12.18For the reaction

4HNO 3 −→4NO 2 +2H 2 O+O 2

a proposed mechanism is

(1) HNO 3 
HO+NO 2

(2) HO+HNO 3 −→further intermediates

where the second step is assumed to be rate-limiting. Find

the rate law predicted by this mechanism.

12.19An alternative mechanism for the reaction of Problem
12.17 is

(1) Cl 2 
2Cl

(2) Cl+Cl 2 
Cl 3

(3) Cl 3 +CO
COCl 2 +Cl

a.Find the forward rate law, assuming step (3) to be

rate-limiting.

b.Find the reverse rate law, assuming step (3) to be

rate-limiting.

c.Show that these expressions are consistent with the

equilibrium constant expression.

(^15) K. J. Laidler,op. cit., p. 301ff (note 3).
12.20The gas-phase reaction
C 2 H 6 +H 2
2CH 4
is thought to proceed by the mechanism
(1) C 2 H 6
2CH 3
(2) CH 3 +H 2 −→CH 4 +H
(3) H+C 2 H 6 −→CH 4 +CH 3
where the back reactions for steps 2 and 3 are negligible.
a.Find the rate law assuming the quasi-steady-state
approximation.
b.Find the rate law assuming that step 2 is rate-limiting.
12.21Consider the hypothetical reaction:
A+2B−→C+D
Assume that the forward rate law is
rate−
d[A]
dt
k[A][B]^2
Propose two different mechanisms that conform to this
rate law. Which of these two mechanisms is more
plausible?
12.22A plausible mechanism for the reaction of H 2 and I 2 is^16
(1) I 2
2I
(2) H 2 +I
H 2 I
(3) H 2 I+I
2HI
a.Obtain the rate law for the forward reaction for this
mechanism using the steady-state approximation
(omit the reverse reaction of step 3). The experimental
rate law is second order, and the reaction was thought
for many decades to be elementary.
b.Obtain the rate law for the reverse reaction using the
steady-state approximation.
c.Equate the forward and reverse rates to obtain an
expression for the equilibrium constant.
12.23Obtain the rate law for the forward reaction for the
mechanism of the previous problem assuming that step 3
is rate-limiting.
(^16) J. H. Sullivan,J. Chem. Phys., 46 , 73 (1967).