Physical Chemistry Third Edition

12.4 Reaction Mechanisms and Rate Laws 555

12.24For the reaction

3HNO 2 −→H 2 O+2NO+H++NO− 3

assume the mechanism

(1) 2HNO 2 
NO+NO 2 +H 2 O

(2) 2NO 2 
N 2 O 4

(3) N 2 O 4 +H 2 O−→HNO 2 +H++NO− 3

Find the rate law, assuming the third step to be

rate-limiting.

12.25 a.Using the steady-state approximation, find the rate
law corresponding to the mechanism

(1) NO 2 NH 2 +OH−
H 2 O+NO 2 NH−

(2) NO 2 NH−−→N 2 O+OH−

b.Tell how you would determine experimentally whether

one or the other of the two steps is rate-determining.

12.26The reaction equation for the nitration of an aromatic

compound in an acidic solution can be written

ArH+HNO 3 −→ArNO 2 +H 2 O

where Ar stands for an aromatic group such as the phenyl

group, C 6 H 5. A proposed mechanism is^17

(1) HNO 3 +HA
H 2 NO+ 3 +A−

(2) H 2 NO+ 3 
H 2 O+NO+ 2

(3) NO+ 2 +ArH−→ArNO 2 H+

(4) ArNO 2 H++A−−→ArNO 2 +HA

where HA represents a weak acid such as HSO− 4.

a.Find the rate law assuming that step (2) is

rate-limiting.

b.Find the rate law assuming that step (3) is

rate-limiting.

c.Find the rate law assuming the steady-state

approximation.

12.27The reaction

2NO+2H 2 −→N 2 +2H 2 O

is found to be second order in NO and first order in H 2

(third order overall). Propose a mechanism that gives this

rate law.

(^17) R. J. Gillespie, E. D. Hughes, C. K. Ingold, and R. I. Reed,Nature, 163 ,
599 (1949).
12.28The reaction
2Cl 2 O+2N 2 O 5 −→2NO 3 Cl+2NO 2 Cl+O 2
is found to be zero order with respect to Cl 2 O and first
order with respect to N 2 O 5. Devise a mechanism for the
reaction that corresponds to this rate law.
12.29The reaction
2NO 2 Cl−→2NO 2 +Cl 2
is assumed to have the mechanism
(1) NO 2 Cl
NO 2 +Cl
(2) Cl+NO 2 Cl−→NO 2 +Cl 2
a.Find the rate law assuming the second step to be
rate-limiting.
b.Find the rate law assuming the steady-state
approximation.
12.30 a.Find the rate law for the reaction
2NO(g)+O 2 (g)−→N 2 O 4 (g)
assuming the mechanism
(1) NO+O 2
NO 3 (fast)
(2) NO 3 +NO−→N 2 O 4
(slow, rate-limiting)
b.Propose a different two-step mechanism that
corresponds to the same rate law.
c.Find the rate law for the same mechanism using the
steady-state approximation.
12.31For the reaction
2ICl+H 2 −→I 2 +2HCl
the forward rate law is found to be
rate
d[I 2 ]
dt
k[ICl][H 2 ]
Propose a mechanism that predicts this rate law.
12.32For the reaction
2ICl+H 2 −→I 2 +2HCl
a proposed mechanism is
(1) 2 ICl
I 2 +Cl 2 (fast in both directions)
(2) H 2 +Cl 2 −→2 HCl (slow, rate-limiting)
Find the rate law that corresponds to this mechanism.