12.4 Reaction Mechanisms and Rate Laws
555
12.24 For 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.
12.26 The 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.
12.27 The reaction
2NO + 2H 2 − → N 2 + 2 H 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).
12.28 The 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.
12.29 The 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.
12.31 For 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.
12.32 For 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.
555
12.24 For 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.
12.26 The 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.
12.27 The reaction
2NO + 2H 2 − → N 2 + 2 H 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).
12.28 The 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.
12.29 The 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.
12.31 For 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.
12.32 For 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.