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12 Chemical Reaction Mechanisms I: Rate Laws and Mechanisms
12.33 a. Find the rate law for the reaction
H
+
+ I
−
+ H 2 O 2 H 2 O + HIO
assuming the mechanism
(1) H + + H 2 O 2 H 3 O
+
2
(fast)
(2) H 3 O
+
4 + I − − → H 2 O + HIO
(slow, rate-limiting)
b. Find the rate law assuming the mechanism
(1) H + + I − HI
(2) H 2 O 2 + HI − → H 2 O + HIO
(slow, rate-limiting)
12.34 The reaction
H 2 O 2 + 3I
−
+ 2 H
+
− → 2H 2 O + I
−
3
obeys the rate law 18
−
d[H 2 O 2 ]
dt
k 1 [H 2 O 2 ][I
− ] + k 2 [H 2 O 2 ][I
− ][H
+ ]
The two terms presumably correspond to two competing
mechanisms. Propose a reasonable mechanism for the
first term, and two different reasonable mechanisms for
the second term.
12.35 The hypothetical reaction
2A − → 2B + C
obeys the rate law
rate
d[C]
dt
k
[A]
2
[B]
Propose a mechanism consistent with this rate law.
12.5
Chain Reactions
Chain mechanisms involve reactive intermediates that are called chain carriers. A chain
mechanism usually contains an initiation step, in which chain carriers are formed; one or
more chain propagation steps in which products are formed and in which chain carriers
are produced as well as being consumed; and a chain termination step in which chain
carriers are consumed without being replaced. Since chain carriers are produced as
well as being consumed, the reaction can continue without further initiation steps.
The following gas-phase reaction has been identified as a chain reaction:
H 2 + Br 2 − → 2HBr
(12.5-1)
The empirical rate law for the forward reaction in the presence of some HBr is
−
d[H 2 ]
dt
k a [H 2 ][Br 2 ] 1/2
1 + k b [HBr]/[Br 2 ]
(12.5-2)
where k a and k b are temperature-dependent parameters. The accepted mechanism for
the forward reaction is 19
(1) Br 2 2 Br
(2) Br + H 2 HBr + H
(3) H + Br 2 − → HBr + Br
(12.5-3)
Step 1 is the initiation step. The forward reactions of steps 2 and 3 are chain propagation
steps, producing the two chain carriers, Br and H. The reverse reaction of step 1 is the
termination step. The reverse reactions of steps 2 and 3 regenerate chain carriers but
consume the product. They are called inhibition processes.
18 D. Benson, Mechanisms of Inorganic Reactions in Solution, McGraw-Hill, New York, 1968, p. 6ff.
19 K. J. Laidler, op. cit., p. 291ff (note 3).
12 Chemical Reaction Mechanisms I: Rate Laws and Mechanisms
12.33 a. Find the rate law for the reaction
H
+
+ I
−
+ H 2 O 2 H 2 O + HIO
assuming the mechanism
(1) H + + H 2 O 2 H 3 O
+
2
(fast)
(2) H 3 O
+
4 + I − − → H 2 O + HIO
(slow, rate-limiting)
b. Find the rate law assuming the mechanism
(1) H + + I − HI
(2) H 2 O 2 + HI − → H 2 O + HIO
(slow, rate-limiting)
12.34 The reaction
H 2 O 2 + 3I
−
+ 2 H
+
− → 2H 2 O + I
−
3
obeys the rate law 18
−
d[H 2 O 2 ]
dt
k 1 [H 2 O 2 ][I
− ] + k 2 [H 2 O 2 ][I
− ][H
+ ]
The two terms presumably correspond to two competing
mechanisms. Propose a reasonable mechanism for the
first term, and two different reasonable mechanisms for
the second term.
12.35 The hypothetical reaction
2A − → 2B + C
obeys the rate law
rate
d[C]
dt
k
[A]
2
[B]
Propose a mechanism consistent with this rate law.
12.5
Chain Reactions
Chain mechanisms involve reactive intermediates that are called chain carriers. A chain
mechanism usually contains an initiation step, in which chain carriers are formed; one or
more chain propagation steps in which products are formed and in which chain carriers
are produced as well as being consumed; and a chain termination step in which chain
carriers are consumed without being replaced. Since chain carriers are produced as
well as being consumed, the reaction can continue without further initiation steps.
The following gas-phase reaction has been identified as a chain reaction:
H 2 + Br 2 − → 2HBr
(12.5-1)
The empirical rate law for the forward reaction in the presence of some HBr is
−
d[H 2 ]
dt
k a [H 2 ][Br 2 ] 1/2
1 + k b [HBr]/[Br 2 ]
(12.5-2)
where k a and k b are temperature-dependent parameters. The accepted mechanism for
the forward reaction is 19
(1) Br 2 2 Br
(2) Br + H 2 HBr + H
(3) H + Br 2 − → HBr + Br
(12.5-3)
Step 1 is the initiation step. The forward reactions of steps 2 and 3 are chain propagation
steps, producing the two chain carriers, Br and H. The reverse reaction of step 1 is the
termination step. The reverse reactions of steps 2 and 3 regenerate chain carriers but
consume the product. They are called inhibition processes.
18 D. Benson, Mechanisms of Inorganic Reactions in Solution, McGraw-Hill, New York, 1968, p. 6ff.
19 K. J. Laidler, op. cit., p. 291ff (note 3).