560
12 Chemical Reaction Mechanisms I: Rate Laws and Mechanisms
where k a , k b , and k c are temperature-dependent parameters. In the complete absence of
oxygen, the photochemical reaction becomes first order in hydrogen and zero order in
chlorine (except for the dependence of J on the concentration of chlorine). However,
k b is sufficiently small that partial pressures of oxygen down to a few hundredths of a
torr are effective in inhibiting the reaction. Another difference between the hydrogen–
chlorine reaction and the hydrogen–bromine reaction is that the recombination of chlorine atoms, analogous to process 1 in Eq. (12.5-9) is unimportant, whereas termination
of chains by combination of chlorine atoms with the surface of the reaction vessel and
with other molecules (such as oxygen) is important. In the thermally initiated reaction
the dissociation of the Cl 2 molecules at the surface of the reaction vessel is apparently important. 22 A third difference is that the hydrogen–chlorine reaction gives off
enough heat that the reaction mixture can heat up, speeding up the reaction and causing an explosion. The mechanisms and the derivations of the rate laws are found in
reference 3.
The hydrogen–iodine reaction was mentioned in the previous chapter:
H 2 + I 2 − → 2 HI
(12.5-14)
This reaction is not primarily a chain reaction except at high temperatures. The reaction
obeys second-order kinetics and was thought at one time to proceed by a bimolecular
elementary mechanism. We now know that several mechanisms compete, including the
elementary mechanism. The chain mechanism analogous to Eq. (12.5-3) is dominant
above 750 K but is unimportant below 600 K. The following non-chain mechanism
appears to be dominant below 600 K: 23
(1) I 2 2I
(fast)
(2) 2I + H 2 − → 2HI (slow)
(12.5-15)
Exercise 12.21
a. Find the rate law for the mechanism of Eq. (12.5-15) using the rate-limiting step approximation.
b. Find the rate law for the mechanism of Eq. (12.5-15) using the steady-state approximation.
Branching-Chain Reactions
The combustion of hydrogen with oxygen is a chain reaction that appears to proceed by
a branching-chain mechanism. This means that some propagation steps produce more
chain carriers than they consume, accelerating the reaction and possibly producing an
explosion. A simplified version of the accepted mechanism of the hydrogen–oxygen
reaction is 24
(1) H 2 + wall − → H(adsorbed) + H (initiation)
(2) H + O 2 − → OH + O
(branching)
(3) O + H 2 − → OH + H
(branching)
(4) OH + H 2 − → H 2 O + H
(propagation)
22 R. N. Pease, J. Am. Chem. Soc., 56, 2388 (1934).
23 K. L. Laidler, op. cit., p. 295ff (note 3). See also J. H. Sullivan, J. Chem. Phys., 46, 73 (1967).
24 S. W. Benson, The Foundations of Chemical Kinetics, McGraw-Hill, New York, 1960, p. 454ff.
12 Chemical Reaction Mechanisms I: Rate Laws and Mechanisms
where k a , k b , and k c are temperature-dependent parameters. In the complete absence of
oxygen, the photochemical reaction becomes first order in hydrogen and zero order in
chlorine (except for the dependence of J on the concentration of chlorine). However,
k b is sufficiently small that partial pressures of oxygen down to a few hundredths of a
torr are effective in inhibiting the reaction. Another difference between the hydrogen–
chlorine reaction and the hydrogen–bromine reaction is that the recombination of chlorine atoms, analogous to process 1 in Eq. (12.5-9) is unimportant, whereas termination
of chains by combination of chlorine atoms with the surface of the reaction vessel and
with other molecules (such as oxygen) is important. In the thermally initiated reaction
the dissociation of the Cl 2 molecules at the surface of the reaction vessel is apparently important. 22 A third difference is that the hydrogen–chlorine reaction gives off
enough heat that the reaction mixture can heat up, speeding up the reaction and causing an explosion. The mechanisms and the derivations of the rate laws are found in
reference 3.
The hydrogen–iodine reaction was mentioned in the previous chapter:
H 2 + I 2 − → 2 HI
(12.5-14)
This reaction is not primarily a chain reaction except at high temperatures. The reaction
obeys second-order kinetics and was thought at one time to proceed by a bimolecular
elementary mechanism. We now know that several mechanisms compete, including the
elementary mechanism. The chain mechanism analogous to Eq. (12.5-3) is dominant
above 750 K but is unimportant below 600 K. The following non-chain mechanism
appears to be dominant below 600 K: 23
(1) I 2 2I
(fast)
(2) 2I + H 2 − → 2HI (slow)
(12.5-15)
Exercise 12.21
a. Find the rate law for the mechanism of Eq. (12.5-15) using the rate-limiting step approximation.
b. Find the rate law for the mechanism of Eq. (12.5-15) using the steady-state approximation.
Branching-Chain Reactions
The combustion of hydrogen with oxygen is a chain reaction that appears to proceed by
a branching-chain mechanism. This means that some propagation steps produce more
chain carriers than they consume, accelerating the reaction and possibly producing an
explosion. A simplified version of the accepted mechanism of the hydrogen–oxygen
reaction is 24
(1) H 2 + wall − → H(adsorbed) + H (initiation)
(2) H + O 2 − → OH + O
(branching)
(3) O + H 2 − → OH + H
(branching)
(4) OH + H 2 − → H 2 O + H
(propagation)
22 R. N. Pease, J. Am. Chem. Soc., 56, 2388 (1934).
23 K. L. Laidler, op. cit., p. 295ff (note 3). See also J. H. Sullivan, J. Chem. Phys., 46, 73 (1967).
24 S. W. Benson, The Foundations of Chemical Kinetics, McGraw-Hill, New York, 1960, p. 454ff.