At this point, we need to keep track of what process we are speaking of when
we are referring to a rate. For elementary processes, the rate law can be deter-
mined directly from the stoichiometry of the process. For net balanced chem-
ical reactions, we can’t. However, we have proposed that we can know the rate
of the overall reaction if we know the rate-determining step. We will see in the
next section how we might be able to use the rate-determining step to relate
to a measurable rate law.(Counter?)Example 20.11
Assume that the rate law for the combination of hydrogen and oxygen is
rate k[H 2 ][O 2 ]
Show that this is not consistent with the hypothesis that the second elemen-
tary process, which is
OHH 2 →H 2 O H
is the rate-determining step in this reaction.Solution
If the second elementary process in our proposed mechanism were the RDS,
we could immediately predict a rate law of
rate k[OH][H 2 ]
In this case, we have [OH] substituting for [O 2 ]. Unless we can be convinced
that the concentration of the hydroxide radical is equal to the concentration
of diatomic oxygen, we would have a difficult time arguing that this rate law
is equivalent to the assumed rate law from the first part of the example. This
would argue against the second step being the RDS.20.8 The Steady-State Approximation
The preceding example points out one obvious problem, and implies another.
The obvious problem is that rate laws for elementary processes are not imme-
diately transferable to rate laws for the overall reaction.
The implied problem is not so obvious. Typically, we determine rate laws in
terms of amounts we can measure.For example, in the reaction between hy-
drogen and oxygen gases, we would want to express a rate law in terms of the
amounts of H 2 and O 2. On the other hand, we certainly do notwant to express
a rate law in terms of, say, the OH radical. Such a chemical species may be an
intermediate, but its existence is so fleeting that it would be extraordinarily dif-
ficult to measure its concentration at any one time, much less determine the
effect its change in concentration has on a reaction rate. No, we typically ex-
press a rate law in terms of concentrations that are easily measured, like the
concentrations of the reactants (and sometimes the products).
If the rate-determining step is the first step in the mechanism, then the rate
law for the overall reaction is simply the rate law from the elementary process.
(And because the first step does not have any intermediates as reactants, by de-
finition the rate law can be expressed in terms of measurable quantities of
chemical species.) Suppose, however, that the rate-determining step is the sec-
ond step. Consider the following hypothetical two steps:710 CHAPTER 20 Kinetics