The Foundations of Chemistry

Similar interpretations apply to most other overall third- or higher-order reactions, as
well as many lower-order reactions. When several steps are about equally slow, however,
the analysis of experimental data is more complex. Fractional or negative reaction orders
result from complex multistep mechanisms.
One of the earliest kinetic studies involved the gas-phase reaction of hydrogen and
iodine to form hydrogen iodide. The reaction was found to be first order in both hydrogen
and iodine.

H 2 (g)
I 2 (g)88n2HI(g) ratek[H 2 ][I 2 ]

The mechanism that was accepted for many years involved collision of single molecules
of H 2 and I 2 in a simple one-step reaction. Current evidence indicates a more complex
process, however. Most kineticists now accept the following mechanism.

(1) I 2 34 2I (fast, equilibrium)

(2) IH 2 
H 2 34 H 2 I (fast, equilibrium)

(3) H 2 I
I 88n 2HI (slow)

H 2 I
I 2 88n 2HI (overall)

In this case neither original reactant appears in the rate-determining step, but both appear
in the rate-law expression. Each step is a reaction in itself. Transition state theory tells us
that each step has its own activation energy. Because step 3 is the slowest, we know that
its activation energy is the highest, as shown in Figure 16-12.
In summary

The experimentally determined reaction orders of reactants indicate the number of

molecules of those reactants involved in (1) the slow step only, if it occurs first, or

(2) the slow step andany fast equilibrium steps preceding the slow step.

Figure 16-12 A graphical representation of the relative energies of activation for a
postulated mechanism for the gas-phase reaction

H 2 
I 2 88n2HI

16-7 Reaction Mechanisms and the Rate-Law Expression 683

H 2

H 2 
 I 2

2HI

H 2 I


 2I 
 I

Ea2

Ea3

overall

Ea

Ea1

Energy

Progress of reaction

Net energy released

Apply the algebraic approach described

earlier to show that this mechanism is

consistent with the observed rate-law

expression.