Physical Chemistry Third Edition

550 12 Chemical Reaction Mechanisms I: Rate Laws and Mechanisms

A. Construct a possible set of steps.

1. The steps must add up to the correct stoichiometry (possibly multiplying one or
   more of the steps by constants before adding).


2. If the mechanism has two steps, there must be at least one reactive intermediate.
   Three steps require two reactive intermediates, etc. Reactive intermediates must
   cancel in the addition of the steps: They must occur on the right-hand side of one
   step equation and on the left-hand side of a later step equation.


3. Let your knowledge of chemistry guide the choice of a proposed mechanism.

i. The breaking of a weak bond is more likely than the breaking of a strong

bond.

ii. Reactive intermediates should have reasonable structures. In a gas-phase reac-

tion, reactive intermediates with nonzero charges are not very likely, but free

radicals are more likely. In a reaction in an aqueous solution, intermediates

with nonzero charges are more likely than are free radicals.

B. Choose the rate-limiting step approximation or the quasi-steady-state approximation.

1. If the experimental rate law has definite orders, try the rate-limiting step approx-
   imation.

i. If no products appear in the rate law for the forward reaction, it is possible

that the first step is the rate-limiting step.

ii. If there are some reactants that do not appear in the rate law for the forward

reaction, these substances occur only in steps after the rate-limiting step.

iii. If negative orders or fractional orders occur in the rate law, the rate-limiting

step cannot be the first step.

iv. Substances with positive orders have a larger sum of stoichiometric coeffi-

cients on the left-hand sides of step equations up to and including the rate-

limiting step, and substances with negative orders have a larger sum of stoi-

chiometric coefficients on the right-hand sides of step equations prior to the

rate-limiting step.

2. If the rate law has a denominator with two or more terms, try the steady-state
   approximation.

C. Deduce the rate law for your proposed mechanism and compare it with the experi-

mental rate law. If it does not agree, try again with another proposed mechanism.

Let us examine a few hypothetical examples.

EXAMPLE12.14

If the stoichiometry of the reaction is

aA+bB−→cC+dD (12.4-35)

and if the rate law is

rateki[A]a[B]b (12.4-36)

find a mechanism that conforms to this rate law.