Physical Chemistry Third Edition

504 11 The Rates of Chemical Reactions

kf

rinitial

[NO]^2 [Cl 2 ]



(7. 1 × 10 −^5 mol L−^1 s−^1 )

(0.0200 mol L−^1 )^2 (0.0200 mol L−^1 )

 8 .9L^2 mol−^2 s−^1

The average value calculated from all three experiments is 8.8L^2 mol−^2 s−^1. This example

could have been solved by inspection, noticing that the rate quadrupled when [NO] was

doubled and doubled when [Cl 2 ] was doubled.

The Method of Isolation

In this method an experiment is carried in which the initial concentration of one reactant

is chosen to be much smaller than the concentrations of the other reactants. During the

reaction the fractional changes in the large concentrations are small, and these concen-

trations are treated as constants. The species having the small concentration is monitored

as in the case of a single reactant. For example, in the reaction of Eq. (11.3-12), if [A]

is much smaller than [B] and [F], the relative changes in [B] and [F] will be small.

We write

−

1

a

d[A]

dt



(

kf[B]β[F]φ

)

[A]α (11.3-15)

where the quantity in parentheses is approximately constant. Data from this kind of

experiment can be treated like data from reactions with a single reactant. For example,

ifα2, Eq. (11.2-11) can be transcribed to obtain

1

[A]t



1

[A] 0

+(kf[B]β[F]φ)t (11.3-16)

Sets of experiments can also be carried out in which [B] is made much smaller than

[A] and [F], and then in which [F] is made much smaller than [A] and [B], in order to

determineβ,φ, andkf.

If a reaction in a solution includes the solvent as a reactant, the concentration of the

solvent is usually much larger than the concentrations of other reactants and is almost

constant. Assume that the solvent S is involved in the reaction

A+S−→products (11.3-17)

and that the forward rate law is

r−

d[A]

dt

kf[S]σ[A]αkapp[A]α (11.3-18)

whereσis the order with respect to the solvent. The quantitykappis equal tokf[s]σis

called anapparent rate constant. The order with respect to substance A and the apparent

rate constant can be determined by any of the methods that apply to a single reactant.

If the reaction is first-order with respect to substance A and of unknown order with

respect to the solvent, the reaction is called apseudo first-order reaction. If the reaction

is second order with respect to substance A, the reaction is called apseudo second-order

reaction, and so on. The actual rate constantkfand the order with respect to the solvent

cannot be determined unless the concentration of the solvent can somehow be varied

to determine the order with respect to the solvent.

The method of isolation applies automatically to a reaction that is catalyzed by a

substance in the same phase as the reactants. For example, the hydrolysis of methyl

acetate is catalyzed by KI. The reaction equation is

CH 3 CO 2 CH 3 +H 2 O→CH 3 CO 2 H+CH 3 OH (11.3-19)