Physical Chemistry , 1st ed.

some connection, then. The connection is simple. We define an equilibrium

constant Kfor this simple reaction as the quotient of the concentration of the

products and the reactants:



[

[

A

B]

]

e

e

q

q

K (20.35)

With this definition and the relationships between the concentrations of A and

B, it can be shown from equation 20.33 that as t→:

[A]eq

(kf

kr

kr)

[A] 0

It follows that for this simple reaction,

[B]eq 1 [A]eq

(kf

kf

kr)

[A] 0

K

k

k

r

f (20.36)

The last equation is especially noteworthy for its simplicity (and its potential

usefulness), although all three equations above are applicable to first-order or

pseudo first-order reactions.* These three expressions (and the concepts used

to derive them) represent one connection between kinetics and thermody-

namics. Other expressions can be derived for higher-order reactions, but they

all mimic similar ideas in mass conservation and the mathematics of differen-

tial equations.

20.5 Parallel and Consecutive Reactions

The previous section used a simple reaction, A →B, to introduce a connection

that does exist between kinetics and thermodynamics. Many chemical equa-

tions are not this simple. For some reactions, more than one product is possi-

ble; these are parallel reactions.And commonly, in other cases, the product of

the first reaction is the reactant of a second reaction, which may in turn be the

reactant of another reaction, and so on. These are examples ofconsecutive

reactions.

A simple parallel reaction can be illustrated as

k 1

A →B

k 2 

↓

C

in which some reactant A can react to form two possible products, labeled B

or C. The rate constants for each individual reaction are labeled k 1 and k 2 ,re-

spectively. As an example, the thermal decomposition of many small hydro-

carbons like CH 4 can occur via several pathways simultaneously, constituting

a set of parallel (also called competingor concurrent) reactions.

Consider a system in which the rate laws of both reactions are first-order

with respect to A. If we start such a reaction with only A present, the initial

rate of disappearance of A can be written as

696 CHAPTER 20 Kinetics

*Equation 20.36 also applies to any forward-and-reverse reactions whose orders are

equal to the stoichiometric coefficients of the reactants for each process. We won’t be con-

sidering any examples of this application here.