Physical Chemistry , 1st ed.

cally controlled.However, over long time intervals, the ultimate ratio of prod-

ucts will depend on the individual equilibrium constants of the separate reac-

tions. Since equilibrium constants are ultimately related to the thermodynam-

ics of the reaction, we say that the ratio of products under these conditions

is thermodynamically controlled.

The ratio of products at any one instant may be completely different de-

pending on whether the ratio is dictated by kinetic control or thermodynamic

control. For example, consider parallel reactions in which k 1  1 10 ^2 and

k 1  1 10 ^4 (which relate to product B) while k 2  1 10 ^3 and k 2 

1 10 ^7 (which relate to product C). The two equilibrium constants K 1 and

K 2 , are 100 and 10,000, respectively.

Initially, because k 1 is 10 times larger than k 2 , more of product B is produced

than product C. We say that B is the kinetically favored product.However, as

equilibria are established over a long period of time, the amount of product C

is much larger because its equilibrium favors products much more than the B

product is favored by its independent equilibrium. We say that product C is the

thermodynamically favored product.Figure 20.11 shows a graph of how prod-

uct B is produced in larger quantities at first, and how this changes over longer

periods of time as equilibria are established. If a chemical producer is inter-

ested in product B, the kinetically favored product, a way to remove B from the

system would need to be developed, or else B will re-react and form C, the

thermodynamically favored product.

There are many cases ofconsecutive reactions,in which the product of a first

reaction is the reactant (or one of the reactants) of a second reaction, and so

on. A simple consecutive reaction scheme can be represented as

k 1 k 2

A →B→C

Radioactive decay series are good examples of consecutive reactions. Assuming

(as is usually the case) that a system starts out with only A present and no B

or C, the rates of change of concentration of the three species in the above se-

quence are



d[

d

A

t

]

k 1 [A]t



d[

d

B

t

]

k 1 [A]tk 2 [B]t (20.46)



d[

d

C

t

]

k 2 [B]t

20.5 Parallel and Consecutive Reactions 699

1.0

0

0

Time (s)

[A]

[B] [C]

700 800

Fraction present

100 200 300 400 500 600

0.8

0.6

0.4

0.2

Figure 20.11 Plots of [A]t, [B]t, and [C]tfor a
long period of time in which equilibria can be
established. Now the relative concentrations of B
and C are dependent on the equilibrium con-
stants of the individual reactions, not just the rate
constants of the two forward parallel reactions.