Physical Chemistry Third Edition

13.1 Catalysis 567

This theory was devised by Irving
Langmuir, 1881–1957, an American
industrial chemist who won the 1932
Nobel Prize in chemistry for his work on
surface chemistry.

Letθrepresent the fraction of the surface sites that are occupied by adsorbed

A molecules. The adsorption is assumed to be an elementary process so that the rate of

adsorption is proportional to the concentration of A in the fluid phase and to 1−θ, the

fraction of surface sites available for adsorption:

rate of adsorptionk 1 [A](1−θ) (13.1-5)

where [A] is the concentration of A in the gas or liquid phase and wherek 1 is a rate

constant that can depend on temperature but not on [A] orθ. The desorption is also

assumed to be an elementary process so that

rate of desorptionk 1 ′θ (13.1-6)

wherek′ 1 is another rate constant. At equilibrium, the rate of desorption equals the rate

of adsorption:

k′ 1 θk 1 [A](1−θ) (13.1-7)

This equation can be solved forθto give theLangmuir isotherm:

θ

k 1 [A]

k′ 1 +k 1 [A]



K[A]

1 +K[A]

(Langmuir isotherm) (13.1-8)

whereKis an equilibrium constant given by

K

k 1

k′ 1

(13.1-9)

The name “isotherm” is used because the formula corresponds to a fixed tempera-

ture. The value ofKcan be determined from a graph of the Langmuir isotherm since

1 /Kis equal to the value of [A] that corresponds toθ 1 /2. Figure 13.2 schematically

depicts the Langmuir isotherm for a hypothetical system.

Exercise 13.2

Show that 1/Kequals the value of [A] that corresponds toθ 1 /2.

1

1

2

0 [A] = 1/K

[A]

Figure 13.2 The Langmuir Isotherm.