Physical Chemistry Third Edition

13.1 Catalysis 569

B 0 .203 g−^1

K

0 .203 g−^1

1. 55 × 10 −^4 mol L−^1 g−^1

1310 L mol−^1

The asymptotic value ofmis equal to 1/B, or 4.93 g.

b.The effective area of the sample is obtained from the assumption that the asymptotic

amount adsorbed corresponds to a full monolayer. Since the molar mass of chloroethane

is equal to 64.515 g mol−^1 , the asymptotic amount adsorbed is equal to 0.0764 mol. The

effective areaAis

A

(

0 .260 nm^2 molecule−^1

)(

6. 022 × 1023 molecule mol−^1

)

(0.0764 mol)

 1. 20 × 1022 nm^2  1. 20 × 104 m^2

Although this area corresponds to the area of a macroscopic square 110 m on a side,

charcoal can be so finely divided that this sample of charcoal might have a mass of only

a few grams.

There are two classes of adsorption processes:physical adsorptionandchemical

adsorption (chemisorption). In physical adsorption, the binding forces are London

dispersion forces, dipole–dipole attractions, and so on. In chemical adsorption covalent

chemical bonds are formed between the atoms or molecules of the surface and the atoms

or molecules of the adsorbed substance. The Langmuir isotherm applies to both classes

if only a monolayer of atoms or molecules can be adsorbed on the surface and if the

adsorbed molecules do not dissociate. There are other isotherms that apply to the case

of multiple layers.^3

When hydrogen molecules are adsorbed on platinum they dissociate into hydrogen

atoms that are covalently bonded (chemically adsorbed) to platinum atoms on the

surface. In this case a different isotherm from that of Eq. (13.1-8) applies. Assume that

a substance A 2 dissociates to form two adsorbed A atoms that occupy two sites on the

surface:

A 2 (g)+2 surface sites
2A(adsorbed) (13.1-12)

If the adsorption is an elementary process,

rate of adsorptionk 1 [A 2 ](1−θ)^2 (13.1-13)

If desorption is an elementary process,

rate of desorptionk′ 1 θ^2 (13.1-14)

The rates of adsorption and desorption are equated and the resulting equation is solved

forθto obtain the equilibrium isotherm:

θ

K^1 /^2 [A 2 ]^1 /^2

1 +K^1 /^2 [A 2 ]^1 /^2

(adsorption with dissociation) (13.1-15)

(^3) K. J. Laidler,op. cit., p. 234 (note 1).