Physical Chemistry Third Edition

568 13 Chemical Reaction Mechanisms II: Catalysis and Miscellaneous Topics

Since the total area of an adsorbing surface and the area occupied by one adsorbed

molecule are probably not known, the value ofθmight not be known. However, the

mass adsorbed is proportional toθ, and a graph of the mass adsorbed will have the same

shape as the graph of Figure 13.2. The asymptote corresponds toθ1, allowing one

to determine whereθ 1 /2 is located on the graph if the asymptote can be accurately

located. If the data suffer from experimental errors, locating the asymptote might be

difficult, so it is desirable to make a plot of a different type, as shown in Figure 13.3.

In this figure, 1/θis plotted as a function of 1/[A], corresponding to the reciprocal of

Eq. (13.1-8):

1

θ



1 +k[A]

k[A]



1

k[A]

+ 1 (13.1-10)

If the Langmuir isotherm is obeyed, this should give a linear plot.

1/[A]

1/

Slope = 1/K

Figure 13.3 Linear Plot of the
Langmuir Isotherm.

0.3

0.2

0.1

0 500 1000

(^1) m/g
1
[A] / mol L–1
Figure 13.4 Plot of 1/mas a Function
of 1/[A].
A plot of the reciprocal of the mass adsorbed is usually made, since this quantity is
proportional to 1/θ. Since a plot of 1/θas a function of 1/[A] has an intercept equal to
unity, it is possible to determine the relationship betweenθand the mass absorbed and
then to determine the value ofKfrom the slope of the line in the plot.
Exercise 13.3
Show that Eq. (13.1-10) is correct.

EXAMPLE13.1

Chloroethane from the gas phase is adsorbed on a sample of charcoal at 273.15 K. The mass

adsorbed for each concentration in the gas phase is

[C 2 H 5 Cl]/mol L−^1 0.00117 0.00294 0.00587 0.0117 0.0176

mass adsorbed/g 3.0 3.8 4.3 4.7 4.8

a.Find the value ofθfor each concentration and the value ofK.

b.If each chloroethane molecule occupies an area of 2. 60 × 10 −^19 m^2 , find the effective

area of the sample of charcoal.

Solution

a.Sincem, the mass absorbed, is proportional toθ,

1

m



B

θ



B

K[C]

+B (13.1-11)

whereBis a proportionality constant and where we abbreviate chloromethane by C. For

each data point, we calculate 1/mand 1/[C].

1

m/g 0.333 0.263 0.233 0.213 0.208

1

[C]/mol L−^1

855 340 170 85.5 56.8

Figure 13.4 shows a graph of 1/mas a function of 1/[C] with the linear least-squares

line. The slope of this line is equal to 1. 55 × 10 −^4 mol L−^1 g−^1 and its intercept is equal

to 0.203 g−^1.