Physical Chemistry , 1st ed.

and then define a proportionality constant (the Greek letter kappa) to relate
the two:

m or 

1

m





1





1



then we can rewrite equation 22.28 in terms of a measurable parameter:



1

m



K

1

[gas]





1

 (22.29)

Equation 22.29 shows that if we plot the reciprocal of the change in mass,
1/ m, as a gas is adsorbed on a surface versus the reciprocal of the concentra-
tion of the gas, we will get a straight line whose yintercept is the reciprocal of
the proportionality constant . Using this value, we can use the slope of the
plot [which equals 1/(K)] to determine the equilibrium constant of the
adsorption/desorption process. Also, instead of m, we can use a change in
concentration; the concepts behind equation 22.29 remain the same.
Finally, since the yintercept corresponds to an infinite value of [gas] (so that
1/[gas] equals 0), its value should correspond to a coverage of 1. Knowing the
approximate size of the molecule, we can determine how many molecules are ad-
sorbed as well as the approximate surface area of the solid. The proportionality
constant thus acts as the conversion factor between mass adsorbed and surface
area of the solid. The following example shows how to use some of these ideas.

Example 22.8

One application of adsorption on surfaces is to measure the ability of acti-

vated charcoal to adsorb acid. (Activated charcoal, a form of treated carbon,

is very porous and is used to adsorb impurities from water. Its use in aquar-

iums typifies this behavior.) In a lab experiment, a student mixes a given

amount of powdered charcoal into a series of acetic acid solutions. The acetic

acid solutions have different initial concentrations. Some of the acid is ad-

sorbed onto the charcoal. By taking aliquots after equilibrium is established,

the student determines the change in acid concentration. Plot a Langmuir

isotherm for the experimental data and determine the equilibrium constant

for the adsorption. The experimental data are as follows:

Original concentration (M) Change in concentration (M)

0.7001 0.00665

0.3694 0.00588

0.1515 0.00553

0.0437 0.00283

0.0169 0.00153

Solution

In order to use equation 22.29 to plot an isotherm and determine a propor-

tionality constant , we need to plot 1/ c, the inverse of the concentration

change, versus 1/[acid]. The following table is determined from the experimen-

tal data given above:

1/[acid] 1/c

1.428 150.

2.708 170.

6.601 181

22.9 353

59.2 654

22.6 Coverage and Catalysis 785