Solid Surfaces—Adsorption - Surface and Colloid Chemistry: Principles and Applications - page 118

N s /N sm = a p/(1 + a p) (5.14)

where p is the pressure and a is dependent on the energy of adsorption. This equation
can be rearranged as

p /N s = (1/[ a N sm ] + p /N sm ) (5.15)

From the experimental data, p /N s versus p can be plotted. The plot will be linear, and
the slope is equal to 1/N sm . The intersection gives a . Charcoal is found to adsorb 15
mg of N 2 as monolayer. Another example is that of adsorption of N 2 on mica surface
(at 90 K). The following data were found:

volume of Gas adsorbed
(at StP) Pressure/Pa

0.3 12

0.5 17

1.0 24

In this equation one assumes that

The molecules adsorb on definite sites.
The adsorbed molecules are stable after adsorption.

The surface area of the solid can be estimated from the plot of p /N s versus p . Most
data fit this equation under normal conditions and are therefore widely applied to
analyze the adsorption process.
Langmuir adsorption is found for the data of nitrogen on mica (at 90 K). The data
were found to be

p = 1/Pa 2/Pa

V s = 24 mm 3 28 mm 3

This shows that the amount of gas adsorbed increases by a factor 28/24 = 1.2 when
the gas pressure increases twofold.

5.5.1.4 various Gas adsorption equations
Other isotherm equations begin as an alternative approach to the developed equation
of state for a two-dimensional ideal gas. As mentioned earlier, the ideal equation of
state is found to be

Π A = k B T (34.1)

In combination with the Langmuir equation, one can derive the following relation
between N s and p :