Page 34 - Adsorbents - fundamentals and applications

EQUILIBRIUM ISOTHERMS AND DIFFUSION 19

The parameter α is the sticking probability or accommodation coefficient for
adsorption (upon a collision on the surface), and β is the rate constant for desorp-
tion. The constant B is called Langmuir constant. At low pressures, the Langmuir
isotherm reduces to a linear form, or Henry’s law form:

q = KP and K = Bq m (3.1b)

where K is Henry’s constant.
All isotherms should reduce to the Henry’s law form at extreme dilution. The
Henry’s constant is the most important factor for purification. From Eq. 3.1a, B
is exponentially proportional to Q, the heat of adsorption. Here Q(Q =− H) is
positive by definition, because H, the enthalpy change for physical adsorption,
must be negative (Yang, 1987). For physical adsorption, Q is equal to the bond
energy between the adsorbate molecule and the sorbent. Therefore, the bond
energy is critical for purification. Strong bonds are needed for ultrapurification.
Zeldowitsch (1934), assuming an exponentially decaying function of site den-
sity with respect to Q, obtained the classical empirical isotherm:

q = KP 1/n (3.2)

which is known as Freundlich isotherm. To avoid indefinite increase in adsorption
with pressure, the following isotherm is consequently proposed (Sipps, 1948;
1950; Yang, 1987):
1/n
q BP
θ = (3.3)
q m 1 + BP 1/n
which is the Langmuir–Freundlich isotherm. This isotherm can be derived from
the Langmuir isotherm by assuming each sorbate molecule occupies n sites
(Yang, 1987). It can also be considered as the Langmuir isotherm on nonuni-
form surfaces.
The Langmuir isotherm for pure-component adsorption can readily be
extended to an n-component mixture, known as the extended Langmuir isotherm
(Yang, 1987):
q mi B i P i
q i = (3.4)
n

1 + B j P j
j=1
In Eq. 3.4, the monolayer amount for component i in the mixed adsorbed phase
remains the same as that in pure component adsorption. It is assumed that each
species maintains its own molecular area (the area covered by one molecule
that is not influenced by the presence of other species on the surface). This
does not meet the requirement of thermodynamic consistency (which requires all
monolayer amounts be equal). An empirical mixing rule is available for dealing
with this problem (Yang, 1987). Nonetheless, Eq. 3.4 remains useful for practical
design purposes.