Lecture 3. Adsorption on the
interphase of liquid-gas
Prepared by PhD Falfushynska Halina
• A mathematical equation, which describes the
relationship between pressure (p) of the
gaseous adsorbate and the extent of
adsorption at any fixed temperature, is called
adsorption isotherm.
• The extent of adsorption is expressed as mass
of the adsorbate adsorbed on one unit mass
of the adsorbent.
Adsorption Isotherms
Data relating adsorbed concentration (g/g of bed
weight) to equilibrium gas phase concentration
(g/ml of stream) is given in terms of adsorption
isotherms.
Wads = f (P,T)
Three common types of isotherms:
 Langmuir
 Freundlich
 BET
Types of adsorption isoterms
Favorable and Unfavorable Adsorption
Langmuir Isotherm
The earliest model of gas adsorption suggested by
Langmuir (1916). The classical Langmuir model is
limited to monolayer adsorption.
It is assumed that gas molecules striking the surface have a
given probability of adsorption.
At equilibrium, equal numbers of molecules desorb and
adsorb at any time. The probabilities are related to the
strength of the interaction between the adsorbent surface
and the adsorbate gas.
Langmuir Adsorption Isotherm
The surface of the adsorbent is
uniform, that is, all the
adsorption sites are
equivalent.
---Adsorbed molecules do not interact.
---All adsorption occurs through the same
mechanism.
---At the maximum adsorption, only a
monolayer is formed.
• The Langmuir equation is expressed here as:
• where K = Langmuir equilibrium constant, c =
aqueous concentration (or gaseous partial
pressure), Γ = amount adsorbed, and Γmax =
maximum amount adsorbed as c increases.
• The equilibrium constant is actually given by :
• The Langmuir equation can be fitted to data by
linear regression and nonlinear regression
methods.
Langmuir Adsorption Isotherm
θ= the number of sites of the surface which are
covered with gaseous molecule,
P= pressure
K =is the equilibrium constant for distribution of
adsorbate between the surface and the gas phase .
Total number of sites, ST
Langmuir Isotherm
Rate of adsorption,
ra  ka P(1   )
Rate of desorption,
rd  kd
At equilibrium,
ka P

ka P  kd
Wads
CP
 
Wmax
1  CP

1-
air
adsorbate
where,
Wads = the mass of gas adsorbed at pressure P;
Wmax = the mass of gas which covers the entire
adsorbing surface with a monolayer;
P = the partial pressure of interest in the gas phase;
 = coverage;
C = a constant for the gas/solid combination = ka/kd;
ka = the adsorption rate coefficient;
kd = the desorption rate coefficient.
Langmuir Isotherm (cont’d)
Some physisorption and most chemisoption
processes follow this isotherm. It is the one
with the best theoretical basis, which
assumes that adsorption is limited to one
monolayer on the surface.
One can obtain the two
constants by linearization
of the isotherm:
P
1
P


Wads CWmax Wmax
Wads
CP
 
Wmax
1  CP
1

S = 1/Wmax
P/Wads
C
J = 1/CWmax
0
P
P
Freundlich Isotherm
The Fruendlich isotherm model is valid for heterogeneous
surfaces, monolayer coverage. Common for most
adsorption work since it fits almost all data. It is
empirical in nature, although some theoretical foundations
do exit.
Freundlich Isotherm
The expression： Wads = KF P 1/n
(KF and n are experimentally determined parameters)
n>1
n=1
Wads
n<1
P
 When n = 1, the reaction is linear and called
“partitioning”.
 When n > 1, the reaction is said to be “favorable” as
the incremental change in amount sorbed decreases
with increasing concentrations.
 While n < 1 is called “unfavorable” because the
reverse is true.
 Most natural adsorbents exhibit either linear or
favorable adsorption.
 The Langmuir and Fruendlich models for n < 1 are
concave downwards, so both models can be
calibrated to similar data..
Freundlich Isotherm Parameters
Available for a wide variety of organic vapors on
various activated carbon types
Wads = KF P 1/n
Example
The Freundlich isotherm can be accepted to represent
equilibrium concentrations of phenol in the g/L
concentration range and x/m represents g phenol/mg C.
a) If the limiting concentration of phenol is set at 0.2g/L
and the source contains 30g/L, calculate the required
dosage of powdered activated carbon.
b) If instead of a single dosage, the carbon was dosed
twice, first to achieve a concentration of 3g/L and then in
a second tank to the final requirement, how much carbon
will be required?
c) How could we minimize carbon requirements over two
dosages?
d) Qualitatively consider the effect of even more tanks and
possibilities of reusing the carbon from tank to tank. The
isotherm may be extrapolated.
Freundlich isotherm for Problem
a) According to the graph, when c = 0.2 
g/L, x/m = 0.019, assuming 1L phenol solution:
(30g / L  0.2g / L)  1L
29.8g
 0.019gphenol / mgC  m 
 1568mgC
m(mg )
0.019gphenol / mgC
b) According to the graph, when c = 3 g/L, x/m = 0.089, assuming 1L phenol solution:
(30g / L  3g / L)  1L
27 g
 0.019gphenol / mgC  m 
 303.4mgC
m(mg )
0.089gphenol / mgC
According to the graph, when c = 0.2 g/L, x/m = 0.019, assuming 1L phenol solution:
(3g / L  0.2g / L)  1L
2.8g
 0.019gphenol / mgC  m 
 147.4mgC
m(mg )
0.019gphenol / mgC
So, the total carbon required is: 303.4 mgC+147.4 mgC = 450.8 mgC
c) In order to minimize the carbon usage over two dosages, a
concentration of the effluent of phenol from the first activated
carbon dosage must be determined. If this concentration is too
close to the initial phenol concentration, the dosage used in the
second step will be decreased while that used in the first step
will be increased, and vice versa. More elegantly, write and
equation of C as a function of PAC dose, differentiate and solve
when = 0. PAC dosages of about 160 mg/L each will represent
the lowest dosage for a two-step process.
d) The total dosage needed will decrease with an increase of
tanks. If the carbon from the last step is recycled towards the
first tank, countercurrent to the water flow, the adsorption
capacity of carbon can be maximized and minimize the carbon
requirement even further. You can see that the PAC from the
last step above would have much adsorption capacity left when
reused in the first tank.
Brunauer-Emmett-Teller (BET) Isotherm
Brunauer, Emmett and Teller (BET) developed several
models for gas adsorption on solids which have
become the effective standard for surface area
measurements.
BET isotherm is valid for multiple layers on
homogeneous surfaces.
The assumptions used to
derive the BET isotherm are
• 1. Gaseous molecules behave ideally
• 2. Multiple nitrogen molecules can be adsorbed
to each site
• 3. Each adsorbed molecule provides a site for the
adsorption of the molecule in the layer above it
• 4. All sites on the surface are equivalent
• 5. No adsorbate - adsorbate interactions
• 6. An adsorbed molecule is immobile
• 7. Nitrogen in the second and higher layers are
assumed to be liquid like