If the adsorbent and
adsorbate are contacted long
enough, an equilibrium will
be established between the
amount of adsorbate
adsorbed and the amount of
adsorbate in solution. The
equilibrium relationship is
described by adsorption
isotherms.
Adsorption Equilibria Ref: faculty.washington.edu/.../Adsorption%20...
Adsorption Equil Principles_483
An adsorption isotherm is a curve relating the
equilibrium concentration of a solute on the surface of an
adsorbent, qe, to the concentration of the solute in the
liquid, Ce, with which it is in contact.
Adsorption Equilibria
The adsorption isotherm is also an equation relating the
amount of solute adsorbed onto the solid and the
equilibrium concentration of the solute in solution at a
given temperature.
Adsorption Equilibria
The adsorption capacity of activated carbon may be
determined by the use of an adsorption isotherm
which can take multiple forms.
Isotherms are found by doing lab tests.
Adsorption Isotherms
Add same initial target chemical concentration, Cinit, in each
Different activated carbon dosage, Csolid, in each
Control
o e o eC -C mg/L C -C .Vmg g mass=
g g g/L mass
e
solid
q or orC X
An adsorption ‘isotherm’ is a qe vs. Ce relationship at
equilibrium.
Isotherm models
There are several models for predicting the
equilibrium distribution.
However, the following four models are most
commonly observed.
Commonly Reported Adsorption Isotherms
max1
L
L
K cq q
K c
linq k c
n
fq k c
Linear: Langmuir:
Freundlich:
Adsorption Equilibria
i. Linear
ii. Langmuir
iii. Freundlich
iv. Brunauer, Emmet, and Teller (BET)
The most commonly used isotherms for the application
of activated carbon in water and wastewater treatment
are the Freundlich and Langmuir isotherms.
Freundlich isotherm is an empirical equation.
Langmuir isotherm has a rational basis.
Linear Isotherm
qe = K. Ce
Langmuir Isotherm
It assumes
1. Monolayer coverage,
2. Equilibrium model,
3. All adsorption sites are equally probable,
4. A second order reaction.
QM
v
[S.A]
[S ][A]
At equilibrium Kad =
ST = [Sv] + [S.A] (moles/m2) Eq’n 2
Combining Eq’n.s 1 & 2
ad
[S.A]+[S.A]
K [A]
Eq’n 1
Consider total number of sites, ST, to be fixed :
(possible if monolayer coverage is assumed)
ST =
Solve for [S.A] and use CA = [A]
[S.A] = ad A TT
ad A
ad A
K .C .SS=
1 1+K .C1+
K .C
Need expression for qA, which is mg adsorbate
g adsorbent
A ad Aq =[S.A].A .MW
M ad AA
ad A
Q .K .Cq =
1+K .C
0
eA
e
b.C .Qq =
1+ b.C
or
QM or Qo = maximum adsorption capacity for
forming single layer.
Ce has units of mg/L.
Kad or b has units of L/mg.
where
Freundlich Isotherm
n and KF are system specific constants.
n1
eFe CKq
It is emprical and very widely
used.
11
n
KF is an indicator of adsorption capacity.
Higher the maximum capacity, higher the KF.
1/n is a measure of intensity of adsorption.
Higher the 1/n value, more favorable is the adsorption.
Generally, n < 1
This is a more general,
multi-layer model. It
assumes that a
Langmuir isotherm
applies to each layer
BET (Brunauer, Emmett and Teller) Isotherm
and that no transmigration occurs between layers.
It also assumes that there is equal energy of
adsorption for each layer except for the first layer.
Qo or QM
0
( ){1 ( 1)( / )}
B ee
S e B e S
K C Qq
C C K C C
BET (Brunauer, Emmett and Teller) Isotherm
CS =saturation (solubility limit) concentration of the
solute. (mg/liter)
KB = a parameter related to the binding intensity for all
layers.
Note: when Ce << CS and KB >> 1 and Kad = KB/Cs
BET isotherm approaches Langmuir isotherm.
qe
Ce
Most favorable one because
even at low concentrations
you can load your surface
with high amounts of material.
The concept of the adsorption isotherm is
very important, because how much you load
the surface at equilibrium depends on how
much is left in water.
Shape of Freundlich Isotherm
n1
eFe CKq
To determine which model to use to describe the
adsorption for a particular adsorbent/adsorbate
isotherms experiments are usually run. Data from
these isotherm experiments are then analyzed
using the following methods that are based on
linearization of the models.
Determination of appropriate model
For the Langmuir model linearization gives:
0 0
1e e
e
C C
q K Q Q
A plot of Ce/qe versus Ce should give a straight line
with intercept :
0
1
K Q
0
1
Q
and slope:
If you obtain a straight line, determine constants
from slope and intercept.
or:
0 0
1 1 1 1
e eq CQ K Q
Here a plot of 1/qe versus 1/Ce should give a
straight line with intercept : 1/Qo
0
1
K Qand slope :
If you obtain a straight line, determine constants
from slope and intercept.
For the Freundlich isotherm use the log-log version :
Clogn
1Klogqlog Fe
A log-log plot should yield an intercept of log KF
and a slope of 1/n.
0 0
1 1
( )
e eB
S e e SB B
C CK
C C q CK Q K Q
0
1
BK Q
B
0
B s
K 1
K Q C
For the BET isotherm we can arrange the isotherm
equation to get:
Intercept =
Slope =
