3. Adsorption Equilibria
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Transcript of 3. Adsorption Equilibria
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If the adsorbent and
adsorbate are contacted long
enough, an equilibrium will
be established between theamount of adsorbate
adsorbed and the amount of
adsorbate in solution. The
equilibrium relationship isdescribed by adsorption
isotherms.
Adsorption EquilibriaRef: faculty.washington.edu/.../Adsorption%20...
Adsorption Equil Principles_483
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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 equationrelating the
amount of solute adsorbed onto the solid and the
equilibrium concentration of the solute in solution at a
given temperature.
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Adsorption Equilibria
The adsorption capacity of activated carbon may be
determined by the use of an adsorption isothermwhich can take multiple forms.
Isotherms are found by doing lab tests.
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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 or C X
An adsorption isothermis a qevs. Cerelationship at
equilibrium.
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Isotherm models
There are several models for predicting the
equilibrium distribution.However, the following four models are most
commonly observed.
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Commonly Reported Adsorption Isotherms
max 1
L
L
K c
q q K c linq k c
n
fq k c
Linear: Langmuir:
Freundlich:
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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 treatmentare the Freundlichand Langmuirisotherms.
Freundlich isotherm is an empirical equation.
Langmuir isotherm has a rational basis.
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Linear Isotherm
qe= K. Ce
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Langmuir Isotherm
It assumes
1. Monolayer coverage,
2. Equilibrium model,
3. All adsorption sites are equally probable,
4. A second order reaction.
QM
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v
[S.A]
[S ][A]
At equilibrium Kad=
ST= [Sv] + [S.A] (moles/m2
) Eqn2
Combining Eqn.s 1 & 2
ad
[S.A] +[S.A]K [A]
Eqn1
Consider total number of sites, ST, to be fixed :
(possible if monolayer coverage is assumed)
ST=
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Solve for [S.A] and use CA= [A]
[S.A] = ad A TT
ad A
ad A
K .C .SS =1 1+K .C
1+K .C
Need expression for qA, which ismg adsorbate
g adsorbent
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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
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QMor Qo= maximum adsorption capacity for
forming single layer.
Cehas units of mg/L.
Kador bhas units of L/mg.
where
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Freundlich Isotherm
n and KF
are system specific constants.
n1
eFe CKq
It is emprical and very widely
used.
11
n
KFis 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
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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 ofadsorption for each layer except for the first layer.
Qo
or
QM
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0
( ){1 ( 1)( / )}
B ee
S e B e S
K C Qq
C C K C C
BET (Brunauer, Emmett and Teller) Isotherm
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CS=saturation (solubility limit) concentration of the
solute. (mg/liter)
KB= a parameter related to the binding intensity for all
layers.
Note: when Ce> 1 and Kad= KB/Cs
BET isotherm approaches Langmuir isotherm.
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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 isvery important, because how much you load
the surface at equilibrium depends on how
much is left in water.
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Shape of Freundlich Isotherm
n
1
eFe CKq
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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
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For the Langmuir model linearization gives:
0 01e ee
C Cq K Q Q
A plot of Ce/qeversus Ceshould give a straight linewith intercept :
0
1
K Q
0
1
Q
and slope:
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If you obtain a straight line, determine constants
from slope and intercept.
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or:
0 01 1 1 1e e
q CQ K Q
Here a plot of 1/qeversus 1/Ce should give a
straight line with intercept : 1/Qo
01
K Qand slope :
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If you obtain a straight line, determine constants
from slope and intercept.
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For the Freundlich isotherm use the log-log version :
Clogn1Klogqlog Fe
A log-log plot should yield an intercept of log KFand a slope of 1/n.
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0 0
1 1
( )
e eB
S e e SB B
C CK
C C q C K Q K Q
01B
K Q
B
0
B s
K 1
K Q C
For the BET isotherm we can arrange the isotherm
equation to get:
Intercept =
Slope =