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Adsorption Equilibria
Ali Ahmadpour
Chemical Eng. Dept.
Ferdowsi University of Mashhad
2
Contents
Introduction
Adsorption isotherm models
Langmuir isotherm
Volmer isotherm
Fowler-Guggenheim isotherm
Hill-deBoer isotherm
Concluding remarks
3
Introduction
Adsorption equilibria is the most important information in
understanding an adsorption process.
No matter how many components are present in the system,
the adsorption equilibria of pure components indicate how
much those components can be accommodated by a solid
adsorbent.
This information can be used in the study of adsorption
kinetics of a single component, adsorption equilibria of
multicomponent systems, and then adsorption kinetics of
multicomponent systems.
4
Adsorption Process
Adsorbent
AdsorbateAdsorptive
5
The Isotherm
The amount of gas adsorbed is a function of
The strength of interaction between gas and solid (intrinsic)
Temperature (fixed)
Pressure (controlled variable)… expressed as relative pressure P/Po
T)(C, fq
T)(P, fV
V : cm3 STP/g ; mole/g ; mole/cm3
q : mole/g ; mole/cm3
Gas-Solid system:
Liquid-Solid system:
6
Adsorption isotherm models
• Some of the famous models describing the adsorptionequilibria are:
• Basic model: Langmuir (1918)
• Extended model: BET (1938)
• Empirical model: Freundlich (1932)
• There are various types of theoretical, empirical andsemi-empirical models for equilibrium of adsorption.
7
Different types of adsorption
isotherms
8
Langmuir adsorption isotherm
(Type I)
bp
1+bp
9
Type II and IV isotherms
Similar to type II
10
Type III and V isotherms
11
The adsorption theory
The Langmuir theory (1918) is the most basic theory in
adsorption. Langmuir described the kinetic behavior of the
adsorption process.
This theory allows us to understand the monolayer surface
adsorption on an ideal surface.
He postulated that at equilibrium, the rate of arrival of
adsorptive (adsorption) and the rate of evaporation of
adsorbate (desorption) were equal.
Furthermore, the heat of adsorption was taken to be constant
and unchanging with the degree of coverage, θ.
I. Langmuir, J. Amer. Chem. Soc., 40, 1368 (1918)
12
• Graduated as a metallurgical engineer from the
School of Mines at Columbia University in 1903.
• 1903-1906 M.A. and Ph.D. in 1906 from
Göttingen.
• 1906-1909 Instructor in Chemistry at Stevens
Institute of Technology, Hoboken, New Jersey.
• 1909 –1950 General Electric Company at
Schenectady where he eventually became
Associate Director.
• 1913 :Invented the gas filled, coiled tungsten
filament incandescent lamp.
Irving Langmuir (1881-1957)
13
• 1919 to 1921, his interest turned to an examination of atomic theory, and
he published his "concentric theory of atomic structure". In it he
proposed that all atoms try to complete an outer electron shell of eight
electrons.
• 1927 Coined the use of the term "plasma" for an ionized gas.
• 1935-1937 With Katherine Blodgett studied thin films.
• 1948-1953 With Vincent Schaefer discovered that the introduction of dry
ice and iodide into a sufficiently moist cloud of low temperature could
induce precipitation.
• 1932 The Nobel Prize in Chemistry "for his discoveries and
investigations in surface chemistry"
Cont.
14
• Langmuir theory describe that the rate of accumulation of
molecules at the flat surface is zero at equilibrium.
• The assumptions of the Langmuir model are:
Homogeneous surface (all adsorption sites energetically identical).
Monolayer adsorption (Adsorption on surface is localized, i.e. adsorbed
atoms or molecules are adsorbed at definite, localized sites).
No interaction between adsorbed molecules (Each site can
accommodate only one molecule or atom).
Langmuir Theory
15
Cont.
Rate of adsorption (the striking rate at the surface)× sticking coefficient (α: the
accommodation coefficient) = Rate of desorption from the surface
The rate of striking the surface (mole / time × area), from the kinetic theory of gas is:
16
Cont.
The rate of adsorption (mole adsorbed/ surface area × time) is:
The rate of desorption, corresponds to fully covered surface (kd ) × fractional
coverage, is:
Ed = Q : activation energy for desorption (is equal to the heat of adsorption for
physically sorbed species)
kd : rate constant for desorption at infinite temperature
17
Cont.
The average residence time of adsorption is defined as:
The higher Ed , the longer
is the time for adsorption
Physisorption: a = 10-13 to 10-9 sec
Chemisorption: a= 10-6 to 109 sec
18
Famous form of Langmuir
isotherm in the gas phase
“b” is affinity constant and a measure of adsorbate-adsorbent attraction forces.
bp
bp
1
)/exp(2
)/exp(TRQb
TMRk
TRQ
k
kb
g
gd
g
d
a
lim bpp 0
lim = 1p
1bpor
19
Behavior of Langmuir model
The Langmuir isotherm reduces to the Henry law isotherm when the pressure is
very low (bP << 1).
When pressure is sufficiently high, the amount adsorbed reaches the saturation
capacity or monolayer coverage (1).
20
Useful form of Langmuir isotherm
for gas phase
P b(T )1
P b(T )CC
μs
RT
QbTb exp
Cμ : amount adsorbed (mole per unit mass or volume).
Cμs : maximum adsorbed concentration corresponding to a
complete monolayer coverage.
μ denote the
adsorbed phase
21
Linear form of equation
P
1
bC
1
C
1
C
1
μsμs
Plotting 1/Cμ against 1/P gives straight line with the slope 1/bCμs
22
Isosteric Heat of Adsorption
• Isosteric heat is the ratio of the small change in the adsorbate enthalpy
to the small change in the amount adsorbed.
• The knowledge of isosteric heat is essential in the study of adsorption
kinetics.
• The isosteric heat may or may not vary with loading. It is calculated
from the van't Hoff equation:
: thermal expansion coefficient
of the saturation concentration
23
Cont.
• The negativity of the enthalpy change indicates that the
adsorption process is an exothermic process.
• For the isosteric heat to take a finite value at high coverage
(that is 1), the parameter must be zero.
• Therefore, the saturation capacity is independent of
temperature, and as a result the heat of adsorption is constant,
independent of loading and temperature (very ideal system).
• Prove that for the Langmuir isotherm:
dEQH
24
emme
Cbq/q/q/ 111
m
VCCq
e
e
)(0
qe : amount adsorbed at equilibrium in the adsorbed phase (mg/g)
qm : Langmuir constant related to maximum adsorption capacity (mg/g)
C0 : initial concentration in the aqueous solution (mg/L)
Ce : equilibrium concentration in the aqueous solution (mg/L)
b : Langmuir constant related to energy of adsorption (L/mg)
V : volume of the solution (L)
m : sorbent dose in the mixture (g)
Form of Langmuir isotherm in
Liquid phase
25
Isotherms based on the Gibbs
thermodynamic approachIf adsorbed phase is treated as a 2D surface, we have the following Gibbs equation for pure component systems:
At equilibrium, the chemical potential of the adsorbed phase is equal
to that of the gas phase, which is assumed to be ideal, i.e.
Substituting μ into the eqn. gives the following Gibbs isotherm:
This is the fundamental equation relating gas pressure, spreading
pressure (Π) and amount adsorbed.
03 nd μVdP:D in
26
Linear isotherm
For an ideal surface at infinite dilution, the EOS relating the spreading pressure and the number of mole on the surface is:
nRTPV:D 3nRTA:D2
Integrating this equation at constant T gives:
At equilibrium the spreading pressure in the
adsorbed phase is linearly proportional to the
pressure in the gas phase.
To relate the amount adsorbed in the adsorbed
phase in terms of the gas phase pressure, we
use EOS to finally get:
Where:
27
Volmer isotherm
If consider the case where allow for the finite size of adsorbed molecules, the EOS for a surface takes the following form:
Ao : the minimum area
occupied by n molecules
The Gibbs equation can be written in terms of the area per unit
molecule as follows:
σ is the area per unit molecule of adsorbate
28
Cont.
we have:
σ0 is the minimum area per
unit molecule of adsorbate
where:
Volmer
Isotherm
Volmer isotherm is a fundamental equation describing
the adsorption on surfaces where the mobility of
adsorbed molecules is allowed, but no interaction is
allowed among the adsorbed molecules.
29
Cont.
Rearranging the volmer equation:
the Volmer equation is similar to the Langmuir isotherm with the
apparent affinity as:
b is constant in the Langmuir mechanism,
bapp decreases with loading in the Volmer mechanism.
30
Fowler-Guggenheim isotherm
From statistical thermodynamics, the simplest equation allowing for
the lateral (adsorbate-adsorbate) interaction is obtained:
z : coordination no. (usually 4 or 6 depending on the packing of molecules)
w : the interaction energy between adsorbed molecules (w>0 means
attraction between adsorbed species and w<0 means repulsion)
w 500-1000 cal/mole
where:
31
Cont.
Plots of the fractional loading versus bP for the FG equation
32
Hill-deBoer isotherm
When EOS of the adsorbate allows for the co-volume term and the
attractive force term, the following van der Waals equation can be used:
Here mobile adsorption and lateral interaction among adsorbed
molecules are considered.
Then, the isotherm equation obtained is:
33
Isotherms derived from the Gibbs equation
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