Langmuir Isotherm

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ADSORPTION
Outline
1) Adsorption Phenomena Adsorption Forces,
Definitions and Types 2) Adsorbents 3)
Adsorption Equilibrium 4) Characterization of
adsorbents 5) Rate processes in adsorption and
simple design methods for fixed bed adsorption 5)
Adsorption Process Cycles 6) Applications
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ADSORPTION EQUILIBRIUM
The amount of a pure gas absorbed by a unit mass
of a given adsorbent is a function of temperature
and pressure alone, q f (P,T)

• where q is the amount of the gas (in cc at STP,
  grams or mols, etc) per unit amount of the
  absorbent. The nature of this function can be
  quite complex and is not generally be
  predictable on totally theoretical grounds, and
  experimental measurements are necessary.
• The results of the absorption experiments are
  commonly presented in the form of adsorption
  isotherms, amount absorbed as a function of
  pressure at contant temperature
• q f (P) at constant temperature

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ADSORPTION EQUILIBRIUM

• Sometimes the results are presented in the form
  of adsorption isobars, the amount of gas adsorbed
  as a function temperature at constant pressure.
• q f (T) at constant pressure
• Occasionally results are presented as
  adsorption isosteres, equilibrium pressure as a
  function of temperature at a fixed amount of gas
  adsorbed.
•  

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Freundlich, Herbert Max Finlay (1880-1941)German
physical chemist who worked on the nature of
colloids, particularly sols and gels. He
introduced the term 'thixotropy' to describe the
behaviour of gels.Freundlich was born in Berlin
and studied at Munich and Leipzig. In 1911 he
became professor at the Technische Hochschule in
Brunswick. He worked at the Kaiser Wilhelm
Institut in Berlin 1914-33. When Adolf Hitler
came to power, Freundlich emigrated first to
Britain and then, in 1938, to the USA, where he
became professor of colloid chemistry at the
University of Minnesota.Freundlich's research
was mainly devoted to all aspects of colloid
science. He investigated colloid optics, the
scattering of light by dispersed particles of
various shapes. He studied the electrical
properties of colloids, since electrostatic
charges are largely responsible for holding
colloidal dispersions in place. He investigated
mechanical properties such as viscosity and
elasticity, and studied the behaviour of certain
systems under other types of mechanical force.
One application of this work has been the
development of nondrip paints.
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Langmuir Isotherm

• Assumptions
• Molecules are adsorbed at a fixed number of
  well-defined localized sites
• Each site can hold one adsorbate molecule
• All sites are energetically equivalent
• There is no interaction between molecules
• adsorbed on neighboring sites.

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Kinetic derivation

• Rate of adsorption ka p (1-?)
• Rate of desorption kd ?
• ?q/qm fractional coverage
• q amount adsorbed per unit amount of adsorbent
• qm amount adsorbed at complete molayer coverage
  f
• At equilibrium
• ka p (1-?) kd ?
• ? / (1-?) (ka/ kd ) P bP
• b ka/ kd equilibrium constant

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rearranging
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When P is small bP ltlt 1, thus Langmuir equation
reduces to
Which is Henrys law, a thermodynanic state all
isotherms must reduce when p ? 0
bbo exp(-?Ho/RT) vant Hoff equation, ?Ho
limiting heat of adsorption
Linearized form of Langmuir isotherm
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Freundlich Isotherm
Empirical, however it can also be developed on
the basis of a logarithmic distribution of
adsorption energies over sites
n gt1
Linearized form
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BET (Brunauer, Emmet and Teller) Isotherm Model
J. A. C. S. 60,309(1938)
ASSUMPTIONS 1) Surface is homogeneous (as of
Langmuir) 2) No lateral interaction among the
adsorbed molecules ( as of Langmuir) However
adsorption is not limited to monolayer (different
from Langmuir), instead , owing to mutual
interaction in vertical direction multilayer
adsorption is assumed to occur occur.
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BET (Brunauer, Emmet and Teller) Isotherm Model
ASSUMPTIONS ( continued) 3) Within each layer
dynamic equilbrium exists For example, for 2nd
layer Rate of desorption from 2nd layerrate of
adsorption on 1st layer
2nd layer
1st layer
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BET (Brunauer, Emmet and Teller) Isotherm Model
ASSUMPTIONS (continued) 4) The heat of adsorption
in all layers above the first layer is equal to
the latent heat of condensation 5) When pressure
P becomes equal to the saturated vapor pressure (
Po ), the adsorbate vapor condenses as an
ordinary liquid on the adsorbed film so that the
number of layers become infinite on the surface.
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• BET Equation

• VmVolume monolayer at STP
• C Constant
• V Volume at STP

• Relative Pressure (P/Po) must be between
  0.05-0.3. At higher P/Po values the BET equation
  is usually inaccurate because of capillary
  condensation effect while at P/P0 values below
  0.05 the amount of adsorbed gas is too small to
  be measured.

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BET (Brunauer, Emmet and Teller) Isotherm Model
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BET (Brunauer, Emmet and Teller) Isotherm Model
Specific surface S (Vm / vm) (N) (a
) Vm Volume of monolayer of gas adsorbed
at STP per gram of adsorbent vm
Molar volume of gas at STP N Avogadros
number a surface area covered by one
molecule
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BET (Brunauer, Emmet and Teller) Isotherm Model
For spherical molecules arranged in in close
two- dimensional packing a 1.091( M/ (N
?L) )2/3 M Molecular weight of
adsorbate ?L Density of liquid sorbate
at the temperature of adsorption N
Avogadros number a surface area
covered by one molecule
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BET (Brunauer, Emmet and Teller) Isotherm Model
For BET usually, adsorption of nitrogen gas
(N2) at 77 K is measured. For nitrogen M28
N6.023 X 1023 ?L0.808 g/cm3 ( at liquid
nitrogen temperature, -195.8 oC, nbp)
a 16.2X 10-16 cm2 per molecule

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BET (Brunauer, Emmet and Teller) Isotherm Model
Although BET surface area may not always
represent the surface area available for
adsorption of a particular molecule , it is
widely used in the characterization of
adsorbents. For microporus adsorbents having
significant pore volumes in pores of diameters
less than 5 Å ( eg. gas-phase activated carbons)
nitrogen molecules at liq. N2 temperature can
not pass easily through the these narrow
micropores (called activated diffusion) and true
equilibrium my not reach within the experimental
time allowed.
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Branuers classification of isotherms
The simplest isotherm is Type I This type of
isotherm is observed for monolayer(unimolecular)
adsorption. The isotherms of most microporous
adsorbents are also of type I. This is because
with such adsorbents there is a definite
saturation limit corresponding to complete
filling of micropores.
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Branuers classification of isotherms
Type II and III .are generally observed only in
adsorbents in which there is a wide range of pore
sizes. In such systems there is a continuous
progression with increasing loading from
monolayer to multilayer adsorption and then to
capillary condensation
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Branuers classification of isotherms
The increase in capacity at high pressures is due
to capillary condensation in pores of increasing
diameter as the pressure is raised. Type III
isotherm. , with its convex nature it is
undesirable because the extent of desorption is
low except at high pressures.According to BET
theory, it corresponds to muitilayer adsorption
where the heat of adsorption of the first layer
is less than succeeding layers. Fortunately,
this type of of isotherm is rarely observed.
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Branuers classification of isotherms
An isotherm of Type IV suggests the formation of
two surface layers either on a plane surface or
on the wall a pore very much wider than the
molecular diameter of the sorbate. If
intermolecular attraction effects are large an
isotherm of Type V . may be observed.
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Kelvin Equation
Amount of sorbate(moles) dn ? r2 dl /vL
o o
vL molar volume of liquid sorbate in pore
? angle of contact o surface tension
P equilibrium vapor pressure of sorbate
in pore
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Kelvin Equation-Capillary condensation
dn ?G dn RT ln P0 /P 2 ? r dl ? cos ? The
work done against surface tension is exactly
equal to the free energy difference.
dn moles liquid are evaporated from the pore
under equilibrium vapor pressure P and condensed
to a liquid on a plane surfaceover which the
vapor pressure is P0
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Kelvin Equation

• s Surface tension
• ? Contact angle
• Vm molar volume
• r pore radius

P equilibrium pressure P0 vapor pressure of
liquid vapor pressure at the same
temperature of adsorption
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Capillary condensation
Taking benzne at 20 0C as an example ? 29
dyne/cm vL 89 cm3/mole ?0 thus cos?1
r50 Å P/P0 0.67 r500 Å
P/P0 0.96 Capillary consation will be
significant only in quite small pores
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Hysteresis
Type III isotherm
P/Pa