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CRE II Heterogeneous Catalysis
L 11
Prof. K.K.Pant
Department of Chemical EngineeringIIT Delhi.
[email protected]
mailto:[email protected]:[email protected]
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Langmuir Adsorption Isotherm
Simple approach toquantitatively describe
an adsorption process
at the gas/solid interface
N = N + N number of vacant sitesVS
Assumptions:
Solids surface is homogeneous and contain a
number of equivalent sites,each of which is
occupied by a single adsorbate molecule.
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A dynamic equilibrium exist between gas
phase reactant and adsorbed species.
No interactions between adsorbed species.
Adsorbed species localised,Hadsisindependent of coverage ..
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Chemisorption rates:
Adsorption data is reported in the form of
isothermsChemisorption may be considered as a
reaction between a reactant molecule and anactive site resulting
in an adsorbed molecule
A + A (or) A + S AS
Turnover Frequency (N): defined as the number
of molecules reacting per active site persecond at the
conditions of the experiment a measure for the activity of the
catalyst
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Langmuir Isotherm - Assumptions:
Surface is uniformly active
All sites are identical
Amounts of adsorbed molecules will notinterfere with further
adsorption
Uniform layer of adsorption
Site balance:
t
vv
sitestotal
sitesvacantofNositesvacantofFraction
.
t
AA
sitestotal
sitesoccupiedofNoAbyoccupiedsitesofFraction
.
1
Av
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Alternately:
numbersAvogadro
massunitsitesactiveofNositesactiveofconcMolarCt
'
/..
numbersAvogadro
massunitsitesvacantofNositesvacantofconcMolarCv
'
/..
numbersAvogadro
massunitAbysitesofNo
AbysitesofconcMolarCAS '
/.
.
tASv CCC
Though other isotherms account for non-uniform surfaces,
they
have primarily been developed for single adsorbing
components.Thus, the extensions to interactions in multi-component
systems is
not yet possible, as with the Langmuir isotherm.
Langmuir isotherms are only used for developing kinetic rate
expressions.
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Effect of increasing reactant concentration:
Increasing the reactant concentration increases
both the driving force and adsorption inhibitionterms.
CA
rate
Volcano shape results from a competition betweenkinetic driving
force and adsorption inhibition terms.
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R k
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For a given mechanism, the driving force is unique,irrespective
of RDS.
The product of equilibrium constant of all steps inthe mechanism
yield the overall eq. constant
In the kinetic term, the rate constant of RDS willappear.
If adsorption of A is not RDS, then KApAwill appearin the
adsorption term.
If desorption of B is not rate limiting, then pB/KD
will appear in the adsorption term. If SR is RDS, then the
adsorption term will be
raised to the power equal to the number of sitesinvolved in the
SR step.
Remarks:
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Simplified rate laws:
Over limited pressure range, the Langmuirisotherm = Kp/(1+Kp)
can be replaced by anapproximation = kpn
In such cases the rate law assumes the form:
r = k pAmpB
npCo
Such rate laws may be reasonably accurate
Example: CO + Cl2COCl2 (Over charcoal)
2)1(2222
22
2
COClCOClClCl
ClCOClCOCOCl
pKpKppKkKr
L-H approach
2/1
22 ClCOCOCl pkpr Simplified equation
