lecturenotes chem220 expt6 bet isotherm spring 2012
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BET Isotherm:
Solid Surface Area Measurementby gas adsorption
Geometric area
Microscopic area
Geometric area
Reading reference: Atkins, Chapter 25
Physical Adsorption, termed Physisorption: Van-der-Waals forces of interaction will act between an adsorbate (the adsorbing molecule) and a substrate (the surface).
Van-der-Waals forces:are weak and long range forces. Energy is released upon physisorption and its magnitude is ~ 20 kJ/mol, which is comparable to the enthalpyof condensation of matter. of condensation of matter.
Energy released
Gas +S(site) → Gasads-site
Vs. chemisorption: energy ~200 kJ/mol
available sites adsorption ofnumber occupied sites adsorption ofnumber =θ
the extent of surface coverage or the coverage fraction θ is given by:
P(gas)Free gas
The variation of fractional coverage θ with pressure at a fixed temperature is called the adsorption isotherm:
Adsorption Isotherm: θ = f(p) at constant T
adsorption sitegasads gas
The simplest adsorption isotherm is the Langmuir isotherm and is based on three basic physical assumptions:
1. Adsorption cannot exceed monolayer coverage.
2. Adsorption sites are all equivalent. This means there is the same energy of adsorption upon adsorption at any site, and therefore there
The Langmuir Isotherm
energy of adsorption upon adsorption at any site, and therefore there are no differences in the atomic structure on the surface.
3. Throughout the adsorption process, the energy of adsorption does not change, it remains invariant. In other words the occupation of neighboring sites will have no effect on adsorption
Gas (g) + Metal ↔ Gasads_Metal
desorptionadsorption dtd
dtd θθ =
Langmuir Isotherm
)1( θθ −= pNkdtd
aadsorption
θθNk
dtd
ddesorption
−=
ka=rate constant for adsorptionkd=rate constant for desorptionp=partial pressure of the gasN=total number of adsorption sitesN(1-θ)=number of vacant sites
d
a
kk
K 1
=+
=KP
Kpθ
monVV=θ
At equilibrium: adsorption rate = desorption ratethe adsorption isotherm is written as:
p/Vslope=1/Vmon
monmon KVVp
Vp 1+=
Manipulating the expression yields:
Plot p/V vs. pSlope=1/VmonIntercept=1/KVmon
p
Intercept=1/KVmon
slope=1/Vmon
d
a
kk
K 1
=+
=KP
Kpθ
θ
K=101
θ
p
K=0.1
2
lnRT
HT
K adθ
θ
∆=�
�
���
�
∂∂
isosteric enthalpyof adsorption
Standard enthalpy of adsorption at constant coverage
BET Isotherm:adsorption can go beyond monolayer coverage
• The BET isotherm, written by Stephen Brunauer, Paul Emmett, and Edward Teller, describes such a behavior and is written as:written as:
})1(1){1( zczcz
VV
mon −−−=
opp
z = RTHH vapo
deso
ec /)( ∆−∆=
po = vapor pressure above a layer of adsorbate more than a molecule thick which resembles a pure bulk liquid
Desorption from a monolayer
Vaporization ofliquid adsorbate
V/Vmon
for different values of c:
RTHH vapo
deso
ec /)( ∆−∆=
z=p/po
1
1001000
BET isotherm
monmon cVzc
cVVzz )1(1
)1(−+=
−
A plot of z/(1-z)V vs. z allows determination of Vmonolayer and the value of c
z
z/(1-z)VSlope=(c-1)/cVmonIntercept=1/cVmon
In this experiment:
1. You will be trained on how to use at BET instrument to measure the surface area of a solid using gas adsorption.
2. This will be applied to determine the surface area of 2 solids (Al2O3 and TiO2) by adsorption of nitrogen gas:
I. By adsorbing nitrogen gas on the solid at liquid nitrogentemperature, the volume of gas adsorbed will be determined as temperature, the volume of gas adsorbed will be determined as a function of the pressure of the gas.
II. BET isotherms linear plots will be constructed to determine cand Vmonolayer.
III. From the volume needed to form a monolayer of gas (Vmonolayer)on the solid, you will calculate the surface area of the solid.
BET system:
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