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: