The BET isotherm extends the Langmuir adsorption isotherm model to account for multilayer adsorption. The BET isotherm equation relates the volume of gas adsorbed to vapor pressure and can be used to calculate the specific surface area of materials. The BET theory models physical adsorption of gas molecules on a solid surface in multilayers based on the hypotheses that adsorption occurs in layers infinitely and the Langmuir model applies to each layer. The BET method is widely used to determine surface areas by measuring adsorbed gas quantities at different relative humidities.

1. BET Isotherm
An isotherm that takes account of the possibility that the monolayer in the Langmuir adsorption
isotherm can act as a substrate for further adsorption. The BET isotherm (named after S.
Brunauer, P. Emmett, and E. Teller) has the form:
V/V mon=cz/{(1 – z)[1 – (1 – c)z]}
where z=p/p* (p* is the vapour pressure above a macroscopically thick layer of liquid on the
surface), V mon is the volume that corresponds to the surface being covered by a monolayer, V and
p are the volume and pressure of the gas respectively, and c is a constant. In the BET isotherm,
the isotherm rises indefinitely at high pressures (in contrast to the Langmuir isotherm). It
provides a useful approximation over some ranges of pressure but underestimates adsorption for
low pressures and overestimates adsorption for high pressures.
Type of Adsorption Isotherm
Five different types of adsorption isotherm and their characteristics are explained below.
Type I Adsorption Isotherm
Type I Adsorption Isotherm
• The above graph depicts Monolayer adsorption.
• This graph can be easily explained using Langmuir Adsorption Isotherm.
• If BET equation, when P/P0<<1 and c>>1, then it leads to monolayer formation and Type I
Adsorption Isotherm is obtained.

2. • Examples of Type-I adsorption are Adsorption of Nitrogen (N2) or Hydrogen (H) on charcoal at
temperature near to -1800C.
Type II Adsorption Isotherm
Type II Adsorption Isotherm
• Type II Adsorption Isotherm shows large deviation from Langmuir model of adsorption.
• The intermediate flat region in the isotherm corresponds to monolayer formation.
• In BET equation, value of C has to be very large in comparison to 1.
•
• Examples of Type-II adsorption are Nitrogen (N2 (g)) adsorbed at -1950C on Iron (Fe) catalyst
and Nitrogen (N2 (g)) adsorbed at -1950C on silica gel.

3. Type III Adsorption Isotherm
Type III Adsorption Isotherm
• Type III Adsorption Isotherm also shows large deviation from Langmuir model.
• In BET equation value if C <<< 1 Type III Adsorption Isotherm obtained.
• This isotherm explains the formation of multilayer.
• There is no flattish portion in the curve which indicates that monolayer formation is missing.
• Examples of Type III Adsorption Isotherm are Bromine (Br2) at 790C on silica gel or Iodine (I2) at
790C on silica gel.

4. Type IV Adsorption Isotherm
Type IV Adsorption Isotherm
• At lower pressure region of graph is quite similar to Type II. This explains formation of
monolayer followed by multilayer.
• The saturation level reaches at a pressure below the saturation vapor pressure .This can be
explained on the basis of a possibility of gases getting condensed in the tiny capillary pores of
adsorbent at pressure below the saturation pressure (PS) of the gas.
• Examples of Type IV Adsorption Isotherm are of adsorption of Benzene on Iron Oxide (Fe2O3) at
500C and adsorption of Benzene on silica gel at 500C.
Type V Adsorption Isotherm
Type V Adsorption Isotherm

5. • Explanation of Type V graph is similar to Type IV.
• Example of Type V Adsorption Isotherm is adsorption of Water (vapors) at 1000C on charcoal.
• Type IV and V shows phenomenon of capillary condensation of gas.
Theory
BET theory aims to explain the physical adsorption of gas molecules on a solid surface and
serves as the basis for an important analysis technique for the measurement of the specific
surface area of a material. In 1938, Stephen Brunauer, Paul Hugh Emmett, and Edward Teller
published an article about the BET theory in a journal for the first time; “BET” consists of the
first initials of their family names.
The concept of the theory is an extension of the Langmuir theory, which is a theory for
monolayer molecular adsorption, to multilayer adsorption with the following hypotheses: (a) gas
molecules physically adsorb on a solid in layers infinitely; (b) there is no interaction between
each adsorption layer; and (c) the Langmuir theory can be applied to each layer. The resulting
BET equation is expressed by (1):
P and P0 are the equilibrium and the saturation pressure of adsorbates at the temperature of
adsorption, v is the adsorbed gas quantity (for example, in volume units), and vm is the monolayer
adsorbed gas quantity. c is the BET constant, which is expressed by (2):
E1 is the heat of adsorption for the first layer, and EL is that for the second and higher layers and
is equal to the heat of liquefaction.

6. BET plot
Equation (1) is an adsorption isotherm and can be plotted as a straight line with 1 / v[(P0 / P) −
1] on the y-axis and φ = P / P0 on the x-axis according to experimental results. This plot is called
a BET plot. The linear relationship of this equation is maintained only in the range of 0.05 < P /
P0 < 0.35. The value of the slope A and the y-intercept I of the line are used to calculate the
monolayer adsorbed gas quantity vm and the BET constant c. The following equations can be
used:
The BET method is widely used in surface science for the calculation of surface areas of solids
by physical adsorption of gas molecules. A total surface area Stotal and a specific surface area S
are evaluated by the following equations:
where vm is in units of volume which are also the units of the molar volume of the adsorbate gas

7. N: Avogadro's number,
s: adsorption cross section of the adsorbing species,
V: molar volume of adsorbate gas
a: mass of adsorbent (in g)
Derivation of the BET Isotherm
Consider a surface:
Definition:
θ0, θ1, ..., θn = Surface area (cm-2
) covered by 0, 1, ..., n layers of adsorbed molecules.

8. At Equilibrium:
θ0 must remain constant.
. Rate of Evaporation Rate of Condensation
. . =
from First Layer onto Bare Surface
K-1 Ѳ 1 = K1 ѲP0
Similarly, at equilibrium θ1 must remain constant.
. Rate of Condensation Rate of Condensation
. . on the Bare Surface on the 1st Layer
+ = +
Rate of Evaporation Rate of Evaporation
from the second layer from the second layer
.
. .
k1Pθ0 + k-2θ2 = k2Pθ1 + k-1θ1
Substituting into (I) gives
k-2θ2 = k2Pθ1
Extending this argument to other layers,
K-I I =K1PI-1 ………………….(2)
K- i Ѳi = ki PѲi-1
Example :
Cement paste
By application of the BET theory it is possible to determine the inner surface of hardened cement
paste. If the quantity of adsorbed water vapor is measured at different levels of relative humidity
a BET plot is obtained. From the slope A and y-intersection I on the plot it is possible to calculate

9. vm and the BET constant c. In case of cement paste hardened in water (T=97°C), the slope of the
line is A = 24.20 and the y-intersection I = 0.33; from this follows
From this the specific BET surface area SBET can be calculated by use of the above mentioned
equation (one water molecule covers s = 0.114nm2
). It follows thus SBET = 156m2
/ g which means
that hardened cement paste has an inner surface of 156 square meters per g of cement.
Activated Carbon
For example, activated carbon, which is a strong adsorbate and usually has an adsorption cross
section s of 0.16 nm2
for nitrogen adsorption at liquid nitrogen temperature, is revealed from
experimental data to have a large surface area around 3000 m² g-1
. Moreover, in the field of solid
catalysis, the surface area of catalysts is an important factor in catalytic activity. Porous
inorganic materials such as mesoporous silica and layer clay minerals have high surface areas of
several hundred m² g-1
calculated by the BET method, indicating the possibility of application for
efficient catalytic materials.

10. vm and the BET constant c. In case of cement paste hardened in water (T=97°C), the slope of the
line is A = 24.20 and the y-intersection I = 0.33; from this follows
From this the specific BET surface area SBET can be calculated by use of the above mentioned
equation (one water molecule covers s = 0.114nm2
). It follows thus SBET = 156m2
/ g which means
that hardened cement paste has an inner surface of 156 square meters per g of cement.
Activated Carbon
For example, activated carbon, which is a strong adsorbate and usually has an adsorption cross
section s of 0.16 nm2
for nitrogen adsorption at liquid nitrogen temperature, is revealed from
experimental data to have a large surface area around 3000 m² g-1
. Moreover, in the field of solid
catalysis, the surface area of catalysts is an important factor in catalytic activity. Porous
inorganic materials such as mesoporous silica and layer clay minerals have high surface areas of
several hundred m² g-1
calculated by the BET method, indicating the possibility of application for
efficient catalytic materials.