Freundlich equation,Brunauer, Emmett, and Teller (BET) Equation, GIBBS ADSORPTION ISOTHERM

1. ASSIGNMENT ON
ADSORPTION ISOTHERMS
SUBMITTED TO- Dr. K. TEDIA
Head of Department
Department of Soil Science and
Agricultural Chemistry
IGKV, RAIPUR
PRESENTED BY- DEEPIKA SAHU
Ph.D. Previous year
Department- Soil Science and
Agricultural Chemistry
College of Agriculture, Raipur
INDIRA GANDHI KRISHI VISHWAVIDYALAYA, RAIPUR

2. CONTENT
INTRODUCTION
Adsorption Phenomena in Soil colloids
Adsorption Isotherms
Adsorption equation
Freundlich equation
Brunauer, Emmett, and Teller (BET) Equation
GIBBS ADSORPTION ISOTHERM
REFERENCE

3. INTRODUCTION
Adsorption Phenomena in Soil
Adsorption is the process through which a net
accumulation of a substance occurs at the common
boundary of two contiguous phases.
Contiguous phases- they are the phases sharing a common
border. Which include following interfaces:
Solid-
Solid
interface
Liquid-Vapour
interface
Solid-
Liquid
interface

4. Adsorption Phenomena in Soil colloids
• Organic colloids - adsorption related to their
functional groups- -COOH, -OH (alcoholic) and –
OH (phenolic).
• Inorganic colloids - pH dependent charged surfaces
– Silaxane
– Oxyhydroxy
– Silanol
– Aluminol
– Ferrol

5. Adsorption Isotherms
The curve relating to the concentration of adsorbed
material at a fixed temperature is called adsorption
isotherm.
Two methods are available in the use of adsorption
isotherms to study the behavior of adsorption
reactions:
I. Identification of shape and curvature of adsorption
isotherms.
II. Statistical formulation, known today as statistical
modeling of adsorption isotherms. In the first method,
four basic types of adsorption isotherms have been
recognized and used for identifying the nature of
adsorption of solutes from aqueous solutions.

7. The S-type represents adsorption reactions when the
solid has a high affinity for the solvent, whereas the L-
type suggests that the solid has high affinity for the
solute.
Both S- and L-type adsorption curves are considered to
predict similar things as the Langmuir adsorption
isotherm.
The H-type curve, also called high affinity curve,
represents adsorption reactions when the solute has a
high affinity for the solid. This type of curve is the
special type of L-curve.
In dilute solution the solute is often completely
adsorbed and no measurable amount is left in the
solution.

8. Four major types of equations have been
formulated and are used today to describe
adsorption processes-
Adsorption Equations
The Freundlich
equation
The Langmuir
equation
The BET (Brunauer,
Emmett and Teller)
equation
The Gibbs equation

9. Freundlich equation
The adsorption isotherm in many dilute solutions is
formulated by Freundlich (1926) as:
x/m= KC1/n -------(1)
By taking the logarithm, Equation 1 changes into
log (x/m) = log K + (1/n) log C
Where,
x = amount of material adsorbed
m = amount of adsorbents
C = concentration of the equilibrium solution
k = Freundlich adsorption constants
n or1/n= Freundlich exponent

10. Langmuir Adsorption Isotherm
Adsorption of gases on solid surface was explained by
Langmuir Adsorption Isotherm. (Langmuir-1918)
Assumptions of Langmuir adsorption isotherm
• Surface of solid contains a fixed number of adsorption
site, only where gaseous molecules can bind.
• Each site can hold only one molecule and the process
involves a constant heat of adsorption. This is identical
for all adsorption site.
• The adsorption is monolayer.
• The gaseous molecules adsorbed different adsorption
site do no interact.
• The process of adsorption involves a dynamic
equilibrium.

11. Langmuir Equation
Adsorption of gases on solid surface was explained by
Langmuir Adsorption Isotherm. Method of statistical
formulation of adsorption reactions given by Langmuir
(1918), originally derived for adsorption gases by
solids, is formulated as follows:
Ɵ = (bP)/(1 + bP)
Where,
Ɵ = amount of gas adsorbed per unit area
b = a constant related to the free energy of
adsorption
P = equilibrium gas pressure
Continued…

12. For adsorption of solute, P can be replaced
by equilibrium concentration C as-
x/m = (k1C)/(1 + k2C)
where,
x = amount adsorbed
m = amount of adsorbents
k1 and k2 = constants
C = concentration of equilibrium solution

13. Brunauer, Emmett, and teller (BET)
Equation
The concept of theory is an extension of Langmuir theory,
which is a monolayer molecule adsorption to multilayer
adsorption with the following hypothesis:
1.The Langmuir theory can be applied to each layer.
2.The enthalpy of adsorption for the first layer is constant
and greater than the second layer ( and higher layer).
3.The enthalpy of adsorption for second (and higher)
layers is the same as the enthalpy of liquefaction.
4.The gas molecules physically adsorb on a solid in many
layers.
Continued…

14. BET Equation-
P/Vt(P-P0)=1/VmC + C-1/VmC (P/P0)
Where,
P = equilibrium vapor pressure
P0 = saturation vapor pressure
V= volume of gas adsorbed
Vm= volume of gas adsorbed when solid is covered
with a monolayer
C= constant related to heat of adsorption
The BET equation was developed by Stehen
Brunauer, Paul Hugh Emmett and Edward Teller in
1938 for adsorption of multilayers of nonpolar gases
(Brunauer et. al., 1938)

15. GIBBS ADSORPTION ISOTHERM
The Gibbs equation describes processes in relation to
surface tension and is formulated as follows:
= - a/RT (dγ/da)
Γ
Where,
Γ= surface concentration of adsorbed material
(moles/cm²)
a= activity of solute in moles
R= gas constant
T= absolute temperature
γ = surface tension in dynes/cm
Continued…

16. •The solute is adsorbed on the surface of the adsorbent is
dγ/da is negative ( Γ = positive).
•This type of adsorption is called positive adsorption.
Therefore, positive adsorption occurs when the plate decreases
surface tension.
•If dγ/da is positive (Γ = negative), the solute is more
concentrated the bulk solution than in the interface region.
•The latter is sometimes called negative adsorption. this case,
the solute increases surface tension.
•The Gibbs equation finds primary application in adsorption at
liquid-gas interfaces.
•It is very difficult to use this equation in adsorption reactions
at solid-liquid interfaces, because it is impossible to measure
the surface tension of solid surfaces.

17. REFERENCE
•Tan, Kim. H. 2017. Principles of Soil Chemistry, CRC Press
Taylor & Francis Group, fourth edition,P-:83-192.
•Brady, Nyle. C. and Weil, Ray. R.,2019, The Nature and
Properties of Soils, fourteenth edition, P:393-394.
•Sanyal, Saroj Kumar.,2018. A Textbook of Soil Chemistry, Daya
Publishing House A division of Astral International Pvt. Ltd, P: 66-
71.
•WWW.Wikipedia.com date- 1/1/2021
•https://youtu.be/CL_X1QA9gNA date- 4/1/2021