This document discusses Langmuir adsorption isotherm, which explains monolayer adsorption of gases onto surfaces. It assumes adsorption occurs at specific identical sites, with no lateral interactions between adsorbed molecules. Langmuir derived an equation showing the relationship between fraction of surface coverage (θ) and gas pressure (P), based on equilibrium between adsorption and desorption rates. This model applies at low pressures and assumes only monolayer coverage, with limitations at high pressures where multilayers can form. The document also outlines assumptions, derivation of the Langmuir equation, and applications for measuring moisture adsorption.

1. Langmuir Adsorption
Isotherm
Presented by:
Ruchika Zalpouri
L-2K19-AE-163-D

2. Adsorption
Adhesion of atoms, ions, bi-molecules or molecules of
gas, liquid or dissolved solids to a surface is called
adsorption.
This process creates a film of the adsorbate on the
surface of the adsorbent.

3. Activated charcoal adsorbs gases like CO2, SO2 and Cl2
etc.
Pt or Ni metal kept in contact with a gas adsorbs the gas -
Hydrogenation of oils.
Animal charcoal, when added to acetic acid solution and
shaken vigorously, adsorbs acetic acid.
Molasses is decolorized by activated charcoal.
Examples:

4. Difference between adsorption and absorption

5. FactorsAffecting
Adsorption
Nature of adsorbate and adsorbent
The surface area of adsorbent
Exothermic nature
Pressure

6. TypesofAdsorption
Physical adsorption
(Physisorption) /
Vander Waal’s adsorption
Chemical adsorption
(Chemisorption) /
Langmuir adsorption

7. Physical Adsorption
• If the force of attraction existing between adsorbate
and adsorbent are Vander Waal’s forces, the
adsorption is called physical adsorption.
• In this, the force of attraction are very weak, therefore
easily reversed by heating or by decreasing the
pressure.
• In this multi-layered adsorption is possible and it is
easily disrupted by increasing temperatures.

8. Chemical Adsorption
If the force of attraction existing between
adsorbate and adsorbent are almost same
strength as chemical bonds, the adsorption is
called chemical adsorption.
In chemisorption the force of attraction is very
strong, therefore adsorption cannot be easily
reversed and monolayer adsorption is possible.

9. Adsorption Isotherm
Adsorption process is usually studied through graphs is known as
adsorption isotherm.
That is the amount of adsorbate on the adsorbent as a function if
its pressure at constant temperature.
Where,
X- Amount of adsorbate
M- Weight of the adsorbent
P- Pressure

10. Langmuir Adsorption Isotherm
 Langmuir (1916) developed a classic kinetic model of
adsorption for EMC estimation.
 It explains the adsorption of monolayer of water
vapour on the internal surfaces of a solid.
 For molecules (water vapours / gas) in contact with a
solid surface at a fixed temperature, Langmuir model
describes the partitioning between gas phase and
adsorped species as a function of applied pressure.

11. Assumptions of Langmuir Isotherm:
1. Adsorption is limited to a monolayer.
2. The surface is homogenous and all sites are identical.
3. The adsorption is localized.
4. Adsorption is reversible.
5. Lateral interactions between adsorbed molecules are
absent.
6. The adsorption sites always contain either a molecule
of the adsorbate or a molecule of the solvent.

12. Derivation of Langmuir Model:
Let,
θ be the number of sites of the surface which are covered with gaseous
molecules.
(1 – θ) - the fraction of surface which are unoccupied by gaseous molecules.
 Condition:
Rate of forward direction (or) rate of adsorption depends upon two factors:
Number of sited available on the surface of adsorbent, (1 – θ) and
pressure, P.
Where, A(g) is un-adsorbed gaseous molecule, B(S) is unoccupied metal surface
and AB is Adsorbed gaseous molecule

13. Rate of adsorption is ∝ Pressure of the gas a, Pa
∝ Number of vacant sites i.e. N (1 – θ)
Where, N = Total number of sites
 Rate of adsorption = Ka Pa N (1 – θ)
Rate of desorption ∝ Number of adsorbed molecules
 Rate of desorption = Kd N θ
At equilibrium condition, Rate of adsorption = Rate of desorption
 Ka Pa N (1 – θ) = Kd N θ

14. Note: K is empirical coefficient and depends upon nature of
adsorbent and adsorbent

15. Special cases of Langmuir Model
 At very low pressure, K Pa < < 1 then θ = K Pa (or ) θ ∝ Pa
This equation shows linear variation between extent of adsorption of gas and
pressure.
 At high pressure, K Pa > > 1 then θ = K Pa / K Pa = 1 = (Pa)0
i.e. zero power of pressure = it is independent of pressure
 At intermediate pressure, θ = K (Pa)n, here the value of n is ranges between 0 to
1. This is a Freundlich adsorption equation
 Amount of gas absorbed per unit mass, a ∝ θ
a = K1 θ
a = (K1 K) (Pa)n
a = K1 (Pa)n , where K1 = K1 K = Constant

16. θ = K Pa / (1 + K Pa)
Writing θ (fraction of surface site occupied) in terms of volume of adsorbed gas ( water
vapour)
Where,
i = no. of adsorbed layer which in this case is either 0 or 1(monolayer)
V0 = Volume of gas adsorbed / cm2 of surface when it is covered with a complete layer
θ = V / V0
i.e. V / V0 = K Pa / (1 + K Pa) ≈> V = V0 K Pa / (1 + K Pa)
Where,
V= Isothermally adsorbed volume of water vapour at vapour pressure P.
K = Constant which depends on temperature and type of solid

17. Moisture content at vapour pressure P

18. Limitations of Langmuir Adsorption Isotherm
At high pressure, it is found that multi layers of the gases are
found.
Surfaces of the solids are heterogeneous, hence may have
different affinities for the gas molecules.
According to this theory, the saturation value of adsorption
should be independent of temperature. But experiments
show that saturation value decreases with rise of
temperature.
The theory holds good only at low pressure.

19. Thank you
have a wonderful day