Langmuir Adsorption Isotherm

Introduction, assumptions, derivation and limitation of Langmuir Adsorption Isotherm

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 CO 2 , SO 2 and Cl 2 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. Factors Affecting Adsorption

6. 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 .

7. 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 .

8. 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

9. 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 .

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

11. 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

12. Rate of adsorption is ∝ Pressure of the gas a, P a ∝ Number of vacant sites i.e . N (1 – θ) Where, N = Total number of sites Rate of adsorption = K a P a 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 K a P a N (1 – θ) = K d N θ

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

14. Special cases of Langmuir Model At very low pressure, K P a < < 1 then θ = K P a (or ) θ ∝ P a This equation shows linear variation between extent of adsorption of gas and pressure. At high pressure, K P a > > 1 then θ = K P a / K P a = 1 = ( Pa) i.e . zero power of pressure = it is independent of pressure At intermediate pressure, θ = K (P a ) 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 = K 1 θ a = (K 1 K) (Pa) n a = K 1 (Pa) n , where K 1 = K 1 K = Constant

15. θ = K P a / (1 + K P a ) 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) V = Volume of gas adsorbed / cm 2 of surface when it is covered with a complete layer θ = V / V i.e. V / V = K P a / (1 + K P a ) ≈> V = V K P a / (1 + K P a ) Where, V = Isothermally adsorbed volume of water vapour at vapour pressure P. K = Constant which depends on temperature and type of solid

16. Moisture content at vapour pressure P

17. 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 .

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