Gibbs Adsorption Isotherm

Gibbs Adsorption Isotherm

1. GIBBS ADSORPTION ISOTHERM

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3. “Adsorption is a technical term coined to denote the taking up of gas, vapour , liquid by a surface or interface”. Adsorption is a surface phenomenon where the surface of a solid has a tendency to attract and to retain molecules of other species(gas or liquid) with which such surfaces come in contact. Absorption is a bulk phenomenon in which the substance assimilated is uniformly distributed throughout the body of a solid or liquid to form a solution or a compound. When adsorption and absorption takes place simultaneously is generally termed as sorption. Water vapour is absorbed by anhydrous calcium chloride while it is absorbed by silica gel. Ammonia is adsorbed by charcoal while it is adsorbed by water to form ammonium hydroxide. ADSORPTION & ABSORPTION

4. Characteristics and Factors affecting adsorption

5. Adsorption isotherm (also A sorption isotherm ) describes the equilibrium of the sorption of a material at a surface (more general at a surface boundary) at constant temperature. It represents the amount of material bound at the surface (the sorbate ) as a function of the material present in the gas phase and/or in the solution. If the temperature is kept constant and pressure is changed, the curve between a and b is known adsorption isotherm. Where, a = amount of adsorbed p = pressure T = temperature Adsorption isotherm a = f (P, T)

6. Gibbs adsorption equation This equation represents an exact relationship between the adsorption and change in surface tension of a solvent due to presence of a solute. This equation was derived by J. Willard Gibbs (1878) and afterwards independently by J.J Thomson , 1888. The dG for 2 comonent system is given by: dG = - SdT + Vdp + µ 1 dn 1 + µ 2 dn 2 + ϒ dA ① Where, ϒ = Surface tension dA = Increase in surface area S = Entropy p= Pressure V = Volume

7. dG = Change in Gibbs free energy Integrating equation no. ① at a constant temperature, pressure, surface tension and chemical potential of the component we obtain the expression G = µ 1 n 1 + µ 2 n 2 + ϒ A ② Where, n 1 = Number of moles of solvent. n 2 = Number of moles of solute. Complete differential of Eq. ② dG = µ 1 n 1 + µ 2 n 2 + n 1 dµ 1 + n 2 d µ 2 + µ dA + Ad ϒ ③ Comparing eq. no. ① & ③ the result is: SdT - Vdp + n 1 dµ 1 + n 2 d µ 2 + µ dA + Ad ϒ = 0 ④

8. At constant temperature and pressure equation no. ④ simplifies to n 1 dµ 1 + n 2 d µ 2 + Ad ϒ = 0 ⑤ We can imagine the system under consideration made of 2 portion: Surface phase – It involves the portion of system affected by the surface process and therefore equation no. ⑤ holds true only for it. Bulk Phase – The remainder of the solution which s unaffected by surface forces is known as bulk phase and therefore Gibbs Duehem equation holds for this only. This Equation is n 1 dµ 1 + n 2 d µ 2 = 0 ⑥

9. Where On multiplying equation ⑥ by n 1 /n 1 and subtracting from equation no. ⑤ we obtain the expression Ad ϒ + (n 2 – n 1 n 2 /n 1 ) dµ 2 = 0 “Or” - d ϒ /d µ = [n 2 - n 1 n 2 /n 1 ]/A ⑦Where, n 2 Represents no. of moles of solute associated with n 1 moles of solvent in the surface phase and n 1 n 2 / n 1 is the corresponding quantity in the bulk phase. It therefore, follows that the quantity [n 2 - n 1 n 2 /n 1 ]/A is the excess concentration of the solute per unit area of the surface and is usually designated by the symbol ‘ᴦ’ Thus equation no. 7 becomes as ᴦ = - d ϒ / dµ 2 ⑧

10. Where ᴦ is independent of n 1 and is dependent only on the nature of surface phase and not on its amount. ᴦ is also called the surface concentration of solute per unit area of interface . For a solution : µ 2 = µ 2 + RT ln a 2 ⑨ Where, a 2 is the activity of solute By differentiating equation no. ⑨ we get: dµ = RT d ln a 2 ⑩ Assuming µ 2 as a constant On substituting eq. no. ⑩ in eq. no. ⑧ we get, ᴦ = 1/ RT ₓ d ϒ /d ln a 2 or ᴦ = -a 2 / RT ₓ d ϒ /da 2 [Since d ln a 2 = da 2 /a 2 ] ⑪ Equation no. ⑪ is known as Gibbs Adsorption Equation.

11. Conclusion Gibbs adsorption isotherm for multi component system is an equation used to relate the changes in concentration of a component in contact with a surface with changes in the surface tension. This equation represents exact relationship between adsorption and change in surface tension of a solvent due to the presence of solute. This equation is corresponds to relatively solute solutions, highly hydrated organic compounds, amphipathic species.

12. Reference Source: Advanced physical chemistry Gurdeep Raj, Krishna Prakashan Media, 2012. Advanced physical chemistry Gurtu-Gurtu , Pragati Prakashan , Meerut, 2011. Net Source: www.wikipedia.com