Adsorption Equilibria Ali Ahmadpour Chemical Eng. Dept. Ferdowsi University of Mashhad
Contents Introduction Adsorption isotherm models Langmuir isotherm Volmer isotherm Fowler-Guggenheim isotherm Hill-deBoer isotherm Concluding remarks 2
Introduction Adsorption equilibria is the most important information in understanding an adsorption process. No matter how many components are present in the system, the adsorption equilibria of pure components indicate how much those components can be accommodated by a solid adsorbent. This information can be used in the study of adsorption kinetics of a single component, adsorption equilibria of multicomponent systems, and then adsorption kinetics of multicomponent systems. 3
Adsorption Process Adsorbate Adsorptive Adsorbent 4
The Isotherm The amount of gas adsorbed is a function of The strength of interaction between gas and solid (intrinsic) Temperature (fixed) Pressure (controlled variable) expressed as relative pressure P/P o Gas-Solid system: V f (P, T) Liquid-Solid system: q f (C, T) V : cm 3 STP/g ; mole/g ; mole/cm 3 q : mole/g ; mole/cm 3 5
Adsorption isotherm models Some of the famous models describing the adsorption equilibria are: Basic model: Langmuir (1918) Extended model: BET (1938) Empirical model: Freundlich (1932) There are various types of theoretical, empirical and semi-empirical models for equilibrium of adsorption. 6
Different types of adsorption isotherms 7
Langmuir adsorption isotherm (Type I) bp 1+bp 8
Type II and IV isotherms Similar to type II 9
Type III and V isotherms 10
The adsorption theory The Langmuir theory (1918) is the most basic theory in adsorption. Langmuir described the kinetic behavior of the adsorption process. This theory allows us to understand the monolayer surface adsorption on an ideal surface. He postulated that at equilibrium, the rate of arrival of adsorptive (adsorption) and the rate of evaporation of adsorbate (desorption) were equal. Furthermore, the heat of adsorption was taken to be constant and unchanging with the degree of coverage, θ. I. Langmuir, J. Amer. Chem. Soc., 40, 1368 (1918) 11
Irving Langmuir (1881-1957) Graduated as a metallurgical engineer from the School of Mines at Columbia University in 1903. 1903-1906 M.A. and Ph.D. in 1906 from Göttingen. 1906-1909 Instructor in Chemistry at Stevens Institute of Technology, Hoboken, New Jersey. 1909 1950 General Electric Company at Schenectady where he eventually became Associate Director. 1913 :Invented the gas filled, coiled tungsten filament incandescent lamp. 12
Cont. 1919 to 1921, his interest turned to an examination of atomic theory, and he published his "concentric theory of atomic structure". In it he proposed that all atoms try to complete an outer electron shell of eight electrons. 1927 Coined the use of the term "plasma" for an ionized gas. 1935-1937 With Katherine Blodgett studied thin films. 1948-1953 With Vincent Schaefer discovered that the introduction of dry ice and iodide into a sufficiently moist cloud of low temperature could induce precipitation. 1932 The Nobel Prize in Chemistry "for his discoveries and investigations in surface chemistry" 13
Langmuir Theory Langmuir theory describe that the rate of accumulation of molecules at the flat surface is zero at equilibrium. The assumptions of the Langmuir model are: Homogeneous surface (all adsorption sites energetically identical). Monolayer adsorption (Adsorption on surface is localized, i.e. adsorbed atoms or molecules are adsorbed at definite, localized sites). No interaction between adsorbed molecules (Each site can accommodate only one molecule or atom). 14
Cont. Rate of adsorption (the striking rate at the surface) sticking coefficient (α: the accommodation coefficient) = Rate of desorption from the surface The rate of striking the surface (mole / time area), from the kinetic theory of gas is: 15
Cont. The rate of adsorption (mole adsorbed/ surface area time) is: The rate of desorption, corresponds to fully covered surface (k d ) fractional coverage, is: E d = Q : activation energy for desorption (is equal to the heat of adsorption for physically sorbed species) k d : rate constant for desorption at infinite temperature 16
Cont. The average residence time of adsorption is defined as: The higher E d, the longer is the time for adsorption Physisorption: a = 10-13 to 10-9 sec Chemisorption: a = 10-6 to 10 9 sec 17
Famous form of Langmuir isotherm in the gas phase bp 1 bp or bp 1 lim bp p 0 lim = 1 p b k k a d exp( k d Q / R 2 MR g g T T ) b exp( Q / R g T ) b is affinity constant and a measure of adsorbate-adsorbent attraction forces. 18
Behavior of Langmuir model The Langmuir isotherm reduces to the Henry law isotherm when the pressure is very low (bp << 1). When pressure is sufficiently high, the amount adsorbed reaches the saturation capacity or monolayer coverage (1). 19
Useful form of Langmuir isotherm for gas phase C C μs 1 b(t ) P b(t ) P μ denote the adsorbed phase b Q RT T b exp C μ : amount adsorbed (mole per unit mass or volume). C μs : maximum adsorbed concentration corresponding to a complete monolayer coverage. 20
Linear form of equation C 1 C 1 μs bc 1 μs 1 P Plotting 1/C μ against 1/P gives straight line with the slope 1/bC μs 21
Isosteric Heat of Adsorption Isosteric heat is the ratio of the small change in the adsorbate enthalpy to the small change in the amount adsorbed. The knowledge of isosteric heat is essential in the study of adsorption kinetics. The isosteric heat may or may not vary with loading. It is calculated from the van't Hoff equation: : thermal expansion coefficient of the saturation concentration 22
Cont. The negativity of the enthalpy change indicates that the adsorption process is an exothermic process. For the isosteric heat to take a finite value at high coverage (that is 1), the parameter must be zero. Therefore, the saturation capacity is independent of temperature, and as a result the heat of adsorption is constant, independent of loading and temperature (very ideal system). Prove that for the Langmuir isotherm: H Q E d 23
Form of Langmuir isotherm in Liquid phase 1 / q 1 / q 1 e m / bq m C e q e ( C C 0 m e ) V q e : amount adsorbed at equilibrium in the adsorbed phase (mg/g) q m : Langmuir constant related to maximum adsorption capacity (mg/g) C 0 : initial concentration in the aqueous solution (mg/l) Ce : equilibrium concentration in the aqueous solution (mg/l) b : Langmuir constant related to energy of adsorption (L/mg) V : volume of the solution (L) m : sorbent dose in the mixture (g) 24
Isotherms based on the Gibbs thermodynamic approach If adsorbed phase is treated as a 2D surface, we have the following Gibbs equation for pure component systems: in 3D : VdP nd μ 0 At equilibrium, the chemical potential of the adsorbed phase is equal to that of the gas phase, which is assumed to be ideal, i.e. Substituting μ into the eqn. gives the following Gibbs isotherm: This is the fundamental equation relating gas pressure, spreading pressure (Π) and amount adsorbed. 25
Linear isotherm For an ideal surface at infinite dilution, the EOS relating the spreading pressure and the number of mole on the surface is: 2D : A nrt 3D : PV nrt Integrating this equation at constant T gives: At equilibrium the spreading pressure in the adsorbed phase is linearly proportional to the pressure in the gas phase. To relate the amount adsorbed in the adsorbed phase in terms of the gas phase pressure, we use EOS to finally get: Where: 26
Volmer isotherm If consider the case where allow for the finite size of adsorbed molecules, the EOS for a surface takes the following form: A o : the minimum area occupied by n molecules The Gibbs equation can be written in terms of the area per unit molecule as follows: σ is the area per unit molecule of adsorbate 27
Cont. σ 0 is the minimum area per unit molecule of adsorbate we have: Volmer Isotherm Volmer isotherm is a fundamental equation describing the adsorption on surfaces where the mobility of adsorbed molecules is allowed, but no interaction is allowed among the adsorbed molecules. where: 28
Cont. Rearranging the volmer equation: the Volmer equation is similar to the Langmuir isotherm with the apparent affinity as: b is constant in the Langmuir mechanism, b app decreases with loading in the Volmer mechanism. 29
Fowler-Guggenheim isotherm From statistical thermodynamics, the simplest equation allowing for the lateral (adsorbate-adsorbate) interaction is obtained: where: z : coordination no. (usually 4 or 6 depending on the packing of molecules) w : the interaction energy between adsorbed molecules (w>0 means attraction between adsorbed species and w<0 means repulsion) w 500-1000 cal/mole 30
Cont. Plots of the fractional loading versus bp for the FG equation 31
Hill-deBoer isotherm When EOS of the adsorbate allows for the co-volume term and the attractive force term, the following van der Waals equation can be used: Then, the isotherm equation obtained is: Here mobile adsorption and lateral interaction among adsorbed molecules are considered. 32
Isotherms derived from the Gibbs equation 33