Lecture 5 Solid surface: Adsorption and Catalysis
Adsorbtion G = H T S DG ads should be negative (spontaneous process) DS ads is negative (reduced freedom) DH should be negative for adsorption processes (driven by enthalpy) Adsorption processes are important for: heterogeneous catalysis (first step of catalysis) characterization of porous materials
Physical and Chemical Adsorption physical adsorption: involves only molecular interaction forces, no chemical bonds formed, -D ads H<20 kj/mol similar to condensation, easily reversible many layers can be formed adsorbate is mobile low temperatures and high pressures close to liquefaction chemical adsorption (chemisorption) involves formation of chemical bonds, -D ads H>80 kj/mol involves specific chemistry on the surface adsorbed atoms are localized difficult to reverse (breaking chemical bonds is required) only monolayers can be formed (however further physisorbed layers can be formed on top) high temperatures, wide range of pressures
Measurement of gas adsorption volumetric methods: change in the gas volume is measured over a range of pressures gravimetric methods: change in a sample mass is measured (e.g. by a microbalance) flow methods: changes in a gas concentration are measured
Measurement of gas adsorption volumetric methods: change in the gas volume is measured over a range of pressures Helium is usually used for calibration: Nitrogen as an adsorbate surface area can be calculated as volume adsorbed divided by the area of N 2 molecule 0.162 nm 2.
Measurement of gas adsorption flow methods: adsorbant gas (e.g. N 2 ) is diluted in diluent gas (e.g. He). changes in a gas concentration are measured used thermal conductivity
Adsorption isotherms adsorption isotherm: the amount of gas adsorbed vs gas pressure at a fixed temperature saturation pressure: pressure of gas in equilibrium with the with liquefied phase (or pressure at which condensation commence). relative pressure: normalized by the saturation pressure
Classification of adsorption isotherms Brunner, Deming, Deming and Teller 1940: isotherms can be classified into 5 groups chemisorption: limited to one layer high affinity between gas and solid
Isotherm equations at very low pressures can be approximated as a straight line: Henry s law region isotherm equation should describe the shape of the isotherm isotherm equation should produce enthalpy of adsorption matching the one deduced by calorimetry
Langmuir adsorption equation Langmuir equation (1918) is based on a chemisorption model: adsorption is limited to a single monolayer number of molecules adsorbed number of molecules in a complete monolayer n n m α p = 1 +α p gas pressure linearized form p 1 p = + n n n α m m
Langmuir adsorption equation Model: dynamic equilibrium between gas and adsorbed phase molecules can only attach to a bare surface rate of adsorption= apa 1 0 rate of desorption = baexp( E / RT) 1 1 1 in equilibrium: apa = baexp( E/ RT) 1 0 1 1 1
Langmuir adsorption equation apa = baexp( E / RT) 1 0 1 1 1 A= A + A 0 1 combining: A1 a1p = A b exp( E / RT) + a p or 1 1 1 n α p a = α = nm 1+ α p b E RT, where 1 exp( 1 / ) 1
Assumptions of the Langmuir equation The enthalpy of desorption E 1 is constant and independent on coverage: uniformity of the surface, no interaction between adsorbed molecules Molecules are immobilized on the surface and cannot move around Each site can only accommodate one molecule Molecules are adsorbed without dissociation
Application of the Langmuir equation n n m α p =, 1 + α p a 1 where α = exp( E1 / RT ) b1 Langmuir equation fits type I curves Increasing a (i.e. E 1 ) leads to steeper adsorption at lower relative pressures Limitations: Applies to only one type of isotherms usually lead to inconsistencies like large variations of n a and E 1 with temperature and adsorbate. applicable only to monolayer adsorption while multilayer adsorption is more common in nature
The BET equation BET equation (1938): the extension of Langmuir isotherm proposed by Brunauer, Emmet and Teller to include multilayer adsorption n { ( )} n = ( p p) 1 + ( Z 1) p/ p m Zp 0 0, {( ) } where Z exp E E / RT 1 v
The BET equation Model: no limit to the number of layers adsorbed the Langmuir equation applies to each layer adsorption and desorption only occurs at exposed surfaces at equilibrium, the distribution of adsorbant between different layers is constant.
The BET equation at equilibrium A = const a pa = b A exp( E / RT ) 0 1 0 1 1 1 A = const a pa + b A exp( E / RT) = 1 2 1 1 1 1 Generally: = apa+ baexp( E / RT) 1 0 2 2 2 apa= baexp( E/ RT) 2 0 2 2 2 apa = ba i i 1 i i ( ) exp( E / RT) { / exp( / )} 1 A = a b p E RT A i i i i i i
The BET equation ( ) { / exp( / )} 1 Ai = ai bi p Ei RT Ai n n A= A n = ia = i m i= 1 i i i= 0 A i= 1 nm Ai i= 0 ia assumptions: E1 = E2 =... = E v b / a = b / a =... = C 2 2 3 3 definitions: = 1 1 1 Y ( a / b) pexp( E / RT) X = (1/ C) pexp( E / RT) Z = Y / X v A i i n ZX = ZX A0 and = n (1 X)(1 X + ZX) m
Application of the BET equation n Zp n = ( p p) 1 + ( Z 1) p/ p m { ( )} 0 0 {( 1 v ) } where Z exp E E / RT the BET equation can describe type II (high Z) and III isotherms (low Z), Limitation of the BET equation: unrealistic picture of the adsorbed film: battered metropolis full enthalpy released irrespective of the number of neighbors
The other isotherms the BET equation for limited adsorption v n ZX 1 ( v+ 1) X + vx = n 1 X 1 + ( Z 1) X ZX m v+ 1 v+ 1 the Freundlich isotherm (empirical) n 1/ κ = βp κ > the Temkin isotherm n n m 0, 1 RT ln( κ p) E β = E 0 enthalpy of desorption when n = 0 the isotherms obtained from the equation of state for an ideal 2D gas on the surface Henry s law: n = Kp
Capillary condensation If the surface is curved the vapour pressure will be different than p 0 : Kelvin equation. c L p γv 1 1 ln = + p RT r r 1 1 1 + = r r 1 1 2 + = r r r
Chemisorption can be described to some extent by Langmuir equation defects on the surface cause various enthalpy at various sites: as adsorption proceeds the enthalpy will decrease usually occurs via physisorption and involves diffusion on the surface
Heterogeneous catalysis Catalyst: increases rate of a chemical reaction doesn t take in the overall chemical reaction is unchanged chemically at the end of the reaction, the amount of catalyst stays the same as well required in a relatively small quantity doesn t affect the position of equilibrium but reduces the barrier
Mechanism of heterogeneous catalysis Steps of the catalytic reaction: diffusion of reactants to the surface adsorption of the reactants reaction within the adsorbed layer desorption of the products diffusion of the products away from the surface Adsorption of the reactants: always involves a chemisorption, although physisorption might occur as well: catalysts are active at high temperature, many catalysts are highly specific, IR spectroscopy shows change in the spectrum of adsorbed components active sites: positions where strength of the chemisorption bond is optimal for the reaction
Mechanism of heterogeneous catalysis Langmuir-Hinshelwood mechanism: reaction takes place between two adjacent chemisorbed atoms or radicals
Mechanism of heterogeneous catalysis The Rideal-Eley mechanism no net breakage of chemical bonds: as one forms another is broken
Kinetics of reaction in the adsorbed layer Unimolecular reaction dpa kα ApA v= = kθ A = dt 1 +α p A A first order if α p 1 zero order if α p 1 A A A A
Kinetics of reaction in the adsorbed layer Bimolecular reaction v= kθ θ θ A v= k A B α ApA α BpB = and θb = 1+ α p + α p 1+ α p + α p A A B B A A B B α p α p A A B B ( 1+ α p + α p ) 2 A A B B Limiting cases: if one of the gases (B) is not chemisorbed: v= k α p p A A B ( 1+ α p ) if A is adsorbed strongly and B weakly: α B pb v= k α p A A A A
Summary adsorption: physisorption and chemisorption methods for measuring gas adsorption: volumetric, flow and gravimetric methods 5 types of adsorption isotherms shapes equations: Langmuir: monolayer, BET: multilayer capillary condensation on porous surfaces: hysteresis heterogeneous catalysis: Langmuir- Hinshelwood and Rideal-Eley mechanism
Problems 8.4 Data for the adsorption of nitrogen gas on silica, when plotted according to the linear form of the BET equation, give a slope of 319 mol -1 and an intercept of 3.35 mol -1. Calculate the surface area of the sample and, using the customary approximation, calculate the enthalpy of adsorption of the first layer. The enthalpy of vaporization of nitrogen at 77 K (the temperature of the experiment) is 5.60 kj mol -1 and the effective cross-sectional area of a nitrogen molecule is 0.162 nm 2. 8.6 The data in the table are for the adsorption of nitrogen on a 10 mg sample of mica at 90 K. Show that the data fit the Langmuir isotherm and evaluate the constants in the expression. Given that the cross-sectional area of a nitrogen molecule is 0.162 nm 2, calculate the specific surface area of the mica. p/pa V /mm 3 (at STP) 0.293 12.0 0.506 17.0 0.973 23.9 1.773 28.2 3.479 33.0 where V is the volume of gas adsorbed at standard temperature (273.15 K) and pressure (101.32 kpa).