Langmuir-Hinshelwood

Steps in a Heterogeneous Catalytic Reaction 7. Diffusion of B from external surface to the bulk fluid (external diffusion) 1. Mass transfer of A to surface 2. Diffusion of A from pore mouth to internal catalytic surface 3. Adsorption of

A onto catalytic surface 6. Diffusion of B from pellet interior to pore mouth 5. Desorption of product B from surface 4. Reaction on surface Ch 10 assumes steps 1,2,6 & 7 are fast, so only steps 3, 4, and 5 need to be considered Langmuir-Hinshelwood HougenWatson(LHHW) model The Langmuir-HinshelwoodHougen-Watson(LHHW) approach is one of the most commonly used way of

deriving rate expressions for fluid solid catalytic reactions. The advantages of this method are that: (1) Rate derived by this method takes into account the adsorption/desorption process occurring over the surface along with the surface reaction. (2) Rate equation derived can be extrapolated more accurately to concentrations lying beyond the experimentally measured values. The chemical rate depends on: (1) chemisorption steps (2) surface reaction steps (3) desorption steps In LHHW model development, the rate equation is

first derived in terms of surface concentration of adsorbed species and vacant sites. Then, these surface concentrations are related to the fluid or bulk concentration that is directly measurable. Adsorption Step The adsorption of A (gas phase) on an active site S is represented by: A A A(g) + S AS I -S-S-S-S-S-SS: open (vacant) surface site AS: A bound to a surface site Rate of adsorption = rate of attachment rate of detachment

rAD k APA Cv k A CA S Conc of sites occupied by A partial pressure of A Molar conc of vacant sites on surface Rate is proportional to # of collisions with surface, which is a function of P A Rate is proportional to # of vacant (active) sites, C v, on the surface Active site: site on surface that can form a strong bond with adsorbed species k In terms of the adsorption equilibrium constant KA where K A A k A k A

rAD k APA Cv k A C A S rAD k A PA Cv CA S k A rAD CAS k A PA Cv K A

Equation I Site Balance Ct: Total number of active sites per unit mass of catalyst divided by Avogadros # (mol/g cat) Cv: Number of vacant sites per unit mass of catalyst divided by Avogadros # Vacant active site Active site occupied by A Active site

occupied by B A B Surface Cv is not measurable, but the total number of sites Ct can be measured In the absence of catalyst deactivation, assume the total number of active sites remains constant: Site balance: Ct = Cv + CAS + CBS We will use the site balance equation to put Cv in terms of measurable species Desorption

Step Products are desorbed into the gas phase CS C + S C I -S-S-S- C -S-S-S- rD,C PCCv kD CCS

K D,C Equation III where KD,C kD k D Note that the desorption of C is the reverse of the adsorption of C rD,C rAD,C Also the desorption equilibrium constant KD,C is the reciprocal of the adsorption equilibrium constant KC

1 KD,C KC Substituting 1/KC for KD,C in the rate equation for product desorption gives: rD,C kD CCS K CPCCv Derive a Rate Law for Catalytic Rxn Postulate catalytic mechanism, and then derive the rate law for that mechanism Assume pseudo-steady state hypothesis (rate of adsorption = rate of surface reaction = rate of desorption) No accumulation of species on the surface or near interface Each species adsorbed on the surface is a reactive intermediate Net rate of formation of species i adsorbed on the surface is 0, r iS=0 One step is usually rate-limiting If the rate-limiting step could be sped up, the entire rxn would be faster

Although reactions involve all 7 steps, only adsorption, surface reaction, or desorption will be rate limiting The surface reaction step is rate limiting ~70% of the time! Steps to derive the rate law Select among types of adsorption, surface reaction, and desorption Write rate laws for each individual step, assuming all are reversible Postulate which step is rate limiting Use non-rate-limiting steps to eliminate the surface concentration terms that cannot be measured Consider A B and assume the following mechanism is correct: C AS rAD k A PA Cv

1. Adsorption: A(g) + S AS K A 2. Surface reaction: 3. Desorption: CBSCv r k C C

AS + S S + BS S S A S v K S PBCv rD kD CBS BS B + S K D We need to select one of these 3 reactions as the rate limiting step, then derive the

corresponding rate equation, and see if this rate eq matches experimental data. Which step is the most logical to start with? a) Adsorption b) Surface reaction c) Desorption d) None of the above e) Any of these would be logical - they all have equal probability of being the rate limiting step The surface reaction step as is rate limiting ~70% of the time

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