Heterogeneous catalysis (C9981) 1.Kinetics 2.Mechanisms of catalytic reactions 3.Diffusional limitations on heterogeneous catalysts Definition •Catalyst is… –A substance that speeds up a chemical reaction –Without being consumed or changed Výsledek obrázku pro beaker Výsledek obrázku pro beaker Výsledek obrázku pro beaker Výsledek obrázku pro beaker + CATA + CATA Výsledek obrázku pro snail Výsledek obrázku pro fastest animal in the world •We get our products –In shorter time; at lower rxn temperature; at lower pressure –cheaper; economical; ecological Catalytic cycle •A + B → P Ea >> Ea(cata); k = A∙e–Ea/RT ΔG = ΔG(cata); ΔG = –RT∙lnK Kinetics •We know kineticsJ (#ChemKin) •Rxns of zero order, first order, and second order • • • • • •But in catalysis also 0.39 order… (many steps, all contribute!) Výsledek obrázku pro zero order kinetics Výsledek obrázku pro first order kinetics Kinetics •An important consideration: type of the reactor –Batch –Continuous (plug flow (fixed bed) reactor (PFR) or continuous stirred tank reactor (CSTR)) •Steady-state approximation (complicated math behind!) •It is not possible to follow changes of concentrations in time Výsledek obrázku pro first order kinetics Kinetics •Important terms –Rate – – – –Arrhenius equation Kinetics •Important terms –Reaction order – – – –For elementary reactions α, β = whole numbers (integers) –For non-elementary reactions (i.e. catalytic reactions) α, β = non-integers Kinetics •Important terms –Reaction order •Can be negative! Kinetics •Important terms –Reaction order •Example: Determination of reaction order Kinetics •Back to Arrhenius equation •k – is the reaction rate constant •k – is not a constant in fact –It depends on temperature and pressure –Its units differ according to the reaction order Kinetics •Important terms –Reaction pseudo-order •Application of one (or more) of the reactants in a big excess so that its concentration in time t virtually equals concentration in time 0 •Simplification of reaction rate equation Kinetics Kinetics Kinetics •Ea (apparent) and A can be estimated by plotting ln k vs. 1/T = Arrhenius plot Kinetics •Summary Homework 1 Homework 1 Mechanisms of catalytic reactions •Langmuir (monomolecular) –A(adsorbed) → P(adsorbed) •Langmuir-Hinshelwood (bimolecular) –A(adsorbed) + B(adsorbed) → P(adsorbed) •Eley-Rideal (bimolecular) –A(adsorbed) + B(gas phase) → P(adsorbed) •Mars-van Krevelen (special case) Mechanisms of catalytic reactions •Langmuir (monomolecular) –A(adsorbed) → P(adsorbed) •Langmuir-Hinshelwood (bimolecular) –A(adsorbed) + B(adsorbed) → P(adsorbed) •Eley-Rideal (bimolecular) –A(adsorbed) + B(gas phase) → P(adsorbed) •Mars-van Krevelen (special case) Langmuir •Hypotheses identical as for Langmuir adsorption isotherm –Monolayer –One molecule per active site –The enthalpy of adsorption independent on surface coverage Θ •All sites identical •No interactions between molecules of adsorbate –Adsorption and desorption in equilibrium Langmuir •Reaction rate ≈ k∙[A] •First order reaction Note: k can be kA→P Or kA-adsorption Langmuir Surface is fully covered with A No change with increasing [A] Reaction rate ≈ k Zero order reaction Note: k can be kA→P Or kP-desorption Mechanisms of catalytic reactions •Langmuir (monomolecular) –A(adsorbed) → P(adsorbed) •Langmuir-Hinshelwood (bimolecular) –A(adsorbed) + B(adsorbed) → P(adsorbed) •Eley-Rideal (bimolecular) –A(adsorbed) + B(gas phase) → P(adsorbed) •Mars-van Krevelen (special case) Langmuir-Hinshelwood •Competition between A and B adsorbates for adsorption sites Mechanisms of catalytic reactions •Langmuir (monomolecular) –A(adsorbed) → P(adsorbed) •Langmuir-Hinshelwood (bimolecular) –A(adsorbed) + B(adsorbed) → P(adsorbed) •Eley-Rideal (bimolecular) –A(adsorbed) + B(gas phase) → P(adsorbed) •Mars-van Krevelen (special case) Eley-Rideal • Mechanisms of catalytic reactions •Langmuir (monomolecular) –A(adsorbed) → P(adsorbed) •Langmuir-Hinshelwood (bimolecular) –A(adsorbed) + B(adsorbed) → P(adsorbed) •Eley-Rideal (bimolecular) –A(adsorbed) + B(gas phase) → P(adsorbed) •Mars-van Krevelen (special case) Mars-van Krevelen •Example: oxidation of toluene over V2O5 –Oxygen comes from crystal lattice (confirmed by isotope studies) •Creation of oxygen vacancies •Regeneration of catalyst with O2 in the feed O2 Note: 1.Catalyst should not change during catalysis! 2.Compare with Langmuir-Hinshelwood and Eley-Rideal Mars-van Krevelen •Possible only with metal oxides, sulphides, etc., where metal can achieve variable oxidation states and coordinations •Catalyst works as a „bank“ –It can borrow you oxygen if needed –It can save oxygen for worse times… •Selectivity might be very high –Specific oxidation species within the crystal lattice •Diffusion in solids needs to be considered –Vacancies play an important role Mars-van Krevelen •Possible only with metal oxides, sulphides, etc., where metal can achieve variable oxidation states and coordinations: –Oxidation of propylene to acrolein over MoO3-x –Reduction of benzoic acid to benzaldehyde over MoO3-x –Hydrodesulfurization of DBT do DB over NiMoS2-x –Oxidation and reduction of gases in car exhausts over CeO2-Ce2O3 • Thermodynamics + steps of cat reaction •A + B → P 1 1: Adsorption of reactants on catalyst surface 2 3 1 3: Desorption of products from catalyst surface 2: Reaction on active site Steps of catalytic rxns •A + B → P 1 1: Diffusion medium→catalyst 2: Adsorption of reactants (3: Diffusion on cat. surface) 4: Reaction on active site (5: Diffusion on cat. surface) 6: Desorption of products 7: Diffusion catalyst→medium 4 6 2 Steps of catalytic rxns 1a: Diffusion of the reactant in the fluid film surrounding the catalysts grain (External diffusion; macroporosity) 1b: Diffusion of the reactant in porous network until reaching surface (Internal diffusion; micro- and mesopores) 2: Adsorption of reactants (3: Diffusion on cat. surface) 4: Reaction on active site (5: Diffusion on cat. surface) 6: Desorption of products 7a: Diffusion of the product in the porous network until reaching the aperture of the pore (Internal diffusion) 7a: Diffusion of the product in the fluid film (External diffusion) Rate determining step •Total: Up to 9 steps; 6 of them diffusion! •All of them more or less contribute to the final reaction rate (kapparent and Eapparent) •Slowest step??? Rate determining step •6 steps based on diffusion –Fick laws –Low dependance on temperature –Ea = 4–8 kJ mol–1 •3 steps based on chemistry –High dependance on temperature –Ea = 20–200 kJ mol–1 Slowest step of the catalytic reaction??? Depends on the temperature!!! k = A∙e–Ea/RT Rate determining step •Low temperature –Chemical steps are limiting –Eapp = Ea of the reaction step Rate determining step •High temperature –The chemical reaction is fast –There is no time for internal diffusion to take place, only external surface employed in catalysis –Diffusional steps are limiting –Eapp = Ea of the diffusion in the fluid film (external diffusion) Rate determining step •Intermediate temperature –Contribution of both chemistry and diffusion (diffusion in the pores, internal diffusion) –Eapp = average of Ea of the reaction step and Ea of internal diffusion Diffusional limitation •kd = diffusion constant; ki = reaction rate constant per m2 of catalysts; S = specific surface area •kd = ki∙S; Surface is supplied with reactants; no diffusional limitation •kd << ki∙S; Internal surface of the catalyst is not supplied with reactants; Diffusional limitation Diffusional limitation •Gradient of reactant concentration in –Fluid film of particle (External diffusion) –Inside the pore (Internal diffusion) – Diffusional limitation •We want to use as many active sites as possible (even deep in the internal pore system) •We want to avoid diffusional limitation • •Effectivenes factor η (observed reaction rate / maximal theoretical reaction rate) depends on Thiele modulus •Thiele modulus φ describes the „quality“ of catalyst grain in terms of internal diffusion: dp = diameter of grain; ki = reaction rate constant per m2 of catalysts; S = specific surface area; ρg = density of the catalyst including pores; De = diffusion coefficient of the reactant in the pores Diffusional limitation •Thiele modulus φ describes the „quality“ of catalyst grain in terms of internal diffusion: • • • • •The higher the Thiele modulus, the higher probability of diffusional limitations to occur •Internal diffusional limitations occur always to some extent • Diffusional limitation •Thiele modulus φ describes the „quality“ of catalyst grain in terms of diffusion: • • • • •Let‘s decrease dp = small catalyst grains •Let‘s decrease ρg = higher pore volume •Let‘s increase De = bigger pores Catalyst synthesis, shaping, thermal treatment… …in order to avoid the internal diffusional limitations as much as possible… Diffusional limitation •Gradient of reactant concentration in –Fluid film of particle (External diffusion) •Viscosity of vector gas •Linear velocity of vector gas •Size of the grains •Diffusion coeff of reactants –Inside the pore (Internal diffusion) – Diffusional limitations •Note: Up to now we have discussed only diffusion of reactants •Same applies for heat diffusion •I.e. diffusional limitations can lead to important issues! –Effectivenes factor η > 1 –Hot spots –Sintering of catalysts –Shift/loss of selectivity –Explosion Industrial point of view Diffusional limitations •Internal diffusional limitations always present to some extent –We can diminish them at the time of catalyst preparation (pore volume, pore diameter, size of catalysts grains) •External can be avoided at the time of catalytic reaction –Linear velocity of vector gas,… •How to reveal external diffusional limitations? Diffusional limitations •How to reveal external diffusional limitations? • •Constant temperature and constant contact time (other parameters can vary) lead to constant conversion, selectivity, and yield Diffusional limitations •How to reveal external diffusional limitations? • •Contact time practically??? 1 unit of catalyst mass 1 unit of catalyst volume 0.5 unit of catalyst mass 0.5 unit of catalyst volume 1 unit of linear gas velocity 1 unit of reactant feed 0.5 unit of linear gas velocity 0.5 unit of reactant feed Conversion, yield, and selectivity are equal! If not, then we encounter external diffusional limitations! Space velocity and contact time •Contact time = 1/space velocity •Space velocity [h–1] –Based on catalyst mass (WHSV, weight hourly space velocity) •weight of reactant per weight of catalyst per hour • –Based on catalyst volume (GHSV or LHSV – gas/liquid…) •Volume of feed gas@STP (reactant + gas vector) per volume of catalyst bed per hour • Be careful, contact time can be based on WHSV, GHSV, or LHSV! Space velocity and contact time •Calculations with volumes always much less convenient than weight… •So…Why is GHSV/LHSV important in heterogeneous catalysis?? • 1 unit of catalyst mass 1 unit of catalyst volume 1 unit of catalyst mass 1 unit of catalyst volume 1 unit of linear gas velocity Feed of reactant constant 0.5 unit of linear gas velocity Feed of reactant constant WHSV is constant. GHSV is different. Conversion, yield, and selectivity are different! Space velocity and contact time 1 unit of catalyst mass 1 unit of catalyst volume 1 unit of linear gas velocity [m3 h–1] 1 unit of reactant feed Výsledek obrázku pro mass flow controller Mass flow controller Manual Bubble Flowmeter (Standard Version) flow meter volume 50 mL, pkg of 1 ea Soap bubble flow meter Výsledek obrázku pro automatic syringe pump Space velocity and contact time 1 unit of catalyst mass 1 unit of catalyst volume 1 unit of linear gas velocity 1 unit of reactant feed [g or cm3 h–1] → gas (= mass flow control, soap…) → liquid Automatic syringe pump Výsledek obrázku pro chem bubbler Vapor saturator (= bubbler) Space velocity and contact time 1 unit of catalyst mass [g] 1 unit of catalyst volume [cm3] 1 unit of linear gas velocity 1 unit of reactant feed → dilute with inert material to a constant volume Remember, GHSV important for catalyst comparison Homework 2 •Selectivity = 90 % in all cases; WHSV = 15.5 h–1 2 -2 MeOH TiO2/SiO2 Temperature [°C] Conversion sample 1 (4.2 wt% Ti) [%] Conversion sample 2 (0.9 wt% Ti) [%] 220 39 8.6 230 48 9.6 240 59 13 250 82 17 260 93 21 •Gas phase transesterification •Continuous flow fixed bed reactor •Create Arrhenius plots for both catalysts (plot ln k [molLD gcat–1 h–1] vs. 1000/T [K–1] •Estimate apparent Ea and A from Arrhenius equation •What makes the difference between these two catalysts? ACS Catal. 2018, 8, 9, 8130–8139