Heterogeneous catalysis (C9981)
1. Kinetics
2. Mechanisms of catalytic reactions
3. Diffusional limitations on
heterogeneous catalysts
styskalik@chemi.muni.cz
styskalik.sci.muni.cz
Definition
• Catalyst is…
– A substance that speeds up a chemical reaction
– Without being consumed or changed
+ CATA + CATA
• 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 kinetics☺ (#ChemKin)
• Rxns of zero order, first order, and second order
• But in catalysis also 0.39 order… (many steps, all
contribute!)
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
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 2
Homework 2
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
LangmuirHinshelwood
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)
Thermodynamics vs. kinetics
• Another representation of the complexity of heterogeneous
catalytic reaction
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)
• The 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:
φ =
𝑑 𝑝
2
𝑘𝑖 ∙ ρ 𝑔 ∙ 𝑆
𝐷 𝑒
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
φ =
𝑑 𝑝
2
𝑘𝑖 ∙ ρ 𝑔 ∙ 𝑆
𝐷 𝑒
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
φ =
𝑑 𝑝
2
𝑘𝑖 ∙ ρ 𝑔 ∙ 𝑆
𝐷 𝑒
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
– Viscosity of vector gas
– Linear velocity of vector gas
– Size of the grains
– Diffusion coeff of reactants
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
Mass flow controller
Soap bubble flow meter
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 pumpVapor 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
HW3: Ethanol dehydration over 192 mg of Al-SiO2
catalyst, gas phase, fixed bed reactor, 240 °C
Feed: 4.4 mol% ethanol, the rest being flowing N2 (40 cm3 min−1 @STP)
Analysis of the products by GC-FID:
2.326 mol% ethylene, 0.332 mol% diethylether, water from
dehydration rxn, ethanol 1.553 mol%, the rest being N2 (constant)
Calculate conversion, selectivity to ethylene and diethylether + their
yields. Calculate carbon balance. Calculate WHSV.
C2H5OH → C2H4 + H2O
2 C2H5OH → C2H5OC2H5 + H2O