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Questions and Answers
What does the symbol β represent in the effectiveness factor equation?
What does the symbol β represent in the effectiveness factor equation?
Which equation represents the calculation of dimensionless activation energy?
Which equation represents the calculation of dimensionless activation energy?
In the provided equations, what does ΔHR stand for?
In the provided equations, what does ΔHR stand for?
What unit is the effective heat conductivity (ke) expressed in?
What unit is the effective heat conductivity (ke) expressed in?
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The dimensionless activation energy (γ) includes which of the following parameters?
The dimensionless activation energy (γ) includes which of the following parameters?
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Which parameter is multiplied by the dimensionless heat of reaction to form the equation for β?
Which parameter is multiplied by the dimensionless heat of reaction to form the equation for β?
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What is the correct measurement for ΔEa in the effectiveness factor equation?
What is the correct measurement for ΔEa in the effectiveness factor equation?
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Which variable reflects the temperature at the external surface of the catalyst pellet?
Which variable reflects the temperature at the external surface of the catalyst pellet?
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What is the primary factor that affects reaction rates in catalytic processes?
What is the primary factor that affects reaction rates in catalytic processes?
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Which term describes the diffusion limitations that occur from the fluid bulk to the surface of the catalyst?
Which term describes the diffusion limitations that occur from the fluid bulk to the surface of the catalyst?
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How does the concentration of a component inside the pores of a catalyst relate to the particle radius?
How does the concentration of a component inside the pores of a catalyst relate to the particle radius?
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Which of the following statements about porous catalysts is true?
Which of the following statements about porous catalysts is true?
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What does the equation $V_c = V_s + V_p$ represent in the context of porous catalysts?
What does the equation $V_c = V_s + V_p$ represent in the context of porous catalysts?
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In a heterogeneous catalytic reaction, reaction rates are proportional to which of the following?
In a heterogeneous catalytic reaction, reaction rates are proportional to which of the following?
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Which type of diffusion limitation occurs during the transportation of reactants through the catalyst pores?
Which type of diffusion limitation occurs during the transportation of reactants through the catalyst pores?
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What happens to the overall reaction rate when both reaction and internal diffusion limitations occur simultaneously?
What happens to the overall reaction rate when both reaction and internal diffusion limitations occur simultaneously?
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What does the specific area Sa measure in a catalyst?
What does the specific area Sa measure in a catalyst?
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What is the effective diameter dp in relation to a catalyst?
What is the effective diameter dp in relation to a catalyst?
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Which diffusion mechanism involves molecules colliding with the walls of the pore but not with each other?
Which diffusion mechanism involves molecules colliding with the walls of the pore but not with each other?
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What does the term εs represent in the context of catalyst characteristics?
What does the term εs represent in the context of catalyst characteristics?
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Which equation represents the molecular diffusivity DAB for binary diffusion?
Which equation represents the molecular diffusivity DAB for binary diffusion?
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What limitation affects the accessibility of catalyst pores despite their surface area?
What limitation affects the accessibility of catalyst pores despite their surface area?
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At which condition does molecular diffusion usually occur?
At which condition does molecular diffusion usually occur?
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What does the term $W_{Az}$ represent in the context of species A?
What does the term $W_{Az}$ represent in the context of species A?
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Which factor is NOT included in the equation for the diffusivity $D_{AS}$?
Which factor is NOT included in the equation for the diffusivity $D_{AS}$?
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In the steady-state equation, what does the term $W_{Ar}$ signify?
In the steady-state equation, what does the term $W_{Ar}$ signify?
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What is the significance of the term τ in the flux equation for species A?
What is the significance of the term τ in the flux equation for species A?
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What condition is implied by the term 'steady-state' in the reaction and diffusion context?
What condition is implied by the term 'steady-state' in the reaction and diffusion context?
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What is the role of activation energy (E) in the context of diffusivity?
What is the role of activation energy (E) in the context of diffusivity?
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Which variable would directly affect the flux WAz as indicated by the equations provided?
Which variable would directly affect the flux WAz as indicated by the equations provided?
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What happens to the effectiveness factor (η) for a first-order reaction as the Thiele modulus (φ1) increases?
What happens to the effectiveness factor (η) for a first-order reaction as the Thiele modulus (φ1) increases?
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According to the Weisz-Prater criterion, what does it indicate if CWP is greater than 1?
According to the Weisz-Prater criterion, what does it indicate if CWP is greater than 1?
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For a first-order reaction with a small Thiele modulus, what can be said about the effectiveness factor?
For a first-order reaction with a small Thiele modulus, what can be said about the effectiveness factor?
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In which scenario does the internal catalyst temperature exceed the surface temperature?
In which scenario does the internal catalyst temperature exceed the surface temperature?
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What is the characteristic length (L) for a cylindrical catalyst shape according to the Thiele modulus formulation?
What is the characteristic length (L) for a cylindrical catalyst shape according to the Thiele modulus formulation?
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How is the Thiele modulus (φn) approximated for a reaction order n and different shapes?
How is the Thiele modulus (φn) approximated for a reaction order n and different shapes?
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What is the relationship between the internal reaction rate and the observed reaction rate in the context of the effectiveness factor?
What is the relationship between the internal reaction rate and the observed reaction rate in the context of the effectiveness factor?
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Which parameter does NOT influence the Thiele modulus in the given equation for different catalyst shapes?
Which parameter does NOT influence the Thiele modulus in the given equation for different catalyst shapes?
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What does the Thiele modulus represent in terms of a chemical reaction?
What does the Thiele modulus represent in terms of a chemical reaction?
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In the context of the Thiele modulus, what does a large value indicate?
In the context of the Thiele modulus, what does a large value indicate?
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What are the boundary conditions for concentration in the given system?
What are the boundary conditions for concentration in the given system?
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Which of the following correctly identifies the units of kn, the reaction rate constant?
Which of the following correctly identifies the units of kn, the reaction rate constant?
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How does the equation $𝜑_n = √{(k_n R^2 c_{As})/D_e}$ relate to the Thiele modulus?
How does the equation $𝜑_n = √{(k_n R^2 c_{As})/D_e}$ relate to the Thiele modulus?
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Study Notes
Diffusion Limitations in Porous Catalysts
- Diffusion limitations arise when transport effects, not just reaction rates, influence the reaction rate in heterogeneous catalysts.
- Reactant concentration gradients exist from the bulk fluid to the catalyst surface due to simultaneous reaction and transport limitations.
- External diffusion limitations occur from the bulk fluid to the catalyst's exterior surface.
- Internal diffusion limitations arise during reactant transport through the catalyst's pores to the reaction sites.
- Internal and External diffusion impacts reaction rate differing from the pore's radius.
- Reaction rate depends on the radius given by the concentration variation.
Catalyst Surface Area
- Reaction rate in heterogeneous catalysts is proportional to the accessible catalyst surface.
- Porous materials, such as catalysts in figure 4.2, have increased surface area due to pores.
- Catalyst volume includes solid and pore volumes.
- Specific surface area (Sa) represents total surface area per unit mass of catalyst [m²/kg].
- Effective pore diameter (dp) is the average pore size [m].
- Catalyst density (pc) represents the catalyst mass per unit volume[kg/m³].
- Catalyst void fraction (ɛs) is the fraction of the catalyst that is occupied by pores.
Diffusion Inside Catalyst Pores
- Fick's Law is applied for component A diffusion: molar flux (Waz) = (DA * dCA/dz)
- DA (diffusivity of A): [m²/s] is the measure of how quickly component A diffuses.
- Different diffusion mechanisms exist: molecular diffusion and Knudsen diffusion.
- Molecular diffusion: molecules colliding with each other but not the pore walls, dominating in large pores at high pressure.
- Knudsen diffusion: molecules collide with pore walls more than each other, dominating in small pores.
- Overall diffusivity can be calculated in series resistances.
Reaction and Diffusion Effects
- When reaction and diffusion occur simultaneously, a material balance can be used.
- For spherical catalysts, deriving a steady-state balance is required, considering generation and accumulation terms within an infinitesimal volume segment.
- A reaction rate equation with respect to the radial position can be derived.
- Surface diffusion exists in which molecules migrate on pore surfaces leading to surface diffusion flux and diffusivity.
Thiele Modulus
- Thiele modulus (Φn) compares surface reaction rate to internal diffusion rate determining whether diffusion or reaction is the rate-limiting step.
- High Thiele modulus values imply internal diffusion limitations affecting overall reaction rate.
- Low Thiele modulus values imply that surface reaction rate limits the overall reaction rate.
- Dimensionless parameters (ψ, λ) represent reaction concentration and radial distance respectively.
Effectiveness Factor
- Effectiveness factor (η) measures the ratio of actual overall reaction rate to reaction rate without internal diffusion effects.
- The effectiveness factor helps correct reaction rate accounting for internal mass transfer limitations.
- Numerical values of η (effectiveness factor) range 0 to 1.
Weisz-Prater Criterion
- Weisz-Prater criterion (Cwp) is used assessing internal diffusion limitations.
- Cwp ≤ 1 implies no significant diffusion limitations
- Cwp >>1 implies internal diffusion limitations. This relates observed reaction rate, catalyst properties, and effective diffusivity.
Thiele Modulus for Different Shapes & Reaction Orders
- Thiele modulus varies accounting for different catalyst geometries and reaction orders.
- Values for Thiele Modulus (Φ) are provided based on different shapes (sphere, cylinder, slab).
Non-isothermal Conditions
- In exothermic reactions, reaction rate increases with temperature.
- Non-isothermal conditions lead to higher temperatures inside particles, potentially exceeding surface temperatures and impacting effectiveness factor, which is related to temperature differences within the particle.
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Description
This quiz explores the various diffusion limitations encountered in heterogeneous catalysts, focusing on both internal and external factors. It discusses the impact of reactant concentration gradients and the significance of catalyst surface area on reaction rates. Understand how transport effects influence catalytic processes.
