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Part D ONLY LAST PART ONLY PLEASE

Part D ONLY LAST PART ONLY PLEASE

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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Part D ONLY LAST PART ONLY PLEASE

**Convection and Diffusion Associated with a Porous Catalyst Layer** **Figure 30-6E Explanation:** This diagram illustrates the process of convection and diffusion within a porous catalyst layer. The following parameters and components are depicted: 1. **Bulk Gas:** - Diffusivity (\(D_{AB}\)) = 0.15 cm²/sec - Concentration (\(C_{A\infty}\)) = 5.0 gmole/m³ 2. **Boundary Conditions and Layers:** - **Boundary Layer** (Top): - Rate of mass transfer coefficient (\(k_c\)) = 0.100 cm/sec - **Porous Catalyst Layer:** - Effective Diffusivity (\(D_{Ae}\))= 0.02 cm²/sec - Reaction rate constant (\(k_1\)) = 0.05 sec⁻¹ - **Impermeable Boundaries:** - Bottom and sides of the catalyst layer are impermeable. 3. **Geometrical Dimensions:** - Thickness of the boundary layer (\(z = \delta\)) = 2.0 cm - Length (\(x\)) of the system ranges from 0 to \(L = 5.0 cm\) 4. **Flow and Concentration:** - \(N_A\) represents the flux of species A entering the porous catalyst. - At the boundary layer interface (\(z = 0\)), the concentration of A is denoted as \(C_A = C_{As}\). This setup is commonly used in chemical engineering to model how a reactant gas interacts with a porous catalyst, taking into account both convective transport and diffusion through the catalyst material. *Figure 30-6E. Convection and diffusion associated with a porous catalyst layer.*
Transcribed Image Text:**Convection and Diffusion Associated with a Porous Catalyst Layer** **Figure 30-6E Explanation:** This diagram illustrates the process of convection and diffusion within a porous catalyst layer. The following parameters and components are depicted: 1. **Bulk Gas:** - Diffusivity (\(D_{AB}\)) = 0.15 cm²/sec - Concentration (\(C_{A\infty}\)) = 5.0 gmole/m³ 2. **Boundary Conditions and Layers:** - **Boundary Layer** (Top): - Rate of mass transfer coefficient (\(k_c\)) = 0.100 cm/sec - **Porous Catalyst Layer:** - Effective Diffusivity (\(D_{Ae}\))= 0.02 cm²/sec - Reaction rate constant (\(k_1\)) = 0.05 sec⁻¹ - **Impermeable Boundaries:** - Bottom and sides of the catalyst layer are impermeable. 3. **Geometrical Dimensions:** - Thickness of the boundary layer (\(z = \delta\)) = 2.0 cm - Length (\(x\)) of the system ranges from 0 to \(L = 5.0 cm\) 4. **Flow and Concentration:** - \(N_A\) represents the flux of species A entering the porous catalyst. - At the boundary layer interface (\(z = 0\)), the concentration of A is denoted as \(C_A = C_{As}\). This setup is commonly used in chemical engineering to model how a reactant gas interacts with a porous catalyst, taking into account both convective transport and diffusion through the catalyst material. *Figure 30-6E. Convection and diffusion associated with a porous catalyst layer.*
### Problem 30-6E A gas stream mixture of A in carrier gas B flows over the porous catalyst layer shown in Figure 30-6E. The bulk gas concentration of species A is \( C_{A\infty} = 5.0 \text{ gmole/m}^3 \). At the condition of flow, the convective mass transfer coefficient for flux of species A across the boundary layer is \( k_c = 0.10 \text{ cm/sec} \). The porous catalyst layer catalyzes a first-order reaction of the form \( R_A = -k_1C_A \), with \( k_1 = 0.050 \text{ sec}^{-1} \), to consume species A. The effective diffusion coefficient of species A in the porous catalyst layer is \( D_{Ae} = 0.020 \text{ cm}^2/\text{sec} \), and the molecular diffusion coefficient of A in the bulk gas mixture is \( D_{AB} = 0.15 \text{ cm}^2/\text{sec} \). The width of the slab is \( L = 5.0 \text{ cm} \) and the thickness of the catalyst layer is \( \delta = 2.0 \text{ cm} \). The process is at steady state. It can be assumed that the concentration of species A does not vary along position \( x \). #### Questions: 1. **What is the Biot number associated with this process?** 2. **The flux of species A must get through both the hydrodynamic boundary layer and the porous catalyst layer. What is the concentration of species A right at the surface of the porous layer, \( C_{As} \)?** 3. **What is the flux \( N_A \) through the process?** 4. **If \( k_c \) is increased, which of the following process parameters also increase? Justify the reason for each selection.** \[ (1) N_A \quad (2) C_{As} \quad (3) Bi \] #### Explanation of Diagram: The figure referenced as **Figure 30-6E** likely illustrates the setup of the gas stream flowing over the porous catalyst layer. The figure is not included here, but we can infer that it includes: - A depiction of the gas stream with species A
Transcribed Image Text:### Problem 30-6E A gas stream mixture of A in carrier gas B flows over the porous catalyst layer shown in Figure 30-6E. The bulk gas concentration of species A is \( C_{A\infty} = 5.0 \text{ gmole/m}^3 \). At the condition of flow, the convective mass transfer coefficient for flux of species A across the boundary layer is \( k_c = 0.10 \text{ cm/sec} \). The porous catalyst layer catalyzes a first-order reaction of the form \( R_A = -k_1C_A \), with \( k_1 = 0.050 \text{ sec}^{-1} \), to consume species A. The effective diffusion coefficient of species A in the porous catalyst layer is \( D_{Ae} = 0.020 \text{ cm}^2/\text{sec} \), and the molecular diffusion coefficient of A in the bulk gas mixture is \( D_{AB} = 0.15 \text{ cm}^2/\text{sec} \). The width of the slab is \( L = 5.0 \text{ cm} \) and the thickness of the catalyst layer is \( \delta = 2.0 \text{ cm} \). The process is at steady state. It can be assumed that the concentration of species A does not vary along position \( x \). #### Questions: 1. **What is the Biot number associated with this process?** 2. **The flux of species A must get through both the hydrodynamic boundary layer and the porous catalyst layer. What is the concentration of species A right at the surface of the porous layer, \( C_{As} \)?** 3. **What is the flux \( N_A \) through the process?** 4. **If \( k_c \) is increased, which of the following process parameters also increase? Justify the reason for each selection.** \[ (1) N_A \quad (2) C_{As} \quad (3) Bi \] #### Explanation of Diagram: The figure referenced as **Figure 30-6E** likely illustrates the setup of the gas stream flowing over the porous catalyst layer. The figure is not included here, but we can infer that it includes: - A depiction of the gas stream with species A
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