Part D ONLY LAST PART ONLY PLEASE
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
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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66d6d299-6dc2-4668-804d-91523295e64a%2Fe99c4874-7ef9-4b02-ae85-3b8971fb2503%2Fly31cda_processed.png&w=3840&q=75)
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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