For the elementary reaction, 2A->B Carried in isothermal CSTRS positioned in series. Feed is pure A and conversion and conversion at 2nd reactor outlet is 0.95. a) Determine the first reactor outlet's conversion b)Find the space time required for each of the reactors
For the elementary reaction, 2A->B Carried in isothermal CSTRS positioned in series. Feed is pure A and conversion and conversion at 2nd reactor outlet is 0.95. a) Determine the first reactor outlet's conversion b)Find the space time required for each of the reactors
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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![### Chemical Engineering Reactor Design: Series CSTR Problem
**Problem Statement:**
Consider the elementary reaction, \( 2A \rightarrow B \), conducted in isothermal Continuous Stirred Tank Reactors (CSTRs) arranged in series. The feed consists of pure A, and the conversion at the outlet of the second reactor is 0.95.
**Tasks:**
a) Determine the conversion at the outlet of the first reactor.
b) Calculate the space time required for each of the reactors.
**Diagrams and Figures:**
* No diagrams or graphs are provided with this problem.
### Solution Approach:
**a) Determining the First Reactor Outlet’s Conversion:**
1. **Write the Mole Balance Equation:**
For any CSTR, the mole balance is given by \[ F_{A0}(1 - X) = F_{A0} - V_rkC_{A0}(1 - X)^2 \]
2. **Conversion Definition:**
The conversion of the reactant \(A\) can be defined as:
\[ X = (C_{A0} - C_A) / C_{A0} \]
3. **Separation into Two CSTRs:**
- Let \( X_1 \) be the conversion at the outlet of the first reactor.
- The overall conversion at the second reactor outlet, \( X_2 \), is given as 0.95.
Use the conversion balance at the first reactor to find \(X_1\).
**b) Space Time for Each Reactor:**
1. **Space Time (τ) Definition:**
Space time is defined by:
\[ \tau = \frac{V_r}{F_{A0}} \]
where \( V_r \) is the reactor volume, and \( F_{A0} \) is the volumetric flow rate of A.
2. **Calculate for Each Reactor:**
Using the conversions and reaction kinetics, calculate the space time required for both reactors.
**Note:** Specific values, kinetic constants, and volumetric flow rates are necessary to perform these calculations, so refer to additional data or experimental results if needed.
This problem approach is a common one in chemical reaction engineering, particularly in designing multiple reactors in series for optimal conversion and efficiency.
### References:
For further study, refer to textbooks such as "Elements of Chemical Reaction Engineering" by H. Scott Fogler, or](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F24b9c3c5-f97f-4bf7-81d0-02a5082b54b2%2Faf75441a-52d9-49b4-b9a3-038da15506ed%2Fikd5cst_processed.png&w=3840&q=75)
Transcribed Image Text:### Chemical Engineering Reactor Design: Series CSTR Problem
**Problem Statement:**
Consider the elementary reaction, \( 2A \rightarrow B \), conducted in isothermal Continuous Stirred Tank Reactors (CSTRs) arranged in series. The feed consists of pure A, and the conversion at the outlet of the second reactor is 0.95.
**Tasks:**
a) Determine the conversion at the outlet of the first reactor.
b) Calculate the space time required for each of the reactors.
**Diagrams and Figures:**
* No diagrams or graphs are provided with this problem.
### Solution Approach:
**a) Determining the First Reactor Outlet’s Conversion:**
1. **Write the Mole Balance Equation:**
For any CSTR, the mole balance is given by \[ F_{A0}(1 - X) = F_{A0} - V_rkC_{A0}(1 - X)^2 \]
2. **Conversion Definition:**
The conversion of the reactant \(A\) can be defined as:
\[ X = (C_{A0} - C_A) / C_{A0} \]
3. **Separation into Two CSTRs:**
- Let \( X_1 \) be the conversion at the outlet of the first reactor.
- The overall conversion at the second reactor outlet, \( X_2 \), is given as 0.95.
Use the conversion balance at the first reactor to find \(X_1\).
**b) Space Time for Each Reactor:**
1. **Space Time (τ) Definition:**
Space time is defined by:
\[ \tau = \frac{V_r}{F_{A0}} \]
where \( V_r \) is the reactor volume, and \( F_{A0} \) is the volumetric flow rate of A.
2. **Calculate for Each Reactor:**
Using the conversions and reaction kinetics, calculate the space time required for both reactors.
**Note:** Specific values, kinetic constants, and volumetric flow rates are necessary to perform these calculations, so refer to additional data or experimental results if needed.
This problem approach is a common one in chemical reaction engineering, particularly in designing multiple reactors in series for optimal conversion and efficiency.
### References:
For further study, refer to textbooks such as "Elements of Chemical Reaction Engineering" by H. Scott Fogler, or
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