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: McGraw-Hill Education
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- A) Construct a complete stoichiometric table for the molar flow rate and gas-phase concentrations using the correct limiting reactant
![### Gas Phase Reaction
The reaction is as follows:
\[ \frac{1}{2} \text{N}_2 + \frac{3}{2} \text{H}_2 \rightarrow \text{NH}_3 \]
This reaction is to be carried out isothermally in a flow reactor. The molar feed composition is 50% \(\text{H}_2\) and 50% \(\text{N}_2\). The reaction conditions are set at a pressure of 16.4 atm and a temperature of 227°C.](https://content.bartleby.com/qna-images/question/d47fc2c3-8f4b-4085-b234-bc909be774e3/d74bf648-024c-4b76-8ced-e6281233dea4/ttju3uc_processed.png)
Transcribed Image Text:### Gas Phase Reaction
The reaction is as follows:
\[ \frac{1}{2} \text{N}_2 + \frac{3}{2} \text{H}_2 \rightarrow \text{NH}_3 \]
This reaction is to be carried out isothermally in a flow reactor. The molar feed composition is 50% \(\text{H}_2\) and 50% \(\text{N}_2\). The reaction conditions are set at a pressure of 16.4 atm and a temperature of 227°C.
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![**C) Suppose by chance, the reaction is elementary with rate constant \( k_{N_2} = \frac{40 \, \text{dm}^3}{\text{mol} \cdot \text{s}} \). Write the rate of reaction solely as a function of conversion for (i) a flow reactor and (ii) a constant volume batch reactor.**
In this problem, you are asked to express the rate of reaction as a function of conversion for two types of reactors: a flow reactor and a constant volume batch reactor. The rate constant \( k_{N_2} \) is given as \( \frac{40 \, \text{dm}^3}{\text{mol} \cdot \text{s}} \), which indicates the reaction follows elementary kinetics.
### Explanation:
- **Flow Reactor:** This typically refers to a plug flow reactor (PFR) or continuous stirred-tank reactor (CSTR), where concentration continuously changes and is related to conversion \( X \). The design equation for flow reactors often comes in the form of:
\[
-r_A = \frac{F_{A0}}{V}X
\]
where \( -r_A \) is the rate of reaction, \( F_{A0} \) is the molar flow rate of the reactant \( A \), \( V \) is the reactor volume, and \( X \) is the conversion.
- **Constant Volume Batch Reactor:** In this setup, the volume of the reactor does not change as the reaction progresses. The rate of reaction is related to the change in concentration over time:
\[
-r_A = \frac{dC_A}{dt}
\]
Given the elementary nature of the reaction, expressions for \( C_A \) can be aligned to conversion \( X \).
Both these scenarios leverage the rate constant to model the system kinetics accurately. Understanding these concepts is crucial for chemical reaction engineering and reactor design.](https://content.bartleby.com/qna-images/question/d47fc2c3-8f4b-4085-b234-bc909be774e3/c500fde3-6589-40a4-a9cc-46cbe9ae959c/d678ulk_processed.png)
Transcribed Image Text:**C) Suppose by chance, the reaction is elementary with rate constant \( k_{N_2} = \frac{40 \, \text{dm}^3}{\text{mol} \cdot \text{s}} \). Write the rate of reaction solely as a function of conversion for (i) a flow reactor and (ii) a constant volume batch reactor.**
In this problem, you are asked to express the rate of reaction as a function of conversion for two types of reactors: a flow reactor and a constant volume batch reactor. The rate constant \( k_{N_2} \) is given as \( \frac{40 \, \text{dm}^3}{\text{mol} \cdot \text{s}} \), which indicates the reaction follows elementary kinetics.
### Explanation:
- **Flow Reactor:** This typically refers to a plug flow reactor (PFR) or continuous stirred-tank reactor (CSTR), where concentration continuously changes and is related to conversion \( X \). The design equation for flow reactors often comes in the form of:
\[
-r_A = \frac{F_{A0}}{V}X
\]
where \( -r_A \) is the rate of reaction, \( F_{A0} \) is the molar flow rate of the reactant \( A \), \( V \) is the reactor volume, and \( X \) is the conversion.
- **Constant Volume Batch Reactor:** In this setup, the volume of the reactor does not change as the reaction progresses. The rate of reaction is related to the change in concentration over time:
\[
-r_A = \frac{dC_A}{dt}
\]
Given the elementary nature of the reaction, expressions for \( C_A \) can be aligned to conversion \( X \).
Both these scenarios leverage the rate constant to model the system kinetics accurately. Understanding these concepts is crucial for chemical reaction engineering and reactor design.
Solution
by Bartleby Expert
Follow-up Question
plz help w next question
Transcribed Image Text:B) Express the concentrations in \(\frac{\text{mol}}{\text{dm}^3}\) of each for the reacting species as a function of conversion.
Evaluate \(C_{A0}, \delta, \varepsilon\) then calculate the concentration of ammonia and hydrogen when the conversion of H\(_2\) is 75%.
Solution
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Follow-up Questions
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Follow-up Question
will u plz help with the last follow up question
Transcribed Image Text:**C) Suppose by chance, the reaction is elementary with rate constant \( k_{N_2} = \frac{40 \, \text{dm}^3}{\text{mol} \cdot \text{s}} \). Write the rate of reaction solely as a function of conversion for (i) a flow reactor and (ii) a constant volume batch reactor.**
In this problem, you are asked to express the rate of reaction as a function of conversion for two types of reactors: a flow reactor and a constant volume batch reactor. The rate constant \( k_{N_2} \) is given as \( \frac{40 \, \text{dm}^3}{\text{mol} \cdot \text{s}} \), which indicates the reaction follows elementary kinetics.
### Explanation:
- **Flow Reactor:** This typically refers to a plug flow reactor (PFR) or continuous stirred-tank reactor (CSTR), where concentration continuously changes and is related to conversion \( X \). The design equation for flow reactors often comes in the form of:
\[
-r_A = \frac{F_{A0}}{V}X
\]
where \( -r_A \) is the rate of reaction, \( F_{A0} \) is the molar flow rate of the reactant \( A \), \( V \) is the reactor volume, and \( X \) is the conversion.
- **Constant Volume Batch Reactor:** In this setup, the volume of the reactor does not change as the reaction progresses. The rate of reaction is related to the change in concentration over time:
\[
-r_A = \frac{dC_A}{dt}
\]
Given the elementary nature of the reaction, expressions for \( C_A \) can be aligned to conversion \( X \).
Both these scenarios leverage the rate constant to model the system kinetics accurately. Understanding these concepts is crucial for chemical reaction engineering and reactor design.
Solution
by Bartleby Expert
Follow-up Question
plz help w next question
Transcribed Image Text:B) Express the concentrations in \(\frac{\text{mol}}{\text{dm}^3}\) of each for the reacting species as a function of conversion.
Evaluate \(C_{A0}, \delta, \varepsilon\) then calculate the concentration of ammonia and hydrogen when the conversion of H\(_2\) is 75%.
Solution
by Bartleby Expert
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