1. Fuel cells have been proposed for use in cars and for power generation as part of a hydrogen economy. They offer the advantages of higher efficiency and cleaner fuel with insignificant pollutants. The balanced reaction is: 2 H₂ + O₂ => 2 H₂O Hydrogen flows into a fuel cell operating at steady state at a rate of 42 lbmol/min. Air enters the fuel cell in a separate stream, at a flow rate that ensures that the oxygen is fed at 50% excess. 90% of the hydrogen entering the reactor gets reacted. Assume that all reactants and products are gaseous phase. All the left over reactants and created products leave the fuel cell in a single stream. Calculate the mole fraction of oxygen in the outlet stream.
1. Fuel cells have been proposed for use in cars and for power generation as part of a hydrogen economy. They offer the advantages of higher efficiency and cleaner fuel with insignificant pollutants. The balanced reaction is: 2 H₂ + O₂ => 2 H₂O Hydrogen flows into a fuel cell operating at steady state at a rate of 42 lbmol/min. Air enters the fuel cell in a separate stream, at a flow rate that ensures that the oxygen is fed at 50% excess. 90% of the hydrogen entering the reactor gets reacted. Assume that all reactants and products are gaseous phase. All the left over reactants and created products leave the fuel cell in a single stream. Calculate the mole fraction of oxygen in the outlet stream.
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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![### Fuel Cells in Hydrogen Economy
Fuel cells have been proposed for use in cars and for power generation as part of a hydrogen economy. They offer the advantages of higher efficiency and cleaner fuel with insignificant pollutants.
#### Reaction:
The balanced chemical reaction for the fuel cell is:
\[ 2 H_2 + O_2 \rightarrow 2 H_2O \]
Hydrogen flows into a fuel cell operating at a steady state at a rate of 42 lbmol/min. Air enters the fuel cell in a separate stream, at a flow rate that ensures that the oxygen is fed at 50% excess. 90% of the hydrogen entering the reactor gets reacted. Assume that all reactants and products are in gaseous phase. All the leftover reactants and created products leave the fuel cell in a single stream. Calculate the mole fraction of oxygen in the outlet stream.
#### Step-by-Step Explanation:
1. **Hydrogen Input:**
- Hydrogen flow rate: 42 lbmol/min
2. **Oxygen Requirement:**
- From the balanced reaction, 2 moles of \( H_2 \) require 1 mole of \( O_2 \).
- Moles of \( O_2 \) required for 42 lbmol/min of \( H_2 \):
\[\frac{42 \text{ lbmol/min}}{2} = 21 \text{ lbmol/min} \]
- With 50% excess oxygen, the oxygen feed rate:
\[ 21 \text{ lbmol/min} \times 1.5 = 31.5 \text{ lbmol/min} \]
3. **Hydrogen Reaction:**
- 90% of 42 lbmol/min of \( H_2 \) react:
\[ 0.9 \times 42 \text{ lbmol/min} = 37.8 \text{ lbmol/min} \]
- Leaving 10% unreacted \( H_2 \):
\[ 0.1 \times 42 \text{ lbmol/min} = 4.2 \text{ lbmol/min} \]
4. **Oxygen Consumption:**
- Corresponding \( O_2 \) consumed for reacted \( H_2 \):
\[\frac{37.8 \text{ lbmol/min}}{2} = 18.9 \text{](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F42d7a143-2adc-420d-86c3-225c6cc98b5a%2Fa2b5e61c-67fa-47d1-b12b-77ffd18b188f%2F5tisyx9_processed.png&w=3840&q=75)
Transcribed Image Text:### Fuel Cells in Hydrogen Economy
Fuel cells have been proposed for use in cars and for power generation as part of a hydrogen economy. They offer the advantages of higher efficiency and cleaner fuel with insignificant pollutants.
#### Reaction:
The balanced chemical reaction for the fuel cell is:
\[ 2 H_2 + O_2 \rightarrow 2 H_2O \]
Hydrogen flows into a fuel cell operating at a steady state at a rate of 42 lbmol/min. Air enters the fuel cell in a separate stream, at a flow rate that ensures that the oxygen is fed at 50% excess. 90% of the hydrogen entering the reactor gets reacted. Assume that all reactants and products are in gaseous phase. All the leftover reactants and created products leave the fuel cell in a single stream. Calculate the mole fraction of oxygen in the outlet stream.
#### Step-by-Step Explanation:
1. **Hydrogen Input:**
- Hydrogen flow rate: 42 lbmol/min
2. **Oxygen Requirement:**
- From the balanced reaction, 2 moles of \( H_2 \) require 1 mole of \( O_2 \).
- Moles of \( O_2 \) required for 42 lbmol/min of \( H_2 \):
\[\frac{42 \text{ lbmol/min}}{2} = 21 \text{ lbmol/min} \]
- With 50% excess oxygen, the oxygen feed rate:
\[ 21 \text{ lbmol/min} \times 1.5 = 31.5 \text{ lbmol/min} \]
3. **Hydrogen Reaction:**
- 90% of 42 lbmol/min of \( H_2 \) react:
\[ 0.9 \times 42 \text{ lbmol/min} = 37.8 \text{ lbmol/min} \]
- Leaving 10% unreacted \( H_2 \):
\[ 0.1 \times 42 \text{ lbmol/min} = 4.2 \text{ lbmol/min} \]
4. **Oxygen Consumption:**
- Corresponding \( O_2 \) consumed for reacted \( H_2 \):
\[\frac{37.8 \text{ lbmol/min}}{2} = 18.9 \text{
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