Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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![### Combustion of Ethane Problem
**Problem Statement:**
5.60 L of \( \text{C}_2\text{H}_6 \) is completely combusted at 0.500 bar and 313 K according to the reaction below. During the reaction, the pressure and temperature change. In the end, 9.23 L of \( \text{CO}_2 \) are produced and the total pressure of the reaction vessel is 1.56 bar. What is the final temperature of the reaction vessel? (R = 0.08314 L·bar/mol·K)
**Chemical Reaction:**
\[ 2\text{C}_2\text{H}_6(g) + 7\text{O}_2(g) \rightarrow 4\text{CO}_2(g) + 6\text{H}_2\text{O}(g) \]
### Explanation:
This problem involves the combustion of ethane (\( \text{C}_2\text{H}_6 \)), which is a hydrocarbon, in the presence of oxygen (\( \text{O}_2 \)) to produce carbon dioxide (\( \text{CO}_2 \)) and water (\( \text{H}_2\text{O} \)). The reaction is conducted in a controlled environment where the initial pressure and temperature are known, and the final pressure and volume of \( \text{CO}_2 \) produced are given.
**Key Concepts:**
1. **Ideal Gas Law:**
Use the ideal gas law \( PV = nRT \) to relate pressure (P), volume (V), temperature (T), and amount of gas (n, in moles).
2. **Stoichiometry:**
The balanced equation provides the molar ratio for the reactants and products, which is crucial for calculating the amounts of substances.
3. **Calculating Final Temperature:**
- Calculate the moles of \( \text{C}_2\text{H}_6 \) initially.
- Determine the moles of \( \text{CO}_2 \) produced using the ideal gas law.
- Use the stoichiometry of the reaction to find the relationship between the reactants and products.
- Apply the ideal gas law again to determine the final temperature of the gas mixture.
This type of problem is common in chemistry courses to demonstrate the application of gas laws](https://content.bartleby.com/qna-images/question/ce0e1f50-5655-4918-bba8-458441e12ec5/4d9d858e-0082-455f-97b1-f62166acc25e/z541cqw_processed.jpeg)
Transcribed Image Text:### Combustion of Ethane Problem
**Problem Statement:**
5.60 L of \( \text{C}_2\text{H}_6 \) is completely combusted at 0.500 bar and 313 K according to the reaction below. During the reaction, the pressure and temperature change. In the end, 9.23 L of \( \text{CO}_2 \) are produced and the total pressure of the reaction vessel is 1.56 bar. What is the final temperature of the reaction vessel? (R = 0.08314 L·bar/mol·K)
**Chemical Reaction:**
\[ 2\text{C}_2\text{H}_6(g) + 7\text{O}_2(g) \rightarrow 4\text{CO}_2(g) + 6\text{H}_2\text{O}(g) \]
### Explanation:
This problem involves the combustion of ethane (\( \text{C}_2\text{H}_6 \)), which is a hydrocarbon, in the presence of oxygen (\( \text{O}_2 \)) to produce carbon dioxide (\( \text{CO}_2 \)) and water (\( \text{H}_2\text{O} \)). The reaction is conducted in a controlled environment where the initial pressure and temperature are known, and the final pressure and volume of \( \text{CO}_2 \) produced are given.
**Key Concepts:**
1. **Ideal Gas Law:**
Use the ideal gas law \( PV = nRT \) to relate pressure (P), volume (V), temperature (T), and amount of gas (n, in moles).
2. **Stoichiometry:**
The balanced equation provides the molar ratio for the reactants and products, which is crucial for calculating the amounts of substances.
3. **Calculating Final Temperature:**
- Calculate the moles of \( \text{C}_2\text{H}_6 \) initially.
- Determine the moles of \( \text{CO}_2 \) produced using the ideal gas law.
- Use the stoichiometry of the reaction to find the relationship between the reactants and products.
- Apply the ideal gas law again to determine the final temperature of the gas mixture.
This type of problem is common in chemistry courses to demonstrate the application of gas laws
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