Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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![**Problem:**
If 67.0 grams of carbonic acid are sealed in a 2.00 L soda bottle at room temperature (298.15 K) and decompose completely via the equation below, what would be the final pressure of carbon dioxide (in atm) assuming it had the full 2.00 L in which to expand?
\[ \text{H}_2\text{CO}_3(\text{aq}) \rightarrow \text{H}_2\text{O}(\text{l}) + \text{CO}_2(\text{g}) \]
**Explanation:**
This problem involves decomposing carbonic acid in a soda bottle to find the final pressure exerted by the carbon dioxide gas produced. Here's a step-by-step guide to solving it:
1. **Calculate the number of moles of carbonic acid (H₂CO₃):**
- Use the molar mass of carbonic acid, which is approximately 62.03 g/mol.
- Number of moles \( n \) = \(\frac{\text{Mass}}{\text{Molar mass}} = \frac{67.0 \ \text{g}}{62.03 \ \text{g/mol}} \).
2. **Determine the moles of carbon dioxide (CO₂) produced:**
- The balanced chemical equation shows a 1:1 molar ratio between carbonic acid and carbon dioxide.
- Therefore, the moles of CO₂ will be the same as the moles of H₂CO₃.
3. **Use the Ideal Gas Law to find the final pressure:**
- Ideal Gas Law: \( PV = nRT \), where:
- \( P \) = pressure,
- \( V \) = volume (2.00 L),
- \( n \) = number of moles of CO₂,
- \( R \) = gas constant (0.0821 L atm / K mol),
- \( T \) = temperature (298.15 K).
4. **Solve for \( P \):**
- Rearrange the Ideal Gas Law to \( P = \frac{nRT}{V} \).
5. **Substitute the values and calculate:**
- Calculate the number of moles of CO₂.
- Plug the values into the appropriate places and solve for the pressure in atm.](https://content.bartleby.com/qna-images/question/44982666-d339-4885-b9e9-36706f6e8dd1/7f17e691-cf17-4539-b76e-52482d879da6/ngv4pdg_processed.png)
Transcribed Image Text:**Problem:**
If 67.0 grams of carbonic acid are sealed in a 2.00 L soda bottle at room temperature (298.15 K) and decompose completely via the equation below, what would be the final pressure of carbon dioxide (in atm) assuming it had the full 2.00 L in which to expand?
\[ \text{H}_2\text{CO}_3(\text{aq}) \rightarrow \text{H}_2\text{O}(\text{l}) + \text{CO}_2(\text{g}) \]
**Explanation:**
This problem involves decomposing carbonic acid in a soda bottle to find the final pressure exerted by the carbon dioxide gas produced. Here's a step-by-step guide to solving it:
1. **Calculate the number of moles of carbonic acid (H₂CO₃):**
- Use the molar mass of carbonic acid, which is approximately 62.03 g/mol.
- Number of moles \( n \) = \(\frac{\text{Mass}}{\text{Molar mass}} = \frac{67.0 \ \text{g}}{62.03 \ \text{g/mol}} \).
2. **Determine the moles of carbon dioxide (CO₂) produced:**
- The balanced chemical equation shows a 1:1 molar ratio between carbonic acid and carbon dioxide.
- Therefore, the moles of CO₂ will be the same as the moles of H₂CO₃.
3. **Use the Ideal Gas Law to find the final pressure:**
- Ideal Gas Law: \( PV = nRT \), where:
- \( P \) = pressure,
- \( V \) = volume (2.00 L),
- \( n \) = number of moles of CO₂,
- \( R \) = gas constant (0.0821 L atm / K mol),
- \( T \) = temperature (298.15 K).
4. **Solve for \( P \):**
- Rearrange the Ideal Gas Law to \( P = \frac{nRT}{V} \).
5. **Substitute the values and calculate:**
- Calculate the number of moles of CO₂.
- Plug the values into the appropriate places and solve for the pressure in atm.
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