Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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![**Determining a Rate Law from Changes in Concentration Over Time**
A chemistry graduate student is analyzing the rate of the following chemical reaction:
\[ \text{H}_2\text{CO}_3 (\text{aq}) \rightarrow \text{H}_2\text{O} (\text{aq}) + \text{CO}_2 (\text{aq}) \]
The student fills a reaction vessel with \(\text{H}_2\text{CO}_3\) and monitors its concentration as the reaction proceeds over time.
The following table presents data on the concentration of \(\text{H}_2\text{CO}_3\) at various time intervals:
| Time (seconds) | \([\text{H}_2\text{CO}_3]\) (M) |
|----------------|--------------------------|
| 0.00 | 0.0100 |
| 0.10 | 0.00499 |
| 0.20 | 0.00333 |
| 0.30 | 0.00250 |
| 0.40 | 0.00200 |
**Using this data, answer the following questions:**
1. **Write the rate law for this reaction.**
The rate law generally takes the form:
\[ \text{rate} = k [\text{H}_2\text{CO}_3]^n \]
where \( k \) is the rate constant, and \( n \) is the order of the reaction which must be determined based on the given data.
2. **Calculate the value of the rate constant \( k \).**
Using the given data:
- Determine the order \( n \) of the reaction.
- Use the initial concentrations and rate to solve for \( k \).
Round your calculated value of \( k \) to 2 significant digits. Ensure your final answer includes the correct unit symbol for \( k \).
**Explanation:**
When studying reaction rates, the concentration of reactants can be monitored over time to determine how quickly the reactants are consumed. By plotting concentration vs. time (or performing calculations), one can determine the reaction order and rate constant. The order of a reaction indicates how the rate is affected by the concentration of reactants, which is critical for understanding reaction kinetics and mechanisms.
**Interactive Components:**
Below the given](https://content.bartleby.com/qna-images/question/4100c518-1a8f-4898-88a2-d0f1a7669694/ed58b9a7-cbee-4461-9385-3103d4cef7b2/594w09k_processed.jpeg)
Transcribed Image Text:**Determining a Rate Law from Changes in Concentration Over Time**
A chemistry graduate student is analyzing the rate of the following chemical reaction:
\[ \text{H}_2\text{CO}_3 (\text{aq}) \rightarrow \text{H}_2\text{O} (\text{aq}) + \text{CO}_2 (\text{aq}) \]
The student fills a reaction vessel with \(\text{H}_2\text{CO}_3\) and monitors its concentration as the reaction proceeds over time.
The following table presents data on the concentration of \(\text{H}_2\text{CO}_3\) at various time intervals:
| Time (seconds) | \([\text{H}_2\text{CO}_3]\) (M) |
|----------------|--------------------------|
| 0.00 | 0.0100 |
| 0.10 | 0.00499 |
| 0.20 | 0.00333 |
| 0.30 | 0.00250 |
| 0.40 | 0.00200 |
**Using this data, answer the following questions:**
1. **Write the rate law for this reaction.**
The rate law generally takes the form:
\[ \text{rate} = k [\text{H}_2\text{CO}_3]^n \]
where \( k \) is the rate constant, and \( n \) is the order of the reaction which must be determined based on the given data.
2. **Calculate the value of the rate constant \( k \).**
Using the given data:
- Determine the order \( n \) of the reaction.
- Use the initial concentrations and rate to solve for \( k \).
Round your calculated value of \( k \) to 2 significant digits. Ensure your final answer includes the correct unit symbol for \( k \).
**Explanation:**
When studying reaction rates, the concentration of reactants can be monitored over time to determine how quickly the reactants are consumed. By plotting concentration vs. time (or performing calculations), one can determine the reaction order and rate constant. The order of a reaction indicates how the rate is affected by the concentration of reactants, which is critical for understanding reaction kinetics and mechanisms.
**Interactive Components:**
Below the given
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