Using the data in the table, determine the rate constant of the Trial [A] (M) [B] (М) | Rate (M/s) reaction and select the appropriate units. 1 0.210 0.360 0.0175 0.210 0.720 0.0175 A + 2B → C +D 3 0.420 0.360 0.0700 k = Units 0.183 M-'s-1 Incorrect
Using the data in the table, determine the rate constant of the Trial [A] (M) [B] (М) | Rate (M/s) reaction and select the appropriate units. 1 0.210 0.360 0.0175 0.210 0.720 0.0175 A + 2B → C +D 3 0.420 0.360 0.0700 k = Units 0.183 M-'s-1 Incorrect
Chemistry
10th Edition
ISBN:9781305957404
Author:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher:Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Chapter1: Chemical Foundations
Section: Chapter Questions
Problem 1RQ: Define and explain the differences between the following terms. a. law and theory b. theory and...
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![### Determining the Rate Constant of a Reaction
**Objective**: Using the data in the table, determine the rate constant \( k \) of the reaction and select the appropriate units.
**Reaction**:
\[ A + 2B \rightarrow C + D \]
### Data Table
| Trial | \([A]\) (M) | \([B]\) (M) | Rate (M/s) |
|-------|-------------|-------------|------------|
| 1 | 0.210 | 0.360 | 0.0175 |
| 2 | 0.210 | 0.720 | 0.0175 |
| 3 | 0.420 | 0.360 | 0.0700 |
### Rate Constant Calculation
**Incorrect Value Entered**:
\[ k = 0.183 \]
**Correct Units**:
\[ \text{Units} = M^{-1}s^{-1} \]
### Explanation
- **Trial Analysis**:
- **Trial 1 and 2**: Comparing the data, \([A]\) remains constant while \([B]\) is doubled, but the rate does not change. This indicates that the reaction rate is independent of the concentration of B.
- **Trial 1 and 3**: Here, \([A]\) is doubled while \([B]\) remains constant, and the rate increases by a factor of 4. This suggests that the reaction order with respect to A is 2.
- **Rate Law Expression**:
\[ \text{Rate} = k[A]^2[B]^0 \]
Simplifies to:
\[ \text{Rate} = k[A]^2 \]
- **Determining \( k \) Using Trial 1**:
\[ 0.0175 \, M/s = k (0.210 \, M)^2 \]
\[ k = \frac{0.0175}{(0.210)^2} \]
\[ k = 0.397 \, M^{-1}s^{-1} \]
#### Conclusion:
\[ k = 0.397 \, M^{-1}s^{-1} \]
The previously entered value \( k = 0.183 \) was incorrect. Based on the data and correct analysis,](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff00f8b75-2bac-4335-a200-62a4fa07a89d%2F7f930bc3-86f4-4345-8bed-e369b6897c69%2Fm6zehwa_processed.png&w=3840&q=75)
Transcribed Image Text:### Determining the Rate Constant of a Reaction
**Objective**: Using the data in the table, determine the rate constant \( k \) of the reaction and select the appropriate units.
**Reaction**:
\[ A + 2B \rightarrow C + D \]
### Data Table
| Trial | \([A]\) (M) | \([B]\) (M) | Rate (M/s) |
|-------|-------------|-------------|------------|
| 1 | 0.210 | 0.360 | 0.0175 |
| 2 | 0.210 | 0.720 | 0.0175 |
| 3 | 0.420 | 0.360 | 0.0700 |
### Rate Constant Calculation
**Incorrect Value Entered**:
\[ k = 0.183 \]
**Correct Units**:
\[ \text{Units} = M^{-1}s^{-1} \]
### Explanation
- **Trial Analysis**:
- **Trial 1 and 2**: Comparing the data, \([A]\) remains constant while \([B]\) is doubled, but the rate does not change. This indicates that the reaction rate is independent of the concentration of B.
- **Trial 1 and 3**: Here, \([A]\) is doubled while \([B]\) remains constant, and the rate increases by a factor of 4. This suggests that the reaction order with respect to A is 2.
- **Rate Law Expression**:
\[ \text{Rate} = k[A]^2[B]^0 \]
Simplifies to:
\[ \text{Rate} = k[A]^2 \]
- **Determining \( k \) Using Trial 1**:
\[ 0.0175 \, M/s = k (0.210 \, M)^2 \]
\[ k = \frac{0.0175}{(0.210)^2} \]
\[ k = 0.397 \, M^{-1}s^{-1} \]
#### Conclusion:
\[ k = 0.397 \, M^{-1}s^{-1} \]
The previously entered value \( k = 0.183 \) was incorrect. Based on the data and correct analysis,
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