Chemistry
10th Edition
ISBN: 9781305957404
Author: Steven S. Zumdahl, Susan A. Zumdahl, Donald J. DeCoste
Publisher: Cengage Learning
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![### Determining the Rate Law and Rate Constant for a Reaction
The following table shows some measurements of the initial rate of a certain reaction:
| \([N_2]\) (M) | \([H_2]\) (M) | Initial Rate of Reaction (M/s) |
|---------------|---------------|-------------------------------|
| 2.38 M | 1.39 M | 0.140 M/s |
| 10.8 M | 1.39 M | 2.88 M/s |
| 2.38 M | 0.584 M | 0.0588 M/s |
Using the provided data, one can determine the rate law for this reaction and calculate the value of the rate constant \( k \).
### Steps to Solve:
1. **Write the Rate Law Expression:**
The general form of the rate law is:
\[
\text{rate} = k [N_2]^m [H_2]^n
\]
where \( k \) is the rate constant, and \( m \) and \( n \) are the orders of the reaction with respect to nitrogen and hydrogen, respectively.
2. **Determine the Reaction Orders \( m \) and \( n \):**
- Compare Experiment 1 and Experiment 2 to determine \( m \):
\[
\frac{\text{rate}_2}{\text{rate}_1} = \frac{k [N_2]_2^m [H_2]_2^n}{k [N_2]_1^m [H_2]_1^n} = \frac{2.88}{0.140}
\]
\[
\frac{[N_2]_2}{[N_2]_1}^m = \frac{10.8}{2.38}^m = 20.57 (simplified)
\]
Solving for \( m \), the change in nitrogen concentration leads to a corresponding change in the rate, so:
\[
m = 2
\]
- Compare Experiment 1 and Experiment 3 to determine \( n \):
\[
\frac{\text{rate}_3}{\text{rate}_1} = \frac{k [N_2]_3^m [H_2]_3^n](https://content.bartleby.com/qna-images/question/550116fe-4392-44b3-9444-167bfb5405dc/e49cd507-59ff-470d-aeef-69b18006442f/nj4fodk_processed.jpeg)
Transcribed Image Text:### Determining the Rate Law and Rate Constant for a Reaction
The following table shows some measurements of the initial rate of a certain reaction:
| \([N_2]\) (M) | \([H_2]\) (M) | Initial Rate of Reaction (M/s) |
|---------------|---------------|-------------------------------|
| 2.38 M | 1.39 M | 0.140 M/s |
| 10.8 M | 1.39 M | 2.88 M/s |
| 2.38 M | 0.584 M | 0.0588 M/s |
Using the provided data, one can determine the rate law for this reaction and calculate the value of the rate constant \( k \).
### Steps to Solve:
1. **Write the Rate Law Expression:**
The general form of the rate law is:
\[
\text{rate} = k [N_2]^m [H_2]^n
\]
where \( k \) is the rate constant, and \( m \) and \( n \) are the orders of the reaction with respect to nitrogen and hydrogen, respectively.
2. **Determine the Reaction Orders \( m \) and \( n \):**
- Compare Experiment 1 and Experiment 2 to determine \( m \):
\[
\frac{\text{rate}_2}{\text{rate}_1} = \frac{k [N_2]_2^m [H_2]_2^n}{k [N_2]_1^m [H_2]_1^n} = \frac{2.88}{0.140}
\]
\[
\frac{[N_2]_2}{[N_2]_1}^m = \frac{10.8}{2.38}^m = 20.57 (simplified)
\]
Solving for \( m \), the change in nitrogen concentration leads to a corresponding change in the rate, so:
\[
m = 2
\]
- Compare Experiment 1 and Experiment 3 to determine \( n \):
\[
\frac{\text{rate}_3}{\text{rate}_1} = \frac{k [N_2]_3^m [H_2]_3^n
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