Some measurements of the initial rate of a certain reaction are given in the table below. [N₂] [H₂] initial rate of reaction 2.38M 1.39 M 0.140 M/s 10.8M 1.39 M 2.88 M/s 2.38M 0.584 M 0.0588 M/s Use this information to write a rate law for this reaction, and calculate the value of the rate constant k. Round your value for the rate constant to 3 significant digits. Also be sure your answer has the correct unit sym

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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
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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