Some measurements of the initial rate of a certain reaction are given in the table below. [₂] [H₂] initial rate of reaction 0.785 M 0.273 M 0.859 M/s 2.30M 0.273 M 2.52 M/s 0.785 M 0.347 M 1.39 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 2 significant digits. Also be sure your answer has the correct unit symbol. rate = & k = x10 X 00 5

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Chapter11: Chemical Kinetics
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### Initial Rate of Reaction Data Analysis

Some measurements of the initial rate of a certain reaction are given in the table below.

| [N\(_2\)] | [H\(_2\)] | Initial Rate of Reaction |
|:---------:|:---------:|:------------------------:|
| 0.785 M   | 0.273 M   | 0.859 M/s                |
| 2.30 M    | 0.273 M   | 2.52 M/s                 |
| 0.785 M   | 0.347 M   | 1.39 M/s                 |

Use this information to write a rate law for this reaction and calculate the value of the rate constant \( k \).

1. **Rate Law Expression**:
   
   The rate law for a reaction can be expressed in the form:
   \[
   \text{rate} = k [N_2]^x [H_2]^y
   \]

2. **Experimental Data Analysis**:
   
   By comparing the initial rates when one concentration is changed while the other is kept constant, you can determine the order of the reaction with respect to each reactant.

3. **Calculate the Rate Constant \( k \)**:

   Rearrange the formula to solve for \( k \):
   \[
   k = \frac{\text{rate}}{[N_2]^x [H_2]^y}
   \]

4. **Significant Figures and Units**:

   Ensure the calculated value for the rate constant is rounded to 2 significant digits and includes the proper unit.

5. **Example Calculation**:
    
    Suppose analysis yields the reaction orders \( x \) and \( y \). Substituting the values allows computation of \( k \), which will have the unit \(\text{M}^{-1}\text{s}^{-1}\) or similar, depending on the reaction orders.

### Editable Areas:

- **Rate Law Expression**:
   \[
   \text{rate} = k [N_2]^x [H_2]^y 
   \]
   Fill in the determined exponents \( x \) and \( y \).

- **Rate Constant \( k \)**:
  \[
  k = \text{value with correct units}
  \]

6. **Graphical/Diagram Descriptions**:

   The provided image includes an interactive space for calculating and entering
Transcribed Image Text:### Initial Rate of Reaction Data Analysis Some measurements of the initial rate of a certain reaction are given in the table below. | [N\(_2\)] | [H\(_2\)] | Initial Rate of Reaction | |:---------:|:---------:|:------------------------:| | 0.785 M | 0.273 M | 0.859 M/s | | 2.30 M | 0.273 M | 2.52 M/s | | 0.785 M | 0.347 M | 1.39 M/s | Use this information to write a rate law for this reaction and calculate the value of the rate constant \( k \). 1. **Rate Law Expression**: The rate law for a reaction can be expressed in the form: \[ \text{rate} = k [N_2]^x [H_2]^y \] 2. **Experimental Data Analysis**: By comparing the initial rates when one concentration is changed while the other is kept constant, you can determine the order of the reaction with respect to each reactant. 3. **Calculate the Rate Constant \( k \)**: Rearrange the formula to solve for \( k \): \[ k = \frac{\text{rate}}{[N_2]^x [H_2]^y} \] 4. **Significant Figures and Units**: Ensure the calculated value for the rate constant is rounded to 2 significant digits and includes the proper unit. 5. **Example Calculation**: Suppose analysis yields the reaction orders \( x \) and \( y \). Substituting the values allows computation of \( k \), which will have the unit \(\text{M}^{-1}\text{s}^{-1}\) or similar, depending on the reaction orders. ### Editable Areas: - **Rate Law Expression**: \[ \text{rate} = k [N_2]^x [H_2]^y \] Fill in the determined exponents \( x \) and \( y \). - **Rate Constant \( k \)**: \[ k = \text{value with correct units} \] 6. **Graphical/Diagram Descriptions**: The provided image includes an interactive space for calculating and entering
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