PROBLEM: Many gaseous reactions occur in a car engine and exhaust system. One such reaction is as follows: NO2(8) + CO(g) NO(g) + CO2(g) rate = k[NO2]"[co]" %3D Use the following data to determine the individual and overall reaction orders. experiment initial rate (mol/L•s) initial [NO2] (mol/L) initial [CO] (mol/L) 1 0.0050 0.10 0.10 2 0.080 0.40 0.10 0.0050 0.10 0.20 Solve for each reactant using the general rate law by applying the method described previously. PLAN:

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### Sample Problem 16.3: Determining Reaction Order from Initial Rate Data

#### Problem:
Many gaseous reactions occur in a car engine and exhaust system. One such reaction is as follows:

\[ \text{NO}_2(g) + \text{CO}(g) \rightarrow \text{NO}(g) + \text{CO}_2(g) \]
\[ \text{rate} = k[\text{NO}_2]^m[\text{CO}]^n \]

Use the following data to determine the individual and overall reaction orders.

#### Data:

<table>
  <tr>
    <th>Experiment</th>
    <th>Initial Rate (mol/L·s)</th>
    <th>Initial [NO<sub>2</sub>] (mol/L)</th>
    <th>Initial [CO] (mol/L)</th>
  </tr>
  <tr>
    <td>1</td>
    <td>0.0050</td>
    <td>0.10</td>
    <td>0.10</td>
  </tr>
  <tr>
    <td>2</td>
    <td>0.080</td>
    <td>0.40</td>
    <td>0.10</td>
  </tr>
  <tr>
    <td>3</td>
    <td>0.0050</td>
    <td>0.10</td>
    <td>0.20</td>
  </tr>
</table>

#### Plan:
Solve for each reactant using the general rate law by applying the method described previously. 

This problem entails calculating the order of reaction with respect to nitrogen dioxide (\(\text{NO}_2\)) and carbon monoxide (\(\text{CO}\)), as well as determining the overall order of the reaction. To achieve this, we need to analyze the changes in the initial rates based on the provided concentration data for each experiment, using the rate law equation provided.
Transcribed Image Text:### Sample Problem 16.3: Determining Reaction Order from Initial Rate Data #### Problem: Many gaseous reactions occur in a car engine and exhaust system. One such reaction is as follows: \[ \text{NO}_2(g) + \text{CO}(g) \rightarrow \text{NO}(g) + \text{CO}_2(g) \] \[ \text{rate} = k[\text{NO}_2]^m[\text{CO}]^n \] Use the following data to determine the individual and overall reaction orders. #### Data: <table> <tr> <th>Experiment</th> <th>Initial Rate (mol/L·s)</th> <th>Initial [NO<sub>2</sub>] (mol/L)</th> <th>Initial [CO] (mol/L)</th> </tr> <tr> <td>1</td> <td>0.0050</td> <td>0.10</td> <td>0.10</td> </tr> <tr> <td>2</td> <td>0.080</td> <td>0.40</td> <td>0.10</td> </tr> <tr> <td>3</td> <td>0.0050</td> <td>0.10</td> <td>0.20</td> </tr> </table> #### Plan: Solve for each reactant using the general rate law by applying the method described previously. This problem entails calculating the order of reaction with respect to nitrogen dioxide (\(\text{NO}_2\)) and carbon monoxide (\(\text{CO}\)), as well as determining the overall order of the reaction. To achieve this, we need to analyze the changes in the initial rates based on the provided concentration data for each experiment, using the rate law equation provided.
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