The rate constant k for a certain reaction is measured at two different temperatures: temperature k 10 116.0 °C 2.9 x 10 227.0 °C 8.4 x 10" Assuming the rate constant obeys the Arrhenius equation, calculate the activation energy Round vour answer to 2 significant digits.

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### Arrhenius Equation and Activation Energy Calculation

The rate constant \( k \) for a specific reaction is measured at two different temperatures as shown in the table below:

| Temperature (°C) | Rate Constant \( k \) (s⁻¹) |
|:-----------------:|:-----------------------------:|
| 116.0 °C          | \( 2.9 \times 10^{10} \)      |
| 227.0 °C          | \( 8.4 \times 10^{11} \)      |

### Objective:
Assuming the rate constant follows the Arrhenius equation, calculate the activation energy \( E_a \) for this reaction. Round your answer to 2 significant digits.

### Equation:
\[ E_a = \boxed{ \ \ \ \text{kJ mol}^{-1} \ \ \ } \]

### Steps to Calculate Activation Energy Using the Arrhenius Equation:

1. **Convert temperatures from Celsius to Kelvin:**
   - \( T_1 = 116.0 + 273.15 = 389.15 \, K \)
   - \( T_2 = 227.0 + 273.15 = 500.15 \, K \)

2. **Determine the natural logarithm of the rate constants:**
   - \( \ln(k_1) = \ln(2.9 \times 10^{10}) \)
   - \( \ln(k_2) = \ln(8.4 \times 10^{11}) \)

3. **Apply the Arrhenius equation in the natural logarithm form:**
   - \[ \ln(k) = \ln(A) - \frac{E_a}{R}\left(\frac{1}{T}\right) \]
   Where:
   - \( k \) is the rate constant,
   - \( A \) is the frequency factor,
   - \( E_a \) is the activation energy,
   - \( R \) is the gas constant (8.314 J/mol·K),
   - \( T \) is the temperature in Kelvin.

4. **Set up two equations with the natural logarithms of the rate constants and the respective temperatures:**

5. **Solve for the activation energy \( E_a \).**

### Conclusion:
After performing the calculations, input the computed activation energy in the boxed area provided in the image.

Note: Use
Transcribed Image Text:### Arrhenius Equation and Activation Energy Calculation The rate constant \( k \) for a specific reaction is measured at two different temperatures as shown in the table below: | Temperature (°C) | Rate Constant \( k \) (s⁻¹) | |:-----------------:|:-----------------------------:| | 116.0 °C | \( 2.9 \times 10^{10} \) | | 227.0 °C | \( 8.4 \times 10^{11} \) | ### Objective: Assuming the rate constant follows the Arrhenius equation, calculate the activation energy \( E_a \) for this reaction. Round your answer to 2 significant digits. ### Equation: \[ E_a = \boxed{ \ \ \ \text{kJ mol}^{-1} \ \ \ } \] ### Steps to Calculate Activation Energy Using the Arrhenius Equation: 1. **Convert temperatures from Celsius to Kelvin:** - \( T_1 = 116.0 + 273.15 = 389.15 \, K \) - \( T_2 = 227.0 + 273.15 = 500.15 \, K \) 2. **Determine the natural logarithm of the rate constants:** - \( \ln(k_1) = \ln(2.9 \times 10^{10}) \) - \( \ln(k_2) = \ln(8.4 \times 10^{11}) \) 3. **Apply the Arrhenius equation in the natural logarithm form:** - \[ \ln(k) = \ln(A) - \frac{E_a}{R}\left(\frac{1}{T}\right) \] Where: - \( k \) is the rate constant, - \( A \) is the frequency factor, - \( E_a \) is the activation energy, - \( R \) is the gas constant (8.314 J/mol·K), - \( T \) is the temperature in Kelvin. 4. **Set up two equations with the natural logarithms of the rate constants and the respective temperatures:** 5. **Solve for the activation energy \( E_a \).** ### Conclusion: After performing the calculations, input the computed activation energy in the boxed area provided in the image. Note: Use
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