The problem involves using the Arrhenius equation to determine the rate constant at a given temperature. Here’s a breakdown of the problem:

Given Information:

1. Activation Energy, $E_a = 191 \, \text{kJ/mol}$
2. Rate constant at 562 K, $k_1 = 3.52 \times 10^{-7} \, \text{L/mol·s}$
3. Two temperatures: $T_1 = 562 \, \text{K}$ and $T_2 = 649 \, \text{K}$
4. The gas constant, $R = 8.3145 \, \text{J/mol·K}$

Formula:

We will use the Arrhenius equation in its logarithmic form for two temperatures: $\ln \left( \frac{k_2}{k_1} \right) = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right)$ Where:

• $k_1$ is the rate constant at $T_1$
• $k_2$ is the rate constant at $T_2$
• $E_a$ is the activation energy
• $R$ is the universal gas constant
• $T_1$ and $T_2$ are the initial and final temperatures, respectively.

Selected Required Information:

The boxes that should be checked are:

• $E_a = 191 \, \text{kJ/mol}$ (This is required to calculate the rate constant using the Arrhenius equation)
• $k_1 = 3.52 \times 10^{-7} \, \text{L/mol·s}$ (This is the known rate constant at $T_1$)
• $T_1 = 562 \, \text{K}$ and $T_2 = 649 \, \text{K}$ (These temperatures are needed to apply the Arrhenius equation)
• $R = 8.3145 \, \text{J/mol·K}$ (This is the gas constant in appropriate units)
• The formula provided: $\ln \left( \frac{k_2}{k_1} \right) = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right)$

Would you like to proceed with the calculation of the rate constant at 649 K?

Relative Questions:

1. How does the activation energy affect the rate constant in a reaction?
2. Can the Arrhenius equation be used for all types of chemical reactions?
3. Why is the rate constant dependent on temperature?
4. What happens to the rate constant when the temperature is significantly increased?
5. How is the gas constant $R$ related to the ideal gas law?

Tip:

Ensure that all units are consistent when applying the Arrhenius equation, particularly converting $E_a$ from kJ/mol to J/mol.