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The problem shown in the image asks for the rate constant \(k_2\) at 335 K for the decomposition reaction of \( \text{N}_2\text{O}_5 \), using the Arrhenius equation, given the rate constant \(k_1 = 6.34 \times 10^{-2} \, \text{min}^{-1}\) at 325 K and an activation energy \(E_a = 103 \, \text{kJ/mol}\).

To solve for \(k_2\), we use the two-point version of the Arrhenius equation:

\[
\ln \left( \frac{k_2}{k_1} \right) = \frac{E_a}{R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right)
\]

Where:
- \( k_1 = 6.34 \times 10^{-2} \, \text{min}^{-1} \) (rate constant at \( T_1 = 325 \, \text{K} \)),
- \( k_2 \) is the unknown rate constant at \( T_2 = 335 \, \text{K} \),
- \( E_a = 103 \, \text{kJ/mol} = 103000 \, \text{J/mol} \),
- \( R = 8.314 \, \text{J/mol·K} \) (the universal gas constant),
- \( T_1 = 325 \, \text{K} \),
- \( T_2 = 335 \, \text{K} \).

Let's compute \( k_2 \).The rate constant \( k_2 \) at 335 K is approximately \( 0.198 \, \text{min}^{-1} \).

Would you like further explanation or details on the steps involved?

Here are 5 related questions for further practice:
1. How does the Arrhenius equation change for reactions with different activation energies?
2. What happens to the rate constant if the temperature increases significantly?
3. How would the rate constant change if the activation energy were lower?
4. Can you apply the Arrhenius equation to reactions in the liquid phase?
5. How does the pre-exponential factor in the Arrhenius equation affect the rate constant?

**Tip:** Always ensure that activation energy and gas constant units are consistent when applying the Arrhenius equation.

The gas phase reaction 2 N2O5(g) → 4 NO2(g) + O2(g) has an activation energy of 103 kJ/mol, and the first order rate constant is 6.34×10^-2 min^-1 at 325 K. What is the rate constant at 335 K?

Learn how to calculate the rate constant for the decomposition of N2O5 at different temperatures using the Arrhenius equation. This problem provides a step-by-step solution to find the rate constant at 335 K, given activation energy and an initial rate constant at 325 K.

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