The rate constant k for the order gas phase decomposition of ethyl iodide, `C_2H_5l rarrC_2H_4+Hl` is `1.60xx10^(-5)s^(-1)` ar 600 K and `6.36xx10^(-3)s^(-1)` at 700 K. Calculate the energy of activation for this reaction.

Explanation

To calculate the energy of activation (Ea) for the decomposition of ethyl iodide, we can use the Arrhenius equation in the form of the logarithmic relationship between the rate constants at two different temperatures. The equation is given by:

\[ \log \left(\frac{k_2}{k_1}\right) = \frac{E_a}{2.303R} \left( \frac{1}{T_1} - \frac{1}{T_2} \right) \]

Where:
- \( k_1 = 1.60 \times 10^{-5} \, s^{-1} \) at \( T_1 = 600 \, K \)
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