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# The rate constant for the decomposition of acetaldehyde, $\mathrm{CH}_3 \mathrm{CHO}$, to methane, $\mathrm{CH}_4$, and carbon monoxide, $\mathrm{CO}$, in the gas phase is $1.1 \times 10^{-2} \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at $703 \mathrm{~K}^{\text {and }} 4.95 \mathrm{~L} \mathrm{~mol}^{-1} \mathrm{~s}^{-1}$ at $865 \mathrm{~K}$. Determine the activation energy for this decomposition.

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To calculate for the frequency factor of the reaction, we can use the Arrhenius equation:

\begin{aligned}k = Ae^{\frac{-E_{a}}{RT}}\end{aligned}

where $k$ stands for the rate constant, $A$ stands for the frequency factor, $E_{a}$ stands for the activation energy, $R$ stands for the gas constant and $T$ stands for the temperature.

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