Chemical Engineering
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The decomposition of acetaldehyde $(X)$ to methane and carbon monoxide follows four-step free radical mechanism. The overall rate of decomposition of $X$ is $$-r_X=k_2 \bigg( \dfrac{k_1}{2k_3} \bigg) ^{1/2} C_X^{3/2} =k_{\text{overall}}C_X^{3/2}$$ where $k_1, k_2$, and $k_3$ denote the rate constants of the elementary steps, with corresponding activation energies (in $kJ \: mol^{-1}$) of $320$, $40$, and $0$, respectively. The temperature dependency of the rate constants is described by Arrhenius equation. $C_X$ denotes the concentration of acetaldehyde. The rate constant for the overall reaction is $k_{\text{overall}}$. The activation energy for the overall reaction (in $kJ \: mol^{-1}$) is _______ (round off to nearest integer).
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