We’re being asked to find the fraction of the ethyl chloride that decomposes in 16 minutes at this 720 K. We first need to calculate the rate constant of the reaction.

This means we need to use the ** Arrhenius Equation**:

$\overline{){\mathbf{k}}{\mathbf{=}}{{\mathbf{Ae}}}^{\raisebox{1ex}{$\mathbf{-}{\mathbf{E}}_{\mathbf{a}}$}\!\left/ \!\raisebox{-1ex}{$\mathbf{RT}$}\right.}}$

where:

**k** = rate constant**E _{a}** = activation energy (in J/mol)

**Given**:**E _{a}**

Ethyl chloride vapor decomposes by the first-order reaction C_{2}H_{5}Cl → C_{2}H_{4} + HCl. The activation energy is 249 kJ/mol and the frequency factor is 1.6×10^{14} s^{-1}.

Find the fraction of the ethyl chloride that decomposes in 16 minutes at this 720 K.

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