The reaction : \( \mathrm{CO}+\mathrm{Cl}_{2} \rightarrow \mathrm{COCl}_{2} \) has the following...

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The reaction : \( \mathrm{CO}+\mathrm{Cl}_{2} \rightarrow \mathrm{COCl}_{2} \) has the following mechanism. Derive the rate expression :
\[
\mathrm{Cl}+\mathrm{CO} \underset{K_{2}^{\prime}}{\stackrel{K_{1}^{\prime}}{\rightleftharpoons}} \mathrm{COCl} \quad \text { (fast) }
\]
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