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Lindemann-Hinshelwood mechanism sample question

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The reaction of CO and Cl2 consists of a series of steps as outlined below: Write an expression for d[COCl]/dt and write the overall reaction.

Step rate constant
Cl2 + M -> 2 Cl + M k1
2 Cl + M -> Cl2 + M k-1
Cl + CO + M -> COCl + M k2
COCl + M -> Cl + CO + M k-2
COCl + Cl2 -> COCl2 + Cl k3
COCl2 + Cl -> COCl + Cl2 k-3

*M is usually taken to be an inert gas. See the Lindemann-Hinshelwood mechanism for details.
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The solution writes an expression and overall reaction for the sample question.

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