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Use lindemann mechanisms to find reaction kinetics

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In the discussion of the Lindemann mechanism, it was assumed that the rate of activation by collisions with another reactant molecule, A, was the same with a non-reactant molecule, M, such as an inert gas. What if the rates of activation for these two process are different? In this case, the mechanism become

k1
A +M ?A* + M
k-1

k2
A +A ?A* + A
k-2

k3
A* ? P

Demonstrate that the rate law expression for this mechanism is:

R= (k3(k1[A][M]+k2[A]^2)/(k-1[M]+k-2[A]+k3)

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