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Question

For the formation of phosgene from CO(g) and chlorine, CO(g)+Cl2(g)COCl2(g), the experimentally determined rate equation is, d[COCl2]dt=k[CO][Cl2]3/2.
Is the following mechanism consistent with the rate equation?
(i) Cl22Cl (fast)
(ii) Cl+COCOCl (fast)
(iii) COCl+Cl2COCl2+Cl (slow)

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Solution

Multiplying equation (ii) by 2 and adding (i), we get:
Cl2+2CO2COCl
K=[COCl]2[Cl2][CO]2
[COCl]=(K)1/2[Cl2]1/2[CO] ....(i)
Slowest step is rate determining, hence,
Rate =k[COCl][Cl2] ...(ii)
From equations (i) and (ii), we get
Rate =kK1/2[Cl2]1/2[Cl2][CO]
Rate =k[Cl2]3/2[CO]
Thus, rate law is in accordance with the mechanism.

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