Derive a rate law from a mechanism (rates of reactions)

[qwedsa]

Homework Statement

The reaction: CO + Cl <-> COCl2
has the rate law: rate = k[CO][Cl2]^(3/2)

Show that this rate law is consistent with the mechanism:

Cl2 <-> 2Cl (fast)
Cl + CO <-> COCl (fast)
Cl2 + COCl -> COCl2 + Cl (slow)

(i don't know how to do superscript and subscript on here. in Cl2, the 2 should be subscsript, and ^(3/2) means that the reaction is 3/2 order with respect to Cl2)

The Attempt at a Solution

when you derive a rate law from a proposed mechanism, you usually start with the slow reaction...

rate = k[Cl2][COCl]

if i didn't know beforehand that the reaction is 3/2 order with respect to Cl2, i'd say k[COCl]=k-1[CO] => rate = k[Cl2][CO] but apparently this is incorrent. i am not sure how to proceed with the problem

 

[epenguin]

While the last reaction is proceeding slowly, the species reacting fast are in equilibrium with each other.

 

[dorebase2006]

Your mechanism looks a bit confusing to me, because the elementary steps don't seem to add up to the overall equation.