At temperatures below 500 K, the reaction between carbon monoxide and nitrogen d

Question

At temperatures below 500 K, the reaction between carbon monoxide and nitrogen dioxide
CO (g) + NO2 (g) CO2 (g) + NO (g)
has the following rate equation: Rate = k[NO2]2. Which of the three mechanisms suggested here agrees with the experimentally observed rate equation?
Mechanism 1: Step 1 Slow NO2 + NO2 NO3 + NO
                      Step 2 Fast NO3 + CO NO2 + CO2
Mechanism 2: Step 1 Fast NO2 + NO2 N2O3 + O
                      Step 2 Slow N2O3 + O + CO CO2 + NO2 + NO
Mechanism 3: CO + NO2 CO2 + NO

The answer is mechanism 1, explain why?

Explanation / Answer

for mechanism 1:
rate depends on slowest step:
rate = k [NO2]^2

For mechanism 2:
rate = k2 [N2O3][O][CO]

from 1st step
rate of forward reaction = rate of backward reacion
kf [NO2]^2 = Kb [N2O3][O]
[N2O3][O] = (Kf/Kb)*[NO2]^2

Put this in rate expression,
rate = k2 (Kf/Kb)*[NO2]^2[CO]
= k * [NO2]^2 [CO]

for mechanism 3:
rate = k [CO][NO2]

But the correct law is:
Rate = k[NO2]^2

Hence the mechanism 1 is correct

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