The rate law for the slowest step (which is the rate-determining step) will give us the overall rate law.
The slow step is: NO2(g) + NO2(g) --> NO(g) + NO3(g)
The rate law for this step can be written as:
rate = k1[NO2][NO2]
The fast step is: NO3(g) + O2(g) --> NO2(g) + O3(g)
The rate law for this step can be written as:
rate = k2[NO3][O2]
Now, we need to eliminate NO3 from the rate law of the overall reaction. We can do this by using the fast step to express [NO3] in terms of [NO2] and [O2]:
k2[NO3][O2] = rate of NO3 consumption = k1[NO2][NO2]
[NO3] = (k1/k2)[NO2]^2[O2]
Substituting this expression for [NO3] into the rate law for the fast step:
rate = k2[(k1/k2)[NO2]^2[O2]][O2] = k1k2[NO2]^2[O2]^2
Therefore, the rate law for the overall reaction is:
rate = k1k2[NO2]^2[O2]^2
The reaction 2 NO2(g)--> 2NO(g)+O2(g) is postulated to occur via the mechanism below:
NO2)g)+ NO2(g)-->NO(g)+NO3(g) ;K1,slow NO3(g)--+O2(g);K2 , fast
What is the rate law for this mechanism
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