[eunChae]

we know that for elementary reactions(one step reactions) we can find the order of reactions just by looking stoichiometry of the reactants. I mean, for example considering the following rxn:
 (just assume that the following rxn is elementary even if it is not) 
       2NO + O2 --> 2NO2
 and the rate law is 
       rate = k[NO]^2*[O2] (NO is second order and O2 is first order reaction.)
       we can do this conclusion just by looking its stoichiometry but my question is that why is this enough? How can we determine the order of the elementary reaction by lookin at their stoichiometry? Any explanation for this rule?
Thanks for any comments in advance...

[Astrokel]

The reason is because the rate law always follows the slowest step of the multiple steps of a reaction. If the reaction is one step, the rate law will just be the same as what you mentioned. Therefore if it has multiple steps, you cannot just look at the stoichiometry of the overall reaction equation but the rate determing step (slowest).

[eunChae]

Well, but why the stoichiometric coefficients are applied as they are the orders in elementary reactions(if it has a simple step)?
In the previous example, the coefficient of NO is 2 and so, the order of NO([NO]) is 2. Similarly, the coeff. of O2 is 1 and the order of it is also 1. This is not coincidence, it is rule. My question occurs here: why do the orders have to be the same as the coefficients in elementary reactions?

[eunChae]

I came up with an idea as i writing the message above:
if we write the reaction as the following
   NO + NO + O2 -->.   and prove that each of the reactants is first order, then we can write the rate law as
   rate= [NO]*[NO]*[O2] = ([NO]^2)*[O2]
question is how we know that each of them is first order?
I dont know maybe it is a stupid idea but i wanted to share it.     

[Astrokel]

Order of reactants can be determined through experimental works.