That's a sample reaction: $$2N_2+3O_2->2N_2O_3\ \ \ r=k_1[N_2]^2[O_2]^3$$ Why can't I write this as $$N_2+\frac{3}{2}O_2->N_2O_3\ \ \ r=k_2[N_2][O_2]^{\frac{3}{2}}$$ Don't bother the elements. Assume it's elementary not mechanism.
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2First kinetic eq. is incorrect, second probably too. – Mithoron Mar 06 '20 at 20:18
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1Furthermore, $N_2$ and $O_2$ have the greatest difficulty to make any reaction at all. And if they react, they will produce $NO$ or $NO_2$, and never $N_2O_3$. – Maurice Mar 06 '20 at 21:32
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1The rate law doesn't change when multiply equation of the reaction – Adnan AL-Amleh Mar 07 '20 at 01:19
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1I'd rather make a sample out of a reaction that actually can occur. – Ivan Neretin Mar 07 '20 at 04:40
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https://chemistry.stackexchange.com/questions/38167/do-coefficients-matter-in-rate-law/38169#38169 – Adnan AL-Amleh Mar 09 '20 at 06:28
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A rate law is never deduced from a theoretical equation. NEVER. It is always obtained form experimental measurements. It may happen that the order of the reaction is equal to the stoichiometric coefficient.
Maurice
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4This is a bit over the top. I agree that a reaction which such a high reaction order is unlikely to be an elementary reaction which book problems often assume. – MaxW Mar 06 '20 at 20:59