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Elementary reactions basically make up an overall non-elementary reaction. Elementary reactions only involve a single step, whereas non-elementary reactions make up multiple single step elementary reactions. It should be noted that when dealing with elementary reactions, the coefficients DO matter for the rate law (they influence the superscript of the concentration), whereas for non-elementary reactions you can't rely on coefficients to determine the superscripts.
Elementary reactions are the specifics of an overall reaction. They're elementary in that there may be species seen, such as intermediates and catalysts, that are not seen in the net reaction that takes place.
It says in the lecture notes that the rate law for each elementary step follows directly from molecularity, which is the number of species. Because of that, we can determine that an elementary step with a first order rate law is unimolecular meaning one species, a second order rate law is bimolecular meaning two species colliding, and third order rate law is termolecular meaning three species colliding. Higher molecularity is rare because it is rarer for more molecules to collide at the same time.
In an elementary reaction, you can use the coefficients as exponents when writing the rate law for the elementary step (cannot be done for overall or non-elementary rates) because it's directly related to molecularity.
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