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We should be prepared to find, for the purposes of this class, the zeroth order, first order, and second order. There are orders higher than that, but they are rare and we are not expected to do calculations involving those.
Find the individual orders of each reaction based on how the rate changes with additional initial concentration of the reactants. Each reactant will have its own individual order and then you will take the sum of the orders of the reactants to find the overall order of the reaction.
The number of reactants do play a role in the overall order, as each contributes a certain exponent to the total that is added to derive this number. I believe that Professor Lavelle said that reactions become less common as their rate orders increase, so we should expect reactions to be of orders: 0, 1, 2, and possibly 3.
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