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In a first order reaction, there will be one reactant present in the rate law. For a second order reaction, you can either have a rate law with one reactant to the second order, or with two reactants both to the first order. I remember it by adding the exponents of all the reactants in the rate law - whatever the exponent is, that's the order of the rate law.
In first-order reactions, the reaction rate is directly proportional to the concentration of one of the reactants. These reactions usually take the form of A → products. In contrast, a second-order reaction is one whose rate is proportional to the square of the concentration of one reactant. Second-order reactions often take the form of either A + B → products or 2A → products.
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