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The units of rate constants vary by 1st, 2nd and Zero Order reactions. For First Order reactions the units are s-1 because when used in k[A] we get the correct units for d[A]/dt which is mol/L*s. For Second order reactions the units of k are in M-1s-1 because when used in the equation k[A]^2 we get the correct units (mol/L*s) for d[A]/dt.
The rate of a reaction is always in so we want a rate constant, which if we have certain inputs (concentrations), we get an answer in . So in the case of a first order reaction where the reaction is dependent on the concentration of a single reactant, we have the units of M. Therefore, we want a rate constant that converts M to . So our solution to that is to have the rate constant divide our concentration by seconds, represented as s-1.
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