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I believe it depends on the order of the reaction. For example, for a second order rate constant rate = k[A][B], if we assume B is in large excess, then we can say rate = k'[A] where k' = k[B]. In this case, the units of k are 1/M*s, so when we multiply this by the concentration of B we get 1/s as the units of k'. This makes sense because in this equation k' is acting as a first order rate constant, and should have the units 1/s.
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