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An easy way to determine the units of k is to understand that the rate needs to have units of M/s so for 0 order rate=k and therefore k=M/s. for 1st order: rate=k[A] where [A] has the units of M and so when multiplied with k, k must have units of s^-1. For second order rate=k[A]^2 where [A]^2 has units of M^2 so in order to get rate = M/s, k must be M^-1 s^-1.
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