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By looking at the rate law, a 0 order equation with be the simplest looking [A]= -kt + [A]. The first order equation always has ln before [A] so , ln[A]= -kt + ln[A]. Finally 2nd order has [A] in a fraction over 1, so 1/[A]= kt + 1/[A].
Yes, by comparing equations with rates and concentrations for different experiments as we did in class you can find the exponents for the differential rate laws and the exponent directly corresponds to the order of the reaction.
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