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One way is based off how the rate varies with concentration. If the concentration increases two-fold and the rate increases two-fold, you know that the reaction is first order. Similarly, if the concentration increases two-fold and the rate increases by a factor of 4, then you know the reaction is second order.
As well as this, another thing to consider is the overall order of the reaction. Depending on the amount of reactants, aA+bB=cC+dD, you must find the order of each reactant, then add the sum of the orders to get the OVERALL order. For example, let's say rate law =k[A]^2 * [B]^2, then the overall order is 2+2=4. From here, they would usually ask to find k. If given the table of values for different concentrations of A and B as well as the rate, then you would simply focus on one line, and plug in k=(rate of reaction)/[A]^2*[B]^2. Then once k is found, you have found the rate law for that reaction by plugging in the value of k to the original equation of the rate law.
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