Order of the reaction is defined as the sum of the concentration of terms on which the rate of the reaction actually depends. It is the sum of the exponents of the molar concentration in the rate law expression.

Elementary reactions are defined as the reactions for which the order of the reaction is same as its molecularity and order with respect to each reactant is equal to its stoichiometric coefficient as represented in the balanced chemical reaction.

For the given reaction:

$aA+bB\rightleftharpoons cC+dD$

$Rate=k[A]^m[B]^n$

In this equation, the order with respect to each reactant is not equal to its stoichiometric coefficient which is represented in the balanced chemical reaction.

Hence, this is not considered as an elementary reaction.

Order with respect to A = m

Order with respect to B = n

Overall order = m+n

Thus order with respect to A is m.

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