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The rate law is an expression for the reaction rate in terms of concentrations of chemical species involved in the reaction. For example, Rate = k [A]m [B]n. where k is a rate constant, m is reaction order with respect to A, n is the reaction order with respect to B, and m+n is the overall reaction order. The rate constant is independent of the concentrations of the chemical species involved in the reaction.
The reaction rate (rate of reaction) or speed of reaction for a reactant or product in a particular reaction is intuitively defined as how quickly or slowly a reaction takes place.