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First-order tells us that an increase in the concentration of the reactant is directly proportional to the rate, so doubling the reactant will double the rate. Second-order means that doubling the reactant will increase the rate by a factor of four, and zero-order means that the rate does not depend on the concentration of reactant.
The order of a reaction explains how that reaction rate varies depending on how the reaction is organized. For example if it was a zeroth order reaction then there would be no correlation between reaction rate and time and first order would have a direct correlation and so on.
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