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Reaction rates are dependent on the concentration of reactants. As a reaction proceeds, the reactants are used up and thus their concentration is lowered. THis means that the maximum rate of reaction will be at or immediately after time zero, when the reaction is only just begun, and the minimum will be when one or more of the reactants' concentrations have reached zero.

Thus, any rate stated for the reaction would only hold for a specific time in the reaction progress and cannot be extrapolated to cover all of that progress. So a mean rate of reaction must be used; this can tell a person, when combined with either the time of beginning, time of ending, or the initial concentrations, what any of the others were for the reaction in question. This is impossible to do if given a specific rate and the time it applied to; you cannot calculate any new information from just those two data.

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Q: When giving the rate of a chemical reaction why would it be significant to know that the reaction rate is an average reaction rate?
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