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Average rate is measured over a time period while instantaneous rate is at a certain time point. If the average rate is measured while the system is constantly at equilibrium, then the average rate will be 0. However, if the average rate is measured when the reaction is not at equilibrium and then reaches equilibrium, the average rate will not be 0. The average rate depends on what two time points that its measured from.
Yes, at equilibrium, the forward and reverse reaction rates are equal which is the reason there is no change in the concentration of the products and the reactants. Also, the instantaneous rate is a more accurate measurement of the rates of the reactants and the products as it takes the smallest time step. Therefore, the average rate should also be zero since for its derivative to be zero, the plot should also reach a point where there is no change.
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