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Rate of a chemical reaction depends on...

Rate of a chemical reaction depends on concentration of reactant is independent on concentration. Why?

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According to law of mass action rate of a reaction is proportional to the concentration of each reactant involved in the reaction.
Rate constant is the rate of reaction at unit concentration of each reactant. Hence rate constant is independent of concentrations of reactants.
Therefore rate is dependent and rate constant is independent on the concentration.
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