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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 recation is proportional to the conectration 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 concentration of reactants.
Therefore rate is dependent and rate constant is independent on the concentration.
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