the value of rate constant vary with reactant concentration
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Rate constant is the constant of proportionality in the rate law equation and is equal to the rate of reaction when the molar concentration of each of the reaction is unity. The rate constant is constant for a particular reaction at a particular temperature and does not depend upon the concentrations of the reactants.
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the rate of a reaction depends on the temperature, and concentration of the reactants, but the value of k, the rate constant does not.
If this ratio is constant, then the value of k will be constant, and will thus not be dependent upon the concentration
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