$\text{A}\to \text{P}$ is a first order reaction. At $300 \text{ K}$ this reaction was started with $[\text{A}]=0.5 \text{ mol}\text{L}^{-1}$. The rate constant of reaction was $0.125 \text{ min}^{-1}$. The same reaction was started separately with $[\text{A}]=1 \text{ mol}\text{L}^{-1}$ at $300 \text{ K}$. The rate constant (in $\text{min}^{-1}$) now is
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The rate constant ($k$) for a chemical reaction is independent of the reactant concentrations. It is affected only by temperature (Arrhenius equation) and the presence of a catalyst. If the temperature and catalyst remain the same, the rate constant must remain the same.