For the reaction R rightarrow P,the half-life | vedclass

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(B) The condition that the half-life $(t_{1/2})$ is independent of the initial concentration $([R]_0)$ is a characteristic property of a first-order r

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(B) The condition that the half-life $(t_{1/2})$ is independent of the initial concentration $([R]_0)$ is a characteristic property of a first-order reaction. For a first-order reaction,the integrated rate equation is $\ln[R] = -kt + \ln[R]_0$,which can also be written as $\log[R] = -\frac{kt}{2.303} + \log[R]_0$ or $\log\frac{[R]_0}{[R]} = \frac{kt}{2.303}$. Graph $A$ ($\ln[R]$ vs $	ext{time}$) is a straight line with slope $-k$,which is correct. Graph $B$ ($[R]$ vs $	ext{time}$) represents an exponential decay curve,not a straight line with a constant negative slope. Therefore,this graph is incorrect for a first-order reaction. Graph $C$ ($\log[R]$ vs $	ext{time}$) is a straight line with slope $-\frac{k}{2.303}$,which is correct. Graph $D$ ($\log\frac{[R]_0}{[R]}$ vs $	ext{time}$) is a straight line passing through the origin with slope $\frac{k}{2.303}$,which is correct.

For the reaction $R \rightarrow P$,the half-life is independent of the initial concentration of the reactant,$R$. Which one of the following graphs is not correct for this reaction?

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