Which of the following plots is(are) correct | vedclass

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(A) The reaction is a $SN^1$ reaction,which follows first-order kinetics.For a first-order reaction:$1$. The half-life $t_{1/2} = \frac{0.693}{k}$ is

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(A) The reaction is a $SN^1$ reaction,which follows first-order kinetics.For a first-order reaction:$1$. The half-life $t_{1/2} = \frac{0.693}{k}$ is independent of the initial concentration $[P]_0$. Thus,the plot of $t_{1/2}$ vs $[P]_0$ is a horizontal line.$2$. The rate of reaction is given by $rate = k[P]$. The initial rate is $rate_0 = k[P]_0$. Thus,the plot of initial rate vs $[P]_0$ is a straight line passing through the origin.$3$. The concentration of product $Q$ at time $t$ is $[Q] = [P]_0 - [P] = [P]_0(1 - e^{-kt})$. Thus,$\frac{[Q]}{[P]_0} = 1 - e^{-kt}$. This plot is an exponential growth curve.$4$. For first-order kinetics,$\ln(\frac{[P]}{[P]_0}) = -kt$. The plot of $\ln(\frac{[P]}{[P]_0})$ vs time is a straight line with a negative slope $-k$ passing through the origin.

Which of the following plots is(are) correct for the given reaction? $( [P]_0$ is the initial concentration of $P$ $)$

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