Which of the following plots is(are) correct for the given reaction?\ ( $[P]_{0}$ is the initial co

Question

Which of the following plots is(are) correct for the given reaction?\ ( $[P]_{0}$ is the initial concentration of $P$ )\

Professor PC Thomas Classes · Answer

(a) : The given reaction is an example of $\mathrm{S}_{\mathrm{N}} 1$ reaction.\ Rate $\propto$ [Conc. of alkyl halide]\ Thus, it is a first order reaction.\ For first order reaction, $t_{1 / 2}=\frac{0.693}{k}$\ Thus, $t_{1 / 2} \propto\left[P_{0}ight]^{0}$. So, graph (a) is correct.\ Also for first order, $P=P_{0} e^{-k t}$\ $\ln \frac{P}{P_{0}}=-k t$\ where, $P=$ Conc. at time $t, P_{0}=$ Initial conc. at $t=0$\ $\frac{P}{P_{0}}=e^{-k t}$\ $1-\frac{P}{P_{0}}=1-e^{-k t}=\frac{P_{0}-P}{P_{0}}=\frac{Q}{P_{0}}$\ (where $Q=P_{0}-P$ )\ Thus, graphs (b), (c) and (d) are incorrect.