For the first order reaction 2 N_2O_{5(g)} ri | vedclass

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(A) For a first-order reaction,the concentration at time $t$ is given by $C_t = C_0 e^{-kt}$,which shows exponential decay. Thus,statement $A$ is corr

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$A, B, D$

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(A) For a first-order reaction,the concentration at time $t$ is given by $C_t = C_0 e^{-kt}$,which shows exponential decay. Thus,statement $A$ is correct.The half-life is $t_{1/2} = \frac{\ln 2}{k}$. Since the rate constant $k$ increases with temperature according to the Arrhenius equation,$t_{1/2}$ decreases as temperature increases. Thus,statement $B$ is correct.For a first-order reaction,$t_{1/2} = \frac{0.693}{k}$,which is independent of the initial concentration $C_0$. Thus,statement $C$ is incorrect.After $n$ half-lives,the remaining reactant is $C_t = \frac{C_0}{2^n}$. For $n = 8$,$C_t = \frac{C_0}{2^8} = \frac{C_0}{256}$.Percentage completion = $\frac{C_0 - C_t}{C_0} 	imes 100 = \frac{C_0 - \frac{C_0}{256}}{C_0} 	imes 100 = (1 - \frac{1}{256}) 	imes 100 \approx 99.6 \%$. Thus,statement $D$ is correct.Therefore,statements $A, B,$ and $D$ are correct.

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