N_2O_5 rightarrow 2NO_{2(g)} + frac{1}{2}O_{2 | vedclass

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(A) For a first order reaction,the rate constant $k$ is given by the equation: $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.Given: $k = 5 	imes 10^

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$2773$

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(A) For a first order reaction,the rate constant $k$ is given by the equation: $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.Given: $k = 5 	imes 10^{-4} \ s^{-1}$,$[A]_0 = 0.2 \ mol \ L^{-1}$,and $[A]_t = 25 \% 	ext{ of } [A]_0 = 0.25 	imes [A]_0$.Substituting the values: $5 	imes 10^{-4} = \frac{2.303}{t} \log \frac{[A]_0}{0.25[A]_0}$.$5 	imes 10^{-4} = \frac{2.303}{t} \log(4)$.Since $\log(4) \approx 0.6021$,we have $t = \frac{2.303 	imes 0.6021}{5 	imes 10^{-4}}$.$t = \frac{1.3866}{5 	imes 10^{-4}} = 2773.2 \ s \approx 2773 \ s$.

$N_2O_5 \rightarrow 2NO_{2(g)} + \frac{1}{2}O_{2(g)}$ is a first order reaction. $k = 5 \times 10^{-4} \ s^{-1}$. The initial concentration of $N_2O_5 = 0.2 \ mol \ L^{-1}$. After how much time will its concentration be $25 \%$ of the initial concentration (in $s$)?

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