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

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(C) For a first-order reaction,the rate constant $k$ is given by $k = \frac{0.693}{t_{1/2}}$.The half-life $t_{1/2} = \frac{0.693}{k}$ is independent

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The half-life of the reaction depends on the initial concentration of the reactant.

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(C) For a first-order reaction,the rate constant $k$ is given by $k = \frac{0.693}{t_{1/2}}$.The half-life $t_{1/2} = \frac{0.693}{k}$ is independent of the initial concentration of the reactant.Therefore,statement $C$ is incorrect because the half-life of a first-order reaction is independent of the initial concentration.For $99.6\%$ completion,the remaining concentration is $0.4\%$ of the initial concentration $([A]_t = 0.004[A]_0)$.Using $t = \frac{2.303}{k} \log(\frac{[A]_0}{[A]_t}) = \frac{2.303}{k} \log(\frac{1}{0.004}) = \frac{2.303}{k} \log(250) \approx \frac{2.303}{k} 	imes 2.398 \approx \frac{5.52}{k}$.Since $t_{1/2} = \frac{0.693}{k}$,then $8 	imes t_{1/2} = 8 	imes \frac{0.693}{k} \approx \frac{5.54}{k}$,which is approximately equal to the time for $99.6\%$ completion.

For the first-order reaction $2N_2O_{5(g)} \rightarrow 4NO_{2(g)} + O_{2(g)}$,which of the following statements is incorrect?

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