What is the half-life of a first-order reacti | vedclass

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(A) For a first-order reaction,the rate constant $k$ is given by $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.Given $[A]_0 = 0.8 \ mol \ dm^{-3}$,$[

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(A) For a first-order reaction,the rate constant $k$ is given by $k = \frac{2.303}{t} \log \frac{[A]_0}{[A]_t}$.Given $[A]_0 = 0.8 \ mol \ dm^{-3}$,$[A]_t = 0.2 \ mol \ dm^{-3}$,and $t = 12 \ hour$.$k = \frac{2.303}{12} \log \frac{0.8}{0.2} = \frac{2.303}{12} \log 4 = \frac{2.303 	imes 0.602}{12} \approx 0.1155 \ hour^{-1}$.The half-life $t_{1/2}$ is given by $t_{1/2} = \frac{0.693}{k}$.$t_{1/2} = \frac{0.693}{0.1155} = 6 \ hour$.Alternatively,since the concentration decreases by a factor of $4$ $(0.8$ $ightarrow 0.4$ $ightarrow 0.2)$,it corresponds to $2$ half-lives. Thus,$2 	imes t_{1/2} = 12 \ hour$,which implies $t_{1/2} = 6 \ hour$.

What is the half-life of a first-order reaction if the time required to decrease the concentration of the reactant from $0.8 \ mol \ dm^{-3}$ to $0.2 \ mol \ dm^{-3}$ is $12 \ hour$ (in $hour$)?

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