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Q.

For the given first order reaction
$A \to B$
the half life of the reaction is 0.3010 min. The ratio of the initial concentration of reactant to the concentration of reactant at time 2.0 min will be equal to ________________
(Nearest integer)

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answer is 100.

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Detailed Solution

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$A \to B t_{1 / 2} = 0.3010 m i n A_{0} / A_{t} a t t i m e 2 m i n = ? K = \frac{2.303}{t} \log [\frac{A_{0}}{A_{t}}] \Rightarrow \frac{0.693}{t_{\frac{1}{2}}} = \frac{2.303}{2} \log [\frac{A_{0}}{A_{t}}] O r \frac{2.303 \times 0.3010}{0.3010} = \frac{2.303}{2} \log \frac{A_{0}}{A_{t}} \log \frac{A_{0}}{A_{t}} = 2 ∴ \frac{A_{0}}{A_{t}} = 10^{2} = 100$

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