The half-life values for two different first- | vedclass

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(A) For a first-order reaction,the rate constant $k$ is related to the half-life $t_{1/2}$ by the formula $k = \frac{0.693}{t_{1/2}}$.Given for reacti

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$2.0$

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(A) For a first-order reaction,the rate constant $k$ is related to the half-life $t_{1/2}$ by the formula $k = \frac{0.693}{t_{1/2}}$.Given for reaction $A$: $t_{1/2, A} = 75 \ min$.Given for reaction $B$: $t_{1/2, B} = 2.5 \ h = 2.5 	imes 60 \ min = 150 \ min$.The rate constant for $A$ is $k_A = \frac{0.693}{75}$.The rate constant for $B$ is $k_B = \frac{0.693}{150}$.The ratio of rate constants is $\frac{k_A}{k_B} = \frac{0.693 / 75}{0.693 / 150} = \frac{150}{75} = 2.0$.Thus,the ratio is $2.0$.

The half-life values for two different first-order reactions $A$ and $B$ are $75 \ min$ and $2.5 \ h$ respectively. What is the ratio of their rate constants $\frac{k_A}{k_B}$?

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