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Question
Obtain the expression for half-life and rate constant of the first-order reaction.
Solution
k = `2.303/t log_10 [A]_0/[A]_t`
Where, `[([A]_0 = "Initial concentration"),([A]_t = "Final concentration")]`
At, t = `t_(1/2), [A]_t = [A]_0/2`
k = `2.303/t_(1/2) log_10 [A]_t/([A]_0/2)`
k = `2.303/t_(1/2) xx log_10 2`
= `2.303/t_(1/2) xx 0.3010`
`t_(1/2) = 0.693/k`
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