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Question
The rate constant of the first order reaction is 1.386 min–1. Calculate the time required for 80% reactant to decompose?
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Solution
Given: [A]0 = 100%, k = 1.386 min–1
To find: Time required for 80% reactant to decompose
Formula: t = `2.303/"k" log_10 ["A"]_"o"/["A"]_"t"`
Calculations: The reactant is 80% decomposed. Hence, [A]t = 20%.
t = `2.303/"k" log_10 ["A"]_"o"/["A"]_"t"`
Substituting the values,
t = `2.303/(1.386 "min"^-1) log_10 100/20`
= `2.303/(1.386 "min"^-1) xx 0.69897`
= 1.16 min × `(60 "s")/(1 "min")`
= 69.6 s
Time required for reducing concentration of reactant to 20 % is 1.16 min or 69.6 s.
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