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Question
Consider a certain reaction \[\ce{A -> Products}\] with k = 2.0 × 10−2 s−1. Calculate the concentration of A remaining after 100 s if the initial concentration of A is 1.0 mol L−1.
Solution
k = 2.0 × 10−2 s−1, T1 = 0, [A]1 = 1.0 M,
T2 = 100 s, [A]2 = ?
k = `1/("T"_2 - "T"_1) ln (["A"]_1)/(["A"]_2)`
2.0 × 10−2 = `1/(100 - 0) ln 1.0/(["A"]_2)`
(2.0 × 10−2) × 100 = `ln 1.0/(["A"]_2)`
2 = `ln 1/(["A"]_2)`
7.389 = `1/(["A"]_2)`
∴ [A]2 = `1/7.389`
= 0.135 mol L−1
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