The rate constant k for the first-order reaction A→3B is 0.527 s−1. After how many seconds will 45.0% of the initial amount of A remain?

2020-11-23 1:43 pm

回答 (1)

2020-11-23 3:54 pm
✔ 最佳答案
Method 1:

ln(A/Aₒ) = -kt
ln(45%) = -(0.527 s⁻¹)t
Time taken, t = -ln(0.45)/0.527 s = 1.52 s

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Method 2:

Let n be the number of half-lives taken.
45% = (1/2)ⁿ
ln(0.45) = ln(0.5)ⁿ
n ln(0.5) = ln(0.45)
n = ln(0.45)/ln(0.5)

Time taken = [ln(0.45)/ln(0.5)] × [ln(2)/0.527 s] = 1.52 s


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