First order kinetics problem?
2016-06-30 4:15 pm
A city's water supply is contaminated with a toxin at a concentration of 0.63 mg/L . For the water to be safe for drinking, the concentration of this toxin must be below 1.5 x 10 ^-3 mg/L . Fortunately this toxin decomposes to a safe mixture of products by first-order kinetics with a rate constant of 0.27 day ^-1 . How long will it take for the water to be safe to drink?
回答 (2)
2016-06-30 5:11 pm
✔ 最佳答案
The decomposition of the toxin is a first-order reaction.Half-life of the toxin
= ln(2) / k
= ln(2) / (0.27 day⁻¹)
= ln(2)/0.27 days
Let n half-lives be the time for the concentration of the toxin decreases from 0.63 mg/L to 1.5 × 10⁻³ mg/L.
(1/2)ⁿ = (1.5 × 10⁻³)/0.63
ln(1/2)ⁿ = ln[(1.5 × 10⁻³)/0.63]
n ln(1/2) = ln[(1.5 × 10⁻³)/0.63]
n = ln[(1.5 × 10⁻³)/0.63] / ln(1.2)
Time taken for the water to be safe to drink
= (ln(2)/0.27 days) × [ln[(1.5 × 10⁻³)/0.63] / ln(1/2)]
= 22.4 days
2016-06-30 4:34 pm
for first order kinetics
ln[A]t = -kt + ln[A]0
[A]0 = 0.6 mg/L
[A]t = 1.5e-3 mg/L
k = 0.27 1/day
solve for t in days
ln[A]t = -kt + ln[A]0
[A]0 = 0.6 mg/L
[A]t = 1.5e-3 mg/L
k = 0.27 1/day
solve for t in days
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