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

Question

Quizplus · Accepted Answer

To solve this problem, we can use the first-order rate law:

ln ([toxin]t/[toxin]0) = -kt

where [toxin]t is the concentration of toxin at time t, [toxin]0 is the initial concentration of toxin, k is the rate constant, and t is time.

We can rearrange this equation to solve for t:

t = (ln ([toxin]0/[toxin]t))/k

Plugging in the given values, we get:

t = (ln (1.5 x 10^-3/0.63))/0.27 = 22 days (rounded to the nearest whole day)

Therefore, it will take 22 days for the water to be safe to drink. So the correct answer is D.

A City's Water Supply Is Contaminated with a Toxin at a Concentration