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 * 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

We can use the first-order reaction equation to determine the time required for the toxin concentration to decrease from 0.63 mg/L to 1.5 x 10^-3 mg/L:

ln([A]/[A]0) = -kt

where [A]0 is the initial concentration (0.63 mg/L), [A] is the concentration at time t, k is the rate constant (0.27 day^-1), and t is the time.

Rearranging and plugging in the values, we get:

ln(1.5 x 10^-3/0.63) = -0.27t

Solving for t, we get:

t = 22 days

Therefore, it will take 22 days for the water to be safe for drinking. Answer choice D is correct.

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