(Solved): 1. A tanker truck carrying 6,000 gallons of the synthetic organic compound Kilu has overturned spil ...

1. A tanker truck carrying 6,000 gallons of the synthetic organic compound Kilu has overturned spilling its entire contents into Cooter's Pond, a swimming hole and recreation area frequented by local teenagers. KilU* has a specific gravity of \( 1.05 \), is highly soluble in water, and is thought to pose a health risk to swimmers at concentrations greater than \( 10.0 \mathrm{mg} / \mathrm{L} \). Fortunately, KilU \( { }^{*} \) is known to decompose naturally according to first-order kinetics with a rate constant of \( 0.05 \) day \( ^{-1} \). Cooter's Pond has an average depth of \( 22.91 \) feet and average surface area of \( 10.02 \) acres (both at the mean water level). The town council has retained the services of your consulting firm to estimate how long the pond will be unsafe for swimming. After thinking a while, you decide to assume that the KilU* will mix into the pond very quickly (and uniformly) and that although a very small stream runs through the pond it would be prudent, under the circumstances, to completely ignore any dilution effect this might have. What do you tell the Town Council about how long swimming should be prohibited? State all assumptions clearly and show all your work.