A “midnight dumper” discharged a tank truck full of industrial waste into a pit.

Question

A “midnight dumper” discharged a tank truck full of industrial waste into a pit. The truck (with no company markings) was spotted there 3 days ago, and a pool of pure waste remains. A laboratory technician determined that the waste has a BOD5 of 80 mg/L with a rate constant of 0.1/day. Three factories in the vicinity generate organic wastes: a winery (ultimate BOD = 275 mg/L), a vinegar manufacturer (ultimate BOD = 80 mg/L), and a pharmaceutical company (ultimate BOD = 200 mg/L). Determine which of the three factories is the source of the waste. (Carbonaceous BOD only.)

Explanation / Answer

ln(Ao/At) = kt

For the first order chemical kinetics

k = 0.1/day, t = 3days

ln(Ao/At) = 0.1/day * 3 days = 0.3

Taking exponential both sides we get

Ao/At = e^(0.3) = At * e^(0.3) = 80 * 1.349 = 107.988 mg/L

The source of the waste must came from either of pharmaceutical company or winery

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