Suppose that a chemical spill occurred in Lake Pleasant, which is a source of dr

Question

Suppose that a chemical spill occurred in Lake Pleasant, which is a source of drinking water for some communities. The chemical concentrations in the Lake were measured on the first day (t=0) as 9.00 ppm. After 3.00 days, the chemical concentrations were determined to be 7.20 ppm. How long (from t=0) would it take for the water concentrations reach the federally-mandated concentrations of 0.500 ppm for safe drinking water? Assume the lake is well mixed and the degradation kinetics follow first order kinetics. The units are days.

Explanation / Answer

Let us find the rate constant k for reaction,

for a first order reaction we have,

ln[A]t = ln[Ao] - kt

with,

[A]t = 7.20 ppm

[Ao] = 9.00 ppm

t = 3 days

Feed values,

ln(7.20) = ln(9.00) - k x 3

k = 0.0744 day^-1

Now for [A]t = 0.500 ppm, the time required would be,

ln(0.50) = ln(9.00) - 0.0744 x t

t = 38.85 days would be needed

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