An ice-covered pond experiences a high deoxygenation rate due to a high rate of

Question

An ice-covered pond experiences a high deoxygenation rate due to a high rate of oxygen demand within the pond sediments. Prior to the freeze-over date, the dissolved oxygen (DO) concentration in the pond is 12.4 mg/L. Assume that the DO transfer occurs at the sediment-water interface according to the relation r=kC, where the rate constant k=0.1 day-1 and C is the DO concentration in the well-mixed pond. The DO lower survival limit is 3 mg/L for the cold-water fish. The dissolved oxygen concentration in the pond 30 days after the freeze-over date is about:

Explanation / Answer

-dC/dT=kC, or - ∫dC/C = K ∫dT , integratin C to C1 to C2 and T to 0 to T, we get ln( C1/C2)= KT

or C1= C2 * e^(KT) , or, C2= C1*e^(-KT) = 12.4 *e^(-0.1 * 30 ) = 0.6 mg/L

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