Question

Due to an unexpected equipment breakdown, a 5-day BOD test was only performed for 3 days at 25°C. The value, BOD₃, is 100 mg/L. The BOD rate constant is 0.20 day⁻¹. Find the expected 5-day BOD result (i.e., BOD₅).

a) 50 mg/L
b) 80 mg/L
c) 125 mg/L
d) 150 mg/L

Answer 1

The expected 5-day BOD result (BOD₅) is approximately 72.58 mg/L.

Step-by-step explanation:

To find the expected 5-day BOD result (BOD₅), we can use the BOD formula:

BODₙ = BODₘ(1 - e^(-kₙtₙ)) / (1 - e^(-kt))

Where:

BODₙ is the BOD at time n

BODₘ is the BOD at time m

k is the BOD rate constant

t is the time period

In this case, BOD₃ is given as 100 mg/L at 3 days, and we need to find the BOD₅. The given rate constant, k, is 0.20 day⁻¹.

Substituting the values into the formula:

BOD₅ = 100 (1 - e^(-0.20(5-3))) / (1 - e^(-0.20*3))

Simplifying:

BOD₅ = 100 (1 - e^(-0.40)) / (1 - e^(-0.60))

BOD₅ ≈ 100 (1 - 0.6703) / (1 - 0.5488)

BOD₅ ≈ 100 (0.3297) / (0.4512)

BOD₅ ≈ 72.58 mg/L

Therefore, the expected 5-day BOD result (BOD₅) is approximately 72.58 mg/L.