The BOD5 of a waste water is determined to be 240 mg/l at 20℃. The k value at 20℃ is known to be 0.23 day-1 . Calculate the BOD7 if the test were run at 10℃.ans.258.12 mg/l224.05 mg/l240 mg/l196.89 mg/l Previous Marked for Review Save & Finish

The BOD (Biochemical Oxygen Demand) is a measure of the amount of oxygen required by bacteria to decompose the organic matter in the water under aerobic conditions. The BOD5 is the BOD after 5 days, and the BOD7 is the BOD after 7 days.

The BOD at any time t can be calculated using the formula:

BODt = BOD0 * (1 - e^(-kt))

where:

• BOD0 is the initial BOD (in this case, the BOD5 is given as 240 mg/l),
• k is the deoxygenation rate constant (given as 0.23 day^-1),
• t is the time (in days),
• e is the base of the natural logarithm (approximately 2.71828).

First, we need to calculate the initial BOD (BOD0) using the BOD5 and the k value. Rearranging the formula for BOD0 gives:

BOD0 = BOD5 / (1 - e^(-k*5))

Substituting the given values:

BOD0 = 240 mg/l / (1 - e^(-0.23*5)) = 240 mg/l / (1 - e^-1.15)

Calculate the value in the bracket:

1 - e^-1.15 = 0.68

So, BOD0 = 240 mg/l / 0.68 = 352.94 mg/l

Next, we can calculate the BOD7 using the BOD0 and the k value. Substituting the values into the formula gives:

BOD7 = BOD0 * (1 - e^(-k7)) = 352.94 mg/l * (1 - e^(-0.237))

Calculate the value in the bracket:

1 - e^-1.61 = 0.80

So, BOD7 = 352.94 mg/l * 0.80 = 282.35 mg/l

However, this is the BOD7 at 20℃. The question asks for the BOD7 at 10℃. The temperature affects the deoxygenation rate constant k. Unfortunately, without information on how the k value changes with temperature, we cannot calculate the BOD7 at 10℃.

The question seems to be incomplete. However, I can explain how to calculate BOD7 from BOD5 and k value.

The formula to calculate BOD at any time 't' from initial BOD (BOD0) and k value is:

BODt = BOD0 * e^(-kt)

Where: BODt = BOD at time 't' BOD0 = Initial BOD (BOD5 in this case) k = deoxygenation rate constant t = time in days

However, the temperature factor is missing in the question. The temperature can affect the rate of deoxygenation (k value). If the temperature were different, we would need to adjust the k value using the following formula:

kT = k20 * θ^(T-20)

Where: kT = k value at temperature T k20 = k value at 20℃ θ = temperature coefficient (usually between 1.04 and 1.07 for waste water) T = temperature in ℃

Once we have the adjusted k value, we can substitute it into the first formula to calculate BOD7.

Please provide the missing temperature coefficient (θ) so that I can help you calculate the BOD7.