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Chapter 18: Problem 50

Sewage causes removal of oxygen from the fresh water into which the sewage is discharged. For a town with a population of 100,000 people, this effluent causes a daily oxygen depletion of 50.0 g per person. How many liters of water at \(8 \mathrm{ppm} \mathrm{O}_{2}\) are \(50 \%\) depleted of oxygen in a day by the population of this town?

Short Answer

Expert verified
The total daily oxygen depletion is (50.0 g/person) × (100,000 people) = 5,000,000 g. The amount of oxygen in a depleted liter of water is \(\frac{1}{2} \times 8\ \mathrm{mg} = 4\ \mathrm{mg}\). The amount of oxygen removed in a depleted liter of water is \(8\ \mathrm{mg} - 4\ \mathrm{mg} = 4\ \mathrm{mg}\). Therefore, the volume of water 50% depleted of oxygen in a day is \( \frac{5,000,000\ \mathrm{g}}{4\ \mathrm{mg/L}} = 1,250,000\ \mathrm{L}\).

Step by step solution

01

Calculate total daily oxygen depletion

First, let's calculate the total daily oxygen depletion caused by the population of the town. To do this, simply multiply the oxygen depletion per person (50.0 g) by the total population of the town (100,000 people). Total daily oxygen depletion = (50.0 g/person) × (100,000 people)
02

Calculate the amount of oxygen in a depleted liter of water

We are given that the normally, the water has \(8\ \mathrm{ppm} \ \mathrm{O}_2\). This means that in one liter of water, there are 8 mg of \(\mathrm{O}_2\). If the water is 50% depleted of oxygen, then the remaining amount of oxygen will be half of 8 mg. Amount of oxygen in a depleted liter of water = \(\frac{1}{2} \times 8\ \mathrm{mg}\)
03

Calculate the amount of oxygen removed in a depleted liter of water

To calculate the amount of oxygen removed in a depleted liter of water, subtract the amount of oxygen in a depleted liter of water (calculated in step 2) from the initial amount of oxygen in a liter (8 mg). Amount of oxygen removed in a depleted liter of water = \(8\ \mathrm{mg} - \frac{1}{2} \times 8\ \mathrm{mg}\)
04

Calculate the volume of 50% depleted water

Now, we can determine the volume of water that is 50% depleted of oxygen in a day by the population of this town. To do this, divide the total daily oxygen depletion (calculated in step 1) by the amount of oxygen removed in a depleted liter of water (calculated in step 3). Volume of water 50% depleted of oxygen = Total daily oxygen depletion / Amount of oxygen removed in a depleted liter of water After calculating all the values, we will obtain the final answer for the volume of water that is 50% depleted of oxygen in a day by the population of this town.

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