Problem 50 - Chemistry: The Central Science in SI Units, Global Edition

Question

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?

Step-by-Step Solution

Answer

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 1: 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)

Step 2: 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 = \(\frac{1}{2} \times 8\ \mathrm{mg}\)

Step 3: 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 = \(8\ \mathrm{mg} - \frac{1}{2} \times 8\ \mathrm{mg}\)

Step 4: 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.

Key Concepts

Oxygen Depletion

Oxygen depletion refers to the reduction of oxygen levels in water, which can have serious consequences for aquatic life. The main reason for this phenomenon in our exercise is the discharge of sewage. As the organic matter in sewage gets broken down by bacteria, they consume oxygen from the water. This reduces the dissolved oxygen levels available for fish and other aquatic organisms.
With a town population of 100,000 people each contributing to an oxygen depletion of 50 g per day, the cumulative effect can be significant. It is crucial to understand this process in order to manage and control it. Knowing the amount of oxygen depletion in a water body helps in predicting the impact on aquatic life and planning remediation strategies.

Water Pollution

Water pollution occurs when harmful substances like sewage enter water bodies, affecting both the water quality and the living organisms within it. This leads to issues such as oxygen depletion, rendering the water unsuitable for aquatic wildlife. In the presented exercise, sewage discharge was primarily responsible for polluting the water and depleting its oxygen levels.
The presence of pollutants not only reduces oxygen but can also introduce other harmful substances such as pathogens and nutrients that can cause algal blooms. These blooms further exacerbate oxygen depletion, creating a cycle that can be very damaging to the ecosystem. Understanding water pollution helps in taking preventive measures to safeguard water resources.

Effluent Impact

Effluent refers to wastewater—like sewage—that is discharged into natural water bodies. The impact of effluents is seen in the form of decreased water quality and adverse effects on ecosystems. Effluent impact assessment is crucial as it tells us how the introduction of sewage affects water bodies.
In our scenario, the daily effluent load from the town’s population leads to considerable oxygen depletion. This happens because the organic matter in the sewage consumes oxygen as it decomposes. Assessing the effluent impact enables authorities to design better wastewater treatment systems to minimize harmful effects on aquatic environments.

Chemical Calculations

Chemical calculations are essential in determining precise amounts of substances and their interactions within aqueous environments. In our exercise, calculating the total oxygen depletion and the volume of water affected involves several steps.

• First, the total oxygen depletion: Multiply the individual depletion rate by the total population.
• Second, we understand the remaining oxygen in a liter after 50% depletion, given in ppm (parts per million), which relates directly to mg/L.
• Lastly, to find the volume of 50% depleted water, use the total daily depletion to calculate how much water's oxygen was consumed.

By mastering these calculations, you gain insight into the extent of pollution and its impact, which is crucial for managing and mitigating environmental effects.