Problem 48 - Chemistry: The Central Science

Question

The average daily mass of \(\mathrm{O}_{2}\) taken up by sewage discharged in the United States is \(59 \mathrm{~g}\) per person. How many liters of water at \(9 \mathrm{ppm} \mathrm{O}_{2}\) are \(50 \%\) depleted of oxygen in 1 day by a population of \(1,200,000\) people?

Step-by-Step Solution

Answer

The total mass of \(\mathrm{O}_{2}\) consumed by \(1,200,000\) people is \(59\,\mathrm{g/person} \times 1,200,000 = 70,800,000\,\mathrm{g}\). In \(1\) liter of water at \(9\,\mathrm{ppm} \mathrm{O}_{2}\), the available oxygen mass is \(9\,\mathrm{ppm} \times 1000\,\mathrm{g} = 9\,\mathrm{g}\). After \(50\%\) depletion, the remaining oxygen mass is \(\frac{1}{2} \times 9\,\mathrm{g} = 4.5\,\mathrm{g}\). The consumed oxygen mass per liter is \(9\,\mathrm{g} - 4.5\,\mathrm{g} = 4.5\,\mathrm{g}\). Hence, the number of liters needed is \(\frac{70,800,000\,\mathrm{g}}{4.5\,\mathrm{g/liter}} = 15,733,333\,\mathrm{liters}\).

Step 1: Calculate the total mass of oxygen consumed by the population in one day.

The total mass of oxygen consumed by \(1,200,000\) people can be calculated using the average daily mass per person: Total mass of \(\mathrm{O}_{2}\) consumed = (Average daily mass per person) × (Number of people) Total mass of \(\mathrm{O}_{2}\) consumed = \(59\,\mathrm{g} \times 1,200,000\) Calculate the total mass of \(\mathrm{O}_{2}\) consumed by the population in one day.

Step 2: Calculate the amount of oxygen available in 1 liter of water at \(9\,\mathrm{ppm}\,\mathrm{O}_{2}\).

To find the mass of \(\mathrm{O}_{2}\) available in \(1\) liter of water at \(9\,\mathrm{ppm}\,\mathrm{O}_{2}\), first, note that \(\mathrm{ppm}\) stands for parts per million and represents the mass of a substance within a total mass of a mixture or solution. We can use the following equation to calculate the available oxygen in \(1\) liter of water: Available \(\mathrm{O}_{2}\) mass = (Concentration in \(\mathrm{ppm}\)) × (Total mass of water) Since \(1\) liter of water weighs approximately \(1000\,\mathrm{g}\), the total mass of water for \(1\) liter is: Total mass of water = \(1000\,\mathrm{g}\) Now, we can calculate the available oxygen in one liter of water: Available \(\mathrm{O}_{2}\) mass = \(9\,\mathrm{ppm} \times 1000\,\mathrm{g}\) Calculate the available \(\mathrm{O}_{2}\) in one liter of water at \(9\,\mathrm{ppm}\,\mathrm{O}_{2}\).

Step 3: Calculate the amount of oxygen remaining in the water after \(50\%\) depletion.

To find the remaining mass of oxygen after \(50\%\) depletion, we can multiply the available oxygen mass found in Step 2 by \(0.5\). Remaining oxygen mass = \(\frac{1}{2}\) × (Initial oxygen mass) Calculate the remaining mass of oxygen in the water after it is \(50\%\) depleted.

Step 4: Calculate the number of liters needed to provide the required amount of oxygen.

To find the number of liters needed to provide the required amount of oxygen, we should divide the total mass of \(\mathrm{O}_{2}\) consumed (found in Step 1) by the oxygen mass consumed in one liter of water. The consumed oxygen mass per liter will be the initial amount minus the remaining amount (found in Step 3). Number of liters = \(\frac{\text{Total mass of } \mathrm{O}_{2} \text{ consumed}}{\text{Consumed oxygen mass per liter}}\) Calculate the number of liters needed to provide the required amount of oxygen for the given population.

Key Concepts

Oxygen Depletion

Oxygen depletion is a significant concern in environmental chemistry, especially when it comes to water systems. It describes the reduction of dissolved oxygen levels in water bodies, which can have harmful effects on aquatic life. Oxygen is crucial for the survival of fish and other aquatic organisms, and when levels drop, these creatures can suffer or even die.

In the context of sewage disposal, such as in our exercise, each person contributes to oxygen consumption, potentially leading to depleted oxygen levels in water. Human waste contains organic materials that are decomposed by bacteria in water. During this decomposition process, bacteria consume oxygen, thus reducing its availability in the water.

• The more organic material discharged, the greater the oxygen demand.
• Sewage discharge without proper treatment can severely impact local water quality.
• Monitoring and managing oxygen levels is vital to maintain ecological balance.

Understanding oxygen depletion helps us appreciate the importance of regulating waste disposal and protecting aquatic ecosystems.

PPM Calculation

PPM stands for parts per million and is used to measure the concentration of a substance in a mixture or solution. It's particularly useful in environmental science to assess contaminant levels in air, water, or soil. In the scenario provided by our exercise, we're dealing with oxygen concentrations in water measured in ppm.

One ppm is equivalent to one part of oxygen per one million parts of water; therefore, it's a weight-to-weight measurement. For instance, a 9 ppm oxygen concentration means there are 9 grams of oxygen in one million grams (or 1000 liters) of water.

• To calculate the mass of a substance using ppm, multiply by the total mass of the solution.
• In our calculation, Available \(\mathrm{O}_2 \) mass = \(9 \, \mathrm{ppm} \times 1000\, \mathrm{g}\).
• PPM calculations help determine if additional treatment is required to meet environmental standards.

By understanding ppm calculations, you can effectively gauge the purity of water and assess various environmental risks.

Water Chemistry

Water chemistry is the study of chemical processes that govern the composition and quality of water. It plays a vital role in environmental science, where preserving the health of aquatic ecosystems is of primary concern. When solving problems such as our exercise, understanding water chemistry fundamentals aids in determining the repercussions of human activities on water systems.

Key factors in water chemistry include:

• Concentration of dissolved substances, such as oxygen.
• The balance of ions and pH levels.
• The presence of pollutants or contaminants from natural or anthropogenic sources.

In our scenario, the chemistry of water focuses on how oxygen levels are influenced by sewage discharge. Assessing the amount of oxygen available before and after certain depletions reveals how human waste impacts water bodies.
Understanding these principles allows us to develop strategies for minimizing pollution, such as advanced water treatment and sewage processing, ensuring the environmental balance is maintained.