Problem 79 - Chemistry: An Atoms-Focused Approach

Question

Sulfur in Coal Suppose 75 metric tons of coal that is \(3.0 \%\) sulfur by mass is burned at a power plant. During combustion, the sulfur is converted into \(\mathrm{SO}_{2} .\) Antipollution scrubbers installed in the smokestacks of the power plant capture 3.9 metric tons of \(\mathrm{SO}_{2} .\) How efficient are the scrubbers in capturing \(\mathrm{SO}_{2} ?\) How many metric tons of \(\mathrm{SO}_{2}\) escape?

Step-by-Step Solution

Answer

Answer: The scrubbers are approximately \(86.67\%\) efficient, and 0.6 metric tons of \(\mathrm{SO}_{2}\) escape.

Step 1: Find the total mass of sulfur in the coal

We're given that the coal is \(3.0 \%\) sulfur by mass. So, we need to find the mass of sulfur in the 75 metric tons of coal. To do this, multiply the coal's mass by the percentage of sulfur. $$ \text{Mass of sulfur} = \text{Total mass of coal} \times \frac{\text{Percentage of sulfur}}{100} $$ $$ \text{Mass of sulfur} = 75\,\text{metric tons} \times \frac{3.0 \%}{100} = 2.25\,\text{metric tons} $$

Step 2: Find the total mass of \(\mathrm{SO}_{2}\) produced

In the combustion process, sulfur is converted into \(\mathrm{SO}_{2}\). To find the total mass of \(\mathrm{SO}_{2}\) produced, we need to use the mass ratio of \(\mathrm{SO}_{2}\) to sulfur. The molar mass of \(\mathrm{SO}_{2}\) is 32 (mass of sulfur) + 2 * 16 (mass of each oxygen) = 64g/mol, while the molar mass of sulfur is 32g/mol. $$ \text{Mass of } \mathrm{SO}_{2}\text{ produced} = \text{Mass of sulfur} \times \frac{\text{Molar mass of } \mathrm{SO}_{2}}{\text{Molar mass of sulfur}} $$ $$ \text{Mass of } \mathrm{SO}_{2}\text{ produced} = 2.25\,\text{metric tons} \times \frac{64\,g/mol}{32\,g/mol} $$ $$ \text{Mass of } \mathrm{SO}_{2}\text{ produced} = 4.5\,\text{metric tons} $$

Step 3: Compute the efficiency of the scrubbers

To find the efficiency of the scrubbers, divide the mass of \(\mathrm{SO}_{2}\) captured by the total mass of \(\mathrm{SO}_{2}\) produced and multiply by 100. $$ \text{Scrubbers' efficiency} = \frac{\text{Mass of } \mathrm{SO}_{2}\text{ captured}}{\text{Total mass of } \mathrm{SO}_{2}\text{ produced}} \times 100 $$ $$ \text{Scrubbers' efficiency} = \frac{3.9\,\text{metric tons}}{4.5\,\text{metric tons}} \times 100 \approx 86.67\,\% $$

Step 4: Calculate the mass of \(\mathrm{SO}_{2}\) escaped

Subtract the mass of \(\mathrm{SO}_{2}\) captured from the total mass of \(\mathrm{SO}_{2}\) produced to find the mass of \(\mathrm{SO}_{2}\) that escaped. $$ \text{Mass of } \mathrm{SO}_{2}\text{ escaped} = \text{Total mass of } \mathrm{SO}_{2}\text{ produced} - \text{Mass of } \mathrm{SO}_{2}\text{ captured} $$ $$ \text{Mass of } \mathrm{SO}_{2}\text{ escaped} = 4.5\,\text{metric tons} - 3.9\,\text{metric tons} = 0.6\,\text{metric tons} $$ The scrubbers are approximately \(86.67\%\) efficient, and 0.6 metric tons of \(\mathrm{SO}_{2}\) escape.

Key Concepts

Sulfur Dioxide

Sulfur dioxide (\(\mathrm{SO}_{2}\)) is a significant component in the chemistry of combustion processes, especially relevant in industrial settings such as power plants. When coal, which often contains sulfur, is burned for energy, the sulfur within the coal reacts with oxygen in the air to form sulfur dioxide. This conversion is an important chemical reaction in combustion chemistry. Sulfur dioxide is not only a byproduct of coal combustion but also derives from various other industrial processes like the refining of oil and the production of concrete.

Sulfur dioxide is a colorless gas with a pungent odor, and it plays a role in environmental chemistry. It can combine with water vapor in the atmosphere to form sulfurous acid, contributing to the phenomenon known as acid rain. Additionally, \(\mathrm{SO}_{2}\) contributes to particulate pollution and can have harmful effects on human health, affecting the respiratory system.

Pollution Control

Pollution control methods, such as the use of scrubbers in power plants, are essential for minimizing environmental damage caused by industrial emissions. Scrubbers are devices installed in smokestacks that help capture and neutralize pollutants emitted during the combustion of coal and other fuels. This process is crucial in mitigating the harmful effects of sulfur dioxide emissions.

There are several types of scrubbers, with wet scrubbers being among the most common. Wet scrubbers use a liquid to wash unwanted pollutants from a gas stream. In the case of sulfur dioxide, the liquid, often a slurry of limestone or lime, reacts with \(\mathrm{SO}_{2}\) to form a solid compound that can be removed and disposed of safely.

Implementing efficient pollution control technologies in power plants is not just about meeting regulatory standards. It is also about protecting air quality and health, reducing the impact of acid rain, and addressing climate change by lowering the concentration of atmospheric pollutants. The efficiency of scrubbers, as in the exercise problem, reflects how effectively they prevent \(\mathrm{SO}_{2}\) from being released into the atmosphere.

Stoichiometry

Stoichiometry is a fundamental concept in chemistry that involves calculating the quantities of reactants and products in chemical reactions. It is grounded in the law of conservation of mass, which states that matter cannot be created or destroyed in a chemical reaction. This principle makes stoichiometry a powerful tool for understanding the conversion of substances.

The exercise problem effectively uses stoichiometry to assess the conversion of sulfur to sulfur dioxide during the combustion of coal. First, it calculates the mass of sulfur in the coal using the percentage composition of sulfur. Then it determines how much \(\mathrm{SO}_{2}\) will be produced by leveraging the molar masses of sulfur and sulfur dioxide, maintaining a mass-to-mass ratio. This step shows how stoichiometry helps translate the theoretical proportions of chemical equations into practical, measurable quantities.

Stoichiometry can also assess the environmental impact of chemical processes. By understanding the stoichiometric relationships in combustion, engineers and scientists can design more efficient processes to reduce emissions, aiding in pollution control and environmental preservation.