Question

Approximately 65 million metric tons of \(\mathrm{SO}_{2}\) enter the atmosphere every year from the burning of coal. If coal, on average, contains \(2.0 \% \mathrm{~S},\) calculate how many metric tons of coal were burned to produce this much \(\mathrm{SO}_{2}\). A 1000-MW power plant burns about 700 . metric tons of coal per hour. Calculate the number of hours the quantity of coal will burn in one of these power plants.

Short answer

1,625 million metric tons of coal were burned; it burns for about 2,321,429 hours.

Step-by-step solution

Calculate the amount of sulfur in metric tons

To find out how much sulfur is used to create the given amount of \( \text{SO}_2 \), we first consider that 65 million metric tons of \( \text{SO}_2 \) are produced. \( \text{SO}_2 \) is made up of sulfur and oxygen. The molar mass of sulfur (S) is approximately 32 grams/mole, and the molar mass of \( \text{SO}_2 \) is about 64 grams/mole. Since sulfur makes up half the molar mass of \( \text{SO}_2 \), then the sulfur content in \( \text{SO}_2 \) is 50%. Therefore, the amount of sulfur needed is 50% of 65 million metric tons. Calculate as follows: \[ \text{Sulfur (S) mass} = 0.5 \times 65 \text{ million metric tons of } \text{SO}_2 = 32.5 \text{ million metric tons of sulfur.} \]

Calculate the total coal burned in metric tons

With sulfur making up 2% of the coal by weight, we can calculate the total amount of coal burned to produce this quantity of \( \text{SO}_2 \). Given 32.5 million metric tons of sulfur needed, we find the coal needed using the proportion: \[ 32.5 \text{ million metric tons of sulfur} = 0.02 \times \text{Total Coal Burned} \] \[ \text{Total Coal Burned} = \frac{32.5 \text{ million metric tons of sulfur}}{0.02} \] \[ \text{Total Coal Burned} = 1625 \text{ million metric tons.} \]

Calculate the number of hours the coal burns in the power plant

We know that a 1000-MW power plant consumes 700 metric tons of coal per hour. To calculate the number of hours required to burn the total coal, use the formula: \[ \text{Number of Hours} = \frac{\text{Total Coal Burned}}{\text{Coal Burned per Hour}} \] \[ \text{Number of Hours} = \frac{1625 \times 10^6 \text{ metric tons}}{700 \text{ metric tons/hour}.} \] \[ \text{Number of Hours} = 2321428.57 \text{ hours (approximately)}. \]

Key concepts

Sulfur Dioxide Emissions

Sulfur dioxide (\(\text{SO}_2\)) emissions result from burning coal. This process is one of the primary sources of air pollution. When coal burns, the sulfur contained within it reacts with oxygen to form sulfur dioxide, a gas that contributes significantly to atmospheric pollution.

Here’s an overview of \(\text{SO}_2\) emissions:

• Sulfur dioxide contributes to respiratory problems in humans and can exacerbate existing health conditions.
• It is also a precursor for acid rain, which can damage crops, forests, and bodies of water.
• Emissions from industrial activities and power plants are a significant environmental concern due to the sheer volume of pollutants released.

To calculate emissions, it's important to understand the chemical composition of the fuel used. Since the problem specifies 65 million metric tons of \(\text{SO}_2\), knowing the percentage of sulfur in coal allows for determining how much coal contributes to these emissions.

This understanding is crucial for developing strategies to reduce emissions, such as desulfurization or switching to lower sulfur fuels.

Coal Combustion

Coal combustion is a chemical process that powers many of the world's energy needs. In this process, coal burns, releasing energy as well as various byproducts, including sulfur dioxide, into the environment. Understanding the specifics of coal's composition, including non-combustibles like sulfur, is essential.

Key points about coal combustion include:

• Coal consists of hydrocarbons and impurities, including sulfur, which varies by coal type.
• During combustion, sulfur in coal converts to sulfur dioxide in the presence of oxygen.
• Managing the sulfur content is crucial to reduce emissions; lower-sulfur coal or technology that removes sulfur from emissions is often used.

In this exercise, we see that coal with a sulfur content of 2% is burned, making it a significant contributor to \(\text{SO}_2\) emissions. By calculating the total coal burned, we understand the scale of combustion required for such emissions.

Proper management of coal combustion involves balancing energy production with minimal environmental impact.

Power Plant Operation

Power plants play a central role in energy production, consuming vast amounts of coal. They are designed to convert the stored energy in coal into electricity, but this also results in substantial sulfur dioxide emissions as a byproduct.

Here's how power plant operations relate to the exercise:

• A 1000-MW power plant can burn around 700 metric tons of coal per hour, highlighting its significant coal consumption.
• Calculating the number of hours a power plant can run on a specific fuel quantity helps in resource planning and environmental impact assessments.
• Power plants must adhere to regulations limiting emissions, often requiring technological solutions like scrubbers to clean emissions before release.

This exercise calculates that burning 1625 million metric tons of coal would require roughly 2,321,428.57 hours at a typical power plant. Thus, efficient operation and planned maintenance are vital in optimizing both energy production and minimizing environmental impact.