Problem 101 - Chemistry The Central Science

Question

Carbon dioxide, which is recognized as the major contributor to global warming as a "greenhouse gas," is formed when fossil fuels are combusted, as in electrical power plants fueled by coal, oil, or natural gas. One potential way to reduce the amount of \(\mathrm{CO}_{2}\) added to the atmosphere is to store it as a compressed gas in underground formations.Consider a 1000 -megawatt coal-fired power plant that produces about \(6 \times 10^{6}\) tons of \(\mathrm{CO}_{2}\) per year. (a) Assuming ideal-gas behavior, 1.00 atm, and \(27^{\circ} \mathrm{C},\) calculate the volume of \(\mathrm{CO}_{2}\) produced by this power plant. (b) If the \(\mathrm{CO}_{2}\) is stored underground as a liquid at \(10^{\circ} \mathrm{C}\) and 120 \(\mathrm{atm}\) and a density of \(1.2 \mathrm{g} / \mathrm{cm}^{3},\) what volume does it possess?(c) If it is stored underground as a gas at \(30^{\circ} \mathrm{C}\) and \(70 \mathrm{atm},\) what volume does it occupy?

Step-by-Step Solution

Answer

The volume of CO₂ produced by the power plant under ideal gas assumption is calculated using the ideal gas law, resulting in \( V_{ideal} = \frac{nRT}{P} \). When stored as a liquid, the volume is found by converting the mass of CO₂ to grams and using the given density, giving \( V_{liquid} = \frac{Mass \, of \, CO_{2}}{Density} \). Finally, when stored as a gas underground, the ideal gas law is again used to find the volume: \( V_{gas} = \frac{nRT}{P} \).

Step 1: Calculate the moles of CO₂ produced under ideal gas assumption

First, we need to determine the number of moles of CO₂ produced by the power plant per year. Given that the power plant produces \(6 \times 10^6\) tons of CO₂ per year, we can convert this to grams, then to moles using the molar mass of CO₂. 1 ton = 2000 pounds 1 pound = 453.592 g Molar mass of CO₂ = 12.01 g/mol (C) + 2 × 16.00 g/mol (O) = 44.01 g/mol Moles of CO₂ = \( \frac{6 \times 10^6 \, tons \times 2000 \, pounds/ton \times 453.592 \, g/pound}{44.01 \, g/mol} \)

Step 2: Calculate the volume of CO₂ produced under ideal gas assumption

Now we have the number of moles of CO₂. We can use the ideal gas law, which is given by: PV = nRT Where P is the pressure, V is the volume, n is the number of moles, R is the ideal gas constant, and T is the temperature in Kelvin. Given the conditions under which the CO₂ is produced: 1.00 atm and 27°C, we can convert the temperature to Kelvin: T = 27 + 273.15 = 300.15 K Plugging in the values, we can solve for V (volume): \( V_{ideal} = \frac{nRT}{P} \)

Step 3: Calculate the volume of CO₂ stored as a liquid

We are given that the CO₂ is stored underground as a liquid at 10°C and 120 atm, with a density of 1.2 g/cm³. To find the volume, we need to first convert the mass of the CO₂ to grams, then find the volume using the given density. First, convert the moles of CO₂ to mass in grams: Mass of CO₂ = Moles of CO₂ × Molar mass of CO₂ Finally, calculate the volume using the given density: \( V_{liquid} = \frac{Mass \, of \, CO_{2}}{Density} \)

Step 4: Calculate the volume of CO₂ stored as a gas underground

We are given that the CO₂ is stored underground as a gas at 30°C and 70 atm. To find the volume, we can use the ideal gas law as before. First, convert the temperature to Kelvin: T = 30 + 273.15 = 303.15 K Plugging in the values, solve for V (volume): \( V_{gas} = \frac{nRT}{P} \) This will give us the volume of CO₂ when stored as a gas underground.

Key Concepts

Greenhouse Gas

Greenhouse gases are substances in the Earth's atmosphere that trap heat, playing a crucial role in regulating the planet's climate. Among them, carbon dioxide (CO₂) is one of the most significant contributors to global warming. When greenhouse gases like CO₂ accumulate in the atmosphere, they create a 'blanket' effect, trapping heat from the sun.
This prevents the heat from escaping back into space and contributes to the planet's rising temperatures. This process is known as the greenhouse effect.

• Carbon dioxide is primarily released through human activities such as burning fossil fuels.
• Natural processes like respiration and volcanic eruptions also contribute to CO₂ emissions.
• The enhanced greenhouse effect caused by the increased concentration of CO₂ is a major driver of climate change.

Understanding the role of CO₂ as a greenhouse gas is crucial for developing strategies to mitigate climate change, such as reducing emissions and enhancing storage solutions.

Fossil Fuels Combustion

Combustion of fossil fuels is a primary source of energy but also a significant source of CO₂ emissions. Fossil fuels, such as coal, oil, and natural gas, are rich in carbon and, when burned, release CO₂ into the atmosphere. This process fuels power plants and vehicles, but it also accelerates the greenhouse effect.
Burning fossil fuels is incredibly energy-efficient, which is why it has been the dominant energy source for decades. However, it comes with environmental costs, as the carbon released contributes directly to global warming.

• Fossil fuels combustion generates approximately 75% of all CO₂ emissions.
• Efforts are being made worldwide to shift from fossil fuels to renewable energy sources.
• Reducing fossil fuel use can significantly decrease greenhouse gas emissions.

By understanding the link between fossil fuels combustion and CO₂ emissions, energy policies can better focus on sustainability and innovation in clean energy technologies.

Carbon Dioxide Storage

Carbon dioxide storage, also known as carbon capture and storage (CCS), is a technology designed to reduce CO₂ emissions by capturing it at the source and storing it underground. By preventing CO₂ from reaching the atmosphere, CCS aims to mitigate the negative impacts of greenhouse gases.
CO₂ can be stored in geological formations such as depleted oil and gas fields, or deep saline aquifers. These storage options provide a secure environment where CO₂ can be trapped for long periods.

• Carbon storage can significantly lower emissions from industrial sources, such as power plants.
• It is a crucial component of strategies to achieve carbon neutrality and limit global warming.
• Developing effective CO₂ storage technologies is vital for any serious effort to combat climate change.

Through CCS, industries can continue to operate while minimizing their environmental footprint, allowing time for the transition to renewable energy.