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 coalfired power plant that produces about \(6 \times 10^{6}\) tons of \(\mathrm{CO}_{2}\) per year. (a) Assuming ideal gas behavior, \(1.00 \mathrm{~atm}\), 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 \(36{ }^{\circ} \mathrm{C}\) and \(90 \mathrm{~atm}\), what volume does it occupy?

Short answer

The volume of CO2 produced by the power plant is \(V = \frac{nRT}{P} = \frac{(6 \times 10^9\text{ kg})(0.0821\text{ L atm/mol K})(27+273.15\text{ K})}{1\text{ atm}}\). When stored as a liquid, the volume is \(V_\text{liquid} = \frac{6 \times 10^{9}\text{ kg}}{1200\text{ kg/m}^3}\). When stored as a gas, the volume is \(V_\text{gas} = \frac{nRT}{P} = \frac{(6 \times 10^9\text{ kg})(0.0821\text{ L atm/mol K})(36+273.15\text{ K})}{90\text{ atm}}\).

Step-by-step solution

a) Finding the volume of CO2

First, we need to find the volume of \(\mathrm{CO_2}\) produced by the power plant. We need to use the Ideal Gas Law formula, which is given by: \(PV=nRT\) Where P is the pressure, V is the volume, n is the number of moles, R is the gas constant, and T is the temperature. The number of moles, n, is given by the mass divided by the molar mass of the substance. The mass of CO2 produced per year is \(6 \times 10^{6}\) tons, or \(6 \times 10^{9}\) kg. The molar mass of CO2 is approximately 44 g/mol, or 0.044 kg/mol. Therefore: \(n = \frac{6 \times 10^{9}\text{ kg}}{0.044\text{ kg/mol}}\) Then, we can find the volume of CO2 using the Ideal Gas Law formula, with P = 1 atm, T = 27°C + 273.15 (to convert to Kelvin), and R = 0.0821 (using appropriate units): \(V = \frac{nRT}{P}\)

b) Volume of CO2 as a liquid

Now, we need to find the volume of CO2 when it's stored underground as a liquid. We're given its density, which is 1.2 g/cm³ or 1200 kg/m³. Using the mass of CO2 we calculated before, now we just need to divide the mass by density to find the volume: \(V_\text{liquid} = \frac{6 \times 10^{9}\text{ kg}}{1200\text{ kg/m}^3}\)

c) Volume of CO2 as a gas

Finally, we need to find the volume of CO2 when it's stored underground as a gas. We'll once again use the Ideal Gas Law formula, but this time with new given conditions: P = 90 atm, T = 36°C + 273.15 (to convert to Kelvin), and R = 0.0821 (using appropriate units): \(V_\text{gas} = \frac{nRT}{P}\) Now we have the three calculated volumes under different conditions.

Key concepts

Greenhouse Gases

Greenhouse gases are a group of compounds that are capable of trapping heat in the Earth's atmosphere. This heat-trapping effect is essential for maintaining the planet’s climate, but excessive amounts can lead to global warming. Carbon dioxide (CO extsubscript{2}), one of the most well-known greenhouse gases, is a byproduct of burning fossil fuels such as coal, oil, and natural gas.

These gases absorb infrared radiation from the sun and emit it in various directions, including back towards the Earth’s surface. This process enhances the natural "greenhouse effect," leading to an increase in global temperatures. Other common greenhouse gases include methane (CH extsubscript{4}), nitrous oxide (N extsubscript{2}O), and water vapor.

• Prevention: Reducing greenhouse gas emissions is crucial in mitigating climate changes. This can be achieved through improved energy efficiency, use of renewable energy sources, and technological innovations such as carbon capture and storage.
• Significant impact: Even small changes in greenhouse gas concentrations can have significant effects on climate and weather patterns due to their ability to trap heat.

Ideal Gas Law

The Ideal Gas Law is a fundamental equation used to relate the four properties of gases: pressure, volume, moles, and temperature. It is usually expressed as:
\[ PV = nRT \] Where

• P denotes pressure,
• V is volume,
• n represents the number of moles of the gas,
• R is the ideal gas constant (0.0821 L atm/mol K when using these units), and
• T is the temperature in Kelvin.

This law is particularly useful for theoretical calculations like determining the volume of carbon dioxide produced from fossil fuel combustion under specific conditions.

While it serves as a good approximation, the Ideal Gas Law assumes that gas particles do not interact with each other and occupy no space. Real gases, however, often show slight deviations from this behavior under high pressure and high temperature conditions.

Fossil Fuels

Fossil fuels are carbon-rich energy sources formed millions of years ago from the remains of living organisms. They include coal, oil, and natural gas, and are extensively used for electricity generation, heating, and powering vehicles.

• Combustion: During combustion, fossil fuels react with oxygen to produce energy, water vapor, and carbon dioxide. This reaction significantly contributes to CO extsubscript{2} emissions, driving global warming.
• Environmental Impact: The extraction and burning of fossil fuels have environmental impacts beyond just carbon emissions. They can lead to land degradation, air and water pollution, and adverse effects on wildlife.
• Transition: To combat climate change, there is a growing shift towards cleaner, renewable energy sources like solar, wind, and hydroelectric power which offer sustainable alternatives to fossil fuels.

Fossil fuels have been a reliable energy source, but their non-renewable nature and environmental consequences necessitate finding balance in energy consumption and sustainable practices.

Global Warming

Global warming refers to the long-term increase in Earth's average surface temperature due to the accumulation of greenhouse gases in the atmosphere. The concern is that continuous warming can trigger catastrophic climate changes, affecting ecosystems and human life.

• Causes: Major factors include the high emissions of carbon dioxide and other greenhouse gases from industrial activities, deforestation, and transportation.
• Consequences: Impacts include melting ice caps, rising sea levels, changes in precipitation patterns, and increased frequency of extreme weather events. These changes can cause habitat loss for many species and have dire consequences on food security and human health.
• Solutions: Effective solutions require a combination of policy change, innovation, and adaptation practices. This might involve enhancing energy efficiency, promoting sustainable agriculture, and improving public transportation infrastructure.

Global warming is a pressing global challenge that requires immediate and coordinated efforts across nations to ensure a sustainable future.