Problem 101 - Chemistry The Central Science In Si Units

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, \(101.3 \mathrm{kPa}\), and \(27^{\circ} \mathrm{C}\), calculate the volume of \(\mathrm{CO}_{2}\) produced by this power plant. \((\mathbf{b})\) If the \(\mathrm{CO}_{2}\) is stored underground as a liquid at \(10^{\circ} \mathrm{C}\) and \(12.16 \mathrm{MPa}\) and a density of \(1.2 \mathrm{~g} / \mathrm{cm}^{3},\) what volume does it possess? \((\mathbf{c})\) If it is stored underground as a gas at \(30^{\circ} \mathrm{C}\) and \(7.09 \mathrm{MPa},\) what volume does it occupy?

Step-by-Step Solution

Answer

(a) CO2 gas occupies 3.362 trillion liters, (b) liquid CO2 occupies 5 billion liters, (c) CO2 gas at high pressure occupies 482.6 million liters.

Step 1: Convert CO2 Mass to Moles

Given mass of \(\mathrm{CO}_2\) is \(6 \times 10^6\) tons per year. To convert this to grams, multiply by \(10^6\). Mass in grams: \(6 \times 10^6 \times 10^6 = 6 \times 10^{12}\) g. Molar mass of \(\mathrm{CO}_2\): \(44 \text{ g/mol}\). Number of moles: \(\frac{6 \times 10^{12}}{44} = 1.364 \times 10^{11} \text{ mol}\).

Step 2: Calculate Ideal Gas Volume

Use the ideal gas law to find the volume. \(PV = nRT\). Given \(P = 101.3 \text{ kPa} = 101300 \, \text{Pa}\), \(T = 27^{\circ} \text{C} = 300 \text{K}\), and \(n = 1.364 \times 10^{11} \text{ mol}\). \(R = 8.314 \text{ J/(mol K)}\). Volume, \(V = \frac{nRT}{P} = \frac{1.364 \times 10^{11} \times 8.314 \times 300}{101300}\). Calculating gives \(V = 3.362 \times 10^{12} \text{ liters}\).

Step 3: Convert Volume for Liquid CO2

Given the density of liquid \(\mathrm{CO}_2\) is \(1.2 \text{ g/cm}^3\), convert the total mass to volume using density: Volume \(= \frac{\text{mass in grams}}{\text{density}} = \frac{6 \times 10^{12}\, \text{g}}{1.2 \text{ g/cm}^3}\). Remembering that \(1\, \text{cm}^3 = 10^{-3}\, \text{L}\), volume in liters is: \(5 \times 10^{12} \text{ cm}^3 = 5 \times 10^{9} \text{ L}\).

Step 4: Calculate Gas Volume at High Pressure

For storage as a gas, we need to use the ideal gas law again.Given \(P = 7.09 \text{ MPa} = 7.09 \times 10^6 \text{ Pa}\) and \(T = 30^{\circ} \text{C} = 303 \text{ K}\). Volume, \(V = \frac{nRT}{P} = \frac{1.364 \times 10^{11} \times 8.314 \times 303}{7.09 \times 10^6}\). Calculating gives \(V = 4.826 \times 10^8 \text{ L}\).

Key Concepts

Carbon Dioxide Storage

Storing carbon dioxide (CO\(_2\)) effectively is crucial in the fight against global warming. Underground carbon storage is one of the methods proposed to prevent excess CO\(_2\) from entering the atmosphere. This involves compressing CO\(_2\) into a liquid or gas and storing it in geological formations deep under the ground. By doing this, the amount of CO\(_2\) in the atmosphere can be significantly reduced.

Some potential sites for CO\(_2\) storage include depleted oil and gas fields, unmineable coal seams, and deep saline aquifers. These formations can safely retain CO\(_2\) for thousands of years, minimizing the risk of leakage.

• **Advantages**: It helps decrease atmospheric CO\(_2\) levels, slows climate change, and repurposes geological formations.
• **Challenges**: Includes ensuring long-term storage safety, the cost of storage, and the need for rigorous monitoring.

Understanding the size required for storage helps decide the feasibility of this solution. For example, storing 6 million tons of CO\(_2\) from a coal-fired power plant requires an understanding of the physical state of CO\(_2\)—whether stored as a gas or liquid—because each state requires different volumes.

Global Warming

Global warming refers to the long-term increase in Earth's average temperature, primarily due to the emission of greenhouse gases such as carbon dioxide (CO\(_2\)), methane, and nitrous oxide. These gases trap heat in the atmosphere, preventing it from escaping into space.

As \CO\(_2\) levels rise, the greenhouse effect intensifies, leading to climate changes, including severe weather events, rising sea levels, and biodiversity losses. Human activities, such as burning fossil fuels and deforestation, are the main contributors to this rise in greenhouse gases.

• **Effects on the Environment**: Increased temperatures can result in the melting of polar ice caps, more instances of extreme weather, and shifts in ecosystems and wildlife patterns.
• **Social Impacts**: Global warming affects agriculture, water supply, and leads to economic strains, especially in vulnerable communities.

To address global warming, reducing CO\(_2\) emissions is crucial, along with practicing other forms of sustainability and conservation.

Coal-Fired Power Plant

Coal-fired power plants are a major source of electrical energy worldwide. They function by burning coal to produce steam, which then spins turbines connected to electric generators. However, this process emits significant amounts of carbon dioxide (CO\(_2\)) into the atmosphere.

Coal-fired power plants are known for their high energy output but are also notorious for their environmental impact due to their CO\(_2\) emissions. A typical 1000-megawatt plant can produce millions of tons of CO\(_2\) annually, contributing heavily to global warming.

• **Operation**: Coal combustion generates heat, converting water to steam to drive electricity-generating turbines.
• **Environmental Concerns**: Apart from CO\(_2\), burning coal releases sulfur oxides, nitrogen oxides, and particulates, which can contribute to air pollution and acid rain.

Efforts to enhance efficiency and reduce emissions in coal plants include improved combustion technology and carbon capture and storage systems.

Greenhouse Gases

Greenhouse gases are atmospheric gases that trap heat from the sun, warming Earth's surface. Carbon dioxide (CO\(_2\)), methane (CH\(_4\)), and nitrous oxide (N\(_2\)O) are the primary greenhouse gases.

While these gases occur naturally, human activities have significantly increased their concentrations in the atmosphere. The burning of fossil fuels releases large quantities of CO\(_2\), contributing to the greenhouse effect and further causing global warming.

• **Sources**: Major sources include power plants, vehicles, agriculture, and industries.
• **Impact**: Higher greenhouse gas levels enhance the warming of the planet, leading to climate instability and a host of environmental issues.

Mitigating the effects of greenhouse gases involves reducing emissions through cleaner energy alternatives, enhancing energy efficiency, and developing technologies for carbon capture and storage. Understanding the role of greenhouse gases helps society develop better policies and practices to curb their adverse impacts.