Problem 94 - 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 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?

Step-by-Step Solution

Answer

(a) The volume of CO2 produced by the power plant is approximately \(2.02 \times 10^{13} \, \text{L}\). (b) The volume of CO2 stored as a liquid is approximately \(5 \times 10^{12} \, \text{cm}^3\). (c) The volume of CO2 stored as a gas underground is approximately \(2.24 \times 10^{12} \, \text{L}\).

Step 1: (a) Volume of CO2 Produced

To determine the volume of CO2 produced by the power plant, we can use the Ideal Gas Law: \(PV = nRT\) Where P is the pressure (atm), V is the volume (L), n is the amount of CO2 (moles), R is the ideal gas constant (0.08206 L*atm/mol*K), and T is the temperature (K). First, we have to convert the given mass of CO2 into moles. Since the power plant produces 6 x 10^6 tons of CO2 per year, we can convert this to moles using the molar mass of CO2 (12 + 16*2 = 44 g/mol): \(6 \times 10^6 \, \text{tons} \, \mathrm{CO}_{2} \times \frac{10^3 \, \text{kg}}{1 \, \text{ton}} \times \frac{10^3 \, \text{g}}{1 \, \text{kg}} \times \frac{1 \, \text{mol} \, \mathrm{CO}_{2}}{44 \, \text{g}}=8.18 \times 10^{10} \, \text{mol} \, \mathrm{CO}_{2}\) Now we can calculate the volume at given temperature and pressure. Remember to convert to temperature in Kelvin (27°C + 273.15 = 300.15K): \(V = \frac{nRT}{P} = \frac{(8.18 \times 10^{10} \, \text{mol})(0.08206 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K})(300.15 \, \text{K})}{1.00 \, \text{atm}} = 2.02 \times 10^{13} \, \text{L}\) The volume of CO2 produced is approximately 2.02 x 10^13 L.

Step 2: (b) Volume of CO2 Stored as Liquid

To determine the volume of CO2 stored as a liquid, we will use the given density and the mass of CO2 produced: Density = mass/volume \(volume=\frac{mass}{density}\) First, convert the mass of CO2 produced into grams: \(6 \times 10^6 \, \text{tons} \, \mathrm{CO}_{2} \times \frac{10^3 \, \text{kg}}{1 \, \text{ton}} \times \frac{10^3 \, \text{g}}{1 \, \text{kg}} = 6 \times 10^{12} \, \text{g} \, \mathrm{CO}_{2}\) Next, calculate the volume using density: \(volume = \frac{6 \times 10^{12} \, \text{g}}{1.2 \, \text{g/cm}^3} = 5 \times 10^{12} \, \text{cm}^3\) The volume of CO2 stored as a liquid is approximately 5 x 10^12 cm^3.

Step 3: (c) Volume of CO2 Stored as Gas

To find the volume of CO2 stored as gas underground, we will again use the Ideal Gas Law and the given temperature and pressure. Convert the temperature to Kelvin (36°C + 273.15 = 309.15K): \(V = \frac{nRT}{P} = \frac{(8.18 \times 10^{10} \, \text{mol})(0.08206 \, \text{L} \cdot \text{atm} / \text{mol} \cdot \text{K})(309.15 \, \text{K})}{90 \, \text{atm}} = 2.24 \times 10^{12} \, \text{L}\) The volume of CO2 stored as a gas underground is approximately 2.24 x 10^12 L.

Key Concepts

Greenhouse Gas

Understanding the impact of greenhouse gases on our environment is pivotal in the battle against global warming. Greenhouse gases, such as carbon dioxide (CO₂), trap heat in the Earth's atmosphere, creating what is known as the greenhouse effect. This effect is essential for life as we know it, as it keeps the planet warm enough to sustain ecosystems. However, human activities, particularly the burning of fossil fuels, have increased the concentration of these gases, thus enhancing the greenhouse effect and contributing to global warming.

The exercises, like the one dealing with CO₂ emissions from power plants, help students apply chemical principles to real-world environmental issues. These problems not only reinforce the scientific concepts of gas behavior but also emphasize the significance of our energy choices on the planet's climate.

CO2 Sequestration

One strategy to mitigate greenhouse gas emissions is through CO₂ sequestration, a process of capturing and storing atmospheric CO₂. It can be stored underground in geological formations, in the ocean, or transformed into another substance.

The hypothetical scenario in our exercise explores CO₂ sequestration by storing the gas in underground formations either as a compressed gas or as a liquid. Understanding the conditions and volumes associated with this process is essential for students to appreciate how chemistry can offer solutions to environmental challenges. Such problems provide insights into the practical aspects of environmental management and the role chemists can play.

Molar Mass Calculation

A fundamental skill in chemistry is the molar mass calculation, which involves determining the mass of one mole of a substance. It is a critical step in converting between the mass of a substance and the number of moles since the molar mass serves as a conversion factor.

The molar mass of a compound like CO₂ is calculated by summing the atomic masses of its constituent elements, measured in grams per mole (g/mol). For example: CO₂ has a molar mass of 44 g/mol (12 g/mol from carbon and 16 g/mol from each of the two oxygen atoms). Accurate molar mass calculations are essential in various chemical calculations, including those of the Ideal Gas Law.

Gas Density and Volume

The concepts of gas density and volume are tightly intertwined in chemistry. Gas density is a measure of a gas's mass per unit volume and can significantly vary with pressure and temperature changes.

The Ideal Gas Law provides a framework to understand how gases will respond to changes in conditions. In the exercise scenario, it is important for students not only to apply the law mathematically but also to conceptualize it in terms of physical changes occurring during the sequestration of CO₂ as its storage conditions change from a gaseous state at one temperature and pressure to either a liquid state or a different set of temperature and pressure.

Environmental Chemistry

Lastly, a grasp of environmental chemistry is critical for understanding human impacts on the environment and for the development of sustainable practices. This field of chemistry studies the chemical and biochemical phenomena occurring in natural places.

The exercises focusing on CO₂ emissions from power plants and their sequestration shed light on environmental chemistry in action. This includes aspects such as anthropogenic emissions, the behavior of chemicals in the atmosphere, and the technological methods to reduce the environmental footprint of industrial activities. It is a bridging concept that connects chemical knowledge with ecological and societal outcomes.