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

01

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 = \( \frac{6 \times 10^6 \, tons \times 2000 \, pounds/ton \times 453.592 \, g/pound}{44.01 \, g/mol} \)

02

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): \( V_{ideal} = \frac{nRT}{P} \)

03

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: \( V_{liquid} = \frac{Mass \, of \, CO_{2}}{Density} \)

04

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.

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