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 CO₂ 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⨉10⁶ tons of CO₂ per year. (b) If the CO₂ is stored underground as a liquid at 10 C and 12.16 MPa and a density of 1.2 g/cm³, what volume does it possess?

Name: Chemistry: The Central Science
Author: Brown
ISBN: 9780134414232

Verified step by step guidance

First, convert the mass of CO2 from tons to grams. Since 1 ton is equal to 1,000,000 grams, multiply the given mass of CO2 (6⨉10^6 tons) by 1,000,000 to get the mass in grams.

Next, use the formula for density, which is \( \text{Density} = \frac{\text{Mass}}{\text{Volume}} \), to solve for the volume. Rearrange the formula to \( \text{Volume} = \frac{\text{Mass}}{\text{Density}} \).

Substitute the mass in grams and the given density (1.2 g/cm^3) into the rearranged formula to calculate the volume in cubic centimeters.

Convert the volume from cubic centimeters to cubic meters. Since 1 cubic meter is equal to 1,000,000 cubic centimeters, divide the volume in cubic centimeters by 1,000,000 to get the volume in cubic meters.

Finally, ensure that all units are consistent and check your calculations for any errors. The volume calculated will be the volume of CO2 stored underground as a liquid at the given conditions.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Ideal Gas Law

The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas through the equation PV = nRT. While the question involves CO2 in a liquid state, understanding gas behavior under varying conditions is crucial for grasping how gases can be compressed and stored. This law helps predict how changes in temperature and pressure affect gas volume.

Density and Volume Relationship

Density is defined as mass per unit volume (density = mass/volume). In this context, knowing the density of liquid CO2 allows us to calculate its volume when a specific mass is given. This relationship is essential for converting the mass of CO2 produced by the power plant into a volume that can be stored underground.

Phase Changes of Substances

Phase changes refer to the transitions between solid, liquid, and gas states of matter, influenced by temperature and pressure. In this scenario, CO2 is stored as a liquid at a specific temperature and pressure, which is critical for understanding how it behaves and can be effectively stored. Recognizing the conditions under which CO2 remains in liquid form is vital for the calculations involved.

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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 CO₂ 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 6×10⁶ tons of CO₂ per year. (a) Assuming ideal-gas behavior, 101.3 kPa, and 27 °C, calculate the volume of CO₂ produced by this power plant.

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