Determining The Phase Of CO2 At 20°C And 25 Atm Using The Phase Diagram

Understanding the phases of matter is a fundamental concept in chemistry and physics. Phase diagrams are graphical representations that depict the conditions of temperature and pressure at which different phases of a substance are thermodynamically stable. Carbon dioxide (CO2) is a common substance that exists in solid (dry ice), liquid, and gaseous phases, depending on the temperature and pressure. In this article, we will delve into the CO2 phase diagram to determine the phase of carbon dioxide at 20°C and 25 atm pressure. This involves interpreting the diagram and pinpointing the region corresponding to the given conditions, ultimately leading to the correct identification of the phase. This exercise will not only enhance our comprehension of phase diagrams but also provide practical insights into the behavior of CO2 under varying conditions.

Understanding Phase Diagrams

Phase diagrams are graphical tools that illustrate the thermodynamically stable phases of a substance under different conditions of temperature and pressure. A typical phase diagram consists of regions representing solid, liquid, and gas phases, separated by phase boundaries or coexistence curves. These curves indicate the temperatures and pressures at which two phases can coexist in equilibrium. The points on these curves represent the conditions where a phase transition, such as melting, boiling, or sublimation, occurs. Understanding these diagrams is crucial for predicting the state of a substance under specific conditions.

The key features of a phase diagram include:

• Phase Regions: Each region represents a specific phase (solid, liquid, or gas) that is stable under the temperature and pressure conditions within that region.
• Phase Boundaries (Coexistence Curves): These lines indicate the conditions (temperature and pressure) where two phases coexist in equilibrium. For example, the solid-liquid boundary represents the melting point curve, and the liquid-gas boundary represents the boiling point curve.
• Triple Point: This is the unique point where all three phases (solid, liquid, and gas) coexist in equilibrium. It is a fixed point with a specific temperature and pressure.
• Critical Point: This point marks the end of the liquid-gas coexistence curve. Beyond the critical point, the distinction between liquid and gas phases disappears, and the substance exists as a supercritical fluid.

To effectively interpret a phase diagram, one must be able to locate a specific temperature and pressure on the diagram and identify the phase region in which that point falls. The phase boundary lines help determine the phase transitions that occur as temperature or pressure changes. For instance, tracing a horizontal line (constant pressure) across the diagram can show the phase transitions that occur as temperature increases, such as melting (solid to liquid) or boiling (liquid to gas). Similarly, tracing a vertical line (constant temperature) can illustrate phase transitions due to pressure changes. Mastering the interpretation of phase diagrams is essential for various applications in chemistry, materials science, and engineering.

The Phase Diagram of Carbon Dioxide (CO2)

To determine the phase of carbon dioxide at a specific temperature and pressure, we need to analyze its phase diagram. The phase diagram of CO2 is a graphical representation that shows the conditions under which CO2 exists in its solid, liquid, and gaseous phases. It is a valuable tool for understanding the behavior of CO2 under different temperature and pressure conditions.

Key Features of the CO2 Phase Diagram

• Solid Phase (Dry Ice): At low temperatures and high pressures, CO2 exists as a solid, commonly known as dry ice. The region representing the solid phase is typically found in the lower-left portion of the phase diagram.
• Liquid Phase: Under moderate temperature and pressure conditions, CO2 can exist as a liquid. The liquid phase region is usually located in the middle of the phase diagram.
• Gas Phase: At high temperatures and low pressures, CO2 exists as a gas. The gas phase region is typically found in the upper-right portion of the phase diagram.
• Triple Point: The triple point of CO2 is at -56.6 °C (216.55 K) and 5.11 atm. At this specific temperature and pressure, solid, liquid, and gaseous CO2 can coexist in equilibrium. The triple point is a critical reference point on the phase diagram.
• Critical Point: The critical point of CO2 is at 31.0 °C (304.3 K) and 72.9 atm. Beyond this point, CO2 exists as a supercritical fluid, where the distinction between liquid and gas phases disappears. Supercritical CO2 has unique properties and is used in various applications, such as supercritical fluid extraction.
• Phase Boundaries: The phase diagram includes lines that represent the equilibrium between two phases:
  • Sublimation Curve: This curve separates the solid and gas phases and shows the conditions under which solid CO2 sublimes (directly converts to gas).
  • Melting Curve: This curve separates the solid and liquid phases and shows the conditions under which solid CO2 melts into liquid CO2.
  • Vaporization Curve: This curve separates the liquid and gas phases and shows the conditions under which liquid CO2 vaporizes into gaseous CO2. This curve ends at the critical point.

By examining the CO2 phase diagram, we can predict the phase of CO2 at different temperatures and pressures. For example, at atmospheric pressure (1 atm), CO2 exists as a solid (dry ice) below -78.5 °C and as a gas above this temperature, directly subliming without passing through the liquid phase. This unique property makes dry ice useful as a refrigerant.

Determining the Phase of CO2 at 20°C and 25 atm

To address the question of what phase carbon dioxide is in at 20°C and 25 atm pressure, we need to utilize the CO2 phase diagram. This involves locating the point corresponding to these conditions on the diagram and identifying the phase region in which it falls. This process provides a clear and accurate way to determine the physical state of CO2 under the specified conditions. Here’s a step-by-step guide to how we can achieve this:

Step-by-Step Analysis

1. Locate 20°C on the Temperature Axis:

   • First, we need to find the position representing 20°C on the temperature axis of the phase diagram. The temperature axis typically runs horizontally, and the scale will indicate where 20°C is located. This temperature is above the triple point temperature of CO2 (-56.6 °C) and below the critical temperature (31.0 °C).

2. Locate 25 atm on the Pressure Axis:

   • Next, we identify the location of 25 atm on the pressure axis. The pressure axis usually runs vertically on the phase diagram. Find the point that corresponds to 25 atm. This pressure is significantly higher than the triple point pressure (5.11 atm) but lower than the critical pressure (72.9 atm).

3. Find the Intersection Point:

   • Now, trace a vertical line from the 20°C mark on the temperature axis and a horizontal line from the 25 atm mark on the pressure axis. The point where these two lines intersect represents the conditions of 20°C and 25 atm on the phase diagram.

4. Identify the Phase Region:

   • Observe which region of the phase diagram the intersection point falls into. In the case of CO2, the phase diagram typically has three main regions: solid, liquid, and gas. At 20°C and 25 atm, the intersection point falls within the liquid phase region. This is because the pressure is high enough to condense CO2 into a liquid at this temperature.

Conclusion

Based on the analysis of the CO2 phase diagram, we can definitively conclude that at 20°C and 25 atm pressure, carbon dioxide is in the liquid phase. This determination is crucial for various applications where CO2 is used, such as in industrial processes, refrigeration, and supercritical fluid extraction. Understanding the phase behavior of CO2 under different conditions is essential for optimizing these processes and ensuring safety.

Multiple Choice Question Answer

Based on our analysis, the correct answer to the question, "Using the phase diagram for CO2, what phase is carbon dioxide in at 20°C and 25 atm pressure?" is:

D. It is in the liquid phase.

This conclusion is reached by locating the point corresponding to 20°C and 25 atm on the CO2 phase diagram and observing that it falls within the region representing the liquid phase.

Explanation of Incorrect Options

To further solidify our understanding, let's briefly discuss why the other options are incorrect:

• A. It is at its melting point: The melting point is the temperature at which a substance transitions from solid to liquid. While CO2 has a melting point, it is not at the specific conditions of 20°C and 25 atm. The melting point line on the phase diagram represents the equilibrium between solid and liquid phases, and the given conditions do not fall on this line.
• B. It is at its boiling point: The boiling point is the temperature at which a substance transitions from liquid to gas. Similar to the melting point, the boiling point of CO2 varies with pressure. At 25 atm, the boiling point of CO2 is higher than 20°C, so CO2 is not at its boiling point under these conditions. The boiling point line (vaporization curve) on the phase diagram represents the equilibrium between liquid and gas phases, and the conditions of 20°C and 25 atm are not on this line.
• C. It is in the gas phase: The gas phase of CO2 is stable at higher temperatures and lower pressures. At 20°C and 25 atm, the pressure is high enough to maintain CO2 in the liquid phase, so it is not in the gas phase. The gas phase region on the phase diagram is located at lower pressures than 25 atm at this temperature.

By understanding why the incorrect options are not valid, we reinforce our comprehension of phase diagrams and the behavior of CO2 under different conditions. This knowledge is invaluable in various scientific and industrial applications, ensuring that we can accurately predict and control the phase of CO2 in different scenarios.

Conclusion

In summary, understanding phase diagrams is crucial for predicting the state of a substance under specific temperature and pressure conditions. By analyzing the CO2 phase diagram, we can determine that carbon dioxide exists in the liquid phase at 20°C and 25 atm pressure. This is achieved by locating the corresponding point on the phase diagram and observing the phase region in which it falls. This exercise not only answers the specific question but also reinforces our ability to interpret phase diagrams, a valuable skill in chemistry, physics, and various engineering disciplines. Understanding the behavior of CO2 under different conditions is essential for applications ranging from industrial processes to environmental science, highlighting the practical importance of mastering phase diagrams.