Question

Solid \(\mathrm{CO}_{2}\) is called dry ice. It sublimes at an atmospheric pressure of \(-78.5^{\circ} \mathrm{C}\). The triple point of \(\mathrm{CO}_{2}\) is \(-56.6{ }^{\circ} \mathrm{C}\) at \(517.8 \mathrm{kPa} . \mathrm{CO}_{2}\) becomes a supercritical fluid at \(31^{\circ} \mathrm{C}\) and 7.487 MPa. Using these data, construct a phase diagram for \(\mathrm{CO}_{2}\). labeling all the regions of your diagram.

Short answer

The phase diagram for \\(\mathrm{CO}_2\\) includes the solid, liquid, gas, and supercritical fluid regions, marked by sublimation, triple, and critical points.

Step-by-step solution

Understanding Key Points

First, identify the key points needed for the phase diagram. We have three important data points: the sublimation temperature at 1 atm (-78.5°C), the triple point (-56.6°C at 517.8 kPa), and the critical point (31°C and 7.487 MPa).

Diagram Axes Setup

Create a graph with the x-axis representing temperature (in °C) and the y-axis representing pressure (in kPa or MPa). Ensure the graph covers the range from below the sublimation point to beyond the critical point.

Plotting the Sublimation Point

Plot the sublimation point at -78.5°C and 1 atm (approximately 101.3 kPa) on the phase diagram. This is where solid \(\mathrm{CO}_2\) transitions directly to gas at atmospheric pressure.

Plotting the Triple Point

Plot the triple point at -56.6°C and 517.8 kPa. This is the only point on the phase diagram where solid, liquid, and gas phases coexist in equilibrium.

Plotting the Critical Point

Plot the critical point at 31°C and 7.487 MPa (or 7487 kPa). Beyond this point, \(\mathrm{CO}_2\) exists as a supercritical fluid, where the liquid and gas phases are indistinguishable.

Connecting the Phases

Draw curves connecting the points: a sublimation curve from the sublimation point to the triple point, a vaporization curve from the triple point to the critical point, and a melting curve (although often not seen in detail for \(\mathrm{CO}_2\)) connecting the triple point downward as pressure increases.

Labeling the Regions

Label the regions: below the sublimation curve as the solid phase, to the right of the sublimation curve as the gas phase, below the vaporization curve as the liquid phase (only between triple and critical points), and beyond the critical point as the supercritical fluid region.

Key concepts

Sublimation

Sublimation is a fascinating process where a substance transitions directly from a solid to a gas without passing through the liquid phase. In the context of carbon dioxide (CO₂), solid CO₂, known as dry ice, sublimes at a temperature of

• -78.5°C
• at atmospheric pressure (1 atm or 101.3 kPa).

This means that under these conditions, dry ice will change directly into CO₂ gas, an effect that can often be seen as fog or mist. Understanding sublimation is crucial because it is one of the main factors influencing the shape and characteristics of a CO₂ phase diagram. This unique property of dry ice makes it useful for a variety of applications such as cooling without leaving any residue, as it does not produce any liquid that would result from melting.

Triple Point

The triple point of a substance is a fascinating concept in thermodynamics. At this specific point, a substance can simultaneously exist in solid, liquid, and gas phases. For carbon dioxide

• the triple point occurs at -56.6°C
• at a pressure of 517.8 kPa.

It's represented on the phase diagram as a single point where the sublimation curve, vaporization curve, and melting curve intersect. This unique behavior underlines the state of physical equilibrium among the three phases and is a critical reference point when drawing a phase diagram.

Critical Point

The critical point marks a significant threshold in the behavior of substances.

• For CO₂, it occurs at 31°C and 7.487 MPa (or 7487 kPa).

Beyond this point, the distinction between the liquid and gas phases vanishes, leading to the formation of a supercritical fluid. What makes the critical point noteworthy is that above this temperature and pressure, it becomes impossible to distinguish between liquid CO₂ and gaseous CO₂, as they morph into one homogenous phase. The critical point reflects the endpoint of the vaporization curve on a phase diagram and signifies a complete change in the physical properties of CO₂.

Supercritical Fluid

A supercritical fluid occurs when a substance is held above its critical temperature and pressure. For CO₂, this state is achieved when the temperature is above 31°C and the pressure exceeds 7.487 MPa. In this supercritical state, CO₂ possesses unique properties:

• it behaves like a gas
  and can diffuse through solids
• yet it has the density of a liquid, allowing it to effectively dissolve materials.

Supercritical CO₂ is widely used in industrial processes such as decaffeination of coffee or the extraction of essential oils due to its efficiency and environmentally friendly characteristics. Understanding the nature of supercritical fluids helps to complete our knowledge of the phase behavior of substances like CO₂ under various conditions.

Phase Transitions

Phase transitions are the processes by which a substance changes from one state of matter to another, owing to shifts in temperature and pressure. In the context of CO₂, common transitions include:

• sublimation (solid to gas)
• melting (solid to liquid)
• vaporization (liquid to gas).

Each of these transitions is represented by a curve on the phase diagram:

• the sublimation curve shows where solid and gas phases coexist
• the melting curve aids in understanding the conversion between solid and liquid
• while the vaporization curve marks the change from liquid to gas.

These transitions help to map out the states in which CO₂ will exist under different environmental conditions, enabling further applications and understanding of its properties.