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

To construct a phase diagram for CO₂, follow these steps: 1. Draw axes for pressure and temperature, labeling them as "Pressure (P)" and "Temperature (T)". 2. Mark the given points on the diagram: sublimation point (-78.5°C, atmospheric pressure), triple point (-56.6°C, 517.8 kPa), and supercritical fluid point (31°C, 7.487 MPa). 3. Define and label the regions for solid, liquid, gas, and supercritical fluid phases of CO₂ using the marked points. 4. Draw the boundaries between different phases: the sublimation line between solid and gas regions, the vaporization line between liquid and gas regions, and the line separating liquid and supercritical fluid regions. The completed phase diagram will have labeled regions and points representing different states of CO₂.

Step-by-step solution

Draw axes for the phase diagram

Draw a vertical axis for pressure and a horizontal axis for temperature. Label the axes as "Pressure (P)" and "Temperature (T)" respectively.

Mark given points on the diagram

Using the given data, mark the following points on the phase diagram: - Sublimation point: (-78.5°C, atmospheric pressure) - Triple point: (-56.6°C, 517.8 kPa) - Supercritical fluid point: (31°C, 7.487 MPa)

Define and label the regions

Using the marked points, we can define the regions for the solid, liquid, and gas phases of CO₂: - Solid region: below and to the left of the sublimation and triple points - Liquid region: between the triple and supercritical fluid points, above the atmospheric pressure line (not including the sublimation point) - Gas region: above and to the right of the sublimation and triple points and below the critical point - Supercritical fluid region: above and to the right of the supercritical fluid point Label each region accordingly on the diagram.

Draw boundaries between regions

Using the marked points, draw the boundaries between different phases: 1. Draw a line from the sublimation point to the triple point. This line represents the boundary between solid and gas regions (sublimation line). 2. Draw a line from the triple point to the supercritical fluid point. This line represents the boundary between liquid and gas regions (vaporization line). 3. Draw a vertical line from the supercritical fluid point. This line represents the boundary between liquid and supercritical fluid regions. Now the phase diagram for CO₂ is complete with labeled regions and points.

Key concepts

Triple Point

The triple point of a substance is a unique set of conditions where all three phases – solid, liquid, and gas – can coexist in equilibrium. It's a special intersection point on a phase diagram that highlights the specific temperature and pressure required for this balance.
A well-known example is the triple point of carbon dioxide (CO₂), which occurs at -56.6 °C and 517.8 kPa. At this precise point, dry ice (solid CO₂), liquid CO₂, and CO₂ gas are all in equilibrium. When CO₂ is at its triple point, small changes in temperature or pressure can push the substance into any one of these phases.
Understanding the triple point is crucial as it provides insight into the stability and behavior of a substance under varying atmospheric conditions. This concept is not only vital for scientists and engineers working with gases but also in manufacturing processes where precise temperature and pressure control is necessary.

Supercritical Fluid

A supercritical fluid is a state of matter that occurs above a substance's critical temperature and pressure. In this state, the substance doesn't behave as a conventional liquid or gas but shares properties of both. Supercritical fluids can diffuse through solids like a gas and dissolve materials like a liquid.
For CO₂, it becomes a supercritical fluid at 31 °C and 7.487 MPa. At this point, CO₂ exhibits unique characteristics valuable for industrial applications, such as supercritical fluid extraction used in food processing, pharmaceuticals, and cosmetics.
Because supercritical fluids can easily penetrate materials while dissolving select compounds, they are extensively utilized in processes that require precise separation and purification. This makes them environmentally friendly alternatives in many industries, reducing the reliance on harsh chemical solvents.

Sublimation

Sublimation is the process where a solid turns directly into a gas without passing through the liquid phase. This occurs under specific conditions of temperature and pressure, representative on a phase diagram by the sublimation line.
For carbon dioxide, sublimation is observed when solid dry ice transitions directly to CO₂ gas at -78.5 °C and atmospheric pressure. This process is straightforward because CO₂ at this pressure never becomes a liquid under atmospheric conditions.
Sublimation is a fascinating chemical process widely used in everyday applications. For instance, it's harnessed in freeze-drying foods and other products, allowing moisture to evaporate without going through a liquid stage, preserving the structural integrity. By understanding sublimation and its conditions, industries can better manage methods for controlling substance phase changes efficiently.