Q. \( \text{Phase diagram for } \mathrm{CO_2}. \)

A full “phase diagram for CO\(_2\)” usually means the standard pressure–temperature map showing the solid, liquid, and gas regions, plus the key phase boundaries (sublimation, fusion/melting, and vaporization/sublimation) and the special points (notably the triple point and the critical point). Below is a detailed, step-by-step guide to what the CO\(_2\) phase diagram looks like and how to read it.

Important note: CO\(_2\) behaves differently from many “simple” substances because its liquid phase exists only at high pressures. At 1 atm, solid CO\(_2\) (dry ice) converts directly to gas (sublimes); it does not melt into a stable liquid phase under normal atmospheric pressure.

1. Identify what axes the diagram uses

The standard phase diagram uses:

• Horizontal axis: Pressure, typically \(P\) (often on a logarithmic scale).

• Vertical axis: Temperature, typically \(T\).

Some textbooks instead plot pressure on a vertical axis; the logic of reading the regions and boundaries stays the same. The key is to label temperatures correctly and interpret the phase boundaries.

2. Label the three main regions

On the diagram for CO\(_2\), you will see three large labeled regions:

• Solid (s): Region where CO\(_2\) is dry ice (solid carbon dioxide).

• Liquid (l): Region where CO\(_2\) exists as a liquid. This region is “small” and only appears at higher pressures.

• Gas (g): Region where CO\(_2\) behaves as a gas (the usual “carbon dioxide gas”).

3. Draw/identify the phase boundaries

Three boundaries separate these regions. Each boundary corresponds to equilibrium between two phases:

3.1 Solid–gas boundary (sublimation curve)

This line separates solid and gas. It is called the sublimation curve for CO\(_2\).

Physically, it represents conditions where solid CO\(_2\) and gaseous CO\(_2\) coexist in equilibrium.

3.2 Solid–liquid boundary (fusion/melting curve)

This line separates solid and liquid. It is the fusion curve.

Physically, it represents the equilibrium melting (or freezing) temperature as a function of pressure.

3.3 Liquid–gas boundary (vaporization curve)

This line separates liquid and gas. It is the vaporization curve (or boiling curve).

Physically, it represents equilibrium between liquid and gas at each pressure.

4. Locate the triple point

The triple point is the single point where all three phases can coexist in equilibrium: solid, liquid, and gas.

For CO\(_2\), the triple point is approximately:

\[
T_{\text{triple}} \approx 216.6\ \text{K}, \qquad P_{\text{triple}} \approx 5.11\ \text{atm}
\]

How to use this:

• At temperatures and pressures below the triple point pressure, the liquid region does not exist as a stable phase.

• The sublimation line (solid–gas) meets the fusion line and the vaporization line at the triple point.

5. Locate the critical point

The critical point is where the distinction between liquid and gas disappears. Beyond this point there is only a single “supercritical” fluid phase.

For CO\(_2\), the critical point is approximately:

\[
T_c \approx 304.1\ \text{K}, \qquad P_c \approx 73.8\ \text{atm}
\]

How to use this:

• The liquid–gas boundary (vaporization curve) ends at the critical point.

• To the right of the critical point (higher pressure), there is a continuous transition (not a phase boundary) between gas-like and liquid-like behavior.

6. What the diagram implies at 1 atm (why dry ice sublimates)

Standard atmospheric pressure is about \(1\ \text{atm}\). On the CO\(_2\) phase diagram:

• \(1\ \text{atm}\) is far below the triple point pressure (\(\approx 5.11\ \text{atm}\)).

• So there is no liquid equilibrium region at \(1\ \text{atm}\).

• As you warm solid CO\(_2\), it crosses the solid–gas (sublimation) boundary, converting directly to gas.

The familiar “dry ice” sublimation temperature near 1 atm is about \(194\ \text{K}\) (approximately \(-79^\circ\text{C}\)). A typical CO\(_2\) phase diagram includes this relationship between pressure and sublimation temperature.

7. Supercritical region

Above the critical temperature and above the critical pressure, CO\(_2\) is in a supercritical state. It is neither “true gas” nor “true liquid.”

• In many diagrams, this appears as a region extending beyond the critical point.

• There is no sharp boundary between gas-like and liquid-like phases in the supercritical region.

8. How to sketch a clean qualitative CO\(_2\) phase diagram (what to draw)

If you need to draw it yourself qualitatively:

1. Draw axes of \(T\) (vertical) and \(P\) (horizontal).

2. Draw a line separating solid–gas (sublimation curve) that extends toward lower temperatures and lower pressures.

3. Mark the triple point at about \((216.6\ \text{K}, 5.11\ \text{atm})\).

4. From the triple point, draw two boundaries:

   • Solid–liquid (fusion) curve

   • Liquid–gas (vaporization) curve

5. Make sure the liquid region sits between the fusion and vaporization curves.

6. End the vaporization curve at the critical point at about \((304.1\ \text{K}, 73.8\ \text{atm})\).

7. Label regions (solid, liquid, gas, and optionally supercritical) clearly.

9. Key facts to remember (useful labels)

• Triple point: \(T \approx 216.6\ \text{K}\), \(P \approx 5.11\ \text{atm}\)

• Critical point: \(T \approx 304.1\ \text{K}\), \(P \approx 73.8\ \text{atm}\)

• At \(1\ \text{atm}\): no stable liquid CO\(_2\); solid sublimes directly to gas.