Phase Diagram

How the model works

A phase diagram shows the stable phase at each pressure and temperature. Lines mark where two phases coexist:

• Vaporisation curve (liquid–gas) runs from the triple point to the critical point. Along it, the vapour pressure follows the Clausius–Clapeyron relation, ln P = −ΔH_vap / RT + C.
• Sublimation curve (solid–gas) is below the triple point.
• Melting curve (solid–liquid) is nearly vertical. For water it leans left, because ice is less dense than liquid water, so pressure lowers the melting point slightly.

At the triple point all three phases coexist. Beyond the critical point, liquid and gas become indistinguishable: a supercritical fluid. CO₂'s triple point is above 1 atm (5.1 atm), which is why dry ice sublimes instead of melting at normal pressure.

Water's boiling curve uses the Antoine equation with NIST constants. CO₂'s curves use Clausius–Clapeyron fitted through its triple and critical points (34.6 atm at 0 °C, against a measured 34.9 atm).

Simplified single-phase-region map; water's many high-pressure ice phases are not shown. Pressure uses a logarithmic axis.

Guided experiments

1. Boil water on a mountain. Water at 0.6 atm (about 4200 m altitude). Prediction: it boils at about 86 °C instead of 100 °C, so pasta takes longer. Water at 0.6 atm
2. Dry ice. CO₂ at 1 atm, warming from −100 °C. Prediction: solid turns straight to gas at about −78.5 °C. There is no liquid at 1 atm. Warm dry ice
3. Pressure cooker. Water at 2 atm. Prediction: the boiling point rises to about 120 °C, which cooks food faster. Water at 2 atm

Challenge

Why can't you make liquid CO₂ in an open container, however cold you make it? What is the lowest pressure at which liquid CO₂ can exist?

References

• OpenStax, Chemistry 2e, §10.4 “Phase Diagrams”.
• NIST Chemistry WebBook, thermophysical properties of water and carbon dioxide.