Critical Constants
of Gases
Tc, Pc, and Vc — the three fundamental constants governing the liquefaction of real gases
What are Critical Constants?
Every real gas possesses three fundamental constants that together define the boundary between its gaseous and liquid phases. These are the critical temperature (Tc), critical pressure (Pc), and critical volume (Vc) — collectively known as the critical constants of the gas.
When a gas is cooled below its critical temperature and simultaneously subjected to sufficient pressure, it undergoes liquefaction. Above the critical temperature, no amount of pressure — however extreme — can force the gas into the liquid state. The molecules simply have too much kinetic energy to be held together by intermolecular forces.
At the critical point (where T = Tc and P = Pc), something remarkable happens: the boundary between the liquid and gaseous phases completely disappears. The two phases become indistinguishable — they share identical densities, identical refractive indices, and the meniscus separating them vanishes entirely. This phenomenon is called the critical phenomenon.
The highest temperature at which a gas can be converted into liquid by applying pressure. Above Tc, the gas cannot be liquefied regardless of pressure.
The critical temperature depends on the strength of intermolecular forces. Gases with stronger attractive forces (e.g. CO₂) have higher Tc values and are easier to liquefy.
The minimum pressure required to liquefy a gas at its critical temperature. At any temperature below Tc, a lower pressure than Pc suffices for liquefaction.
Pc represents the pressure needed to overcome the kinetic energy of gas molecules at precisely the critical temperature.
The volume occupied by one mole of a gas at its critical temperature and critical pressure. At the critical point, the molar volumes of the liquid and gas phases are equal.
Vc is related to the size of gas molecules. Larger, heavier molecules typically have larger critical volumes.
Understanding the Critical Point
The critical point is the unique state where a gas exists at both its critical temperature and critical pressure simultaneously. At this precise condition, the distinction between the liquid phase and the vapour phase ceases to exist — both phases coexist and are completely identical in all their physical properties.
This has a profound physical meaning: the meniscus (the interface between liquid and gas) disappears. The density of the liquid decreases and the density of the vapour increases as you approach the critical point, until they become equal at Tc. This equal density is the critical density, ρc = M / Vc.
The transition of a gas into liquid at the critical point without any phase boundary is called a critical phenomenon or supercritical transition. Above the critical point, the substance exists as a supercritical fluid — it has properties intermediate between a gas and a liquid.
Molecular Simulation — Liquefaction
Adjust the temperature and pressure below to observe how gas molecules behave. Watch the transition from gaseous state to liquid state as you cool the gas and increase pressure. The critical point is where the phase boundary disappears.
Critical Constants of Common Gases
The table below lists the experimentally determined critical constants for common gases. Note how gases with stronger intermolecular forces (polarity, hydrogen bonding) have higher Tc values — they are easier to liquefy at ordinary temperatures.
| Gas | Formula | Tc (K) | Pc (atm) | Vc (cm³/mol) | Compressibility Zc | Liquefy at 25°C? |
|---|---|---|---|---|---|---|
| Water | H₂O | 647.1 | 218.3 | 56.0 | 0.229 | Yes (cool) |
| Ammonia | NH₃ | 405.6 | 112.8 | 72.5 | 0.242 | Yes |
| Carbon Dioxide | CO₂ | 304.2 | 72.8 | 94.0 | 0.274 | Yes |
| Chlorine | Cl₂ | 417.0 | 76.1 | 124.0 | 0.276 | Yes |
| Sulphur Dioxide | SO₂ | 430.8 | 77.8 | 122.0 | 0.268 | Yes |
| Oxygen | O₂ | 154.6 | 50.1 | 73.4 | 0.288 | No (pre-cool) |
| Nitrogen | N₂ | 126.2 | 33.5 | 90.1 | 0.290 | No (pre-cool) |
| Hydrogen | H₂ | 33.2 | 12.8 | 65.0 | 0.305 | No (very hard) |
| Helium | He | 5.2 | 2.3 | 57.8 | 0.308 | No (hardest) |
| Methane | CH₄ | 190.6 | 45.4 | 99.0 | 0.286 | No (pre-cool) |
Van der Waals Equation & Critical Constants
Real gases deviate from ideal behaviour due to (1) finite molecular volumes and (2) intermolecular attractive forces. The van der Waals equation corrects for both:
Leave a Comment