Critical Constants and Liquefaction of Gases Explained

Every gas has a critical temperature above which no amount of pressure can liquefy it — the molecules simply move too fast for attractions to hold them together. The critical temperature (Tc), critical pressure (Pc) and critical volume (Vc) together mark the end of the liquid–gas boundary: beyond this critical point, liquid and gas become one indistinguishable fluid.

This matters because liquefying gases is how we store and transport oxygen for hospitals, LNG for energy and nitrogen for industry. The whole technology rests on one rule: cool the gas below its critical temperature first, then compress it. Skip the cooling step and compression alone will never work.

Key Concepts

• Critical temperature (Tc): the highest temperature at which a gas can be liquefied by pressure alone. Above Tc, the substance is a supercritical fluid.
• Critical pressure (Pc): the minimum pressure needed to liquefy the gas exactly at Tc.
• Critical volume (Vc): the molar volume of the substance at the critical point.
• Critical point: the (Tc, Pc) point on a phase diagram where the liquid–vapour curve ends and meniscus disappears.
• van der Waals relations: Tc = 8a/(27Rb), Pc = a/(27b²), Vc = 3b, linking critical constants to the a and b of the gas.
• Liquefaction methods: (1) cool below Tc then compress; (2) Joule–Thomson expansion — a compressed gas cools when it expands through a throttle (below its inversion temperature); (3) the Linde and Claude processes, which recycle the cooled gas to chill the incoming stream.

Formulas

• Tc = 8a/(27Rb): kelvin; a in L²·bar/mol², b in L/mol, R = 0.08314 L·bar/mol·K.
• Pc = a/(27b²): same pressure units as used for a.
• Vc = 3b: litres per mole.

These follow from the van der Waals equation and are approximate — measured critical constants differ slightly.

Worked Example

Estimate the critical temperature of CO₂ from a = 3.59 L²·bar/mol² and b = 0.0427 L/mol, and check against the measured 304.2 K.

1. Use Tc = 8a/(27Rb).
2. Numerator: 8 × 3.59 = 28.72.
3. Denominator: 27 × 0.08314 × 0.0427 = 27 × 0.003550 = 0.09585.
4. Divide: Tc = 28.72 / 0.09585 = 299.6 K.
5. Compare: the measured value is 304.2 K, so the estimate is within about 2%.

Estimated Tc ≈ 300 K, close to the true 304.2 K.

Common Misconceptions

• Any gas can be liquefied by squeezing hard enough. False above Tc — oxygen (Tc = 154 K) will never liquefy at room temperature no matter the pressure; it must be cooled first.
• The critical temperature is the same as the boiling point. The normal boiling point is measured at 1 atm; Tc is always higher (for water: boiling point 373 K, Tc = 647 K).
• Liquefaction and condensation are different phenomena. Liquefaction of a gas is condensation — the terms describe the same gas-to-liquid change.

Real-World Applications

• Hospitals store liquid oxygen (Tc = 154 K) in cryogenic tanks for patients and surgery.
• LNG (liquefied natural gas, mostly methane, Tc = 191 K) is shipped across oceans in insulated tankers.
• Liquid nitrogen (Tc = 126 K) freezes food, preserves biological samples and cools superconductors.
• Supercritical CO₂ (above 304 K and 73.8 bar) decaffeinates coffee and extracts essential oils.
• Cryogenic rocket propellants (liquid H₂/O₂) depend on large-scale liquefaction plants.

Cool below Tc, then compress — that is the whole secret of liquefaction. The critical constants Tc = 8a/(27Rb), Pc = a/(27b²) and Vc = 3b connect a gas's molecular attractions and size to the exact point where gas and liquid merge.