Critical Constants
of Gases

Critical constants of gases are the characteristic temperature, pressure and molar volume associated with the critical point of a substance. These three quantities are called critical temperature (T_c), critical pressure (P_c) and critical volume (V_c). They help explain why some gases can be liquefied by compression while others require substantial cooling first.

In ordinary conditions, a gas can often be converted into a liquid by lowering its temperature and increasing its pressure. However, pressure alone cannot turn a substance into a distinct liquid phase when its temperature is above the critical temperature. Above this limit, the substance can become a supercritical fluid when both its temperature and pressure exceed their critical values.

The critical constants of gases are important in physical chemistry because they connect molecular attractions, molecular size, real-gas behaviour and phase equilibrium. They are also used in industrial gas processing, refrigeration, chemical engineering and the design of systems that operate at high pressures.

The critical point is the state at which the liquid–vapour boundary disappears. As a liquid is heated towards its critical temperature, its density generally decreases, while the density of the vapour increases. At the critical point, the two densities become equal, and the visible meniscus separating liquid from vapour disappears.

The critical constants of gases therefore describe a limit of ordinary liquid–vapour equilibrium. At temperatures below T_c, compression can produce a liquid phase under suitable conditions. At temperatures above T_c, there is no separate liquid–vapour transition produced simply by increasing pressure.

A substance above both its critical temperature and critical pressure is in the supercritical region. A supercritical fluid is neither an ordinary liquid nor an ordinary gas. Its density and solvent properties can resemble those of a liquid, while its ability to diffuse through materials can resemble that of a gas. Supercritical carbon dioxide, for example, is used in processes such as coffee decaffeination and selective extraction.

The ideal gas equation assumes that molecules have negligible volume and experience no intermolecular attraction. Real gases do not satisfy these assumptions perfectly, especially at high pressure and low temperature. The van der Waals equation accounts approximately for molecular attraction and excluded volume.

For one mole of a gas, using molar volume V_m, the equation is:

How the critical values are derived

Write the van der Waals equation in pressure form:

At the critical point, the P–V isotherm has a horizontal inflection point. Therefore, its first and second derivatives with respect to molar volume are both zero at constant temperature. Differentiating gives:

Solving these simultaneous conditions gives V_c = 3b. Substituting this result into the derivative equations gives T_c = 8a/(27Rb). Substituting the critical temperature and volume into the original equation then gives P_c = a/(27b²). These results form the standard van der Waals expressions for the critical constants of gases.

Use this simplified molecular animation to explore how temperature and pressure relate to critical constants of gases. Select a substance and adjust the sliders. The animation illustrates qualitative trends rather than calculating a precise phase equilibrium.

The following approximate reference values show how critical constants differ among substances. Values can vary slightly between data sources because of rounding and reference conditions. Critical volume is molar volume at the critical point.

1. Liquefaction of gases

Critical temperature helps determine whether cooling is necessary before a gas can be liquefied by compression. This is fundamental to gas storage and separation processes.

2. Refrigeration and cooling systems

Refrigerant selection depends on pressure–temperature behaviour and critical properties. Engineers use critical data to understand the operating limits of refrigeration and heat-pump cycles.

3. Chemical process design

Critical constants are used in equations of state to estimate gas density, phase equilibrium and fluid behaviour under high-pressure conditions. More advanced equations of state may provide better accuracy than the van der Waals model.

4. Supercritical extraction

Supercritical carbon dioxide is used as an extraction medium for selected food, fragrance and pharmaceutical processes. Its solvent properties can be adjusted by changing pressure and temperature.

5. Understanding intermolecular forces

Van der Waals constants connect molecular attractions and excluded volume with predicted critical properties. The attraction parameter a tends to increase with stronger attractive interactions, while b represents an approximate molecular-volume correction.

• Mixing up critical temperature and critical pressure: T_c is a temperature limit for pressure-induced liquefaction; P_c is the pressure at the critical point.
• Using the wrong volume: The displayed van der Waals formulas use molar volume. If the equation is written for n moles using total volume V, the equation must include n consistently.
• Forgetting absolute temperature: Critical temperature is expressed in kelvin, not degrees Celsius, when used in gas equations.
• Assuming Z_c is always 0.375: This is the van der Waals prediction. Experimental critical compressibility factors depend on the substance.
• Calling every compressed gas a liquid: Above T_c, a substance does not become an ordinary liquid merely because pressure increases.
• Confusing the critical point with the triple point: The triple point is where solid, liquid and vapour coexist; the critical point marks the end of the liquid–vapour boundary.

Use the video panel below to study the topic alongside the written notes, formulas and practice quiz.

The critical constants of gases provide a practical way to describe the end of the liquid–vapour equilibrium curve. Critical temperature defines the temperature limit for pressure-induced liquefaction, critical pressure is the pressure at the critical point, and critical molar volume is the molar volume at that state.

The van der Waals equation gives the useful relationships T_c = 8a/(27Rb), P_c = a/(27b²) and V_c = 3b. Remember that these are model predictions and that measured values may differ. Use the molecular simulation, P–V graph, reference table and MCQ quiz on this page to reinforce the key concepts.

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