Critical constants

The critical constants of a real gas describe the conditions for liquefaction of the gas.

Thomas Andrews, an Irish chemist, conducted experiments on the liquefaction of gases in the 1860s and developed the concept of critical constants, which is summarised as follows:-

Consider a gas, Y, confined by a piston in a cylinder. The diagram below shows the pressure of the gas in the cylinder as the piston is pushed to vary the volume at various temperatures with T1 > T2 > T3 > T4 > T5. Each coloured line, called an isotherm, describes the change in pressure versus the change in molar volume of the gas at a specific temperature.

The isotherms at higher temperatures have smooth curves, while those at lower temperatures consist of horizontal portions. As we compress the gas at point A at temperature T5, its pressure increases until just to the left of point B, where the gas starts to condense into its liquid form (it exists in both the liquid and gaseous phases with a defined surface separating the two). The system is now at equilibrium, where Y(g)\rightleftharpoons Y(l). The fact that the gas condenses into a liquid implies that it is a real gas (an ideal gas is devoid of intermolecular interactions).

As we manually compress the system further, more liquid is formed, as the system reacts according to Le Chatelier’s principle: the system counteracts the increase in pressure (decrease in volume) by shifting the position of the equilibrium of Y(g)\rightleftharpoons Y(l) to the right to reduce the pressure, resulting in the pressure of the gas being constant. Hence, the curve from B to C is horizontal and is called a tie line. The pressure corresponding to the tie line is known as the vapour pressure of the liquid atT5. At point C, all the gas is condensed into liquid with the piston touching the surface of the liquid.

The volume hardly changes when we compress the system further from C to D, as the liquid state of a substance is relatively incompressible. If we repeat the entire compression process at higher temperatures, we find that the width of the tie line shortens, e.g. for T4, where it reduces to a maximum point (marked X) at T3. We call this point the critical point of the substance and the isotherm that passes through it, the critical isotherm.

The temperature that produces the critical isotherm is called the critical temperature, Tc, e.g. Tc for CO2 is 31.040C. The pressure and molar volume at the critical point is known as the critical pressure, pc, and critical molar volume, Vc, respectively. pc, Vc, and Tc are collectively called the critical constants of a substance.

The gas that is described by isotherms at temperatures above Tc cannot be compressed into a liquid regardless of the pressure applied. Due to the high pressure environment at temperatures above Tc, the gas has a density that is closer to that of a liquid and is called a supercritical fluid even though it is by definition a gas.

The density of a supercritical fluid and hence its solubility can be optimised for a particular application by adjusting its pressure. Supercritical CO2, for example, is used to dissolve and extract caffeine from coffee beans and as a dry-cleaning solvent.

Generally, the regions shaded yellow, blue, pink and grey in the above graph represent the gas phase, the liquid-gas phase, the liquid phase and the supercritical fluid phase respectively.

Lastly, it is important to note that at points B, C, X and all other points on the boundary separating the liquid-gas zone from the other zones, the substance exists only in one phase. For example, at the critical point, the meniscus between the liquid and gas (supercritical fluid) phases disappears, as there is no difference in densities of the liquid and gas (supercritical fluid).


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