Non-ideal behaviour, liquefaction and plasma

Chemistry · Gases. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.

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The idea

An ideal gas obeys PV = nRT under all conditions. Real gases do not. We measure the difference with the compressibility factor, Z = PV/nRT, which is 1 for an ideal gas. Real gases deviate most at low temperature and high pressure, when the molecules are close together and slow.

Two postulates of the kinetic theory are at fault: that molecules have no volume and that they do not attract each other. The van der Waals equation corrects both.

The attractions are what allow gases to be liquefied. A gas must first be cooled below its critical temperature. At very high temperatures atoms lose electrons and the gas becomes plasma.

Rules to remember

Real gases are nearly ideal at high temperature and low pressure
Z = PV/nRT. Z < 1: attractive forces dominate. Z > 1: the volume of the molecules dominates. H₂ and He have very weak attractions
van der Waals equation: (P + an²/V²)(V − nb) = nRT. The constant a corrects for attractive forces; b is the excluded volume of one mole of molecules
Critical temperature T_c = the temperature above which a gas cannot be liquefied, however high the pressure. Critical pressure = the pressure needed to liquefy the gas at T_c
Stronger intermolecular forces give a higher T_c, so the gas is easier to liquefy (approximately: NH₃ 406 K, CO₂ 304 K, O₂ 154 K, N₂ 126 K)
Joule-Thomson effect: a highly compressed gas cools when it expands suddenly through a jet into a region of low pressure. Linde's method repeats compression, cooling and expansion until the air liquefies
Plasma, the fourth state of matter: a mixture of free electrons, positive ions and neutral atoms. It is neutral overall, conducts electricity, and is found in the sun, stars, lightning, neon signs and fluorescent tubes

Common mistake

Students mix up the two van der Waals constants. Remember that a is for attraction and goes with the pressure term; b is for the size of the molecules and goes with the volume term.

Worked example

The critical temperature of carbon dioxide is about 31 °C and that of ammonia is about 132 °C. Which of these gases can be liquefied by pressure alone at 40 °C?

A gas can be liquefied by pressure only if its temperature is at or below its critical temperature.
40 °C is above 31 °C, so carbon dioxide cannot be liquefied at 40 °C, whatever the pressure.
40 °C is below 132 °C, so ammonia can be liquefied at 40 °C if enough pressure is applied.

Answer: Ammonia only. Its molecules attract each other more strongly (hydrogen bonding), which is why its critical temperature is higher.

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Chapter 3: Gases

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