Deviation from Ideal Behaviour

Real gases do not perfectly obey the ideal gas laws, especially at high pressures and low temperatures or when they are about to condense to a liquid. These deviations occur due to intermolecular forces between gas molecules. Repulsive forces aid expansion and are significant when molecules are very close together, typically at high pressure. Attractive forces assist compression and have a longer range, being effective over several molecular diameters. They become significant when molecules are close but not necessarily in contact, and they diminish when the molecules are far apart.

At low pressures, where molecules are widely spaced and intermolecular interactions are minimal, gases behave nearly ideally. At moderate pressures, attractive forces exceed repulsive forces, making the gas more compressible than an ideal gas. At high pressures, repulsive forces dominate, causing the gas to be less compressible.

The compression factor, Z, is used to quantify the deviation of a real gas from ideal behavior. It's the ratio of the measured molar volume of a gas to the molar volume of an ideal gas at the same pressure and temperature. An ideal gas has Z = 1 at all pressures. Real gases have Z ≈ 1 at very low pressures, behaving nearly perfectly. At high pressures, Z > 1 due to dominant repulsive forces, and at intermediate pressures, most gases have Z < 1, indicating that attractive forces are reducing the molar volume relative to that of an ideal gas.

The ideal gas law (pV_m = RT) is a good first approximation for real gases at high temperatures and large molar volumes. The virial equation of state refines this by adding terms for pressure variables. The compression factor, Z, and virial coefficients, which depend on temperature, measure deviations from ideal behavior. Although a real gas may align with the ideal gas behavior at low pressures, not all its properties necessarily coincide with those of an ideal gas. The Boyle temperature is where the real gas properties match the ideal gas as pressure approaches zero.