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Real gases deviate from ideality because intermolecular forces and molecular volume become significant at high pressures and low temperatures. At these conditions, attractive forces between molecules reduce compressibility, while repulsive forces at very high pressures increase it. The van der Waals equation accounts for these deviations by incorporating terms for molecular interactions and excluded volume.

The compression factor Z is the ratio of a real gas's molar volume to an ideal gas's molar volume at identical pressure and temperature. For ideal gases, Z equals one at all pressures. Real gases have Z ≈ 1 at very low pressures, Z < 1 at moderate pressures due to attractive forces dominating, and Z > 1 at high pressures when repulsive forces dominate.

At low pressures, molecules are widely spaced and intermolecular forces are negligible, so gases behave nearly ideally. At moderate pressures, attractive forces exceed repulsive forces, making gases more compressible than ideal. At high pressures, repulsive forces dominate because molecules are forced close together, reducing compressibility and causing the gas to behave less ideally.

Real gases closely follow the ideal gas law at low pressures and high temperatures, where molecules remain far apart and intermolecular attractions and repulsions become negligible. Under these conditions, the molar volume is large enough that molecular volume is insignificant, and the gas equation pVm = RT provides an accurate approximation of behavior.

The virial equation refines the ideal gas law by adding temperature-dependent terms that account for deviations from ideal behavior. It uses the compression factor Z and virial coefficients to quantify how real gases deviate from ideality. This approach provides a more accurate description of gas behavior across a wider range of pressures and temperatures than the simple ideal gas equation.

The Boyle temperature is the specific temperature at which real gas properties match ideal gas behavior as pressure approaches zero. At this temperature, the compression factor Z approaches one, indicating that the real gas behaves ideally under low-pressure conditions. This temperature is unique to each gas and represents a point where attractive and repulsive forces balance in their effects.

Molecular spacing determines whether intermolecular forces significantly affect gas behavior. When molecules are far apart at low pressures, interactions are minimal and gases behave ideally. As pressure increases and molecules move closer together, attractive forces become significant at moderate pressures, while repulsive forces dominate at very high pressures, causing substantial deviations from ideal behavior.