Q1(a). Conditions for ideal behaviour of real gases

Answer in brief

Real gases behave ideally at low pressure and high temperature (best near the Boyle temperature TB = a/Rb), where molecular volume and attraction are both negligible.

Key points

• Two ideal-gas assumptions fail: molecules have finite volume (b, repulsion) and attract each other (a); ideal behaviour needs both corrections to vanish, i.e. a large Vm.
• Low pressure (P → 0): molecules far apart, Vm ≫ b and a/Vm² → 0 ⇒ Z → 1 for every gas.
• High temperature: kinetic energy ≫ attraction energy (a/RT small); at the Boyle temperature the low-pressure slope vanishes, TB = a/Rb.
• Gases far above their critical temperature with weak forces (H₂, He, N₂, O₂) are nearly ideal at room conditions; NH₃, SO₂ and CO₂ deviate most.