Q1(b). Compressibility factor and Z against P plots

Answer in brief

Z = PVm/RT. Ideal gas: Z = 1. Real gases: Z < 1 where attraction dominates, Z > 1 where repulsion (molecular size) dominates; all curves start at Z = 1 as P → 0.

Key points

• Compressibility factor: Z = PVm/RT = Vm(real)/Vm(ideal); a pure number, Z = 1 at all P and T for an ideal gas.
• Initial slope (∂Z/∂P) at P → 0 = (b − a/RT)/RT: positive for H₂ (small a), negative for N₂, CH₄, CO₂ at 300 K.
• At 300 K: H₂ rises at once; N₂ dips slightly (0.96); CH₄ to about 0.8; CO₂ (320 K) deepest (0.38 near 100 bar).
• Depth of the minimum grows with a, i.e. with ease of liquefaction: CO₂ > CH₄ > N₂ > H₂.
• At very high P every curve rises with nearly the same slope: repulsion (b) dominates.