Q1(f). ΔG for compressing a real gas, from fugacities

Answer in brief

ΔG = RT ln(f₂/f₁) = +4.70 kJ mol⁻¹ (an ideal gas would need +5.71 kJ mol⁻¹).

Key points

• At constant T, (∂G/∂P)T = Vm; for a real gas the fugacity replaces pressure: dG = RT d ln f.
• Integrating: ΔG = RT ln(f₂/f₁).
• ΔG = 8.314 × 298.15 × ln(120/18) = 2478.8 × 1.8971 = 4703 J mol⁻¹ = +4.70 kJ mol⁻¹.
• Ideal gas: RT ln(200/20) = 5708 J mol⁻¹; the real gas needs less because the fugacity coefficient falls from 0.90 to 0.60 (attraction dominates).
• ΔG > 0: compression is not spontaneous; work must be done on the gas.