4. Ideal Gases and the Compressibility Factor 1 mol, 300K for various gases A high pressure, molecules are more influenced by repulsive forces. V real > V ideal  Z > 1 The effect of molecular attraction causes: V real < V ideal  Z < 1

5. Effect of Pressure on Compressibility Factor CH 4, various temperatures Lower temperatures Little thermal motion of molecules Attractive forces dominate: V real < V ideal  Z < 1 Higher temperatures More influenced by repulsive forces: V real > V ideal  Z > 1

6. Comparing Various Equations of State Ethane, 400K van der Waals Redlich-Kwong Peng-Robinson Solid line – experimental

7. Second Virial Coefficient and Intermolecular Potentials The second virial coefficient is the most important. Can be determined by plotting Z vs. P. 373 K Ideal gas Ammonia B 2V = -0.142 dm 3 mol -1 at 373 K Z P / bar slope = B 2P (T) = B 2V (T)/RT 1.000 0.998 0 0.1

8. The effect of temperature At high T B 2V increases Boyle temperature: Temperature at which B 2V (T) = 0. Repulsive and attractive interactions cancel and gas behaves ideal

9. The Lennard-Jones Potential The long range 1/r 6 attractive term The short range 1/r 12 repulsive term u(r)/ε r/σ 0 1 0 23 Contributions: Dipole-dipole (including H-bonding) Induced dipole London dispersion attraction ε