1. Real Gases Deviation from ideal gas Law: -Gas particles have volume - Attraction exists between gas particles (liquefication) Ideal gas law applies only at low gas density: high T, low p

2. isotherm

3. Van der Waal’s Equation Ideal gas law needs modification: - Let’s consider the molecular volume: b: size of 1 mole of gas molecules For 1 mole of gas: V m,total = V m,space + b

4. - Let’s consider the attraction forces between molecules: - Due to attraction: - velocity decreased, - colliding less with wall, - pressure drops

5. - How big is this drop in pressure? attraction force 1f 2f 3f attraction force 1f 2f 3f

6. - How big is this drop in pressure?

7. drop in pressure proportional to attraction force drop in pressure indirectly proportional to square of V m

8. VdW Equation of state

9. b: volume of 1 mole of gas molecules. a: represents strength of attraction.

11. Maxwell construction a1 = a2

12. Many other equations of state Mostly empirical Virial Equation to correct, develop in a series (additional correction terms: B,C, …: second, third, … virial coefficients: exp. determined

13. Compression factor z describes deviation from ideal gas behavior. For ideal gas, z=1

14. At a given temperature, z depends on the nature of gas Why?

15. Let’s find for a VdW gas at p → 0 The slope of the curve z=f(p) in the previous diagram.

17. slope at p → 0

18. > 0 = 0 < 0

19. b: volume of 1 mole of gas molecules. represents repulsive forces a: represents strength of attraction Size effect > attraction Size effect = attraction Size effect < attraction

20. Explain the trend!

21. Critical Point V m range in which L and G phases coexist shrink to a single point Above T c, L and G phases can not be distinguished from each other: Density (L) = Density (G) No Interface

23. Experimental measurements of p c and T c are more accurate than that of V c, a and b are calculated from the experimental values of p c and T c.

24. Is it possible to find an equation of state that doesn’t contain material specific constants? The law of corresponding states Reduced properties:

25. Two gases at the same T r and p r have the same V r. These two gases are in “corresponding states’’. Ar (302 K and 16 atm) ↔ ethylene (381 K and 18 atm)