1. Real gas 1.molecules not always in motion (condense phase can be formed) 2.molecular size is non-negligible (there is molecular repulsion) 3.Molecules do interact (there is molecular attraction)

2. - Compression factor (Z) V m = molar volume or volume per mole If Z < 1 molar volume of real gas is less than ideal gas molecular attraction is dominant Z > 1 molar volume of real gas is larger than ideal gas molecular repulsion is dominant Substitute

3. The variation of the compression factor, Z, with pressure for several gases at 0 o C

4. -Equation of state is equation that represents the state of system Ideal gas equation is the equation of state for gas

5. Virial equation in search for equation of state for real gas, one looks at P dependent of Z or Since and are 2 nd, 3 rd, …, virial coefficient respectively

6. Replacing Z by virial equation of state virial coefficients vary with gas type So does the virial equation of state

7. PV plot for real gas The experimental isotherms of CO 2 at several temperatures.

8. Critical constants

9. - Reduced properties The compression factors of four gas.

10. Van der waals equation another attempt to find equation of state for real gas To correct what’s wrong in kinetic molecular model, Van der waals proposed molecular attraction reduces impact force to wall volume of gas is the space where gas can travel in a container Ideal gas has no molecular volume, volume of gas is volume of container real gas has molecular volume (repulsion), space that gas can travel is less than volume of container

11. P (rate of collision) x (impact force Attraction reduces rate of collision and impact force Reduction in pressure (due to attraction) From ideal gas equation

12. Substitute V in (1) with V - nb then “Van der waals ‘s equation” a, b = van der waals parameter (obtained from experiment) real gas volume is less than ideal gas Given b as molecular volume

13. Since Van der Waals equation comes from modification of kinetic molecular model (theory) while a, b comes from experiment Van der waals equation is “semi-empirical” virial equation is “empirical”

14. Van der waals parameters of gas.

15. - Van der waals loop Isotherms calculated by using the van der waals equation of state.

16. Comparing ideal and real gas V = 10 L,n = 1 mol P (atm) Ideal gasV d wVirial* 273 K N2N2 2.2392.2342.236 CO 2 2.2392.2122.205 O2O2 2.2392.232 Air**2.2392.233 600 K N2N2 4.9204.9264.931 CO 2 4.9204.9054.914 O2O2 4.9204.922 Air4.9204.925 ** AIR = 80%N 2 + 20%O 2 *

17. Example 2.1 Estimate the molar volume of CO 2 at 500 K and 100 atm by treating it as a van der waals gas. From

18. must solve for roots of cubic equation a = 3.610 L 2 atm mol -2; b = 4.29 x 10 -2 L mol -1

20. assume V m = 0.366 L mol -1