1. Chapter 8
Real Gases

2. Compression Factors Physical Chemistry
Real Gases
Compression Factors
Real gases do not obey the perfect gas equation exactly. The measure of the deviation from ideality of the behavior of a real gas is expressed as the compression factor Z:
(8.1) Z P H2
1.2 1
0.8
0oC N2
CH4 Z P
200 K
500 K
1000 K 3 2 1
CH4

3. Real Gas Equations of State
Physical Chemistry
Real Gases
Real Gas Equations of State
(8.2)
van der Waals equation
Ideal Gas Law/Perfect Gas Equation:
PV = nRT (1.18)*

4. Van der Waals Equation of State
Physical Chemistry
Real Gases
Van der Waals Equation of State
: to correct the effect of intermolecular attractive forces on the gas pressure
b: the volume excluded by intermolecular repulsive forces

5. Real Gas Equations of State
Physical Chemistry
Real Gases
Real Gas Equations of State
Redlich-Kwong Equation
(8.3)
Virial Equation of State
(8.4)
The limited accuracy of the data allows evaluation of only B(T) and sometimes C(T).

6. Virial Equation of State
Physical Chemistry
Real Gases
Virial Equation of State
Power series in 1/Vm
(8.4)
Power series in P
(8.5)
(8.6)
low P
(8.7)
(8.2)
vdW gas

7. Gas Mixtures Physical Chemistry
Real Gases
Gas Mixtures
For a mixture of two gases, 1 and 2, use a two-parameter equation,
(8.10)
x1 and x2: the mole fractions of the components
b: a weighted average of b1 and b2
a: related to intermolecular attractions
(a1a2)1/2: intermolecular interaction between gases 1 and 2
(8.11)
mean molar volume

8. Condensation Physical Chemistry T < 374 oC P H
Real Gases
Condensation
T < 374 oC P H
gas condenses to liquid when P
H2O
T = 300 oC Y G
R(vapor)S(saturated vapor), P, V U T S W M R
400 oC
S(saturated vapor)W(saturated liquid), P, V  J N
374 oC L V
300 oC L
200 oC
L + V
W(saturated liquid)Y(liquid), P , V K Vm
Isotherms of H2O

9. H2O phase diagram: P — T Physical Chemistry solid liquid gas
Real Gases
H2O phase diagram: P — T D C
218 atm Y I
solid
liquid S
P / 10 5 Pa
1 atm R
gas A O
0.0024
0.01
99.974
374.2 Tf T3 Tb
t/℃

10. Condensation Physical Chemistry T  374 oC Isotherms of H2O P Vm U R J
Real Gases
Condensation
T  374 oC
Isotherms of H2O P Vm U R J N Y
374 oC
300 oC
200 oC
H2O
L + V L V G H T S K M W
Fig. 8.3
No amount of compression will cause the separation out of a liquid phase in equil. with the gas.
400 oC
T = 374 oC
Critical temperature Tc
Critical pressure Pc
Critical volume Vm,c
Critical constants

11. Critical T (Tc), Tc(CO2)=304.2 K
Physical Chemistry
Real Gases
Isotherms of CO2
{P}
{Vm,c} T3 c Tc g b a l T1 T2
Critical constants
Critical T (Tc), Tc(CO2)=304.2 K
Critical P (Pc), Pc(CO2)=7.38 MPa
Critical molar V (Vm,c), Vm,c(CO2)=94×10-6 m3·mol-1

12. Table 8.1 Critical Constants
Physical Chemistry
Real Gases
Table 8.1 Critical Constants
Species Tc / K Pc / atm Vm,c / cm3·mol-1 Ar Ne N
H2O
D2O
H2S CO
HCl
CH3OH

13. Fluid Physical Chemistry
Real Gases
Fluid
There is a continuity between the gaseous and the liquid states. In recognition of this continuity, the term fluid is used to mean either a liquid or a gas.
An ordinary liquid can be viewed as a very dense gas. Only when both phases are present in the system is there a clear-cut distinction between liquid and gaseous states.
For a single-phase liquid system it is customary to define as a liquid a fluid whose temperature is below Tc and whose molar volume is less than Vm,c.
If these two conditions are not met, the liquid is called a gas. So a further distinction between gas and vapor can be made, but these two words are used interchangeably in this book.

14. Supercritical fluid T > Tc and P > Pc Physical Chemistry
Real Gases
Supercritical fluid
A supercritical fluid is one whose T and P satisfy
T > Tc and P > Pc
A supercritical fiquid usually has liquidlike density but its viscosity is much lower than typical for a liquid and diffusion coefficients in it are much higher than in liquids.

15. CO2 o Supercritical fluid C Physical Chemistry
Real Gases
CO2
-60
-40
-20 20 40 60 80
100 B 5 10 15 25 30 35
-56.6 ℃ t
c=31.06 t/ o C
gas
liquid
solid
200
300
400
500
600
700
800
900
1000
1100
1200 p
/MPa P c
=7.38MPa A
0.518MPa
Supercritical fluid
Supercritical CO2 is used commercially as a solvent to decaffeinate coffee.

16. Critical data and equations of state
Physical Chemistry
Real Gases
Critical data and equations of state
At the critical point:
(8.12)
Differentiating the van der Waals equation (8.2)
and
Application of the conditions (8.12) gives
and
(8.13)

17. Critical data and equations of state
Physical Chemistry
Real Gases
Critical data and equations of state
From van der Waals equation:
(8.14)
Division of the first equation in (8.13) by the second yields
(8.15)
Use of (8.15) in the first equation in (8.13) gives
and
(8.16)

18. Critical data and equations of state
Physical Chemistry
Real Gases
Critical data and equations of state
Substitution of (8.15) and (8.16) into (8.14)
(8.15)
(8.16)
(8.14)
gives
(8.17)

19. Critical data and equations of state
Physical Chemistry
Real Gases
Critical data and equations of state
Substitution of (8.15) and (8.16) into (8.14)
(8.15)
(8.16)
(8.17)
Three equations for two parameters, a and b
vdW gas
(8.18)

20. Critical data and equations of state
Physical Chemistry
Real Gases
Critical data and equations of state
Combination of (8.15) to (8.17)
(8.15)
(8.16)
(8.17)
Predicts the compressibility factor at the critical point
(8.19)
Van der waals equation

21. Critical data and equations of state
Physical Chemistry
Real Gases
Critical data and equations of state
Van der waals equation
(8.19)
ideal gas
R-K equation
(8.20)
(8.21)
(8.22)

22. Selected equations of state
Physical Chemistry
Real Gases
Selected equations of state
Equation
Critical
constants
Perfect gas
van der Waals
Berthelot

23. Selected equations of state
Physical Chemistry
Real Gases
Selected equations of state
Equation
Critical
constants
Perfect gas
R-K
virial

24. The law of corresponding states
Physical Chemistry
Real Gases
The law of corresponding states
The critical constants are characteristic properties of gases
The reduced variables of a gas by dividing the actual variable by the corresponding constant.
(8.27)
reduced pressure
reduced volume
reduced temperature
The observation that the real gases at the same reduced volume and reduced temperature exert the same reduced pressure is called the law (principle) of corresponding states.
(8.28)