Real Gases
Real gases
¾
Real Gases are gases whose behavior does not conform to the
assumptions underlying ideality.
14.1 Corresponding states
¾
Any gas should have the same reduced volume at the same reduced
temperature and reduced pressure.
¾
The law of corresponding states expresses the idea that in the
critical state all substances should behave alike.
14.2 Critical state (point)
¾
For a pure component it means the maximum temperature and
corresponding pressure at which liquid and vapor can coexist.
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
¾
The critical state for the gas-liquid transition is the set of physical
conditions at which the density and other properties of the liquid and
vapor become identical.
¾
A supercritical fluid is a compound in a state above its critical point.
Supercritical fluids are used to replace solvents such as methylene
chloride
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
14.3 Reduced Variables
¾
Are corrected or normalized conditions of temperature, pressure, and
volume, normalized (divided) by their respective critical conditions.
¾
The law of corresponding states indicates that any compound should
have the same reduced volume at the same reduced temperature and
reduced pressure so that a universal gas law might be:
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
1 4.4 Compressibility
¾
Is a common way to modify the ideal gas law by inserting an
adjustable
coefficient
z,
the
compressibility
factor
which
compensates for the nonideality of the gas
¾
The ideal gas law is turned into a real gas law, a generalized
equation of state.
or
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
14.5 Compressibility Charts
¾
Are graphs of the compressibility factor as a function of reduced
temperature, reduce pressure, and ideal reduced volume.
¾
Compressibility factor is a factor that introduced into the ideal gas low
to compensate for nonideality of gas.
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
¾
Instead of the reduced specific volume, a third parameter shown on the
charts is the dimensionless ideal reduced volume defined by:
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
Example: Liquid oxygen is used in the steel industry, in the chemical
industry, in hospitals, as a rocket fuel oxidant, and for wastewater
treatment as well as many other applications. A hospital tank of 0.0284
m3 volume is filled with 3.500 kg of liquid O2 that will vaporize at -25°C.
Will the pressure in the tank exceed the safety limit of the tank
specified as l04 kPa?
Solution
Basis: 3.500 kg O2
From Appendix D, for oxygen
Tc = 154.4 K
pc = 49.7 atm or 5.035 kPa
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
because you do not know the pressure of the O2 in the tank'to begin
with. Thus, you need to use the pseudoparameter, Vri , that is available
as a parameter on the'Nelson and Obert charts
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
From the Nelson and Obert chart (Figure 14.4(b)) you can read
pr = 1.43
The pressure of l04 kPa will not be exceeded.
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
14.7 Real Gas Mixtures
In Kay's method, pseudocritical values for mixtures of gases are
calculated on the assumption that each component in the mixture
contributes to the pseudocritical value in the same proportion as the mol
fraction of that component in the gas. Thus, the pseudocritical values are
computed as follows:
where yi is the mole fraction, p'r is the pseudocritical pressure and T'r is
the pseudocritical temperature.
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
The respective pseudoreduced variables are:
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
Example: A gaseous mixture has the following composition (in mole
percent):
Methane, CH4
20
Ethylene, C2H4
30
Nitrogen. N2
50
at 90 atm pressure and 100°C. Compare the volume per mole as
computed by the
methods of: (a) the ideal gas law and (b) the pseudoreduced
technique (Kay's method).
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
Solution
Basis: 1 g mol of gas mixture
a. Ideal gas law:
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
b. According to Kay's method, you first calculate the pseudocritical values
for the mixture:
p'c = pc yA + pc yB + pc yc = (45.8)(0.2) + (50.5)(0.3) + (33.5)(0.5) = 41.1 atm
A
B
C
T'c = Tc yA + Tc yB + Tc yc = (191)(0.2) + (283)(0.3) + (126)(0.5) = 186K
A
B
C
Then you calculate the pseudoreduced values for the mixture:
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani
Real Gases
You can find from Figure 14.4b that
z T'r = 1.91 and thus z = 0.95 Then:
ChE 201: Introduction to Chemical Engineering
Dr Saad Al-Shahrani