1. Chapter 5 Single Phase Systems

2. Introduction
Before carrying out a complete material balance, we usually need to determine various physical properties of materials in order to derive additional relationship among the system variables.
As an example we need the density to relate the volumetric flow rate to mass flow rate or vice versa.
3 ways to obtain the values of physical properties (such as density, vapor pressure, solubility, heat capacity, etc)
Handbook or database
- Perry’s Chemical Handbook, CRC Handbook of Chemistry & Physics, TRC Database in Chemistry & Engineering, etc
Estimation using empirical correlations
Experimental work

3. Density of Liquid and Solid
Temperature dependence: modest but sometimes important (liquid and solid expanded during heating and density decrease)
Pressure dependence: usually negligible (solid and liquid are incompressible with pressure).
2 methods to estimate the density of a mixture of n liquid (n is number of different type of liquid)
Method 1: Volume Additivity
Work best for mixture of liquid species with similar molecular structure
Method 2: Average Pure Component Densities

4. Ideal Gases Equation of state
Relates the molar quantity and volume of a gas to temperature and pressure.
Ideal gas equation of state
Simplest and most widely used
Used for gas a low pressure and high temperature
Derived from the kinetic theory of gases by assuming gas molecules
have a negligible volume;
Exert no forces on one another;
Collide elastically with the wall of container or
The use of this equation does not require to know the gas species:
1 mol of an ideal gas at 0˚C and 1 atm occupies liters, whether the gas is argon, nitrogen, mixture of propane and air, or any other single species or mixture of gases

5. Ideal Gas Equation of State
P = absolute pressure
V = volume of the gas
n = number of moles of gas
R = gas constant which the unit depend on unit of P, V, n, T
T = absolute temperature
Ideal gas equation of state can also be written as
Which ; specific molar volume of gas.
Unit for gas constant, R or

6. Ideal Gas Equation of State
Density of ideal gas ( M is average molecular weight-refer back previous chapter Eq )
Rule of thumb for when it is reasonable to assume ideal gas behavior.
Let Xideal be a quantity calculated using ideal gas equation of state (X can be pressure, volume, temperature or mole).
Error is estimated value is ε
Let say quantity to be calculate is ideal specific molar volume,
If error calculte is satifies this criterion, the ideal gas equation of state should yield an error less than 1%

7. Class Discussion
Example 5.2-1

8. Standard Temperature and Pressure (STP)
A way to avoid the use of gas constant, R when using ideal gas equation
For ideal gas at arbitrary temperature, T and pressure, P
For the same ideal gas at standard reference temperature, Ts and standard reference pressure, Ps (refer to STP).
Divide eq. 1 to eq. 2
Value of standard conditions (Ps, Ts, Vs) are known, above equation can be used to determine V for a given n or vice versa
Standard cubic meters (SCM) : m3 (STP)
Standard cubic feet (SCF) : ft3 (STP)
Let say 18 SCMH mean 18 m3 (STP)/h

9. Standard Conditions for Gases
System Ts Ps Vs ns Vs
SI 273K 1atm m3 1 mol m3/kmol
cgs 273K 1atm L 1 mol L/mol
English 492˚R 1atm ft3 1 lb-mole ft3/lb-mole

10. “ Saya pasti akan berjaya kerana saya telah kehabisan benda-benda yang tidak berjaya”
Thomas Eddison

11. Class Discussion
Example 5.2-2

12. Class Discussion
Example 5.2-3

13. Class Discussion
Example 5.2-4

14. Ideal Gas Mixture
Suppose nA moles of species A, nB moles of species B, nc moles of species C and so on, contained in a volume, V at temperature, T and pressure, P
Partial pressure, pA
The pressure that would be exerted by nA moles of species A alone in the same total volume, V at the same temperature, T of the mixture.
Pure component volume, vA
The volume would be occupied by nA moles of A alone at the same total pressure, P and temperature, T of the mixture.
Ideal gas mixture
Each of the individual species component and the mixture as whole behave in an ideal manner

15. Ideal Gas Mixture Dalton’s Law
The summation of partial pressure of the component of an ideal gas mixture is equal to total pressure
Amagat’s Law
Volume fraction = vA/V; percentage by volume (%v/v)= (vA/V )x 100%
For an ideal gas mixture, the volume fraction is equal to the mole fraction of the substance:
70% v/v C2H6 = 70 mole% C2H6

16. Class Discussion
Example 5.2-5

17. Equation of State for Nonideal Gases
Critical temperature (Tc)- the highest temperature at which a species can exist in two phases (liquid and vapor), and the corresponding pressure is critical pressure (Pc)
Other definition: highest temperature at which isothermal compression of the species vapor results in the formation of a separate liquid phase.
Critical state- a substance at their critical temperature and critical pressure.
Species below Pc:
Species above Tc- gas
Species below Tc- vapor
Species above Pc and above Tc- supercritical fluids

18. Virial Equation of State
B,C,D- second, third, fourth virial coefficient respectively
Truncated virial equation
Tr=T/Tc
ω – acentric factor from Table 5.3-1
Tc,Pc from Table B.1

19. Class Discussion
Example 5.3-1

20. Kebebasan tanpa tanggungjawab membawa kehancuran

21. Cubic Equations of State
Refer as cubic equation because when the equation is expanded, it become third order equation for the specific volume
To evaluate volume for a given temperature and pressure using cubic equation of state, we need to do trial and error procedure.
Two famous cubic equation of state
Van der Waals equation of state
Soave-Redlich-Kwong (SRK) equation of state

22. Van der Waals Equation of State
(a/V2) - account for attractive force between molecules
b - correction accounting for the volume occupied by the molecules themselves

23. Soave-Redlich-Kwong (SRK) equation of state

24. Class Discussion
Example 5.3-2

25. Compressibility Factor Equation of State
If z=1, equation become ideal gas equation of state
Value of z is given in Perry’s Chemical Engineering Handbook pg
Alternatively; can use generalized compressibility chart
Figure – generalized compressibility chart
Fig to Fig – expansion on various region in Fig

27. Steps to Read Compressibility Factor
Find Tc and Pc
If gas is either Hydrogen or Helium, determine adjusted critical temperature and pressure form Newton’s correction equation
Calculate reduced pressure and reduced temperature of the two known variables
Read off the compressibility factor from the chart

28. Class Discussion
Example 5.4-2

29. Nonideal Gas Mixtures
Kay’s Rule: estimation of pseudocritical properties of mixture as simple average of pure a component critical constants
Pseudocritical temperature (Tc’)
Tc’= yATcA + yBTcB +……
Pseudocritical pressure (Pc’)
Pc’= yAPcA + yBPcB +……
Pseudocritical reduced temperature (Tr’)
Tr’= T/Tc’
Pseudocritical reduce pressure (Pr’)
Pr’= P/Pc’
Compressibility factor for gas mixture, Zm

30. Class Discussion
Example 5.4-3

31. ANY QUESTION?