Single Phase Systems

1. CHE1023
Chemical Process Calculations
Week 9 (1st session): Material Balance
Single Phase Systems

2. 2
Single Phase Systems
Real situations:
physical properties of process materials is not readily available -
must find it:
1) literature (handbook, library or web sources)
2) estimation techniques (correlation or theory)
3) measurement (most expensive but sometimes required)
use to derive relations among system variables to solve for
unknowns

3. 3
Single Phase Systems
Liquid and Solid Densities
• usually independent of temperature in most process
• similarly with pressure - called INCOMPRESSIBLE fluids
So how do we obtain data in absence of literature values?

4. 4
Single Phase Systems
Liquid and Solid Densities
Estimate from component mass fractions and pure densities in 2
ways:
1. Volume additivity: thus
or
∑
= i
V
V ∑
=
i
i
w
ρ
ρ
1
∑
∑
=
=
i
i
i
i
V
x
M
x
V
M
ˆ
ˆ
ρ

5. 5
Single Phase Systems
Liquid and Solid Densities
Estimate from component mass fractions and pure densities in 2
ways:
2. Pure components’ density average:
ρ = Σ xi ρi

6. 6
Single Phase Systems
Gas provides more difficult ways of estimation
Ideal Gas concept is usually the best way:
• relation between specific volume and temperature and
pressure must be established
• or P,V,T relationship

7. 7
Single Phase Systems
Ideal Gas (Perfect Gas)
Use “Equation of State” relates P,V and T.
For ideal gas the equation of state is:
PV = nRT or PV = nRT
where R is the gas constant
P = RT
= V/n ; specific molar volume
V
ˆ
V
ˆ

8. 8
Single Phase Systems
Non-Ideal Gas
Need to put in a correction factor:
Compressibility factor:
z = 1 for ideal gases
RT
V
P
z
ˆ
=

9. 9
Single Phase Systems
Standard conditions:
1) scientific 0oC, 1 atm
1 mol (at std. conditions) ⇒ 22,400 cm3 or 22.4 m3
1 lbmol ⇒ 359 ft3
2) natural gas industry 60oF, 14.7 psia
1 lbmol ⇒ 379 ft3

10. 10
Single Phase Systems
Calculations: usually involve converting from one set of
conditions to another
or
1
2
1
1
2
2
ˆ
ˆ
T
T
V
P
V
P
=
1
1
2
2
1
1
2
2
T
n
T
n
V
P
V
P
=

11. 11
Single Phase Systems
Ideal gas mixtures
Partial pressure of component A:
Note: This is used as the definition of "partial pressure", even
for non-ideal gases. It is equal to the pressure that would be
exerted if A alone occupied the container only for ideal gases.
A
A Py
p =

12. 12
Single Phase Systems
Ideal gas mixtures
Total pressure = sum of partial pressures:
)
1
(
P
y
P
Py
P i
i =
=
= ∑
∑

13. 13
Single Phase Systems
Ideal gas mixtures
Similarly:
Total volume = sum of partial volumes.
PV = nRT can also be written PvA= nART
where vA is partial volume of component A in a
mixture an nA is its mole fraction.

14. 14
Single Phase Systems
Ideal gas mixtures
PvA= nART ; divide this by PV = nRT, we obtain,
vA / V = nA/n = yA
or vA = yAV

15. 15
Single Phase Systems
Ideal gas mixtures
PvA= nART ; divide this by PV = nRT, we obtain,
vA / V = nA/n = yA
or vA = yAV (cf. pA= yAP)

16. 16
Single Phase Systems
Ideal gas mixtures
PvA= nART ; divide this by PV = nRT, we obtain,
vA / V = nA/n = yA
or vA = yAV (cf. pA= yAP)
volume fraction = mole fraction
for ideal gases only.