2. An ideal gas is defined as one in which there are no
intermolecular attractive forces between atoms.
An ideal gas can be characterized by three state variables:
absolute pressure (P),
volume (V), and
absolute temperature (T).
The relationship between them is called the ideal gas law
Where:
n = number of moles
R = universal gas constant = 8.3145 J/mol K
How do we deal with gases composed of a mixture of two or
more different substances?
3. The total pressure of a mixture of gases equals the
sum of the pressures that each would exert if it
were present alone
The partial pressure of a gas: The pressure exerted
by a particular component of a mixture of gases
Dalton's Law of Partial Pressures:
Mathematically, this can be represented as:
If each of the gases behaves independently of the
others then we can apply the ideal gas law to each
gas component in the sample:
1 2 .....
total n
pressure pressure pressure pressure
4. For the first component, n1 = the number of moles
of component #1 in the sample
The pressure due to component #1 would be:
For the second component, n2 = the number of
moles of component #2 in the sample
The pressure due to component #2 would be:
5. And so on for all components. Therefore,
the total pressure Pt will be equal to:
All components will share the same temperature, T, and volume V,
therefore, the total pressure Pt will be:
Pa / P = na / n Pa= (na / n) * P
where :(na / n) = mole fraction
Then Pb = (nb / n) *P Pc = (nc / n) * P
Partial Pressure = mole fraction * total Pressure
6. A gaseous mixture made from 10 g of oxygen and 5 g of
methane is placed in a 10 L vessel at 25 C.
What is the partial pressure of each gas, and what is the total
pressure in the vessel?
Solution:
No. of moles of O2 = (10 g O2)(1 mol/32 g) = 0.313 mol O2
No. of moles of methane = (10 g CH4)(1 mol/16 g) = 0.616
mol CH4
V=10 L
T=(273+25)=298K
Use
8. The ratio of the partial pressure of one component
of a gas to the total pressure is:
The value (n1/nt) is termed the mole fraction of the
component gas
The mole fraction (X) of a component gas is a dimensionless
number, which expresses the ratio of the number of moles of
one component to the total number of moles of gas in the
sample.
The ratio of the partial pressure to the total pressure is equal
to the mole fraction of the component gas
9. The above equation can be rearranged to
give:
The partial pressure of a gas is equal to its
mole fraction times the total pressure
10. a) A synthetic atmosphere is created by blending 2 mol percent CO2, 20 mol
percent O2 and 78 mol percent N2. If the total pressure is 750 torr, calculate
the partial pressure of the oxygen component.
Solution:
Torr. is = mm Hg ( 1atm.=760 mmHg)
Mole fraction of oxygen is (20/100) = 0.2
Therefore, partial pressure of oxygen = X Pt=(0.2)(750 torr) = 150 torr
b) If 25 liters of this atmosphere, at 37C, have to be produced, how many
moles of O2 are needed?
PO2 = 150 torr (1 atm/760 torr) = 0.197 atm
V = 25 L
T = (273+37)=310K
R=0.0821 L atm/mol K
PV = nRT
no2 = (Po2 V)/(RT) = (0.197 atm * 25 L)/(0.0821 L atm/mol K * 310K)
n = 0.194 mol
11. An appropriate starting point in the study of multi-component
– multiphase systems is the background to the phase-rule.
The purpose of this rule is to determine the number of
variables that can be independently changed in defining the
state of a system with C (components )distributed among P
(phases).We refer to this as the number of degrees of
freedom, F
The total number of degrees of freedom is thus given by:
F = C - P + 2.
12. For a two phase system
of single component
P=2, C = 1
Then F= 1
Therefore, for the single component system,
specifying either T or P fixes all intensive variables.
VLE for Pure Components
0
200
400
600
800
270 320 370 420
Temperature: K
Pressure:
kPa
Acetonitrile Nitromethane
13. Pure liquid Water
◦ F = 1 - 1 +2 = 2
Mixture of Ice and Water
◦ F = 1 - 2 + 2 = 1
VLE of acetone + nitrogen
◦ F = 2 - 2 +2 = 2
(example)
T and P
(example)
T or P
(example)
T and x
P and x
T and P
:
F = C - P + 2.
14. The following Antoine equation describes the
dependence of vapor pressure of a pure chemical
species i on temperature.
Where A,B and C are constants for a particular
compounds. where T in º C
ln( )
sat
i
B
P A
C T
15. Pi
sat, or the vapour pressure of component i, is commonly represented by Antoine Equation
(Appendix B, Table B.2, SVNA 7th ed.):
For acetonitrile (Component 1):
For nitromethane (Component 2):
These functions are the only component properties needed to characterize ideal VLE behavior
C
T
B
A
P
ln sat
i
224
C
/
T
47
.
2945
2724
.
14
kPa
/
P
ln sat
1
209
C
/
T
64
.
2972
2043
.
14
kPa
/
P
ln sat
2
16. Consider a system with two phases (vapor and liquid) at given values of
pressure and temperature, What we want to know is the equilibrium
relationship between the measurable variables P, T, yi, xi in this system.
The simplest relationship is Raoult’s law,
which is based on assumptions of ideal gas for
the vapor phase and ideal liquid solution for the liquid phase:
Where: Xi mole fraction of component i in the liquid phase.
is the sat. vapor pressure of comp. i at the temperature of the system.
Σ Pi= P (total pressure) so we can determine the yi =Pi/P
P
T
V
L
i
sat
i
i x
P
Py =Pi
17. y
P x
P
i
i
sat
i
1
So, The mole fraction in vapor phase (y)
The V-L equilibrium ratio (K-Value):
i
i
i
Y
K
X
18. we demonstrate use of
Antoine's equation to plot
the saturation pressure of
pure water as a function of
temperature.
For water between 60 and
150 degrees C
A = 7.96681; B = 1668.21;
C = 228
ln( )
sat
i
B
P A
C T
19. The components A and B form an ideal mixture. The following
Antoine equations:
Calculate
P and ya, yb for t=353.15K and xa=0.25, xb=0.75
Also, plot the x,y diagram .(ASSIGNMENT)
Assume : x1=0.1 -1 and the rest will be x2 , then calculate P total
and y1 &y2 for every x . Then plot x-y diagram
0
3640
ln 16.678
53.54
3816.44
ln 16.62287
46.13
o
a
b
p
t
p
t
20. What is bubble point of a liquid?
It is the temperature at which the first bubble of vapor
forms when the liquid is heated slowly at constant
pressure.
What is dew point of gas ?
It is the temperature at which the first droplet of
liquid formed when vapor is slowly cold at constant
pressure.
Raoult’s Law
21. Bubble point calculations are performed when
the composition of the liquid phase is known
and which to calculate the composition of the
vapor phase.
There are two cases:
◦ Bubl. T: When the pressure of the system &Xi are
known.
◦ Bubl. P :When the temperature of the system &Yi are
known.
22. Bubble-point temperature problem -- P,x given -- T,y unknown.
A trial and error procedure must be followed, where
T is assumed, the vapor pressures calculated using
Antoine equation, and then see if the correct total
pressure is obtained (or the vapor mole fractions sum
to unity).
y
P x
P
i
i
sat
i
1
23. Bubble-point pressure problem -- T,x given -- P,y unknown.
This is a straight-forward calculation. The vapor
pressures are found at the given temperature through
Antoine equation, which allows direct calculation of
the pressure and vapor mole fractions:
Py P P x
y
P x
P
i i
sat
i
i
i
sat
i
24. Dew-point pressure problem -- T, y given -- P, x
unknown.
No trial and error is needed, as P can be directly
calculated.
x
Py
P
x
P
y P
i
i
i
sat i
i i
sat
1
1
/
25. Dew-point temperature problem -- P,y given --
T,x unknown.
Guess a T, find the vapor pressures, and see if the
liquid mole fractions sum to unity.
x
Py
P
i
i
i
sat
1
