CCB 1064: Professor Saibal Ganguly

Lecture Set 8A:

Vapor-Liquid Equilibria for

Multi-component Systems

Professor Dr. Saibal Ganguly

Universiti Teknologi PETRONAS

May2012

1

CCB 1064: Professor Saibal Ganguly

Lecture Set 8: OBJECTIVES

At the end of the lecture, students should be able to:

Non-ideal gas Equation of State

Use Raoult’s law & Hendry law to predict the partial pressure

of a solute and a solvent

Calculate the composition of multi-component systems at

equilibria between the liquid and vapor phases

Understand Partial Saturation & Humidity

2

CCB 1064: Professor Saibal Ganguly

Recap: Vapour Pressure

Definition

The vapour pressure of a species is a measure of

its volatility.

Higher vapour pressures or higher volatility means

that the species tend to exist in the vapour phase

than the liquid phase.

3

CCB 1064: Professor Saibal Ganguly

Recap: Vapour Pressure

Antoine Equation (for ideal species):

A, B, C Antoine constants, T (°C),

p* = Vapour pressure (mmHg)

Antoine Constants are given in Tabular form in text books

and reference books

4

CT

BApLog *10

CCB 1064: Professor Saibal Ganguly

Raoult’s Law

Raoult’s Law is used primarily for a component

whose mole fraction approaches to unity. Partial

pressure is given as,

P = p

1+p

2+…. = x

1p

1* + x

2p

2* +……

4

iiii xppPy *

CCB 1064: Professor Saibal Ganguly

Equilibrium Constant

The ratio of yi and x

i is known as equilibrium constant

or partition coefficient, K.

This equation provides good estimate of K values at low

pressures for components below their critical

temperatures, but yields values too large for components

above the critical temperatures, at high pressures and or

for polar compounds

i

ii

x

yK

CCB 1064: Professor Saibal Ganguly

Equilibrium Constant

The equilibrium constant, Ki can be used to calculate the

following:

1. Bubble point temperature of a liquid mixture given the

total pressure and liquid composition.

2. Dew point temperature of a vapor mixture given the

total pressure and vapor composition.

3. Equilibrium vapor-liquid composition over the range

mole fractions from 0 to 1 as a function of temperature

given the total pressure

7

CCB 1064: Professor Saibal Ganguly

Example 1

Determine the composition of the first vapor

(saturated condition/ equilibrium) formed if a

liquid mixture of 4.0% n-hexane in n-octane

vaporised at 1 atm. Given the Antoine equation

constants as below:

A B C

n-hexane (C6)

15.8737 2697.55 -48.784

n-octane (C8)

15.9798 3127.60 -63.633

CCB 1064: Professor Saibal Ganguly

9

836.0164.01

164.0)040.0(760

3114

661)(

3114)(

3.393

960.0633.63

60.31279787.15exp040.0

784.48

55.26978737.15exp760

8

6

*

66

8

*

6

*

C

C

tot

CC

y

xp

py

mmHgCp

mmHgCp

KT

TT

CCB 1064: Professor Saibal Ganguly

Raoults Law (Equilibrium/saturated condition)

yiP

i = p*

i(T)

yiP

i < p*

i(T) - Superheated vapour

yiP

i = p*

i(Tdp) - Dew point

10

CCB 1064: Professor Saibal Ganguly

Example 2:

Derive the model equations for a flash drum (a single

equilibrium stage separator) using the partition

coefficient or equilibrium constant K.

11

)/()(

1

KiLLFFx

y

Fi

i

CCB 1064: Professor Saibal Ganguly

Example 3:

Calculate the fraction of liquid that will remain at

equilibrium when a mixture of 68.6% hexane and

31.4% toluene is vaporized at 80 degree C and 1 atm

pressure.

Vapor pressure data at 80 degree C are 1020 mm Hg

(hexane) and 290 mmHg (toluene)

Answer: L/F = 0.745

12

CCB 1064: Professor Saibal Ganguly

Henry’s Law

Henry’ Law is used for a component whose mole fraction

approaches zero, such as a dilute gas dissolved in as

liquid. Partial pressure is given as,

The value Hi when x

i approaches to zero can be obtained

from handbooks. Mole fraction in vapor phase is given as,

13

iii xHp

tot

ii

tot

ii

p

xH

p

py

CCB 1064: Professor Saibal Ganguly

Example 4

Determine the partial pressure of CO2 when it is

dissolved in water at 40o

C having H=69,600 atm/mol

fraction. Given xCO2

=4.2 x10-6

.

Answer: PCO2

=69,600(4.2x10-6

)=0.29 atm

14

CCB 1064: Professor Saibal Ganguly

End of Lecture Set 8A

THANK YOU

15