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Dr.T.M 1

Concept of EquilibriumThe separation process considered arebased on the equilibrium stage concept

i.e. the streams leaving a stage are inequilibrium

What do we meant byEquilibrium?

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The objective is:

To understand the concept of equilibrium

Able to estimate the concentration in vapour and liquid

phases

Chapter : 2

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Dr.T.M 3

Vapour-Liquid Equilibrium

Consider a vapor and liquid that are in contactwith each other as shown:

vapor condensing + liquid vaporizing

Pliquid , Tliquid

Pvapour , Tvapour

A B

A B

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Phase Rule and Equilibrium

F = C - P + 2

degrees

of freedom

number

of components

number

Of phases

Degrees of freedom is the number of intensive variables that must

be specified to define the equilibrium state of a system.

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Intensive variables: P, T, or molefraction which do not depend on the total

amount of material presentExtensive variables: number of moles,flow rate, volume, which depend on the

amount of material present

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100oC

Tbp

1 atm

One ComponentExample:Water

2 variables: T and P

V&L

T

P

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Two Components Example: A and B

- 3 variables: T, P and compositionBoiling Point Diagram @Txy diagram at P= 1 atm

L

V

Tbp of A

V&L

Tbp of B

mole fraction A

Tdew

Tbp

bubble pointwhen heating

a subcooled liquid, the

temperature at which the firstbubble forms

dew pointwhen cooling a

superheated vapour, the

temperature at which the first

drop of dew forms

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x

tie line

y

T

Two ComponentsA and B

x = mole fraction of more

volatile component in

liquid phase

y = mole fraction of more

volatile component in

vapour phase

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Raoults law: pi=xi P*i

Ideal Solutions Obey Raoults Law

Consider an ideal solution in equilibrium with an ideal gas to

predict the Txy diagram. Assume we are at some temperaturefor which both phases co-exist at equilibrium

Let P = total pressure

P*i= vapour pressure of pureI

xi, yi= mole fractions in liq or vap at equil

piyi P = partial pressure of component i

Partial Pressure = Vap.Pressure X Conc.

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Ideal Binary Mixtures

Now, we consider to a system with only 2 components, which we

will call A and B.

The mole fractions must sum to one for each phase, so we can

express the mole fraction of B in terms of that for A:

xB= 1xA and yB= 1 - yA

Applying Raoults law to each component:

pA= xA P*A = yA P (1)

pB=(1-xA)P*B = (1yA)P (2)

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Adding the partial pressures from (1) and (2), we obtain the total

pressure:

P =pA +pB=xA P*A + (1-xA)P*B

Solving for the mole fractionxA :

(3)

From (1): yA = xA P*A/P (4)

If you specify a Tand P, the vapour pressure can be determinedand calculate the compositions which will be at equilibrium from

(3) and (4). Thus, you can construct a complete phase diagram

using only vapour pressure data for the pure components.

**

*

BA

BT

A

PP

PPX

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T-x-y Diagram

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Txy diagram

xy diagram

(used in distillation

calculations)

tie line

x y

T

x

y

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Relative Volatility

Relative volatility is a measure of the differences in volatility

between 2 components. It indicates how easy or difficult a

particular separation will be. The relative volatility of component i

with respect to componentj is shown with the relationship

betweenx andy :

ij Ki / Kj

Where Ks are called the distribution coefficient which in turn

are defined as: Ki yi / xi

j

j

i

i

ij

x

y

x

y

i.e.,

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The normal boiling points of the pure, n-heptane and n-octane

are 98.4 oC and 125.6 oC, respectively. The vapor pressure

data are given below. Estimate the mole fraction of n-heptane

in both liquid and vapor phase.

Example - 1

Temp VP mm Hg0C n- heptane Octane

98.4 760 333

105 940 417

110 1050 484

115 1200 561120 1350 650

125.6 1540 760

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T (oC) heptane octane x y

98.4 760 333 1.000 1.000

105 940 417 0.656 0.811

110 1050 484 0.488 0.674

115 1200 561 0.311 0.492

120 1350 650 0.157 0.279

125.6 1540 760 0.000 0.000

Mole Fraction n-heptane

at 1 atm

Vapour Pressure (mmHg)

Vapour Pressure and Equilibrium-Mole-Fraction Data forheptane-octane system

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98

100

102

104

106

108

110112

114

116

118

120

122

124

126

0.000 0.200 0.400 0.600 0.800 1.000

mole fraction of heptane

Temperature(degC)

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