school of chemical & biological engineering, konkuk university

School of Chemical & Biological Engineering, Konkuk University

Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-2

Lecture 22

• Temperature-composition diagrams

• Liquid-liquid phase diagrams

Ch. 6 Phase Diagrams


• Another choice for phase diagram of a two-component mixture

is the temperature-composition diagram (at a fixed pressure).

• This diagram is used to discuss distillation of the mixture.

• Consider an ideal mixture of A and B (A is

more volatile than B).

• Note that the liquid phase now lies in the

lower part of the diagram.

• The region between the lines is a two-

phase (V + L) region where F’ = 1 (fixed p).

V

L

V+L

• Therefore, at a given T (F’=0), the compositions of the phases

in equilibrium are fixed.


V

L

V+L

• Consider heating the ideal mixture of A

and B (A is more volatile than B).

• By heating a liquid (a1), when T reaches

T2, the liquid mixture boils.

xA = a1 = a2 (Most of A and B are liquid.)

yA = a2’ (A trace of A and B is vapor.)

If p = 1 atm, this T is Tb,A.

Tb,B


• In a simple distillation, all the hot vapors

produced are immediately channeled into

a condenser which cools and condenses

the vapors.

• As a result, simple distillation is usually used only to separate

liquids whose boiling points differ greatly (rule of thumb is

25 °C), or to separate liquids from involatile solids or oils.

• Therefore, the distillate will not be pure - its composition will

be identical to the composition of the vapors at the given

temperature and pressure, and can be calculated from Raoult’s

law.


• In fractional distillation, the boiling and

condensation cycle is repeated successively.

• This technique is used to separate volatile liquids.


• In a fractional distillation of A from A/B

mixture, when a first condensate of

composition a3 is reheated, this mixture

boils at T3 and yields a vapor of

composition a3’.

• Then the vapor is draw off, and the first

drop condenses to a liquid of composition

a4.

• The cycle can then be repeated until almost pure A is obtained.


• The efficiency of a fractionating column is expressed in terms

of the number of theoretical plates (the number of effective

vaporization and condensation steps).

• To achieve a condensate of a specified composition from a

given distillate, the fractionating column must have plates of

which the number corresponds to the number of theoretical

plates.

3 theoretical plates 5 theoretical plates

• More similar partial pressures, more plates.


• When the favorable A-B interactions reduce the vapor

pressure of the mixture below the ideal value, a maximum in the

T-z phase diagram (minimum in the P-z diagram) may occur.

• The A-B interactions stabilize the liquid.

• GE < 0 (more favorable to mixing than ideal)

Chloroform(1)/tetrahydrohuran(2)


• When the unfavorable A-B interactions increase the vapor

pressure of the mixture above the ideal value, a minimum in the

T-z phase diagram (maximum in the P-z diagram) may occur.

• The A-B interactions destabilize the liquid.

• GE > 0 (less favorable to mixing than ideal)

Ethanol(1)/toluene(2)


• Consider a liquid of composition a on the

right of the maximum.

• After removal (condensation elsewhere) of

the vapor (a2’), VLE moves to a composition

(a3) that is richer in B.

• After repeating the processes, VLE reaches the composition b

in which the vapor and liquid have the same composition b.

• In the point, evaporation occurs without change of composition.

the mixture is said to be form an azeotrope. (From the Greek

words for ‘boiling without changing’)

• When the azeotropic composition has been reached,

distillation cannot separate the two liquids.


• A high-boiling azeotrope: When the liquid of

composition a is distilled, the composition of

remaining liquid changes towards b but no

further.

Ex) A mixture of HCl/H2O is azeotropic at 80

w% of water, and boils unchanged at 108 oC.

• A low-boiling azeotrope: When the mixture at a

is fractionally distilled, the vapor in equilibrium in

the fractionating column moves towards b and

then remains unchanged.

Ex) A mixture of ethanol/H2O is azeotropic at 4

w% of water, and boils unchanged at 78 oC.


• Consider the distillation of two immiscible liquids,

such as octane and water.

• Both liquids are saturated with a tiny amount of

the other component, so the total vapor pressure of

the mixture is close to:

• The distillation of two immiscible liquids can be regarded the

joint distillation of the separated components.

• The presence of the saturated solutions means that the mixture

boils at a lower temperature than either component would alone,

because boiling begins when the total vapor pressure reaches

the atmospheric pressure, not when either vapor pressure does.

****

BABBAABA pppxpxppp Boil at

different T


• The steam distillation enables some heat-sensitive , water-

insoluble organic compounds to be distilled at a lower

temperature than their Tb.

• The only disadvantage is that the composition of the

condensate is proportional to the vapor pressures of the

components. Low volatility, low abundance.


• Consider a system consisting of pairs of partially miscible

liquids (partially immiscible, P = 2) which are liquids that do not

mix in all proportions at all temperatures.

• Ex) hexane and nitrobenzene

22222 PCF• When P = 2,

• The selection of a temperature (F’ = 0)

implies that the compositions of the

immiscible liquid phases (P = 2) are fixed.

• When P = 1 (fully mixed phase), F = 3

and F’ = 1 at a constant p and a fixed T.

The composition may be adjusted.

pconstant at 1F

Hexane/nitrobenzene

at 1 atm


• The region below the curve corresponds

to the compositions and temperatures at

which the liquids are partially miscible.

• The upper critical solution temperature

(Tuc) is the temperature above which the

two liquids are miscible in all proportions.

Completely

miscible

(P = 1)

Partially miscible (P = 2)

The major (A saturated with B): a’

The minor (B saturated with A): a’’

Relative abundance: Lever rule

• Consider adding B into A.

richA

richB

richB

richA

l

l

n

n

richBrichBrichArichA lnln


Completely miscible (P = 1)

Partially miscible (P = 2)

The major (A saturated with B)

The minor (B saturated with A)

Relative abundance: Lever rule

• Consider raising T which increases the

miscibility.

(See Ex. 6.2)


• The upper critical solution

temperature (Tuc) is the highest T at which

phase separation occurs.

• Above Tuc, phase separation does not

occur whatever the composition. also

called the upper consolute temperature.

• This temperature exists because the greater thermal motion

overcomes the tendency of like molecules to stick together and

therefore to form two phases.


• The upper critical solution temperature (Tuc) is also

observed in solid solutions.

Ex) Palladium/hydrogen system

Solid solution of

H2 in Pd

Palladium

hydride (PdHx)

Tuc = 300 oC


• In the formation of an ideal solution by mixing of liquids,

BBAAmix xxxxnRTG lnln

BBAAmix xxxxnRS lnln

0 Hmix

0 Vmix

• The driving force for mixing is the increasing

entropy of the system, and the enthalpy of

mixing is zero.

• The average energy of A-B interactions in the

ideal solution is the same as the average

energy of A-A and B-B interactions in the pure

liquids.

• mixG < 0 for all compositions and T, so the

mixing is spontaneous in all proportions.


• In the formation of a regular solution (HE 0 but SE = 0) by

mixing liquids,

BABBAAmix xxxxxxnRTG lnlnBAmix

E xRTxnHH

• If < 0, mixing is exothermic

(A-B interactions more favorable).

• If > 0, mixing is endothermic

(A-B interactions less favorable).

• For > 2, two minima separated by a maximum. The

system will separate spontaneously into two phases with

compositions corresponding to the minima. Partially miscible


• For > 2, phase separation occurs in the

compositions corresponding to the minima.

• The compositions are obtained by

BABBAAmix xxxxxxnRTG lnln

0 Amix xG

0)21(1

ln

AA

A xx

x

• As decreases, two minima move together

and merge when =2.

BA x x 1 Using


• Some systems show a lower critical solution

temperature (Tlc, also called the lower

consolute temperature).

• Below Tlc, liquids mix in all proportions.

Ex) water/trimethylamine mixture

• At low T, the two components are more miscible because they

form a weak complex.

• At high T, the complexes break up and the two components

are less miscible.


• Some systems have both upper and lower

critical solution temperatures.

• T < Tlc: the two components form a weak

complex.

• Tlc < T < Tuc: the weak complexes have

been disrupted.

• T > Tuc: the thermal motion homogenizes

the mixture again.

Ex) water/nicotine system


• Reading: page 200 ~ 208

• 강의 평가 할 것.

school of chemical & biological engineering, konkuk university

Documents