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
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-3
• 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.
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-4
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
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-5
• 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.
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-6
• In fractional distillation, the boiling and
condensation cycle is repeated successively.
• This technique is used to separate volatile liquids.
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-7
• 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.
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-8
• 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.
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-9
• 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)
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-10
• 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)
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-11
• 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.
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-12
• 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.
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-13
• 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
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-14
• 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.
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-15
• 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
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-16
• 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
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-17
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)
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-18
• 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.
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-19
• 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
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-20
• 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.
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-21
• 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
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-22
• 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
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-23
• 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.
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-24
• 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
Prof. Yo-Sep Min Physical Chemistry I, Spring 2009 Ch. 6-25
• Reading: page 200 ~ 208
• 강의 평가 할 것.