Transcript STATE OF MATTER AND PHASE EQUILIBRI

Phase Rule and Phase
Equilibria

Phase (p):
A form of matter that is homogeneous in chemical
composition and physical state. Typical phases are solid,
liquid and gas. , Two immiscible liquids separated by a
distinct boundary are counted as two different phases.
Homogeneous phases: pure liquids or solutions

Two phases systems: immiscible liquids (or solutions) ,

One phase system: a mixture of gases, because the mixture is

since there is a definite boundary between them.
homogeneous and there are no bounding surfaces between the
different gases in the mixture.
Two phase system
One phase system
Number of components of a system (C):

Is the smallest number of constituents by which the
composition of each phase in the system at equilibrium
can be expressed in the form of a chemical formula or
equation.

Ice , water , water vapor (3-phase system) the number of
components is 1 (formula is H2O).

A mixture of salt and water is a two component system
since both chemical species are independent & different .
Phase Equilibria and the Phase Rule
The Phase Rule:
Relation between the effect of the least number of
independent variables (temperature, pressure and
concentration).
upon
various phases (solid, Liquid and gaseous) that exist in an
equilibrium system.
Phase Rule also known as Gibbs phase
rule
F = C–P + 2
Degree of
freedom or the
number of
independent
variables
Number of
component
2 variables
(temperature
and pressure)
The number
of phases
Degrees of freedom ( f ):
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
Number of degrees of freedom is the number of
variable conditions i.e. (temperature, pressure &
concentration) that must be known, so that the
condition of the system at equilibrium may be
completely defined.
The relationship between the number of phases (P),
components (C) and degrees of freedom (F) for
equilibria that are influenced only by temperature,
pressure and concentration is given by equation (the
phase rule):
F
=
C
P
+
2
The application
depends on the number of
components present in separate systems.
Phase diagrams:

Represent the effects of temperature, pressure and
composition on the phase equilibria , showing the
variation of transition temperature such as boiling or
melting point with pressure or compression.

Representation of the effect of three variables would
require three axes. This can be achieved with threedimensional models but if one variable is fixed the
resulting planar diagram can be regarded as a section
through such a model.

Systems containing one component

Systems containing two liquid components.

Systems containing two components (liquid &
solid).
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Systems containing three components.
Systems Containing One Component
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The
difficulties
associated with the
representation of 3 variables do not arise in
systems containing one C.
The areas each correspond to a single P. The
no. of degrees of F is therefore given from the
equation :
F=
1- 1+2 =2
(2) means that temperature & pressure can be
varied independently within these areas. (bivariant)
Standard phase diagram for one component system
B
A
Critical
point
Vapor region
O
C
t
t
t1
Ct
System corresponding to a point that lies on one of
the lines AO , BO, or CO,
The number of degrees of
freedom is reduced
because from equation (1)
F=1- 2+2=1
This means that a
single variable exists
when equilibrium is
established between 2
phases. (univariant)
Melting Point: (M.P)
The boundary BO represents the coexistence of liquid water
in solid ice at various temperature and pressures.
BO therefore indicates the effect of pressure on M.P of ice
(-ve slope of BO)
the M.P
To maintain equilibrium conditions
between the two phases, the
temperature & pressure must not
be varied independently of each
other.
as the pressure
.
Boiling Points:
AO
vapor pressure curve,
represents the coexistence of
liquid water and water vapor
under various conditions.
The T & P again cannot be
varied independently.
Two phase system
One phase system.
The critical temperature (374oC)
(upper limit of the vapor pressure)
This temperature above which it
is impossible to liquefy water
vapor even if you increase the
pressure.
Triple Point :
Point O , which is the only point in
the diagram where three phases may
coexist in equilibrium.
F=1 - 3+ 2 = 0
The system is therefore invariant ,
i.e. any change in pressure
or temperature will result in an alteration
of the number of phases that are present.
Sublimation and Sublimation Drying (Freeze Drying):
CO
the sublimation pressure
curve for ice (coexistence of vapor and
solid phases in equilibrium).
A mass of ice
heating
<
water vapor by
on condition
pressure is
triple point pressure.
Important
in drying compounds
that are sensitive to the higher
temperature usually associated with
drying techniques.
Lyophilization, Gelsiccation, Freeze drying
1-It is drying by sublimation from the
frozen condition , i.e. (drying of blood
plasma, blood serum and penicillin).
2-Freezing the solution of the material
(-l0o C to -30o C ) in suitable
containers connected to a high vacuum
system (0.1 - 0.3 mm Hg).
3-A partial pressure of water vapor,
less than that of the material being
dried, is attained.
4-water sublimes from the frozen mass
until the material is desiccated.
Standard phase diagram for carbon dioxide (CO2)
Two Component Systems Containing Liquid
Phases:
miscible
partially miscible
immiscible
ethyl alcohol and water
phenol and water
water and mercury
Phenol and water system:
miscible
Partially miscible
Two factors affecting
misciblity:
1- Concentration of
phenol in water.
2- Temperature.
Two component systems:
water
Phenol / water
Phenol
The curve g b h c i shows limits of temperature and
concentration within which two liquid phases exist in
equilibrium.
2 phases
1 phase
Point A
100% water
10 % phenol
11 % phenol
water rich phase
contains water+ phenol(11%)
Phenol rich phase
contains Phenol (63%)+ water
> 63 % phenol
1 phase
24% phenol
The curve g b h c i shows limits of temperature &
concentration within which two liquid phases exist in
equilibrium.
Point A
100% water (pure water)
Phenol
Point B (11 % phenol)
2 phases
water rich phase& phenol rich phase
More Phenol
Point C ( >63% phenol)
1 phase
Completely miscible
The Tie Line
It is always parallel to the base line
in two component systems.
All systems prepared on a tie line,
at equilibrium, will separate into
phases of constant composition.
known as conjugate phases.
Any system represented by a point
on the line bc , at 50oC.
separates to give a pair of
conjugate phases whose
composition is 11% phenol
in water rich phase (A) & 63 %
phenol in phenol rich phase.
Importance of Tie line:

Calculation of the composition of each phase.
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Determination of the weight of each phases.
(calculation of the distribution of phenol (or
water) throughout the system as a whole.
• The relative weights of the two phases can be
calculated using the tie line using the following
formula:
W eight of P haseA
Lengt hdc

W eight of P haseB
Lengt hbd
The use of Tie line in calculations:
As an example, let us suppose that we mixed 24 g of
phenol with 76 g of water, warmed the mixture to 50oC,
and allowed it to reach equilibrium at this temperature.
 Weight phase A = dc = 63-24
= 39 = 3
weight of phase B
bd 24 -11
13 1
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Weight of A= ¾ x 100= 75, wt. of B = ¼ x 100= 25
Phase A=75 gm ,
phase B =25 gm.
Amount of phenol in A=75 x 11/100= 8.25 gm
Amount of phenol in B= 25 x 63/100= 15.75 gm
24
gm
Application of Tie line:


To formulate systems containing more than one
component where it may be advantageous to
achieve a single-phase product.
Handling of solid phenol, a necrotic agent
(caustic agent), is facilitated in the pharmacy if a
solution of phenol and water is used. The most
convenient formulation of a single liquid phase
solution was 80% w /v, equivalent to about 76%
w / w. This mixture has a freezing point of
about 3.5oC
The Critical Solution Temperature: CST


Is the maximum temperature at which the 2-phase
region exists (or upper consolute temperature). In the
case of the phenol-water system, this is 66.8oC (point h)
All combinations of phenol and water > CST are
completely miscible and yield 1-phase liquid systems.
Systems Showing a Decrease in Miscibility
with Rise in Temperature:

A few mixtures, exhibit a lower
critical solution temperature
(low CST), e.g. triethylamine
plus water. The miscibility
with
in temperature.

In the preparation of paraldehyde
enemas, (consist of a solution of
paraldehyde in normal saline).

Cooling the mixture during
preparation allows more rapid
solution, and storage of enema in
a cool place is recommended.
Systems Showing Upper and Lower CSTs
The miscibility with
temp. in
systems having a lower CST is not
indefinite.
> a certain temperature miscibility
starts to again with further in
temperature.
Closed-phase diagram, i.e. nicotinewater system.
The Effects of Added Substances on CST:
Type of
CST
Solubility of additive in
each component
Effect on
CST
Effect on
miscibility
Upper
Approx. equally soluble in
both components
Lowered
Increased
Raised
Decreased
Raised
Increased
Lowered
Decreased
Upper
Lower
Lower
Readily soluble in one
component but not in the
other
Approx. equally soluble in
both components
Readily soluble in one
component but not in the
other
Added of
substances on
Systems with
lower CST
Examples:
If 0.1 M naphthalene is added to a mix. of phenol and
water, it dissolves only in the phenol and raises the CST
about 20°C
If 0.1 M KCl is added to a phenol-water mix, it dissolves
only in water and raises the CST approximately 8°C.
Blending :
The
in miscibility of two liquids due to the
addition of a third substance.
Example : the formulation of solution of cresol
with soap BP 1968, which contains 50% cresol.
Cresol is only partially miscible with water, but the
soap in this preparation decreases the upper CST
and produces complete miscibility at ordinary
temperature.
Addition of substance
That equally miscible
In 2 phases.
Two-component Systems Containing Solid
and Liquid Phases:
Solid- liquid mixtures in which 2 components
are completely miscible in the liquid state and
completely immiscible as solid.
Examples of such systems are:
 Salol & thymol.
 Salol & camphor.

100% salol
100% thymol
Increasing the % of thymol in the mixture till reaching 100 %.
The phase diagram for the salol thymol system:
(i) Single liquid phase,
(ii) Region containing solid salol and a conjugate
liquid phase,
(iii) Region in which solid thymol is in equilibrium with
a conjugate liquid phase.
(iv) Region in which both components are present as
pure solid phases.
Those regions containing two phases (ii, iii, and iv) are
comparable to the two-phase region of the phenolwater system.
F=2-2+1=1
System is represented by point X (60% by weight of
thymol in salol)
temperature (50 o C)
On cooling the system, the following sequence of the
phase occurs:
 The system remains as a single liquid until 29oC.
 At 29oC
a minute amount of solid thymol
 At 25oC, (system X1)
a liquid phase, a1 (53%
thymol in salol) and b1 (pure solid thymol).
 At 20oC, (system X2)
the liquid phase is a2 (45%.
by weight of thymol in salol), b2 (pure solid thymol).
 At 15oC, (system X3)
the liquid phase a3 is 37 %
thymol in salol and b1 (pure solid thymol).
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Below 13 o C the liquid phase disappears
altogether and the system contains two solid
phases of pure salol and pure thymol.
At 10oC (point X4), the system contains an
equilibrium of a4 & b4 (pure solid thymol +
pure solid salol).
The lowest temperature at which liquid
phase coexists is known as eutectic point.
In case of thymol / salol system the eutectic
point is 13 o C ( 3 phases
liquid, solid salol &
solid thymol)
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The eutectic point therefore denotes an
invariant system for, in a condensed system
F = 2 - 3 + 1 = 0.
Substances forming eutectic mixtures (e.g.,
camphor, chloral hydrate, menthol, and
betanaphthol).
If such combinations is dispensed as dry
powder, drying may be achieved by the addition
of an absorbent powder such as kaolin or light
magnesium oxide.
Phase Equilibria in Three-Component System

In systems containing three components but only
T
constant
one phase,
F = 3 - 1 + 2 = 44
condensed
P
C1


C2
For non-condensed system. The four degrees of
freedom are temperature, pressure & the
concentration of 2 of the 3 components.
For condensed & the temperature is kept
constant, then F = 2 .
Ternary System with One Pair of Partially
Miscible Liquids:
Water and benzene are partially miscible system
two-phase system.
2 – phase
system
benzene saturated with
water
water saturated with
benzene
Addition of alcohol
(solvent effect)
1- phase system
Mixture = 60% B, 20%
A, 20% C.
Alcohol
water
benzene
A, B & C represent water, alcohol & benzene, respectively.
AC
binary mixture of A and C.
a & c are the limits of solubility of C in A and A in C.
 System (g) after reaching equilibrium, will separate into two
phases, (f ) and ( i).
 weight of phase f /weight of phase I = gi / fg.
 Mixture h, mid point of the tie line, will contain equal weights of
the two phases at equilibrium.
 The curve a f d e i c,
a binodal curve
(the extent of the two-phase region).
 The remainder of the triangle contains one liquid
phase.
The directions of the tie lines are related to the shape
of binodal, (depends on the relative solubility of 3rd
component (alcohol) in the other 2 components).
 when the added component acts equally on the other
two components to bring them into solution
binodal be symmetric & the tie lines are parallel
to the base line.
Effect of Temperature:
 Changes in temperature will cause the area of immiscibility, (the
binodal curve) to change.
 Area of the binodal
as the temperature is
& miscibility is
 A point is reached at which complete miscibility is obtained and the
binodal vanishes.
Ternary Systems with Two or Three Pairs of Partially
Miscible Liquids:
A & C , B & C show partial miscibility. A and B are completely
miscible at the temperature used.
Temperature gradually leads to a reduction in the areas of the two
binodal curves & their eventual disappearance. (c)
Temperature expands the binodal curves.
At a sufficiently low temperature, they meet and fuse to form a single
band of immiscibility as shown in (a).
Systems containing three pairs of partially
miscible liquids
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
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3 binodal curves meet, a central region appears in which 3
conjugate liquid phases exist in equilibrium.
In this region, D, which is triangular, F = 0 ( condensed system
under isothermal conditions).
All systems lying within this region consist of 3 phases whose
composition are always given by the points x, y & z.
The only quantity that varies is the relative amounts of these 3
conjugate phases.
One phase
2 phases
3 phases
X
Y
Z
A, B, C
Arrangement of three phases:
It depends on the composition of the phases
At point D , F = 0 ??????