Ch2.phase equlibrium

Bule Hora University
College of Health and Medical Sciences
Department Of Pharmacy
INTEGRATED PHYSICAL PHARMACY AND PHARMACEUTICS I
CHAPTER 2
PHASE EQUILIBRIUM
By: Aliyi Gerina [BSc, B.pharm]
4/5/2022
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Phase Equilibrium By Aliyi Gerina

Out Line
 Introduction to intermolecular force
 The phase rule
 Phase equilibrium of
 single,
 two and
 three component systems (principles and
applications)
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Introduction to intermolecular
force
 There are three states of matters such as gas, liquid,
and solid.
 The pharmacist will encounter three of these
» through dispensing them
» consulting on these pharmaceutical preparations.
 Examples of the three states of matter would include
– gas in metered dose inhalers,
– liquids in syrups and
– solid dosage forms of tablets and capsules.
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Introduction to intermolecular forces…
 What makes some substances be gas, some liquid, some
solid?
 The reason is differences in attractive forces between
particles;
» particles of water have greater affinity for one another
than particles of O2 have for each other.
 There are two types of forces in matters:
• Intramolecular forces
• Intermolecular forces
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 The Intermolecular Forces (forces between molecules)
are weaker than Intramolecular Forces.
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Intramolecular forces
Definition
 An intramolecular force (or primary forces)
 is any force that binds atoms together making up a
molecule or compound,
 Not to be confused with intermolecular forces, which are
the forces present between molecules.

Ionic bonds
 Ionic compounds contain oppositely charged particles
held together by extremely strong electrostatic
interactions.
 These are the strongest intramolecular forces.
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Covalent bond
 Formed between the non metallic elements of the
periodic table.
 It is formed by electron sharing.
H·+·H → H:H or H━H

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Intermolecular Forces
Definition
 Intermolecular forces are forces of attraction and
repulsion that exist between molecules or ions.
 These forces help hold the ions and molecules of a
substance together.

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Overview of Intermolecular Forces
 We know that atoms in a molecule are held together by
chemical bonds. But what holds these molecules together?
 The forces that hold one molecule to another in a substance
are called intermolecular forces.
 Intermolecular forces are
 highest among the molecules of solids and
 least among the molecules of gases.
 Attractive intermolecular forces were first classified by
Johannes Diderik van der Waals and are known as Van der
Waals forces. Does the same force exist between every
particle?

 The forces that exist between two molecules or ions
depend upon the type of molecules or ions that interact:
Ion-Dipole Forces(IDF)
Dipole-Dipole Forces(DDF)
Ion-Induce Dipoles Forces(IIDF)
Dipole-Induced Dipole Forces(DIDF)
London Dispersion Forces (Induced Dipole -
Induced Dipole )(LDF)
Hydrogen Bonding(HB)
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Ion-dipole forces
 Exists between an ion and a dipole molecule.
 A positive ion will be attracted to the negative pole of the
polar molecule, while
 a negative ion will be attracted to the positive pole of the
polar molecule.
 Example: NaCl dissolves in water
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Dipole-dipole Forces
 Results from all polar molecules (an unequal
distribution of electrons around these polar
molecules results in a “dipole’, positive and
negative sides that attract similar molecules).
 HCl is a polar molecule with the partial
positive charge on the H and the partial
negative charge on the Cl.
 A network of partial + and - charges attract
molecules to each other.
• Example: CH3CL, SO2 and H2S
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Ion-induced dipole Force
 Interactiton between an ion and a non-polar molecule.
 The charge of the ion causes distortion of the electron cloud on
the non-polar molecule.
 So we have an non-polar molecule in iteracttion with an ion &
 this ion produces a induced dipole from a non-polar molecule.
 Fe2+ ion in the interaction with a non-polar molecule O2.

Dipole-Induced Dipole Forces
 A non-polar molecule turns into a
induced dipole when it interacts with a
polar molecule.
 E.g Interaction between the non-
polar molecule O2 and the
polar H2O molecule.
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London Dispersion forces (Induced Dipole
-Induced Dipole )
 Weakest of the intermolecular forces
 The only intermolecular force of attraction between
non polar molecules.
 The attractive force between positive and negative
charges that results from temporary dipoles.
 In the Ne atom the induced dipole in one atom influences
the electron distribution in other atom and atoms attract.
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 Even though CH4 has no net dipole,
at any one instant its electron
density may not be completely
symmetrical,
 resulting in a temporary dipole.
 This can induce a temporary dipole in
another molecule.
 The weak interaction of these
temporary dipoles constitutes
 van der Waals forces.
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Hydrogen Bond
 Hydrogen bonding typically occurs
when a H atom bonded to F, O, or N
atom,
 is electrostatically attracted to a lone
pair of electrons on an O, N, or F
atom in another molecule.
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 Interactions b/n H2O molecules.
The hydrogen bond if formed
between O2 [red] and H [white].

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Physical Properties
affected by intermolecular forces
Boiling point(BP)
 The BP of a compound is the temperature at which liquid
molecules are converted into gas.
 In boiling, energy is needed to overcome the attractive forces
in the more ordered liquid state.
 The stronger the intermolecular forces, the higher the BP.
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Physical Properties,…
Melting point (MP)
 The MP is the temperature at which a solid is converted to its liquid
phase
 In melting, energy is needed to overcome the attractive forces in
the more ordered crystalline solid
 The stronger the intermolecular forces, the higher the MP
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The stronger the intermolecular forces between the
molecules of a substance , the higher the melting point
and boiling point of a substance.
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Physical Properties,…
Solubility
 Like dissolves like
– Polar solutes dissolve in polar solvents
– Nonpolar solutes dissolve in nonpolar solvents
 Molecules with similar intermolecular forces will mix freely.
 In dissolving a compound, the energy needed to break up the
interactions between the molecules or ions of the solute .
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Phase rule and Phase diagram
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Out line
 Phase Rule
 Phase equilibrium of
 Single component systems
 Two component systems and
 Three component systems
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Phase Rule
 It was first presented by Gibbs in 1875.
 It is very useful to understand the effect of intensive
variables,
 such as temperature, pressure, or concentration,
 on the equilibrium between phases as well as between chemical
constituents.
 It is used to deduce the number of degrees of freedom
(f) for a system. Sometimes called: “the variance of the
system”.
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Phase Rule,…
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It states that :
 When the equilibrium between any number of phases is
 influenced only by temperature, pressure and concentration
but
 not influenced by gravity, or electrical or magnetic forces or
by surface action then
 the number of Degrees of Freedom (F) of the system is
related to the number of Components (C) and Phases (P)
by the phase rule equation:
F = C - P + 2

Phase Rule,…
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phase
 defined as: any homogeneous part of a system
having all physical and chemical properties the
same throughout.
 In another word , a uniform part of a system in
equilibrium is termed a ‘ phase’.
 Represented by P in the phase Rule equation.

Phase Rule,…
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 A system may consist of one phase or more than one
phases.
 A system containing only liquid water is one-phase or (P = 1)
 A system containing liquid water and water vapor (a gas) is a
two-phase or (P = 2)
 A system containing liquid water, water vapor and solid ice is
a three-phase or(P = 3)

Phase Rule,…
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 A system consisting of one phase only is called a
homogeneous system.
 Water, ice, water vapor, sugar dissolved in water, gases in
general, etc.
 A system consisting of two or more phases is called a
heterogeneous system
 A cube of ice in water. (same chemical compositions but
different physical states)
Ice ↔ water ↔ vapour: Phases in equilibrium

Phase Rule,…
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 CaCO3(s) ↔CaO(s) + CO2(g)
– Phases: P = 2 solid + 1 gas = 3

Phase Rule,…
Substances comments
Phases
(P)
Oxygen gas (O2) Homogeneous gas 1
Liquid benzene (C6H6) Homogeneous liquid 1
Mixture of water and
alcohol
Miscible liquids 1
Mixture of water and oil
Immiscible,
heterogeneous
2
Solution of Nacl in water Solution, homogeneous 1
Mixture of ice-water- Equilibrium,
3
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Phase Rule,…
Components(C)
 The term component is defined as the least number of
independent chemical constituents
 in terms of which the composition of every phase can be
expressed by means of a chemical equation. .
 A system ‘C’ in the Phase Rule equation stands for the number of
components of a system in equilibrium.
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Phase Rule,…
System component
Number of
component
s
Phase
Ice-water Water (H2O) 1 2
Ice-vapour Water (H2O) 1 2
Mixture of oxygen
and nitrogen
O2 and N2 2 1
Sodium chloride
solution
Nacl and
water
2 1
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Phase Rule,…
Degrees of freedom (F):
 defined as the least number of variable factors (concentration,
pressure and temperature) which must be specified
 so that the remaining variables are fixed automatically and the
system is completely defined.
 Represented by F in the phase Rule equation (F = C – P + 2)
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Phase Rule,…
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 A system with F = 0 is known as non variant or having
=>no degree of freedom.
 A system with F = 1 is known as univariant or having
=> one degree of freedom.
 A system with F = 2 is known as bivariant or having
=> two degrees of freedom.
i.e F = 0 => Neither temperature nor pressure can be varied
independently.
F = 1 => Only one out of temperature and pressure can be
varied independently
F = 2 => Both temperature and pressure can be varied

Phase Rule,…
Substance/system Degree of freedom Intensive properties
Pure gas
F=1-1+2=2
(bivariant)
Pressure &
temperature
Mixture of two gases
F=2-1+2=3
(Trivariant)
Press, temp &
concentration
Water & water vapor in
equilibrium
F=1-2+2=1
(univariant)
Vapor press or
temperature
Saturated NaCl solution
with undissolved solid &
vapor
F=2-3+2=1
(univariant)
Temperature
Ice-water-water vapour
F=1-3+2=0
(Invariant)
No need of mention
any properties. Which
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Phase Rule,…
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phase diagram
 is a plot showing the conditions of pressure and
temperature under which two or more physical states can
exist together in a state of dynamic equilibrium
 They are one of the most important sources of information
concerning the behavior of elements, compounds and
solutions as a function of T, P & C.
 They also show the preferred physical states of matter at
different T and P .

Phase Rule,…
Depending on number of components
 One component system
 Two component system
 Three component system
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One component system,
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F=2
F=0
F=1

One Component System
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 For a one-component system the phase rule equation as:
F = C – P + 2 =
=1 – P + 2
=3 – P
 Three cases may arise:
Case 1.
 When only one phase is present
F = 3 – 1
= 2
 Thus the system is bivariant.
 It can be completely defined by specifying
 the two variables T and P. Or both the T and P can be varied independently.

One Component System,…
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Case 2.
 When two phases are in equilibrium,
F = 3 – 2
= 1
 The system then has one degree of freedom and
 is termed uni-variant or mono variant.
 This means that the pressure cannot be changed independently
if we change the temperature.
 The pressure is fixed automatically
 for a given temperature.

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Case 3.
 When three phases are in equilibrium,
F = 3 – P = 3 – 3 = 0 ,
F = 0
 The system has zero degree of freedom and
 is termed non variant or invariant.
 This special condition can be attained at a definite T and P.
 At this point the three phases (solid, liquid, vapor)
 are in equilibrium and,
 therefore, it is called Triple point.

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Triple Point
 The triple point of a substance is the T and P at which the three
phases (gas, liquid and solid) of that substance coexist in
thermodynamic equilibrium.
For example,
 Triple point of water is 273.16 K at 611.2Pa (0.00980C at 4.58
mm of Hg).

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 A triple point shows the conditions under which all three
phases
 can coexist in equilibrium.
 Thus, the system at the triple point may be represented as:
Solid ⇌ Liquid ⇌Vapor
 Applying the phase rule equation we have
 F = C – P + 2
= 1 – 3 + 2
= 0
 This predicts that the system has no degree of freedom at its
triple point.

The Water System
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 ‘Water’ is a three-phase, one-component system.
 The total number of phases which can exist in
equilibrium any time
 depends on the conditions of temperature and pressure.

Phase Diagram of water
system
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Phase Diagram of water,…
 The phase diagram or P-T graph of
the system/ water/ice/vapour is
shown in the Figure.
 The salient features of the phase
diagram are listed below.
(1) The Curves OA, OB, OC
(2) The Triple Point O
(3) The Areas AOC, AOB, BOC
 Let us proceed to discuss the
significance of each of these
features.
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1. The Curves OA, OB, OC
 These three curves meet at the point O and
 divided the diagram in to three region or area.
Curve OA, the Vapor Pressure curve
 It represents the vapour pressure of liquid
water at different temperatures.
 The two phases water and water vapour
coexist in equilibrium along this curve.
Liquid ⇌Vapor
 The curve OA terminates at A’,
 the critical point (218 atm, temp. 374ºC) at
this point the liquid and vapour
 are indistinguishable from each other. 4/5/2022
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Curve OB, the Sublimation curve.
 It shows the vapour pressure of
solid ice at different temperatures.
 The two phases solid ice and
vapour coexist in equilibrium along
this curve.
Solid ⇌ Vapor
 The curve terminates at the point B,
 where no vapour exists.
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Curve OC, the Fusion curve.
 It depicts the effect of pressure on
the melting point of ice.
 Here ice and water coexist in
equilibrium.
Solid ⇌ Liquid
 The OC slopes to the left
indicates
 the melting point of ice
decreases with increase of
Pressure.
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 Along the curves OA, OB, OC
 there are two phases in equilibrium and
one component.
Therefore,
F = C – P + 2 = 1 – 2 + 2
= 1
Hence each two-phase system :
 Liquid ⇌ Vapor represented by OA
 Solid ⇌ Vapor represented by OB
 Solid ⇌ Liquid represented by OC
 has one degree of freedom
i.e., is mono variant.
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F=1

2.The Triple point ‘O’
 The curves OA, OB and OC meet at the
triple point ‘O’ where
 all the three phases liquid water/
ice/vapour are in equilibrium.
Solid ⇌ Liquid ⇌Vapor
 This occurs at 0.00980ºC and vapour
pressure 4.58 mmHg.
 Since there are three phases and one
component, we have
 F = C– P + 2 = 1 – 3 + 2 = 0
i.e., the system is non variant.
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F=0

3. Area AOC, AOB, BOC
 Within the areas a single is capable of
stable existence. Thus,
 Area AOC represents conditions for the
one-phase system water.
 Area AOB represents conditions for the
one-phase system water vapour.
 Area BOC represents conditions for the
one-phase system ice.
 In all the three areas there being one-
phase and one component, we have
F = C – P + 2 = 1 – 1 + 2 = 2
Thus the system is bi-variant. 4/5/2022
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F=2

Why ice skating is possible??
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Summary for one component system
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TWO COMPONENT SYSTEM
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Cont’d,…
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 When a single phase is present in a two component
system,the degree of freedom is three,
F = 2 – 1 + 2 = 3
 This means that three variables must be specified in
order to describe the condition of the phase.
 Thus in such a system, in addition to P and T.
 the concentration of one of the components
has also to be given.

Cont’d,…
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 For graphic representation of these variables,
three coordinate axes at right angles to each other
would be required.
 Therefore the phase diagram obtained would be a
solid model.
 For the sake of having simple plane diagrams we
generally consider only two variables,
 the third one being a constant.

Cont’d,…
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For example, for a solid-liquid equilibrium, the gas phase
is usually absent and
the effect of pressure on the equilibrium is very small.
Thus, when a two-component system consists of solid and
liquid phases only,
the effect of pressure may be disregarded.
Then it is necessary to take into account the remaining
variables , temperature and concentration.
Such a solid/liquid system with the gas phase absent is
Called Condensed System.

Cont’d,…
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 Since the degree of freedom in such a case is reduced by one,
we may write the Reduced Phase rule as
F' = C – P + 1
Where, F' gives the remaining degrees of freedom of the
system.
 The reduced phase rule is more convenient to apply to
 solid/liquid two-component condensed system.

Cont’d,…
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 Since the only variables for two-component solid/liquid
systems are temperature and composition,
 the phase diagrams for such systems consist of Temperature-
Concentration graphs(TC graphs).

Two-Component Systems Containing
Solid and Liquid Phases:
Eutectic Mixtures
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 Component which completely miscible but do not
react.
 The general form of the phase diagram of such a 2-
component condensed system is shown in Figure.
 Here the two components A and B are completely
miscible in the liquid state, and
 these solutions on cooling yield only pure A or pure B as
solid phases.

Phase diagram of Eutectic Mixtures
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phase diagram,…
Curve AC; the Freezing
point curve of A.
 The point A represents the
freezing point of A.
 The curve AC shows that the
freezing point of A falls by
the addition of B to A.
 Thus along this curve, the
solid A is in equilibrium with
the liquid solution of B in A.
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phase diagram,…
Curve BC; the Freezing
point curve of B.
 The point B shows the freezing
point of B.
 The curve BC exhibits the fall
of freezing point by the
addition of A to B.
 Along this curve, the solid B is
in equilibrium with the liquid
solution of A in B.
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phase diagram,…
 Applying the reduced phase
rule equation to the
equilibrium represented by the
curve AC & CB
i.e., solid A/solution and solid
B/solution respectively,
 we have
F’ = C – P + 1 = 2 – 2 + 1 = 1
The degree of freedom is one
 i.e., both equilibrium are mono
variant.
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phase diagram,…
The Eutectic point C.
 The two curves AC and BC meet at the
point C.
 Here both the solids A and B must be in
equilibrium with the solution phase
(solution of A and B).
 The number of phases is 3.
 By applying the reduced phase rule
equation , we have
F' = C – P + 1 = 2 – 3 + 1 = 0
 Thus, the system represented by the point
C is non variant.
 In other words, both temperature and
composition of the system solid A-solid B-
solution are fixed.
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phase diagram,…
 The mixture of components A and B
as at point C,
 melts at the lowest temperature TE
indicated on the graph.
 The point C is therefore, called the Eutectic
point (Greek eutectos = easy melting).
 The corresponding composition (CE) and
temperature (TE) are known as the eutectic
composition and the eutectic temperature
respectively of the system.
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phase diagram,…
The Area above the curves AC
and BC.
 Here the two components A and B are
present as liquid solutions of varying
compositions.
 As a homogeneous solution of A and B
constitutes one phase only, this system
is bivariant.
F’ = C – P + 1 = 2 – 1 + 1 = 2
 Therefore, to define the system at any
point in this area, both temperature
and composition have to be specified.
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phase diagram,…
Effect of Cooling
 When the A/B solution at any point in the
area above ACB is cooled,
 the cooling dashed line meets the curve AC,
say at Y.
 Here solid A separates and the equilibrium
shifts down along the curve AC.
 The change of composition and T
continues till the eutectic point C is
reached when solid B also separates.
 Thus in the area below AC and above TE line,
 there exist two phases, solid A and solution A/B, and
the system is bivariant.
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phase diagram,…
 Similarly, cooling of solution B/A on the other
side of eutectic, on reaching the curve BC would
yield solid B/solution system.
 Thus, the area below BC up to TE line would
represent solid B and solution.
 the system is bivariant.
 If the solution just below the eutectic point is
cooled,
 a solid mixture (eutectic mixture) of eutectic
composition CE.
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Two component system containing liquid
phases
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There are liquids:
 Showing complete miscibility e.g. water & ethyl alcohol
 Showing complete immiscibility e.g. water & mercury
 Showing partial miscibility e.g. water & phenol

phases…
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 The components of an ideal solution are miscible in all proportions.
 e.g. ethanol and water, under normal conditions.
 Attractions between the molecules of one component are greater
than those between its molecules and those of the other component,
i.e. if a positive deviation from Raoult's law occurs, the miscibility of the
components may be reduced.
 The greater the strength of the self-association the greater the
immiscibility,the greater the degree of +ve deviation from Raoult's
law.
e.g. large +ve deviat.: water and Hg binary system.

phases…
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In cases of partial miscibility
 Degree of miscibility may be dependent on Temperature.
1. Solubility with in temperature (water-phenol)
2. Solubility with in temperature
(water-triethylamine)
3. Solubility with & in temperature (water-nicotine)
4. Solubility not affected by temperature
 In case of three component system
 the third liquid may influence the degree of solubility of the 2
liquid systems.

phases…
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 Effect of temperature variation on the degree of miscibility
in these systems is described by means of phase diagrams.
Phase diagrams
= graphs of temperature versus composition at constant P.

1. Systems showing an increase in
miscibility with rise in temperature
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 A +ve deviation from Raoult's law due to difference in
the cohesive forces that exist between the molecules
of each component in a liquid mixture.
T => +ve deviation => miscibility
 Each phase consists of a saturated solution of one
component in the other liquid.
 Such saturated solutions are known as conjugate solutions

Phenol and water system phase diagram.
 Two factors affecting
miscibility of phenol &
water.
1- Concentration of
phenol in water
2- Temperature
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Phenol and water system phase diagram…
 Increasing quantities of phenol from b
to c ,
we form systems in w/c
 the amount of the phenol-rich phase (B)
continually increases.
 At the same time the amount of the
water-rich phase (A) decreases.
 Once the total conc. of phenol exceeds
63 % at 50 0 C
 a single phenol-rich liquid phase is
formed.
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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 critical solution temperature
(upper consolute temperature):
 Is the maximum T at which
 the two phase region exists.
 In the case of the phenol-water
system this is 66.8° (point h).
 All combinations of phenol and
water above this temperature
 are completely miscible and
 yield one-phase liquid systems.
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 Line bc drawn across the region
containing two phases is termed as tie
line.
 It is always parallel to the base line.
 All system prepared on a tie line at
equilibrium will separate into phase of
constant composition.
» These phase are called conjugate phases
 Phenol rich (63% phenol) (c)&
water rich (11% phenol)(b) layers
(phases) at 50 0C.
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PHASE COMPOSITION AND LEVER RULE
 Lever rule: the fractional amounts of two phases are
inversely proportional to their distances along the tie
line from the bulk composition axis.
 Tie line can be used to determine the weight and
composition of the phases.
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Cont’d,…
• The lengths of dc and bd can be measured with a ruler
in centimeters or inches from the phase diagram.
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Cont’d,…
 Example 1
– point d = 24% b = 11%, c = 63%,
𝑑𝑐
𝑏𝑑
=
63−24
24−11
=
39
13
=
3
1
 For every 10 g of a liquid
system in equilibrium at
point d
 Phase A = 7.5 g &
 Phase B = 2.5 g
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Cont’d,…
 At point f =50%
𝑓𝑐
𝑏𝑓
=
63−50
50−11
=
13
39
=
1
3
– For every 10 g of system f
Phase A = 2.5 g &
phase B 7.5
 At Point e = 37 %
𝑒𝑐
𝑏𝑒
=
63−37
37−11
=
26
26
=1
Equal weight of phase A & phase
B .
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2. Systems showing a decrease in miscibility
with rise in T.
 Systems showing a decrease in miscibility
with rise in T.
 E.g : triethylamine-water
 Below TCST the two liquids are miscible
because
 they can form weak complexes
(internal forces).
 Above T CST increases, these weak
complexes break up and
 immiscible systems is being formed.
 Cooling mixture during ppn allows more
solution.
 Such systems should be store in cool place
is recommended
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3. Systems showing upper and lower critical
solution T.
 Other systems show both an upper
and lower consolute temperatures.
 Such systems are known as closed
miscibility loops:
Example: nicotine-water system
 After the weak complexes have been
disrupted, the two liquids are show
only partial miscibility at an
intermediate temperature region
 The thermal motion at higher T
homogenizes the mixture again .
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4. Systems with no critical solution T
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 The pair, ethyl ether and water,
 has neither an upper nor a lower consolute temperature
and
 shows partial miscibility over the entire temperature
range at which the mixture exists.

THREE COMPONENT SYSTEM
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Three-component system (Ternary system)
 The addition of a third liquid to a binary liquid system
produce
 a ternary or three-component system.
 The mutual solubility of the original pair will be
decreased If the third liquid is
 Soluble in only one of the two original liquids or
 Its solubility in the two original liquids is markedly
different,
 The addition of a liquid having roughly the same
solubility in both components of the original pair will
 result in an increase in their mutual solubility
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Three-component system (one phase)
In non condensed system
 In systems containing three component but only one phase
F = C – P + 2
F = 3 - 1+ 2 = 4
F = 4 (P,T, Conc. of two of the three components).
In condensed system and constant temp
 If we regard the system as condensed system(p constant) and hold
the T constant
F = C – P + 0
F = 3 – 1 + 0
F = 2 (conc. of 2 component)
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Rules of triangular diagrams
 Planar diagram to illustrate the phase equilibrium
 An equilateral-triangle graph may be used to represent ternary
system.
 Each side of the triangle represent 0% of one of the
components and
 the apex opposite that side represent 100% of that component
 A point on one of the sides of the triangle will give the composition of a
mixture in which only two components are present, While
 a point within the triangle will represent the composition of a ternary
mixture.
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Rules of triangular diagrams,…
 The area within the triangle
represents all the possible
combinations of A, B, and C
to give three component
systems.
 The location of a particular
three component system
within the triangle,
e.g. point x may be undertaken
as follows:
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X

 The line AC, opposite apex B ,
represents systems, containing
A and C. B is absent, i.e., B.= 0
.
 The horizontal lines running
across the triangle parallel to
AC indicate increasing % of B
from B = 0 (on line AC) to B =
100 (at point B).
 The line parallel to AC which
cuts point x is equivalent to 15
% B; consequently, the system
contains 15 percent of B and 85
percent of A and C together.
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X

 Applying similar arguments to the other
two components in the system,
 we can say that along the line AB, C=0.
 As we proceed from the line AB towards
C across the diagram, the concentration of
C increases until at the apex, C = 100
percent.
 The point x lies on the line parallel to AB,
that is equivalent to 30 percent of C.
 Therefore the concentration of A is
100 - (B + C) = 100 - (15 + 30) = 55%
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X

Ternary Systems with One Pair of Partially
Miscible Liquids
A, B and C represent water,
alcohol, and benzene,
respectively.
The line AC represents binary
mixtures of A and C
The curve afdeic termed a
binodal curve
marks the extent of the two
phase region
The remainder of the triangle
contains 1 liquid phase
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Ternary Systems with One Pair of Partially Miscible
Liquids,…
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 Ternary systems water, benzene and alcohol contains one pair
of partially miscible liquids.
 Water and benzene are miscible only to a slight extent and
 so a mixture of the 2 produces a 2 phase system,
 water saturated with benzene and benzene saturated with water.
 On the other hand, alcohol is completely miscible with both
benzene and water.
 Thus, the addition of alcohol to a two phase system of benzene and
water would produce a single liquid phase
 in which all 3 components are miscible.

Liquids,…
Tie line fi
 Systems g and h prepared along
the tie line fi both rise to two
phases having the compositions
denoted by the points f and i.
 For example, system g, after
reaching equilibrium, will
separate into two phases, f and i.
 The ratio of phases f to phase i,
on a weight basis, is given by the
ratio gi : fg.
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Liquids,…
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Effect of Temperature
 The area of binodal decrease as the temp. is
raised &
 miscibility increase till it is completely miscible &
 the binodal disappear.

Another Examples of tertiary component systems
Chloroform-water-acetic acid Oil-Alcohol-Water
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Applications of Three-component system
 Application of three component system diagram
– Surfactant/oil/water system
– Flavor/water/alcohol system
– Drug/water/propylene glycol system
 The pharmacist can pick any combination from
the region miscible depending on
 safety, efficacy, stability or cost .
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Thank You!!
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105

Ch2.phase equlibrium

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