CHEM%20212

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CHEM 212

• Chapter 5
• Phases and Solutions

Dr. A. Al-Saadi
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Things to be Covered in This Chapter

• Substances can exist in more than one phase.
• Introduction to phases, phase recognitions and
  equilibrium between phases.
• Clapeyron equation and Clausius-Clapeyron
  equation for phase changes.
• Troutons Rule (relationship between enthlapy
  and entropy of vaporization).
• Gibbs equation (variation of vapor pressure with
  external pressure).
• First-order and second-order phase transitions.
• Raoults and Henrys Laws for ideal solutions.
• Gibbs-Duhem equation (relationship between
  volumes and concentrations).
• The chemical potential.
• Thermodynamics of solutions.
• The colligative properties.

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Homogeneous and Heterogeneous Phases

• Phase can be defined as a state of aggregation.
• Homogeneous phase is uniform throughout in its
  chemical composition and physical state. (no
  distinction or boundaries)
• Water, ice, water vapor, sugar dissolved in
  water, gases in general, etc.
• Heterogeneous phase is composed of more than one
  phase These phases are distinguished from each
  other by boundaries.
• A cube of ice in water. (same chemical
  compositions but different physical states)
• Oil-water mixture.
• The two phases are said to be coexistent.

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Phase Distinctions in the Water Systems

• Phase diagram shows the phase equilibria with
  respect to pressure and temperature.
• Pure states.
• Coexistence of two phases at equilibrium.
• Metastable state not the thermodynamically most
  stable state.
• Water phase diagram is not that representative
  because of the ve slope.

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Phase Distinctions in the Water Systems

• Polymorphism takes place at an extremely high
  pressure (order of 2000 bar) at which different
  crystalline forms of ice may exist.
• Triple point is where all the three phases
  coexist. It is also known as the invariant point.

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Phase of Liquid Crystals

• Liquid crystal is an intermediate phase between
  solid and liquid and has some properties of both
  phases.
• Mesogens are the building units of liquid
  crystals. They are long, cylinder-shaped in their
  structure and fairly rigid.
• The liquid-like properties come from the fact
  that they can flow easily one past another.
• The solid-like properties come from the fact
  that during flow they dont disturb their
  structure.

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Phase of Liquid Crystals
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Phase of Liquid Crystals
Texture of LC in the nematic phase when is put
under microscope. It shows the optical properties
of such a phase.
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Phase Equilibria of One-Component System, Water
as an Example
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Phase Equilibria of One-Component System, Water
as an Example
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Phase Equilibria of One-Component System, Water
as an Example

1. Compare slopes.
2. Points of intersection of the curves of the three
   phases.
3. iGm for pure phases. Example 5.1
4. Entropy of the three phases.

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Phase Equilibria of One-Component System, Water
as an Example

1. Heat capacity dependence.
2. Effect of decrease of pressure.
3. Effect of increase of pressure.
4. Triple point.
5. Sublimation

Interesting mathematics link
http//www-rohan.sdsu.edu/jmahaffy/courses/s00a/m
ath121/lectures/graph_deriv/diffgraph.html
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Effect of Pressure Decrease
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Phase Equilibria of One-Component System, Water
as an Example

1. Heat capacity dependence.
2. Effect of decrease of pressure.
3. Effect of increase of pressure.
4. Triple point.
5. Sublimation

Interesting mathematics link
http//www-rohan.sdsu.edu/jmahaffy/courses/s00a/m
ath121/lectures/graph_deriv/diffgraph.html
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Thermodynamics of Vapor Pressure

• Two phases of a pure substance can coexist if ?G
  0 at a given T and P.
• If we are at one of the phase-equilibrium lines
  and either P or T has been varied, one phase will
  disappear, and ?G ? 0.
• How can we maintain the equilibrium while P or T
  is changing.

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Clapeyron Equation
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Clausius-Clapeyron Equation
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Clausius-Clapeyron Equation
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Troutons Rule
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Troutons Rule
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Troutons Rule
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The Vapor Pressure of a Liquid
Vapor pressure is the pressure of a vapor in
equilibrium with its non-vapor phases. All
liquids and solids have a tendency to evaporate
(escape) to a gaseous form, and all gases have a
tendency to condense back into their original
form (either liquid or solid). At any given
temperature, for a particular substance, there is
a pressure at which the gas of that substance is
in dynamic equilibrium with its liquid or solid
forms. This is the vapor pressure of that
substance at that temperature.
Vapor pressure
Liquid or solid
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The Vapor Pressure of a Liquid
Vapor pressure is the pressure of a vapor in
equilibrium with its non-vapor phases. All
liquids and solids have a tendency to evaporate
(escape) to a gaseous form, and all gases have a
tendency to condense back into their original
form (either liquid or solid). At any given
temperature, for a particular substance, there is
a pressure at which the gas of that substance is
in dynamic equilibrium with its liquid or solid
forms. This is the vapor pressure of that
substance at that temperature.
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The Vapor Pressure of a Liquid
Vapor pressure
Increasing T
Liquid or solid
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Effect of Nonvolatile Solutes on Vapor Pressure
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Effect of External Pressure on Vapor Pressure

• External pressure may be applied either by
• compressing the condensed phase, or by
• mixing the vapor with inert gas.
• In both cases the vapor pressure of the condensed
  phase increases.

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Effect of External Pressure on Vapor Pressure
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First-Order and Second-Order Phase Transitions
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Lambda (?) Phase Transitions
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Ideal Solutions

• A Solution is any homogeneous phase that contains
  more than one component. These components cant
  be physically differentiated.
• A Solvent is the component with the larger
  proportion or quantity in the solution. A Solute
  is the component with the smaller proportion or
  quantity in the solution.
• The idea of Ideal Solutions is used to simplify
  the study of the phase equilibrium for solution.
  The solution is considered to be ideal when
• its components are assumed to have similar
  structures and sizes, and when
• it represents complete uniformity of molecular
  forces (basically attraction forces).

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Ideal Solutions
When considering a binary system, we are often
interested to study the behavior of that system
in terms of the variables P, T and n.
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Raoults Law
Recall that the vapor pressure is a measure of
the tendency of the substance to escape from the
liquid. For an ideal solution composed of two
components (binary systems) , Raoults law
relates between the vapor pressure of each
component in its pure state (P) to the partial
vapor pressure of that component when it is in
the ideal solution (P).
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Raoults Law
To know what partial vapor pressure a component
in a solution has is important. This is because
it gives you information about the cohesive
forces in the system.
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Raoults Law

• If the solution has partial vapor pressures that
  follow

then the system is said to obey Raoults law and
to be ideal, taken into consideration T is fixed
for the solvent and solution.

• Examples include
• Benzene toluene.
• C2H5Cl C2H5Br.
• CHCl3 HClCCCl2.

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Application of Raoults Law
Problem 5.21 Benzene and toluene form nearly
ideal solutions. If at 300 K, P(toluene) 3.572
kPa and P(benzene) 9.657 kPa, compute the
vapor pressure of a solution containing 0.60 mole
fraction of toluene. What is the mole fraction of
toluene in the vapor over this liquid?
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Deviations from Raoults Law

• Deviations from Raoults law occur for nonideal
  solutions.
• Consider a binary system made of A and B
  molecules.
• Positive deviation occurs when the attraction
  forces between A-A and B-B pairs are stronger
  than between A-B. As a result, both A and B will
  have more tendency to escape to the vapor phase.
• Examples
• CCl4 C2H5OH system.
• n-C6H14 C2H5OH system

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Deviations from Raoults Law

• For a binary system made of A and B molecules.
• Negative deviation occurs when the attraction
  force between A-B pairs is stronger than between
  A-A and B-B pairs. As a result, both A and B will
  have less tendency to escape to the vapor phase.
• Examples
• CCl4 CH3CHO system.
• H2O CH3CHO system

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Deviations from Raoults Law
Another important observation is that at the
limits of infinite dilution, the vapor pressure
of the solvent obeys Raoults law.
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Henrys Law

• The mass of a gas (m2) dissolved by a given
  volume of solvent at constant T is proportional
  to the pressure of the gas (P2) above and in
  equilibrium with the solution.
• m2 k2 P2
• where k2 is the Henrys law constant.

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Henrys Law

• For a mixture of gases dissolved in a solution.
  Henrys law can be applied for each gas
  independently.
• The more commonly used forms of Henrys law are
• P2 k x2
• P2 k c2

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Henrys Law

• The vapor pressure of a solute, P2 , in a
  solution in which the solute has a mole fraction
  of x2 is given by
• P2 x2 P2
• where P2 is the vapor pressure of the solute in
  a pure liquefied state.
• It is also found that at the limits of infinite
  dilution, the vapor pressure of the solute obeys
  Henrys law.

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Application of Henrys Law
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Partial Molar Quantities

• The method using partial molar quantities
  enables us to treat nonideal solutions. In this
  method we consider the changes in the properties
  of the system as its compositions change by
  adding or subtracting.
• The thermodynamic quantities, such as U, H, and
  G, are extensive functions, i.e. they depend on
  the amounts of the components in the system. Also
  they depend on the P and T. For example, G G(P,
  T, n1, n2, n3, ).

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Partial Molar Volume

• In this treatment, the volume is used as starting
  point to lead to the thermodynamic functions in
  terms of partial molar quantities.
• The volume occupied by H2O molecules added is
  dependent on the nature of surrounding molecules.

V(H2O) 18 mL
Vtot Vw 18 mL
Vtot Vw 14 mL
ethanol V Veth
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Partial Molar Quantities

• Partial molar volume is defined as

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Partial Molar Quantities
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Partial Molar Volumes
Exercise The partial molar volumes of acetone
and chloroform in a solution mixture in which
mole fraction of chloroform is 0.4693 are 74.166
cm3/mol and 80.235 cm3/mol, respectively. What is
the volume of a solution of a mass 1.000 kg?
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Chemical Potential

• The chemical potential (µi) of a thermodynamic
  system is the amount by which the energy of the
  system would change if an additional particle
  (dni) were introduced.
• If a system contains more than one species of
  particles, there is a separate chemical potential
  associated with each species (µi , µj , ).

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Chemical Potential

• The chemical potential (µi) of a thermodynamic
  system is the amount by which the energy of the
  system would change if an additional particle
  (dni) were introduced.
• If a system contains more than one species of
  particles, there is a separate chemical potential
  associated with each species (µi , µj , ).

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Chemical Potential
In spontaneous processes at constant T and P,
system moves towards a state of minimum Gibbs
energy. (dG lt 0) In the condition of equilibrium
at constant T and P, there is no change in Gibbs
energy (dG 0)
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Chemical Potential
dG (µiß µia) dni In a spontaneous processes,
dG lt 0 at constant T and P. dni moves from phase
a to phase ß to have negative change in free
energy. The spontaneous transfer of a substance
takes place from a region with a higher µi to a
lower µi. The process continues to equilibrium
where dG 0, and µi and µi become equal.
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Chemical Potential
dG is negative
dnia
dniß
dni?
dG 0
dnja
dnjß
dnj?
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Thermodynamic of an Ideal Solution
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Colligative Properties
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Colligative Properties
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Colligative Properties
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Colligative Properties
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Colligative Properties
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Colligative Properties
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Colligative Properties
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Colligative Properties
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Colligative Properties