Colligative Properties

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Colligative Properties

• Kausar Ahmad
• Kulliyyah of Pharmacy

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Introduction

• Solutions, especially liquid solutions, generally
  have markedly different properties than either
  the pure solvent or the solute.
• For example, a solution of sugar in water is
  neither crystalline like sugar nor tasteless like
  water. Some of the properties unique to solutions
  depend only on the number of dissolved particles
  and not their identity.
• Such properties are called colligative
  properties.
• Colligative Properties are those properties of a
  liquid that may be altered by the presence of a
  solute.

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Definition

• Colligative property
• A property that depends only on the amount of
  solute in a solution
• and not the identity of the solute
• Non-colligative properties
• depend on the identity of the dissolved solute
  and the solvent

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Colligative vs Non-colligative

• compare the properties of a 1.0 M aqueous sugar
  solution to a 0.5 M solution of table salt (NaCl)
  in water.
• Despite the concentrations, both solutions have
  precisely the same number of dissolved particles
  because each sodium chloride unit creates two
  particles upon dissolution - a sodium ion, Na,
  and a chloride ion, Cl-.
• Therefore, any difference in the properties of
  those two solutions is due to a non-colligative
  property.
• Both solutions have the same freezing point,
  boiling point, vapor pressure, and osmotic
  pressure because those colligative properties of
  a solution only depend on the number of dissolved
  particles.

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Non-Colligative Properties

• The sugar solution is sweet and the salt solution
  tastes salty.
• Therefore, the taste of the solution is not a
  colligative property.
• Another non-colligative property is the color of
  a solution.
• A 0.5 M solution of CuSO4 is bright blue in
  contrast to the colorless salt and sugar
  solutions. Other non-colligative properties
  include viscosity, surface tension, and
  solubility.

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Examples of Colligative Properties

• vapor pressure,
• freezing point depression (melting)
• boiling point elevation,
• osmotic pressure.
• All of these properties ultimately relate to the
  vapor pressure.

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Effect of Solute on Vapour Pressure

• When a nonvolatile solute is dissolved in a
  solvent, the vapor pressure of the resulting
  solution is lower than that of the pure solvent.
• The amount of the vapor pressure lowering is
  proportional to the amount of solute and not its
  identity.
• Therefore, vapor pressure lowering is a
  colligative property.
• The equation that describes that phenomenon is
  called Raoult's law.

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The Vapor Pressure of a Solution is Lower than
that of the Pure Solvent On the surface of the
pure solvent (shown on the left) there are more
solvent molecules at the surface than in the
right-hand solution flask. Therefore, it is more
likely that solvent molecules escape into the gas
phase on the left than on the right. Therefore,
the solution should have a lower vapor pressure
than the pure solvent.
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Boiling point

• Boiling point elevation is a colligative property
  related to vapor pressure lowering.
• The boiling point is defined as the temperature
  at which the vapor pressure of a liquid equals
  the atmospheric pressure.
• Due to vapor pressure lowering, a solution will
  require a higher temperature to reach its boiling
  point than the pure solvent.

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Freezing Point

• Every liquid has a freezing point - the
  temperature at which a liquid undergoes a phase
  change from liquid to solid.
• When solutes are added to a liquid, forming a
  solution, the solute molecules disrupt the
  formation of crystals of the solvent.
• That disruption in the freezing process results
  in a depression of the freezing point for the
  solution relative to the pure solvent.

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Osmotic Pressure

• When a solution is separated from a volume of
  pure solvent by a semi-permeable membrane that
  allows only the passage of solvent molecules, the
  height of the solution begins to rise.
• The value of the height difference between the
  two compartments reflects a property called the
  osmotic pressure of a solution.

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Phase Diagrams and the effect of solutes on
freezing and boiling points
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Factors that affect the magnitude of the changes
in melting point and boiling point.

• Concentration
• Effect of ionic compounds

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Raoult's Law

• The French chemist Francois Raoult discovered the
  law that mathematically describes the vapor
  pressure lowering phenomenon.
• Raoult's law states that the vapor pressure of a
  solution, P1, equals the mole fraction of the
  solvent, X1 , multiplied by the vapor pressure of
  the pure solvent, Po.
• P1 P1o x X1

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Total Vapour Pressure

• In an ideal solution made up of two volatile
  components
• P p1 p2
• In an ideal solution made up of one volatile
  component
• P p1

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A Visual Demonstration of Raoult's Law

• Description The intensity of color of bromine
  vapor is reduced by placing a colorless volatile
  liquid into the same container.
• Source Journal of Chemical Education - Vol. 67
• Year or vol 1990 page 598

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Deviations from Raoult's law

• the "law" is approximately obeyed by most
  solutions, some show deviations from the expected
  behavior.
• Deviations from Raoult's law can either be
  positive or negative.
• A positive deviation means that there is a higher
  than expected vapor pressure above the solution
• P1 gt P1o x X1
• A negative deviation means that we find a lower
  than expected vapor pressure for the solution
• P1 lt P1o x X1

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Reason for the deviation

• consideration of the vapor pressure lowering
  event - we assumed that the solute did not
  interact with the solvent at all.
• If the solute is strongly held by the solvent,
  the solution will show a negative deviation from
  Raoult's law, because the solvent will find it
  more difficult to escape from solution.
• If the solute and solvent are not as tightly
  bound to each other as they are to themselves,
  then the solution will show a positive deviation
  from Raoult's law because the solvent molecules
  will find it easier to escape from solution into
  the gas phase.

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Ideal Solutions

• Solutions that obey Raoult's law are called ideal
  solutions because they behave exactly as we would
  predict.
• Solutions that show a deviation from Raoult's law
  are called non-ideal solutions or real solutions
  because they deviate from the expected behavior.
• Very few solutions actually approach ideality,
  but Raoult's law for the ideal solution is a good
  enough approximation for the non- ideal solutions
  that we will continue to use Raoult's law.

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Deviation from Raoults Law end of lecture
1/3
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Vapor Pressure of a Mixture Raoult's Law

• The measurement of pressure exerted by a vapour
  is demonstrated using barometers.
• Vapor pressure varies with the strength of the
  intermolecular forces in the liquid.
• We can calculate the vapor pressure of a mixture
  using Raoult's law.

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Example Consider a solution that contains 0.6
mole fraction of decane and 0.4 mole fraction of
diethyl ether.
We can calculate the vapor pressure of a mixture
using Raoult's law P P1o x X1 P2o x X2
(5 x 0.6) (460 x 0.4) 187
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Change in Boiling Point

• One consequence of Raoult's law is that the
  boiling point of a solution made of a liquid
  solvent with a nonvolatile solute is greater than
  the boiling point of the pure solvent.
• For a solution, the vapor pressure of the solvent
  is lower at any given temperature.
• Therefore, a higher temperature is required to
  boil the solution than the pure solvent.
• The change in boiling point is

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• m is molality, because molality is temperature
  independent.
• Kb is a boiling point elevation constant that
  depends on the particular solvent used.
• i is the van't Hoff factor and represents the
  number of dissociated moles of particles per mole
  of solute.
• The van't Hoff factor is 1 for all
  non-electrolyte solutes and equals the total
  number of ions released for electrolytes.
• Therefore, the value of i for Na2SO4 is 3 because
  that salt releases three moles of ions per mole
  of the salt.

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Change in Freezing Point

• In order for a liquid to freeze it must achieve a
  very ordered state that results in the formation
  of a crystal.
• If there are impurities in the liquid, i.e.
  solutes, the liquid is inherently less ordered.
• Therefore, a solution is more difficult to freeze
  than the pure solvent so a lower temperature is
  required to freeze the liquid.
• The change in freezing point is
• Note that the sign of the change in freezing
  point is negative because the freezing point of
  the solution is less than that of the pure
  solvent.

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Awan Q Why can adding salt to ice water make the
ice melt slower? Adding salt to the ice/water
mix causes a temperature drop that slows the
melting rate and increases the freezing rate 3.
The net result is that the ice melts more and
more slowly after the initial addition of salt.
Why does salt melt ice? In pure water, at 0C,
ice melts just as fast as water freezes. You
won't see any of the ice melt as long as the
freezing rate and melting rates are exactly equal
1. Adding salt (or any foreign substance) to
the water upsets the delicate balance between
freezing and melting. Fewer water molecules reach
the surface of the ice in a given time, so water
freezes more slowly. The melting rate isn't
changed by the salt, so melting "wins" 2.
Does adding salt to ice and water cause a
temperature drop? Yes. This is how old-fashioned
ice cream makers lowered the temperature of the
ice cream below water's ordinary freezing point.
A mixture of rock salt, ice, and water packed in
the bucket around the ice cream mix can bring the
temperature down as low as -21C. Why does the
temperature drop? Energy is required to snap the
hydrogen bonds that hold the ice together. The
melting ice draws that energy from the
surrounding solution as heat. See these
previous questions for more "Why does salt melt
ice?" (includes a Flash simulation of freezing
point depression) Author Fred Senese
senese_at_antoine.frostburg.edu http//antoine.frostb
urg.edu/chem/senese/101/solutions/faq/why-salt-coo
ls-icewater.shtml
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Molal Boiling Point Elevation and Freezing Point
Depression Constants at 1 Atm pressure
Thus the boiling point of water would increase
0.52 oC for a one molal solution, while the
freezing point of this solution would decrease by
1.86 oC.
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Effect of ionic compounds

• A tenth of a mole of sugar or a tenth of a mole
  of glycerine dissolved in water will have exactly
  the same effect on the boiling and freezing
  points even though sugar is a much bigger
  molecule.
• However, a tenth of a mole of an ionic compound
  such as NaCl,, has an effect on the melting and
  boiling points that is almost twice what we would
  observe for sugar.
• The simple reason for this effect is that salt
  ionizes into Na and Cl- ions in water
• these ions act as independent particles on the
  vapor pressure of water.
• Thus, to a first approximation, we may simply
  multiply the concentration of the salt by the
  number of ions it will form when dissolved in
  water.
• Thus NaCl, NaNO3, and CaCO3 would have
  multipliers of two, while Na2SO4, and CaCl2 would
  have multipliers of three.

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Vant Hoff factor

• In dilute solutions, ionic compounds have simple
  multiple effects, but as the solution
  concentration increases the multiplier effect
  diminishes.
• This phenomenon was first discovered by van't
  Hoff and is generally called the van't Hoff
  factor.
• As concentration increases, some of the ions
  floating in solution find one another and form
  ion pairs, in which two oppositely charged ions
  briefly stick together and act as a single
  particle.
• the higher the concentration, the more likely it
  is that two ions will find one another.

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Osmotic Pressure

• When a solution and the pure solvent used in
  making that solution are placed on either side of
  a semipermeable membrane, more solvent molecules
  flow out of the pure solvent side of the membrane
  than solvent flows into the pure solvent from the
  solution side of the membrane.
• That flow of solvent from the pure solvent side
  makes the volume of the solution rise.
• When the height difference between the two sides
  becomes large enough, the net flow through the
  membrane ceases due to the extra pressure exerted
  by the excess height of the solution chamber.
• Converting that height of solvent into units of
  pressure gives a measure of the osmotic pressure
  exerted on the solution by the pure solvent.
• P rgh
• P stands for pressure, r is the density of the
  solution, and h is the height of the solution.

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Setup for Measuring the Osmotic Pressure of a
Solution
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Effect of concentration on osmotic pressure

• PV inRT
• Since n / V gives the concentration of the solute
  in units of molarity, M.
• P iMRT

End of lecture 2/3
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Application of Raoults LawDistillation
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DISTILLATION
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Distillation of Binary MixtureIdeal Solution

• When a liquid and its vapour are in equilibrium,
  vapour is richer in the more volatile component
  compared to liquid mixture
• At equilibrium, liquid and vapour phase can be
  separated and analysed

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Binary Mixtures Obeying Raoults Law Ideal
Solution

• Attractive forces between molecules of different
  component equal those of the same component.A-B
  A-A B-B
• Without a maximum or minimum at intermediate
  compositions.
• No change in properties of components (except
  dilution to form solution).
• Vapour pressure, refractive index, surface
  tension and viscosity of solution are averages of
  properties of pure individual constituents.
• No heat evolved or absorbed during mixing
  process.
• No change in solution temperature.
• Final properties of solution are additive
  properties of individual constituents.
• No shrinkage or expansion.
• E.g. methyl alcohol-water, benzene-toluene,
  methanol-ethanol.

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Definition - Azeotropic Mixture

• Describes a mixture of miscible liquids which
  boils at a constant composition and thus the
  composition cannot be changed by simple
  distillation
• Composition of vapour similar to that of liquid
• The composition as well as the boiling point of
  an azeotropic mixture changes with pressure
• If a liquid mixture represented by a composition
  X1 is distilled, the vapour has composition X2
  and condenses to form a liquid of that
  composition.
• Distillation starting at composition X1 produces
  an azeotropic mixture Z as the distillate, and
  the residue tends towards pure B
• Similarly, a mixture of composition Y1, yields an
  azeotropic mixture as distillate, and pure A as a
  residue

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Positive Deviation from Raoults Law

• Vapour pressure greater than expected from
  Raoults law.
• The two components differ in properties e.g.
  polarity
• Attractive forces A-B lt A-A or B-B
• Escaping tendency higher
• The extent of deviation is expressed
  quantitatively as activity coefficient (f) of the
  component.
• A max is found in vapour pressure-composition
  curve
• Heat is absorbed during the mixing process
• Solution temperature decreases
• Final volume of solution increases
• Expansion
• Presence of azeotropic mixtures lead to min
  boiling point
• Examples 1. ethyl, isopropyl, n-propyl alcohol
  - water,2. volatile drug (methyl amphetamine)
  chloroform - ethanol

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Positively deviated solution mixturewith a
minimum boiling point

• The mixture shows positive deviation from
  Raoults law
• A minimum boiling point is obtained
• The solution has an azeotropic mixture whose
  vapour pressure is the highest and boiling point
  is the lowest
• example of a positive azeotrope is 95.6 ethanol
  and 4.4 water (by weight). Ethanol boils at
  78.4C, water boils at 100C, but the azeotrope
  boils at 78.1C

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Distillation of positive azeotrope 95.6 ethanol
and 4.4 water

• distillation of any mixture will result in the
  distillate being closer in composition to the
  azeotrope than the starting mixture.
• E.g. if a 50/50 mixture of ethanol and water is
  distilled once, the distillate will be 80
  ethanol and 20 water i.e. closer to the
  azeotropic mixture than the original.
• Distilling the 80/20 mixture produces a
  distillate that is 87 ethanol and 13 water.
• Further repeated distillations will produce
  mixtures that are progressively closer to the
  azeotropic ratio of 95.5/4.5.
• increasing distillations will not give distillate
  that exceeds the azeotropic ratio.

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Negative Deviation from Raoults Law

• Vapour pressure of solution less than that
  expected from Raoults law
• Attractive forces A-B gt A-A or B-B
• Escaping tendency lower
• Heat is evolved during the mixing process
• Solution temperature increases
• Final volume of solution decreases
• Shrinkage
• A min is found in vapour pressure composition
  curve
• Presence of azeotropic mixtures lead to max
  boiling point
• E.g. pyridine-acetic acid, chloroform-acetone
  (formation of loose compounds from hydrogen
  bonding), formation of hydrates, nitric
  acid-water, sulfuric acid-water.

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Negatively deviated solutionwith maximum boiling
point

• Mixtures showing negative deviation from Raoults
  law
• A maximum boiling point is obtained
• The solution has an azeotropic mixture whose
  vapour pressure is the lowest and the boiling
  point is the highest
• example of a negative azeotrope is 20.2 hydrogen
  chloride and 79.8 water (by weight). Hydrogen
  chloride boils at 84C and water at 100C, but
  the azeotrope boils at 110C

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Distillation of negative azeotrope 20.2
hydrogen chloride and 79.8 water

• distillation of any mixture of those constituents
  will result in the residue being closer in
  composition to the azeotrope than the original
  mixture.
• E.g. hydrochloric acid solution contains less
  than 20.2 hydrogen chloride,
• boiling the mixture will give a solution that is
  richer in hydrogen chloride than the original.
• If the solution initially contains more than
  20.2 hydrogen chloride, boiling will give a
  solution that is poorer in hydrogen chloride than
  the original.
• Boiling of any hydrochloric acid solution long
  enough will cause the solution left behind to
  approach the azeotropic ratio.

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Application of Raoults Law in Aerosol Formulation

• Vapour pressure of propellant control the spray
• As pressure increases, spray rate increases -gt
  fine spray, propellant gas vapourises fast
• As pressure decreases, spray rate decreases -gt
  coarse spray, propellant gas vapourises slowly -gt
  wet
• Thus, improvise by using appropriate mixture of
  propellant
• Examples of components
• HFA-125 pentafluoroethane CHCF5
• HFC-134a tetrafluoroethane CHCHF4
• HFA-152 difluoroethane CH3CHF2
• HFA-227 heptafluoropropane CHFCF3CF3

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Exercise Application of Raoults Law in Aerosol
Formulation

• The vapour pressure of pure propellant 11 (MW
  137.4) at 21oC is P110 13.4 psi
• The vapour pressure of pure propellant 12 (MW
  120.9) at 21oC is P120 84.9 psi
• A total of 100 g propellants consisting of 5050
  mixture by gram weight was used.
• n11 50/137.4 0.364 mole
• n12 50/120.9 0.414 mole
• n11 n12 0.778 mole
• P11 P110X11 P110(n11/(n11 n12) 13.4 x
  0.364/0.778 6.27 psi
• P12 P120X12 P120(n12/(n11 n12) 84.9 x
  0.414/0.778 45.2 psi
• P P11 P12 51.5 psi
• Conversion psi to psig (Subtract atmospheric
  pressure of 14.7 psi)
• Thus, P 51.5 14.7 36.8 psig

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Variation of Vapour Pressure with Temperature
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Clausius-Clapeyron Equation

• The variation of vapour pressure with temperature
  in terms of molar enthalpy of the liquid, ?Hvap
• ?V is the difference in molar volume of the two
  phases
• Since molar volume of vapour is very much greater
  than the molar volume of liquid, ??V approaches
  volume of vapour, Vv

• Assuming that the vapour obeys ideal gas
  behaviour,
• PV RT
• V RT/P
• Thus, Vv RT/P
• The equation becomes
• Assuming ?Hvap to be constant

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Application of Clausius-Clapeyron Equation

• To estimate vapour pressure at any temperature.
• To calculate enthalpy of vaporisation based on
  the slope of plot
• To study phase transition important to
  determine the extent of weight loss during
  processing or testing.
• End lecture 3/3

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References

• Please click below
• Vapor Pressure of a Mixture - Raoult's Law
• In addition to required/recommended texts