TwoComponent Systems

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Two-Component Systems

• Two miscible liquids have similar chemical
  structures/intermolecular interactions
• The individual components are free to diffuse
  throughout the two-component system at a single
  phase
• Benzene Toluene form an ideal system
• Raoults law partial vapor pressure PA?APAo
  Pao is the vapor pressure of the pure component,
  ?A is the mole fraction of the liquid in the
  mixture
• Total vapor pressure Ptotal PA PB (Daltons
  law)
• Ptotal ?APAo ?B PBo for an ideal 2-component
  mixture

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Raoults Law for Ideal Two-component System

• Upon mixing, the intermolecular forces are just
  the same as those existing in separate components
  of the ideal mixture
• The energy consumed in overcoming the forces
  holding the molecules together in the separate
  pure liquids should be provided by the same
  forces reforming between the very similar
  molecules in the ideal mixture
• There is no volume change and no enthalpy change
  when an ideal mixture is formed

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Graphical representation of Raoults Law
Vapor pressure - composition curve for an ideal
mixture
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Vapor pressure - liquid/vapor composition phase
diagramof an ideal mixture at constant
temperature

• Most ideal solutions contain one component which
  is more volatile (higher v.p. when pure) than the
  other
• The vapor forming above the mixture is richer in
  the more volatile component
• a represents the liquid composition of a mixture
  whose vapor pressure is 1 atm. b represents the
  composition of the vapor in equilibrium with the
  liquid
• b has a larger XB value than a because the
  vapor is richer in the more volatile component B.

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Vapor pressure - liquid/vapor composition phase
diagram of an ideal mixture at constant
temperature
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From vapor pressure/composition diagram to
boiling point/composition diagram for an ideal
solution

• The normal b.p. of a liquid mixture is the
  temperature at which its total vapor pressure is
  1 atm.
• Vapor pressure (and hence boiling point) of two-
  component systems depends on its composition
• When XB0.8, the vapor pressure of the mixture is
  1 atm. at 70oC so the b.p. for the mixture is
  70oC
• When XB0.3, vapor pressure of the mixture
  reaches 1 atm. at 85oC so the b.p. for the
  mixture is 85oC With decreased amount of volatile
  component B in a mixture, the b.p. increases
  accordingly

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Variation of vapor pressure/boiling point with
composition Fig.22.3

• At a certain liquid composition, the total vapor
  pressure of the ideal solution increases with
  temperature. When XB0.3, vapor pressure is 1
  atm. at 85oC (b.p.) but reaches 1.2 atm. at 90oC
• To find the b.p. of a mixture of given
  composition, just read off the temperature at
  which the total vapor pressure reaches 1
  atmosphere (100 kPa)
• At all temperatures above the 1 atm. line the
  stable state of the system is as a vapor

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A boiling point - liquid/vapor composition phase
diagram (at constant pressure) of an ideal
solution
Fig 22.4
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Applications in Fractional Distillation

• The components of an ideal mixture can be
  separated by fractional distillation which makes
  use of vapor pressure (b.p.) differences of the
  components for their separation from a miscible
  liquid mixture
• During distillation, the vapor is richer in the
  more volatile component as it evaporates
  preferentially.
• With more volatile component in it, the first
  distillate condensed boils at a lower temperature
  than the original ideal mixture

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Fractional distillation
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The Principle of Fractional Distillation

• Fractional distillation is equivalent to a series
  of consecutive simple distillations, where the
  condensed vapor from a previous distillation is
  used as the liquid for the next distillation. The
  lower-boiling condensate from the previous
  distillation can be distilled again higher up the
  fractionating column at a lower boiling
  temperature. The process can be repeated many
  times until the final distillate contains mainly
  the more volatile component and a negligible
  amount of the less volatile component.

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Deviations from Raoults Law

• The total vapor pressure of a non-ideal liquid
  mixture at a constant temperature does not vary
  linearly with composition
• positive deviation the liquid mixture has vapor
  pressure greater than expected from ideal system
  the greater tendency to escape arises from
  energetically unfavorable interactions upon
  mixing (that is, the force of attraction between
  A-B molecules is less than that between A-A and
  B-B molecules
• Ethanol-water, ethanol-chloroform,
  ethanol-toluene, ethanol-hexane are systems with
  positive deviations

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Positive deviations from ideality
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Negative deviation from Raoults Law

• Due to favorable interactions between the
  components on mixing, non-ideal solutions show
  negative deviation
• Mixtures with very large negative deviations have
  a minimum in the vapor pressure curve and the
  b.p. curve passes through a maximum which is
  higher than that of either pure component
• At constant pressure, nitric(V) acid water form
  a maximum boiling azeotrope the maximum occurs
  at 68 nitric acid by mass boiling unchanged at
  121oC

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Fractional distillation of non-ideal solutions

• It is convenient to use boiling point-composition
  diagrams at a fixed pressure instead of
  vapor-pressure-composition diagrams in
  considering fractional distillation of non-ideal
  mixtures
• For vapor pressure-composition diagrams with no
  minimum or maximum, the deviation is relatively
  small
• Methanol water have very similar structures and
  hence identical interactions their vapor
  pressure-composition diagram shows no maximum or
  minimum
• By repeating the boiling-condensing-boiling
  process in one operation using a fractionating
  column, pure methanol can be obtained from a 10
  methanol (90 water) mixture

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Fractional distillation of non-ideal mixtures
whose boiling-point-composition diagram shows a
maximum

• At the maximum point M the liquid and vapor have
  the same composition.That is, if a mixture having
  composition M is distilled, the vapor formed at
  T1 has exactly the same composition as the liquid
  and no separation of the components is achieved.
• If a mixture of composition Z is heated, the
  vapor initially formed at T2 has a composition Y
  which is richer in the more volatile component A,
  so that the residue in the flask becomes richer
  in the less volatile component B. If this vapor
  is then condensed redistilled, the vapor formed
  will have composition X, still richer in volatile
  A
• By fractional distillation, pure A is obtained in
  the distillate, leaving the maximum, constant
  boiling azeotrope in the flask

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