Simple Mixtures

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Chapter 7

• Simple Mixtures

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Partial Molar Volume

• The partial molar volume of a substance A in a
  mixture is the change in volume per mole of A
  added to a large volume of the mixture.
• The partial molar volumes of the components of a
  mixture vary with composition because the
  environment of each type of molecule changes from
  pure A to pure B.
• This changing molecular environment, and the
  consequential modification of the forces acting
  between molecules, results in the variation of
  the thermodynamic properties of a mixture as its
  composition is changed.

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One way to measure partial molar volume is to
measure the dependence of the volume on the
composition and to fit the observed volume to a
function of the amount of substance by using a
curve fitting program. The slope of the function
can then be found by diffentiation.
Molar volumes can also be negative!
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Partial Molar Gibbs Energies

• For a pure substance, m G.
• For a substance in a mixture, the chemical
  potential is the partial molar Gibbs Energy.

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Wider Significance of m
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Gibbs-Duhem Equation
The chemical potential of one component of a
mixture cannot change independently of the
chemical potentials of the other components In
a binary mixture, if one increases, the other
must decrease.
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Thermodynamics of Mixing
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Chemical Potentials of Liquids

• At equilibrium, the chemical potential of a
  substance as a vapour must be equal to its
  chemical potential in the liquid.
• If a solute is present in the liquid

Raoults Law (after a series of experiments)
When components are structurally similar, they
follow Raoults Law
Mixtures that obey this law are ideal
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Raoults Law

• The rate at which A molecules leave the surface
  is ? of them at the surface.
• Rate of vaporization kxA
• The rate at which molecules condense ?
  concentration in the gas phase which is ? to the
  partial pressure.
• Rate of condensation kpA
• At equilibrium they are equal.

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Ideal-Dilute Solutions

• In ideal solutions, the solute and solvent obey
  Raoults Law.
• In a dilute solution the solvent molecules are in
  an environment very much like the one they have
  in the pure liquid.
• In contrast, the solute molecules are surrounded
  by solvent molecules, which is entirely
  different.
• Therefore, the solvent behaves like a pure liquid
  and the solute behaves differently obeying
  Henrys Law
• For real solutions at low concentrations, Henrys
  Law applies
• pB xBKB where KB is an empirical constant.

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Liquid Mixtures
These are valid for ideal liquids. Gas perfection
/ solution ideality Perfect gas no interaction
between molecules and DH 0, driving force for
mixing is DS gt 0. Ideal solution A-B
interaction in mixture is the same as A-A and B-B
interaction. Real solutions These interactions
are very different. There may be an enthalpy
change in mixing and also and increased order,
decreasing entropy and DG gt 0. Then these liquids
do not mix or partially mix, meaning they are
miscible only over a certain range of composition.
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Excess Functions

• Excess functions, XE, is the difference between
  the observed thermodynamic function of mixing and
  the function for an ideal solution. (e.g.
  SEDmixS - DmixSideal)
• This indicates the extent to which solutions are
  nonideal.
• Regular solution is a solution for which HE 0
  but SE 0.

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Colligative Properties

• Boiling-point elevation
• Freezing-point depression
• Osmotic pressure
• These properties depend only on the number of
  solute particles present, not their identity.
• Assumption 1 Solution is dilute.
• Assumption 2 Solute is not volatile
• Assumption 3 Solute does not dissolve in the
  solid solvent.
• All colligative properties stem from the
  reduction of chemical potential of the liquid
  solvent as a result of the presence of solute.
  (mA to mA RT lnxA)

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Elevation of Boiling Point
Depression of Freezing Point
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Osmosis
Osmosis is the spontaneous passage of a pure
solvent into a solution separated from it by a
semi-permeable membrane. The osmotic pressure, P,
is the pressure that must be applied to the
solution to stop the influx of solvent. Osmometry
is the determination of molecular mass by the
measurement of osmotic pressure.
pP
p
mA(p)
mA(pP)
Equal at eq.
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Vant Hoff equation
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Activities

• Deviations from ideal behaviour can be taken into
  account by introducing activity.

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Solute Activity
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Activities in terms of Molalities
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