Colligative Properties

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Colligative Properties

• Nathaniel P. Dugos
• Adamson University
• Manila, Philippines

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Colligative properties

• Properties determined by the number of particles
  in solution rather than the type of particles.
• Vapor pressure lowering
• Freezing point depression
• Boiling point elevation
• Osmotic pressure

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How Vapor Pressure Lowering Occurs

• Solute particles take up space in a solution.
• Solute particles on surface decrease number of
  solvent particles on the surface.
• Less solvent particles can evaporate which lowers
  the vapor pressure of a liquid.

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Vapor Pressures of Pure Water and a Water
Solution The vapor pressure of water over pure
water is greater than the vapor pressure of water
over an aqueous solution containing a nonvolatile
solute.
Solute particles take up surface area and lower
the vapor pressure
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Vapor Pressure Lowering
Let component A be the solvent and B the solute.
solute B is nonvolatile
Applying Raoults Law
vapor pressure of the solvent in solution
vapor pressure of the solution
where
vapor pressure of the pure solvent
mole fraction of the solvent
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The lowering in vapor pressure,
where
mole fraction of solute
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Sample Problems (Vapor Pressure Lowering)

• What mass of urea, CON2H4, must be added to
• 450 g water to get a solution with a vapor
  pressure of 29.3 mmHg? The vapor pressure of
  pure water is 31.8 mmHg at this temperature.

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Sample Problems (Vapor Pressure Lowering
2. The vapor pressure of 2-propanol is 50.00 kPa
at 338.8oC, but fell to 49.62 kPa when 8.69
g of an involatile organic compound was
dissolved in 250-g of 2-propanol. Calculate
the molar mass of the compound.
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Boiling Point Elevation
When a non volatile solute is added to solvent
Vapor pressure of solvent is lowered solution
formed must be heated to higher temperature than
boiling point of pure solvent to reach a vapor
pressure of 1 atm. This means that non
volatile solute elevates the boiling point of the
solvent which we call boiling point elevation
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Boiling Point Elevation
(for dilute solutions)
where
is the molar mass of the solvent and
the molality of the solute in mol/kg
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Boiling Point Elevation
for dilute solutions
where
boiling point constant or ebullioscopic
constant of the solvent
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Freezing Point Depression
Addition of a nonvolatile solute to a solution
lowers the freezing point of the solution
relative to the pure solvent.
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Freezing Point Depression
(for dilute solutions)
molal freezing point depression constant or
cryoscopic constant
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What is the value of the freezing point constant
for water? The enthalpy of fusion at 273.15 K is
6.00 kJ mol-1
The molal freezing point depression constant of
benzene is 5.12. A 0.450 solution of
monoclinic sulfur in benzene freezes 0.088 K
below the freezing point of pure benzene. Find
the molecular formula of the sulfur in benzene.
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Osmosis
There are many times in nature when a solvent
will pass spontaneously through a semipermeable
membrane, which is a membrane permeable to
solvent, but not solute
The osmotic pressure, ?, is the pressure that
must be applied to stop the influx of solvent
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Osmosis

• Examples
• the transport of fluids through living cell
• membranes
• (b) basis of osmometry, the determination of
• molecular mass by measurement of osmotic
• pressure

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Osmosis Eventually the pressure difference
between the arms stops osmosis.
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Osmosis
To treat osmosis thermochemically, we note that
at equilibrium, the chemical potential on each
side of the membrane must be equal
Equilibrium is established when the hydrostatic
pressure of the solution in the column is equal
to the osmotic pressure
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A solution of polystyrene in benzene contains 10
g/L. The equilibrium height of the column of
solution (density 0.88 g cm-3) in the osmometer
corrected for capillary rise is 11.6 cm at 25oC.
What is the molar mass of polystyrene, assuming
the solution is ideal.
The osmotic pressure of an aqueous solution at
300 K is 120 kPa. Calculate the freezing point of
the solution.
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Osmometry
Osmotic pressure is easily measured, and is quite
large. Osmometry can be applied for the
determination of molecular weights of large
molecules (proteins, synthetic polymers), which
dissolve to produce less than ideal solutions.
The Vant Hoff equation can be rewritten in
virial form where B is the
empirically determined osmotic virial
coefficient
? B RT 1 B B ...
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Consider the example of poly (vinyl chloride)
PVC, in cyclohexanone at 298 K
Pressures are expressed in terms of heights of
solution, ?0.980 g cm-3 in balance with the
osmotic pressure
c (g L-1) 1.00 2.00 4.00 7.00
9.00 h (cm) 0.28 0.71 2.01 5.10
8.00
Use ? B RT 1 B B with B c/M,
where c is the mass concentration and M is the
molar mass. The osmotic pressure is related to
the hydrostatic pressure by ? ?gh, where g
9.81 m s-2. Then
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Plot h/ c vs. c to find M, expecting a straight
line with intercept RT/ ?gM at c 0.
Data set c(g L-1) 1.00 2.00 4.00
7.00 9.00 h/c(cm g-1 L) 0.28 0.36 0.53
0.729 0.889
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The data give an intercept of 0.21 g/mL
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The data give an intercept of 0.21 cm g-1 L,
which is equal to RT/ ?gM Thus
where we have used 1 kg m2 s-21J