Colligative Properties

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Colligative Properties

• Properties which do not depend upon the nature of
  the solute particles, only their concentration.
• Vapor pressure lowering
• Boiling point elevation
• Freezing point depression
• Osmotic pressure
• Consider a solvent A and a nonvolatile solute B,
  i.e., only the solvent has a vapor pressure.

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Figure 11.9 An Aqueous Solution and Pure Water
in a Closed Environment
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Figure 11.10The Presence of a Nonvolatile Solute
Inhibits the Escape of Solvent Molecules from the
Liquid
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• Vapor Pressure Lowering
• We saw in Figure 11.9 that the solution has a
  lower vapor pressure than the pure solvent.
• The change in vapor pressure upon dissolving a
  nonvolatile solute is symbolized as ?PA.
• ?PA PA PA
• where PA vapor pressure of pure solvent
• and PA vapor pressure of solvent in solution
• Raoults Law PA PA ?A
• Substituting ?PA PA (PA ?A) PA (1?A)

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• It is usually more useful to express solution
  properties in terms of the solute concentration.
• We know that ?A ?B 1, so ?B 1 ?A
• Thus, the expression for ?PA becomes
• ?PA PA ?B
• Ideal Solution a solution in which all
  components obey Raoults Law. Ex., for a
  2-component soln
• PA PA ?A and PB PB ?B

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Figure 11.11A Solution Obeying Raoults Law
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Figure 11.12Total Vapor Pressure of a Solution
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Figure 11.13Vapor Pressure for a Solution of Two
Volatile Liquids
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Figure 11.14 Vapor Pressure Lowering, Boiling
Point, and Melting Point
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• Boiling Point Elevation
• ?Tb Kb mB
• where ?Tb change in boiling point of the
  solvent
• mB molality of solute
• Kb molal b.p. elevation constant for the
  solvent.
• (or ebullioscopic constant)
• Table 11.5 has Kb values for various solvents
• ex. For H2O, Kb 0.5121 C kg/mol

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• Freezing-Point Depression
• ?Tf Kf mB
• where ?Tf change in freezing point
• mB molality of solute
• Kf molal f.p. depression constant for the
  solvent
• (or cryoscopic constant)
• ex. Kf for H2O 1.856 C kg/mol

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• Now, what can we do with these phenomena?
• Find the Tb or Tf of a given solution.
• Find the amount of solute that must be added to a
  given amount of solvent to produce a certain Tb
  or Tf
• (ex. Find the amount of antifreeze needed to
  protect a car radiator from freezing to a
  temperature of -30)
• 3) Find the molar mass of an unknown solute by
  observing its effect on the Tb or Tf of a
  solvent.

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• Ex. 1 What mass of ethylene glycol (C2H6O2)
  must be added to 37.8 g of water to give a Tf of
  -0.150C?
• Ans. ?Tf Kf mB

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• Ex. 2 A solution of 0.205 g of white phosphorus
  in 25.0g of CS2 had a Tb 0.159C higher than that
  of the pure CS2. The Kb 2.40C kg/mol for CS2.
  Determine the molar mass of white phosphorus.
• Ans. We know the mass in grams of the solute.
• We must find how many moles there are.
• This will be related to the molality of the
  solution.
• Proceed as before to calculate the number of
  moles of solute 0.00166 mol of phosphorus
• Then, 0.205 g P/ 0.00166 mol P 123 g/mol

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• Osmotic Pressure
• A pressure differential developed across a
  semipermeable membrane due to a concentration
  difference across the membrane.
• Semipermeable membrane pore size allows
  passage of solvent molecules but not solute
  molecules.
• Observed result solvent flows from the side of
  lower solute concentration to the side of higher
  solute concentration.

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Figure 11.16Osmotic PressureLink to Movie
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Osmosis Figure 11.17Link to Simulation
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• Let ? the osmotic pressure of a solution in atm
• Then, ?V nRT
• where V solution volume in liters
• n number of moles of solute
• T temperature in kelvin
• R the ideal gas constant
• 0.08206 L atm/mol K
• Now, since n/V molarity of solute, M
• ? MRT

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• Uses of Osmotic Pressure
• Measure ? to determine the molar mass of a solute
  (see sample exercise 11.11)
• Determine the amount of solute needed in order to
  produce a given osmotic pressure (see sample
  exercise 11.12)
• Isotonic Solutions
• Solutions having identical osmotic pressure.
• ex. For intravenous solutions.
• Reverse Osmosis to purify water

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• Colligative Properties of Electrolyte Solutions
• Ex. NaCl(s) ? Na(aq) Cl(aq)
• Each mole of NaCl produces 2 moles of solute
  particles
• Define the vant Hoff i-factor

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• The concentration term in colligative property
  equations must be multiplied by i for solutions
  of electrolytes (soluble salts, strong acids or
  bases)
• Ex. For freezing-point depression ?Tf K f mB
  i
• Actual values of i are generally slightly smaller
  than the expected whole numbers.
• Ex. For NaCl, i 1.9
• For MgCl2,i 2.7 See Table 11.6

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• Colloids Not truly solutions, they are actually
  heterogeneous, although they may not appear to be
  so.
• Colloids are a suspension in which the suspended
  particles are of the order of 1 1000 nm in
  size.
• Tyndall Effect scattering of light as it passes
  through a colloidal suspension, making the light
  beam visible. This does not happen with a true
  solution.
• Examples aerosols (fog, smoke), emulsions
  (milk), foams (whipped cream)