Module 2: Solutions PART 2

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Module 2 Solutions PART 2

• Alyssa Jean-Mary
• Reference Modular Study Guide for CHM1046 by
  Marta E. Goicoechea-Pappas Anthony J. Papas

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Colligative Properties of Nonelectrolyte Solutions

• Unless otherwise noted, the solvent in the
  solution is water
• In water, noneletrolytes ionize almost 0, as
  opposed to strong electrolytes, which ionize
  100, and weak electrolytes, which ionize only
  slightly
• Colligative Properties physical properties of
  solutions that depend on the number of solute
  particles present in the solution, instead of on
  the kind of solute particles present
• There are four colligative properties for a
  solution containing nonvolatile solutes, which
  affect the solution by
• Lowering its vapor pressure
• Raising its boiling point
• Lowering its freezing (melting) point
• Generating an osmotic pressure

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Raoults Law and Vapor Pressure Lowering 1

• If a solution contains two substances, one
  substance is the solute and the other substance
  is the solvent
• The total vapor pressure of such a solution is
  the sum of the partial pressure of the solute and
  the partial pressure of the solvent
• Psolution Psolute Psolvent
• Raoults Law at a given temperature and
  pressure, the partial pressure of a substance
  (i.e. the solute or the solvent) in an ideal
  solution is
• PA XAPA
• PA partial pressure of substance A in the
  solution
• XA mole fraction of substance A in the solution
• PA vapor pressure of pure substance A

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Raoults Law and Vapor Pressure Lowering 2

• Solutions that contain liquid or solid solutes
  with low vapor pressure (i.e. nonvolatile
  solutes) always lower the vapor pressure of the
  solution. Thus, the Psolute in (Psolution
  Psolute Psolvent) is negligible, which causes
  the total vapor pressure of the solution to be
  almost entirely only dependent on the partial
  pressure of the volatile solvent in the solution
  (Psolution Psolvent)
• ?Psolvent is the lowering of the vapor pressure
  of the solution, or the relatively volatile
  solvent present in the solution, that results
  when nonvolatile-nonionizing (i.e.
  nonvolatile-nonelectrolyte) solutes are added
• ?Psolvent Psolvent (pure) Psolvent (in
  solution) Psolvent XsolventPsolvent
• If Psolvent is factored out, ?Psolvent
  Psolvent(1 Xsolvent), and, since Xsolute 1
  Xsolvent, ?Psolvent PsolventXsolute

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Boiling Point Elevation

• In order for a solution whose vapor pressure was
  lowered by the presence of a nonvolatile solute
  to get its vapor pressure to be equal to
  atmospheric pressure, it must be heated to a
  higher temperature than the pure solvent needs to
  be heated to
• This elevation of the boiling point of the
  solution is expressed, in accordance with
  Raoults Law, by
• ?Tb Kbm
• ?Tb the boiling point elevation bp(solution)
  bp(solvent)
• Kb molal boiling point constant, which is
  different for every solvent
• M molality of solute
• Experiments on Boiling Point Elevation can be
  used to determine the molar mass of solutes
• ?Tb Kbm Kb(molsolute/kgsolvent)
  Kb(gsolute/MMsolute/kgsolvent) ? MMsolute (Kb x
  gsolute)/(?Tb x kgsolvent)

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Some Common Properties of Solvents
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Freezing Point Lowering

• The freezing point of a solution will always be
  less than the freezing point of the pure solvent
• Using antifreeze, ethylene glycol, in radiators
  is a good example of the utility of this concept.
  It lowers the freezing point of the solution,
  which is good for cold weather, and it raises the
  boiling point of the solution, which is good for
  hot weather.
• The depression of the freezing point of solutions
  that contain nonvolatile solutes is expressed by
• ?Tf Kfm
• ?Tf the freezing point lowering fp(solvent)
  fp(solution)
• Kf molal freezing point constant, which is
  different for every solvent
• M molality of solute
• Experiments on Freezing Point Elevation can be
  used to determine the molar mass of solutes
• ?Tf Kfm Kf(molsolute/kgsolvent)
  Kf(gsolute/MMsolute/kgsolvent) ? MMsolute (Kf x
  gsolute)/(?Tf x kgsolvent)

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Generation of an Osmotic Pressure

• The above picture illustrates the phenomenon of
  osmotic pressure
• The two compartments are separated by a
  semipermeable membrane, which allows some
  molecules (i.e. small solvent molecules (e.g.,
  H2O)) to pass though, but blocks the passage of
  other molecules (i.e. the larger solute
  molecules)
• Initially (i.e. at the start), both levels are
  equal
• After a certain amount of time, the level in the
  right tube (i.e. the tube with the solution)
  begins to rise, and it continues to rise until
  equilibrium is reached. As the level in the right
  tube rises, the level in the left tube (i.e. the
  tube with the pure solvent) lowers.
• Osmosis is this net movement of solvent molecules
  through a semipermeable membrane from the less
  concentrated (i.e. more dilute) solution or side
  (i.e. the pure solvent side) to the more
  concentrated solution or side (i.e. the solution
  side)

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Osmotic Pressure

• Osmotic Pressure (p) the pressure needed to
  stop osmosis
• For very dilute solutions, the osmotic pressure
  of the solution can be found by using one of the
  following equations
• pV nRT (g/MM)RT ? p MRT (n/V)RT
• p osmotic pressure (atm or torr)
• V volume of solution (L)
• n moles of solute
• R gas constant (0.0821 (L?atm)/(mol?K) or 62.4
  (L?torr)/(mol?K))
• T temperature (K)
• g grams of solute
• MM molar mass of solute (g/mole)
• M molarity of solution (molsolute/Lsolution)
• Comparing osmotic pressures
• Two solutions are isotonic if they have equal
  osmotic pressures (i.e. if they have equal
  effective concentrations or osmolarities (see
  below))
• If the two solutions have solutes that are
  neither acids, bases, or salts (i.e. those that
  are not ionic) and have concentrations (i.e. wt,
  m, or M) that are the same, they are assumed to
  have the same effective concentration
• If two solutions have unequal osmotic pressures
• The solution that is more concentrated is
  hypertonic
• The solution that is less concentrated (i.e. more
  dilute) is hypotonic

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Colligative Properties of Aqueous Electrolyte
Solutions 1

• Remember that colligative properties depend on
  the number of solute particles present in the
  solution
• For nonionizing solutes (i.e. nonelectrolytes,
  whose general formula CxHyOz), 1 mole of solute
  produces 1 mole of particles
• C6H12O6 (s) ---H2O---gt C6H12O6 (aq)
  
• 1 mole of C6H12O6 1 mole of particles
• C3H6O3 (s) ---H2O---gt C3H6O3 (aq)
• 1 mole of C3H6O3 1 mole of particles
• For ionizing solutes (i.e. electrolytes, strong
  acids bases and soluble salts), 1 mole of
  solute produces more than 1 mole of particles
• KCl (s) ---H2O---gt K (aq) Cl- (aq)
  
• 1 mole of KCl 2 moles of particles
• K3PO4 (s) ---H2O---gt 3K (aq) PO43- (aq)
  
• 1 mole of K3PO4 4 moles of particles
• V2(SO4)3 (s) ---H2O---gt 2V3 (aq) 3SO42- (aq)
  
• 1 mole of V2(SO4)3 5 moles of particles

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Colligative Properties of Aqueous Electrolyte
Solutions 2

• For strong electrolytes, those that ionize
  completely, the effective concentration of
  solute in solution is assumed to equal its
  osmolarity or osmolality
• Osmolality (Osm) i x m
• i number of particles m molality of
  solution
• Osmolarity (OsM) i x M
• i number of particles M molarity of
  solution
• This is an assumption because the effective
  concentration is actually less, especially the
  more concentrated the solution, because of ion
  association. The vant Hoff factor, i, used
  above, is a multiplier that converts the stated
  concentration into the effective concentration,
  so, in addition to what is expressed above
• meffective i x m, where i lt the number of
  particles
• Meffective i x M, where i lt the number of
  particles
• However, for nonelectrolytes, its osmolarity
  equals its molarity, and its osmolality equals
  its molality
• For ionizing solutes, the equations used for
  nonionizing solutes are redefined, using Osm for
  m OsM for M
• Boiling Point Elevation ?Tb Kb x Osm
• Freezing Point Elevation ?Tf Kf x Osm
• Osmotic Pressure Generation p OsM x R x T

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The End