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Colligative Properties
• Changes in colligative properties depend only on the number of solute particles present, not on the identity of the solute particles.
• Among colligative properties are– Vapor pressure lowering – Boiling point elevation– Melting point depression– Osmotic pressure
Colligative Properties:
•Vapor Pressure•Freezing Point Depression•Boiling Point Elevation•Osmotic Pressure
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Vapor Pressure
Because of solute-solvent intermolecular attraction, higher concentrations of nonvolatile solutes make it harder for solvent to escape to the vapor phase.
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Raoult’s Law
PA = XAPA
where– XA is the mole fraction of compound A, and
– PA is the normal vapor pressure of A at that temperature.
NOTE: This is one of those times when you want to make sure you have the vapor pressure of the solvent.
Vapor Pressure:
• Raoult’s Law: Psolution = XsolventPoH2O
12g Sucrose (C12H22O11)is dissolved in 250.0g water at 90 °C.
What is the vapor pressure of water over this solution?
(PoH2O = 525.8 mmHg- from data table)
• Ans. 524 mmHg
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Boiling Point Elevation and Freezing Point Depression
Nonvolatile solute-solvent interactions also cause solutions to have higher boiling points and lower freezing points than the pure solvent.
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Boiling Point Elevation• The change in boiling point
is proportional to the molality of the solution:
Tb = Kb m
where Kb is the molal boiling point elevation constant, a property of the solvent.
Tb is added to the normal boiling point of the solvent.
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Boiling Point Elevation• The change in freezing
point can be found similarly:
Tf = Kf m
• Here Kf is the molal freezing point depression constant of the solvent.
Tf is subtracted from the normal boiling point of the solvent.
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Boiling Point Elevation and Freezing Point Depression
Note that in both equations, T does not depend on what the solute is, but only on how many particles are dissolved.
Tb = Kb m
Tf = Kf m
Freezing Point Depression:
• Freezing Point Depression: ΔTfp = Kfpmsolution
• A solution is prepared by adding 0.50g of caffeine (C8H10O2N4) to 100g of benzene (C6H6).
• Calculate the freezing point of this solution.
• The freezing point of pure benzene is 5.50°C• Kfp for benzene = 5.23 °C/m)
Ans.: 0.132 ° CTfreezing= 5.37C
Boiling Point Elevation:
• Boiling point elevation: ΔTbp = Kbpmsolute
• A glycerol solution (C3H8O3) in water is prepared by dissolving glycerol is 500g water. The boiling point of the solution is 100.42°C at 760mmHg. What mass of glycerol was dissolved to make this solution?
• Kbp = 0.5121 °C/m
Ans: 38 g glycerol
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Colligative Properties of Electrolytes
Since these properties depend on the number of particles dissolved, solutions of electrolytes (which dissociate in solution) should show greater changes than those of nonelectrolytes.
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van’t Hoff Factor
• We modify the previous equations by multiplying by the van’t Hoff factor, i.
Tf = Kf m i
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van’t Hoff Factor
• Reassociation is more likely at higher concentration.
• Therefore, the number of particles present is concentration-dependent.
Role of Electrolytes on Colligative Properties:
• Van’t Hoff Factor: ΔTfp = Kfpmsolutei
• A 0.0711m aqueous solution of Sodium sulfate freezes at -0.32C. What is the actual value (i) of the van’t Hoff factor? Kfp = 1.86 °C/m
Ans: i = 2.42
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Osmosis
In osmosis, there is net movement of solvent from the area of higher solvent concentration (lower solute concentration) to the are of lower solvent concentration (higher solute concentration).
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Osmotic Pressure
The pressure required to stop osmosis, known as osmotic pressure, , is
nV
= ( )RT = MRT
where M is the molarity of the solution.
If the osmotic pressure is the same on both sides of a membrane (i.e., the concentrations are the same), the solutions are isotonic.
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Osmosis in Blood Cells
• If the solute concentration outside the cell is greater than that inside the cell, the solution is hypertonic.
• Water will flow out of the cell, and crenation results.
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Osmosis in Cells
• If the solute concentration outside the cell is less than that inside the cell, the solution is hypotonic.
• Water will flow into the cell, and hemolysis results.
Osmotic Pressure
• Osmotic Pressure: π= MRT
• What is the osmotic pressure of a 0.1M solution of sucrose at 25C?
(remember: R= .08206 L-atm/mol-K)
Ans: 2.45 atm
Another Osmotic pressure problem.
• 100. mg of a protein are dissolved in enough water to make 10.0 mL of a solution.
• If this solution has an osmotic pressure of 13.3 mmHg at 25°C, what is the molar mass of the protein?
Ans: 1.4 x 104 g/mole