Back to Secs 13.4-5: Properties of Solutions
Quantitative ways of expressing solution concentration
1. Mass percentage
The mass percentage of a component in a solution is
given by
Mass % of component =
mass of component
x100
total mass of solution
e.g., What is the mass per cent of solute in a solution
containing 3.25 g of Ba(NO3)2 in 100 g H2O?
For work with very dilute solutions, concentrations may be
expressed in parts per million (ppm) or parts per billion
(ppb):
A solution whose concentration is 1 ppm contains 1 g
solute per 106 g solution
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E.g., seawater contains 0.412 g of Ca2+ per kg of water.
What is the concentration of Ca2+ in ppm?
2. Mole fraction, X
Mol fraction of a component is defined as
Xcomponent =
mol component
total mol all components
E.g., what is the mol fraction of CH3OH in a solution which
contains 6.00 g of CH3OH dissolved in 480 g of H2O?
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3. Molarity, M
As in Ch 4, M =
mol solute
liters solution
4. Molality, m
Defined as the number of mol of solute per kilogram of
solvent:
m=
mol solute
kg solvent
Notice that molality is defined in terms of solvent mass
Note also that molarity is defined in terms of solution
volume
E.g., find the molality of a solution that contains 36.5 g of
napthalene (C10H8) in 420 g of toluene (C7H8)
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What other information would we need to calculate the
molarity of this solution?
Colligative Properties of Solutions
Depend upon the concentration but not the kind of solute
particles
Include:
vapor-pressure reduction
freeze-point lowering,
boiling-point elevation
osmotic pressure
Review: what is the difference between an ionic and a
molecular solute?
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E.g., Calculate the concentration of sodium ions in 0.135 M
Na3PO4 solution.
1. Vapor-pressure reduction
Vapor pressure over a liquid is a dynamic
equilibrium (Ch 11)
A nonvolatile solute added to a volatile
solvent reduces the capacity of the
solvent molecules to move from liquid to
vapor phase (how?)
BUT the rate at which solvent
molecules move from vapor to liquid
phase is not changed
The extent to which the vapor pressure is
lowered is proportional to the solute
concentration
How to calculate the vapor pressure
above a solution?
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Raoult's Law
P = XAPAo
P = vapor pressure of solution
XA = mol fraction of solvent
PAo = vapor pressure of pure solvent
Ideal solutions are said to obey Raoult's Law
E.g., find the vapor pressure of H2O above a solution
prepared by adding 10.00g of lactose (C12H22O11) to 100 g
water at 338 K (the vapor pressure of H2O is 187.5 mm Hg)
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When do solutions not obey Raoult's Law? What is
responsible for deviations from ideal behavior?
What if both the solvent and solute are volatile?
How to calculate vapor pressure?
2. Boiling-point elevation
How does the vapor pressure of a pure liquid respond to
increasing temperature?
What effect does the addition of a nonvolatile solute have
upon the vapor pressure of a volatile solvent?
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Vapor Pressure vs Temperature curves: recall the
discussion of phase diagrams from Ch. 11.........
Since the addition of solute decreases the vapor pressure
of the solvent, the boiling point of the solvent increases....
The increase in boiling point, Tb, is proportional to the
concentration of solute
Express in terms of molality:

Tb = Kbm
Kb = molal boiling point elevation constant
m = molality of solute particles
3. Freezing point depression
Tf = Kfm
Kf = molal freeze-point depression constant
m = molality of solute particles
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E.g., find the freezing and boiling points of a solution of
100 g of ethylene glycol, C2H6O2, in 900 g of H2O (Kf = 1.86
oC/m; K = 0.52 oC/m)
b
Remember: colligative properties depend upon the total
number of solute particles, independent of their nature
E.g., arrange the following aqueous solutions in order of
increasing boiling point:
0.030 m glycerin; 0.020 m KBr; 0.030 m benzoic acid,
HC7H5O2
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4. Osmosis
Movement of solvent through a semipermeable membrane
Solvent moves from a region of low solute concentration
to a region of high solute concentration
The pressure required to prevent osmosis is known as the
osmotic pressure, , of the solution
The osmotic pressure  is given by the relation
π  MRT
Where M = molarity of solution and R = gas constant
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E.g., What is the osmotic pressure of an aqueous solution
containing 1.10 g of urea, (NH2)2CO, in 100 mL of solution
at 20oC?
What is meant by a hypertonic solution? By a hypotonic
solution?
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Problems du Jour
The density of acetonitrile, CH3CN, is 0.876 g/mL, and the
density of methanol, CH3OH, is 0.791 g/mL. A solution is
made by dissolving 20.0 mL of CH3OH in 100.0 mL CH3CN.
Calculate the mol fraction of CH3OH.
Calculate the molality of CH3OH in the solution.
Assuming the volumes are additive, find the molarity of
CH3OH.
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Problems du Jour
Calculate the vapor pressure of water above a solution
made by adding 5.00 g sodium sulfate to 115 g H2O at 338
K (the vapor pressure of water = 187.5 torr at 338 K)
Calculate the freezing and boiling points of a solution
made by adding 2.75 g MgCl2 to 80.0 mL of water (Kf =
1.86oC/m; Kb=0.52oC/m for water)
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Problem du Jour
Calculate the mass of ethylene glycol, C2H6O2, that must
be added to 1.00 kg of ethanol, C2H5OH, to reduce its
vapor pressure by 13.2 torr at 35oC. The vapor pressure of
pure C2H5OH is 100 torr at 35oC.
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Problem du Jour
The cooling system of a car is filled with a solution formed
by adding equal volumes of water (density=1.00 g/mL) and
ethylene glycol (density = 1.12 g/mL). Calculate the
freezing and boiling points for the mixture. (Kf = 1.86oC/m;
Kb=0.52oC/m for water)
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