Molality and Mole Fraction
b
1.
In Chapter 5 we introduced two
important concentration units.
% by mass of solute
mass of solute
% w/w =
 100 %
mass of solution
2.
Molarity
moles of solute
M =
Liters of solution
Molality and Mole Fraction
b
Molality is a concentration unit
based on the number of moles of
solute per kilogram of solvent.
moles of solute
m
kg of solvent
in dilute aqueous solutions molarity and
molality are nearly equal
Molality and Mole Fraction
b
Calculate the molarity and the molality of an aqueous
solution that is 10.0% glucose, C6H12O6. The density of the
solution is 1.04 g/mL. 10.0% glucose solution has several
medical uses. 1 mol C6H12O6 = 180 g
Molality and Mole Fraction
b
Calculate the molality of a solution that contains 7.25 g of
benzoic acid C6H5COOH, in 2.00 x 102 mL of benzene,
C6H6. The density of benzene is 0.879 g/mL. 1 mol
C6H5COOH = 122 g
Molality and Mole Fraction
•
•
Mole fraction is the number of moles of one component
divided by the moles of all the components of the
solution
– Mole fraction is literally a fraction using moles of one
component as the numerator and moles of all the
components as the denominator.
In a two component solution, the mole fraction of one
component, A, has the symbol XA.
number of moles of A
XA 
number of moles of A + number of moles of B
Molality and Mole Fraction
b
The mole fraction of component B - XB
number of moles of B
XB 
number of moles of A + number of moles of B
Note that X A  X B  1
The sum of all the mole fractions must equal 1.00.
Molality and Mole Fraction
b
What are the mole fractions of glucose and water in
a
10.0% glucose solution?
Colligative Properties of Solutions
b
b
Colligative properties are properties of solutions
that depend solely on the number of particles
dissolved in the solution.
• Colligative properties do not depend on the
kinds of particles dissolved.
Colligative properties are a physical property of
solutions.
Colligative Properties of Solutions

There are four common types of colligative
properties:
1. Vapor pressure lowering
2. Freezing point depression
3. Boiling point elevation
4. Osmotic pressure
 Vapor pressure lowering is the key to all four of
the colligative properties.
Lowering of Vapor Pressure and Raoult’s
Law
b
Addition of a nonvolatile solute to a solution
lowers the vapor pressure of the solution.
• The effect is simply due to fewer solvent molecules
at the solution’s surface.
• The solute molecules occupy some of the spaces
that would normally be occupied by solvent.
b
Raoult’s Law
X models
 1this
- Xeffect in ideal solutions.
solute
solvent
0
Psolvent  X solute Psolvent
which is Raoult' s Law
Lowering of Vapor Pressure and
Raoult’s Law
b
This graph shows how the solution’s vapor pressure
is changed by the mole fraction of the solute, which
is Raoult’s law.
Fractional Distillation
•
•
Distillation is a technique used to
separate solutions that have two
or more volatile components with
differing boiling points.
A simple distillation has a single
distilling column.
– Simple distillations give reasonable
separations.
•
A fractional distillation gives
increased separations because of
the increased surface area.
– Commonly, glass beads or steel wool
are inserted into the distilling
column.
Boiling Point Elevation
b
b
Addition of a nonvolatile solute to a solution raises the
boiling point of the solution above that of the pure
solvent.
• This effect is because the solution’s vapor pressure is
lowered as described by Raoult’s law.
• The solution’s temperature must be raised to make
the solution’s vapor pressure equal to the
atmospheric pressure.
The amount that the temperature is elevated is
determined by the number of moles of solute dissolved
in the solution.
Boiling Point Elevation
b
Boiling point elevation relationship
is:
Tb  K b m
where : Tb  boiling point elevation
m  molal concentrat ion of solution
K b  molal boiling point elevation constant
for the solvent
Freezing Point Depression

Relationship for freezing point depression is:
Tf  K f m
where: Tf  freezing point depression of solvent
m  molal concentration of soltuion
K f  freezing point depression constant for solvent
Freezing Point Depression
•
Notice the similarity of the two
relationships for freezing point depression
and boiling point elevation.
 Tf  K f m vs.  Tb  K b m
•
Fundamentally, freezing point depression and boiling
point elevation are the same phenomenon.
– The only differences are the size of the effect which is
reflected in the sizes of the constants, Kf & Kb.
•
This is easily seen on a phase diagram for a solution.
Freezing Point Depression
Boiling Point Elevation
b
What is the normal boiling point of a 2.50 m glucose,
C6H12O6, solution?
Freezing Point Depression
b
Calculate the freezing point of a solution that contains 8.50 g
of benzoic acid (C6H5COOH, MW = 122) in 75.0 g of
benzene, C6H6.
Determination of Molecular Weight by
Freezing Point Depression
•
•
The size of the freezing point depression depends
on two things:
1. The size of the Kf for a given solvent, which are
well known.
2. And the molal concentration of the solution
which depends on the number of moles of
solute and the kg of solvent.
If Kf and kg of solvent are known, as is often the
case in an experiment, then we can determine # of
moles of solute and use it to determine the
molecular weight.
Determination of Molecular Weight by
Freezing Point Depression
b
A 37.0 g sample of a new covalent compound, a
nonelectrolyte, was dissolved in 2.00 x 102 g of water. The
resulting solution froze at -5.58oC. What is the molecular
weight of the compound?
Colligative Properties and
Dissociation of Electrolytes
b
b
b
Electrolytes have larger effects on boiling point elevation and
freezing point depression than nonelectrolytes.
• This is because the number of particles released in solution
is greater for electrolytes
One mole of sugar dissolves in water to produce one mole of
aqueous sugar molecules.
One mole of NaCl dissolves in water to produce two moles
of aqueous ions:
• 1 mole of Na+ and 1 mole of Cl- ions
Osmotic Pressure
•
•
Osmosis is the net flow of a solvent
between two solutions separated by a
semipermeable membrane.
– The solvent passes from the lower
concentration solution into the higher
concentration solution.
Examples of semipermeable membranes
include:
1. cellophane and saran wrap
2. skin
3. cell membranes
Osmotic Pressure
b
b
Osmosis is a rate controlled phenomenon.
• The solvent is passing from the dilute solution into the
concentrated solution at a faster rate than in opposite
direction, i.e. establishing an equilibrium.
The osmotic pressure is the pressure exerted by a column of
the solvent in an osmosis experiment.
  MRT
where:  = osmotic pressure in atm
M = molar concentration of solution
L atm
mol K
T = absolute temperature
R = 0.0821
Osmotic Pressure

For very dilute aqueous solutions,
molarity and molality are nearly
equal.
Mm
  mRT
for dilute aqueous solutions only
Osmotic Pressure
b
b
Osmotic pressures can be very large.
• For example, a 1 M sugar solution has an
osmotic pressure of 22.4 atm or 330 p.s.i.
Since this is a large effect, the osmotic
pressure measurements can be used to
determine the molar masses of very large
molecules such as:
1. Polymers
2. Biomolecules like
Osmotic Pressure
b
A 1.00 g sample of a biological material was dissolved in
enough water to give 1.00 x 102 mL of solution. The osmotic
pressure of the solution was 2.80 torr at 25oC. Calculate the
molarity and approximate molecular weight of the material.