Transcript Document 7414503

Molality and Mole Fraction
•
In Chapter 3 we introduced two important
concentration units.
1. % 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
• 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
• 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
• 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.
XA 
number of moles of A
number of moles of A + number of moles of B
Molality and Mole Fraction
• 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
• What are the mole fractions of glucose and water in a
10.0% glucose solution?
Colligative Properties of Solutions
• 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.


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
• 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.
X 1- X
solvent
• Raoult’s Law models solute
this effect
in ideal solutions.
Psolvent  X P
0
solute solvent
which is Raoult' s Law
Lowering of Vapor Pressure and
Raoult’s Law
• 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
• 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
• 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
Tf  K f m
is:
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
• What is the normal boiling point of a 2.50 m glucose,
C6H12O6, solution?
Freezing Point Depression
• 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
• 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
• 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
• 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
R = 0.0821
mol K
T = absolute temperature
Osmotic Pressure
 For very dilute aqueous solutions, molarity
and molality are nearly equal.
 Mm
  mRT
for dilute aqueous solutions only
•
Osmotic Pressure
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
•
•
proteins
ribonucleotides
Osmotic Pressure
• 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.