Molality and Mole Molality and Mole FractionFractionMolality and Mole Molality and Mole FractionFraction

In Chapter 5 we introduced two important concentration units.

1. % by mass of solute

%100solution of mass

solute of mass = w/w%

2. Molarity

solution of Liters

solute of moles = M

Molality and Mole Molality and Mole FractionFractionMolality and Mole Molality and Mole FractionFraction

m moles of solute

kg of solvent

in dilute aqueous solutions molarity and

molality are nearly equal

Molality is a concentration unit based on the number of moles of solute per kilogram of solvent.

Molality and Mole FractionMolality and Mole FractionMolality and Mole FractionMolality 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 FractionMolality and Mole FractionMolality and Mole FractionMolality 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 FractionMolality and Mole FractionMolality and Mole FractionMolality 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.

B of moles ofnumber +A of moles ofnumber

A of moles ofnumber AX

Molality and Mole FractionMolality and Mole FractionMolality and Mole FractionMolality and Mole Fraction

The mole fraction of component B - XB

1.00. equalmust fractions mole theall of sum The

1 that NoteB of moles ofnumber +A of moles ofnumber

B of moles ofnumber

A

B

B

XX

X

Molality and Mole FractionMolality and Mole FractionMolality and Mole FractionMolality and Mole Fraction What are the mole fractions of glucose and water in

a 10.0% glucose solution?

Colligative Properties of Colligative Properties of SolutionsSolutionsColligative Properties of Colligative Properties of SolutionsSolutions

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 Colligative Properties of SolutionsSolutionsColligative Properties of Colligative Properties of SolutionsSolutions

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 Lowering of Vapor Pressure and Raoult’s LawRaoult’s LawLowering of Vapor Pressure and Lowering of Vapor Pressure and Raoult’s LawRaoult’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.

Raoult’s Law models this effect in ideal solutions.

Lowering of Vapor Pressure Lowering of Vapor Pressure and Raoult’s Lawand Raoult’s LawLowering of Vapor Pressure Lowering of Vapor Pressure and Raoult’s Lawand 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 DistillationFractional DistillationFractional DistillationFractional 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 ElevationBoiling Point ElevationBoiling Point ElevationBoiling 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 ElevationBoiling Point ElevationBoiling Point ElevationBoiling Point Elevation

solvent for the

constantelevation point boiling molal K

solution ofion concentrat molal

elevationpoint boiling T :where

KT

b

b

bb

m

m

Boiling point elevation relationship is:

Freezing Point DepressionRelationship for freezing point depression is:

T K

where: T freezing point depression of solvent

molal concentration of soltuion

K freezing point depression constant for solvent

f f

f

f

m

m

Freezing Point DepressionFreezing Point DepressionFreezing Point DepressionFreezing Point Depression

• Notice the similarity of the two relationships for freezing point depression and boiling point elevation.

• 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.

mm bbff K T vs.KT

Freezing Point DepressionFreezing Point DepressionFreezing Point DepressionFreezing Point Depression

Boiling Point ElevationBoiling Point ElevationBoiling Point ElevationBoiling Point Elevation What is the normal boiling point of a 2.50 m glucose,

C6H12O6, solution?

Freezing Point DepressionFreezing Point DepressionFreezing Point DepressionFreezing 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 Determination of Molecular Weight by Freezing Point Weight by Freezing Point DepressionDepression

Determination of Molecular Determination of Molecular Weight by Freezing Point Weight by Freezing Point DepressionDepression

• 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 Determination of Molecular Weight by Freezing Point Depressionby Freezing Point DepressionDetermination of Molecular Weight Determination of Molecular Weight by Freezing Point Depressionby 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 Colligative Properties and Dissociation of ElectrolytesDissociation of ElectrolytesColligative Properties and Colligative Properties and Dissociation of ElectrolytesDissociation 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 PressureOsmotic PressureOsmotic PressureOsmotic 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 wrap2. skin3. cell membranes

Osmotic PressureOsmotic PressureOsmotic PressureOsmotic 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.

M

M

RT

where: = osmotic pressure in atm

= molar concentration of solution

R = 0.0821L atm

mol KT = absolute temperature

Osmotic PressureOsmotic PressureOsmotic PressureOsmotic Pressure

For very dilute aqueous solutions, molarity and molality are nearly equal. M m

m

for dilute aqueous solutions only

RT

Osmotic PressureOsmotic PressureOsmotic PressureOsmotic 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 PressureOsmotic PressureOsmotic PressureOsmotic 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.