SOLUTIONS II

1
SOLUTIONS II

• COLLIGATIVE PROPERTIES
• Chapter 11.5-11.10 McM
• Chapter 13.6 Silberberg

2
Goals Objectives

• See the following Learning Objectives on pages
  543-544.
• Understand these Concepts
• 13.15-20.
• Master these Skills
• 13.5-10.

3
Colligative Properties

• Colligative properties depend on the number,
  rather than the kind, of solute particles.
• Colligative properties are physical properties of
  solutions.

4
Colligative Properties

• Examples of colligative properties include
• change in vapor pressure
• if solute is volatile
• lowering of vapor pressure
• if solute is not volatile
• freezing point depression
• boiling point elevation
• if solute is not volatile
• osmotic pressure

5
Colligative Properties
Raoults Law (vapor pressure of a solvent above a
solution, Psolvent)
Psolvent csolvent X P0solvent where
P0solvent is the vapor pressure of the pure
solvent
P0solvent - Psolvent DP csolute x P0solvent
Boiling Point Elevation and Freezing Point
Depression
DTb Kbm
DTf Kfm
Osmotic Pressure
????M R T where M is the molarity, R is the
ideal gas law constant and T is the Kelvin
temperature
6
Phase diagrams of solvent and solution.
Figure 13.27
7
Freezing Point Depression

• The freezing point of a solvent is lowered when a
  solute is dissolved in the solvent.
• The lowering of the freezing point is directly
  proportional to the molality of the solution.
• If the solute ionizes, the freezing point is
  directly proportional to the modality of the ions
  in solution.

8
Colligative Properties of Electrolyte Solutions
For electrolyte solutions, the compound
formula tells us how many particles are in the
solution.
The vant Hoft factor, i, tells us what the
effective number of ions are in the solution.
For vapor pressure lowering ?P
i(?solutex P0solvent)
For boiling point elevation ?Tb
i(?bm)
For freezing point depression ?Tf
i(?fm)
For osmotic pressure ?
i(MRT)
9
Figure 13.30
Nonideal behavior of electrolyte solutions.
10
Freezing Point Depression

• DTf kfm
• kf the molal freezing point depression constant
• kf for water, H2O 1.86?C/m
• kf for benzene, C6H6 5.12?C/m
• kf for t-butanol, (CH3)3COH 8.09?C/m
• kf for camphor 37.7?C/m

11
Table 13.6 Molal Boiling Point Elevation and
Freezing Point Depresssion Constants of Several
Solvents
Boiling Point (0C)
Melting Point (0C)
Solvent
Kb (0C/m)
Kf (0C/m)
Acetic acid
117.9
3.07
16.6
3.90
Benzene
80.1
2.53
5.5
4.90
Carbon disulfide
46.2
2.34
-111.5
3.83
Carbon tetrachloride
76.5
5.03
-23
30.
Chloroform
61.7
3.63
-63.5
4.70
Diethyl ether
34.5
2.02
-116.2
1.79
Ethanol
78.5
1.22
-117.3
1.99
Water
100.0
0.512
0.0
1.86
at 1 atm.
12
SAMPLE PROBLEM 13.7
Determining the Boiling Point Elevation and
Freezing Point Depression of a Solution
SOLUTION
1.00x103 g C2H6O2
16.1 mol C2H6O2
16.1 mol C2H6O2
3.62 m C2H6O2
4.450 kg H2O
DTbp
0.512 0C/m
3.62m
x
1.850C
DTfp
1.86 0C/m
3.62m
x
BP 101.85 0C
FP -6.73 0C
13
Freezing Point Depression

• Calculate the freezing point of 2.50m glucose
  solution.
• Calculate the freezing point of a solution that
  contains 8.50g of benzoic acid, C6H5COOH, in
  75.0g of benzene, C6H6.
• kf for benzene, C6H6 5.12?C/m
• MW for benzoic acid 122 g/mole
• Freezing point of benzene 5.5?C

14
(No Transcript)
15
(No Transcript)
16
Determination of Molar Masses by Freezing Point
Depression

• A 37.0g sample of a new covalent compound, a
  nonelectrolyte, was dissolved in 200g of water.
  The resulting solution froze at ?5.58?C.
• Determine the molecular weight of the compound.
  (V-3)

17
(No Transcript)
18
The three types of electrolytes.
Figure 13.25
19
(No Transcript)
20
(No Transcript)
21
Boiling Point Elevation

• The boiling point of a solvent is raised when a
  nonvolatile, nonelectrolyte is dissolved in the
  solvent.
• The elevation of the boiling point depends upon
  the molality of the solution.
• DTb kbm

22
Boiling Point Elevation

• kb the molal boiling point elevation constant
• kb for water, H2O 0.512?C/m
• kb for benzene, C6H6 2.53?C/m
• kb for camphor 5.95?C/m

23
Boiling Point Elevation

• Determine the normal boiling point of a 2.50 m
  glucose, C6H12O6, solution.

24
(No Transcript)
25
Osmotic Pressure

• When a dilute and a concentrated solution are
  separated by a semipermeable membrane, the
  solvent passes through the membrane from the
  solution of lower solute concentration into the
  solution of higher solute concentration. This
  spontaneous process is called osmosis. This
  passage of solvent creates osmotic pressure.

26
The development of osmotic pressure.
Applied pressure needed to prevent volume increase
Figure 13.28
osmotic pressure
pure solvent
solution
net movement of solvent
solute molecules
solvent molecules
27
Osmotic Pressure
28
(No Transcript)
29
Osmotic Pressure

• P MRT
• Where
• p osmotic pressure in atmospheres
• M molarity of the solution
• R 0.0821 L-atm/mole-K
• T temperature in Kelvin

30
Osmotic Pressure

• Determine the osmotic pressure of a 1.00 M
  solution of glucose at 25OC.

31
(No Transcript)
32
SAMPLE PROBLEM 13.8
Determining Molar Mass from Osmotic Pressure
3.61 torr
SOLUTION
M

2.08 x10-4 M
(0.0821 Latm/molK)(278.1 K)
(1.50 mL)
3.12x10-8 mol
21.5 mg
6.89 x104 g/mol
33
Osmotic Pressure

• A 1.00 g sample of a protein was dissolved in
  enough water to give 100 mL of solution. The
  osmotic pressure of the solution was 2.80 torr at
  25?C. Calculate the molarity and the approximate
  molecular weight of the material.
• 2.80 torr/ 760 torr 0.00368 atm

34
(No Transcript)
35
Vapor Pressure Raoult's Law

• Raoults Law states that the vapor pressure of a
  volatile component in an ideal solution decreases
  as its mole fraction decreases.
• Psolution (XA)(P?A)(XB)(P?B)(XC)(P?C)
• When a nonvolatile solute is dissolved in a
  liquid, the vapor pressure of the liquid is
  always lowered.
• Psolution (Xsolvent)(P?solvent)
  (Xsolute)(P?solute)

36
Vapor Pressure Raoult's Law

• When an ionic solute is dissolved in a liquid,
  the vapor pressure of the liquid is lowered in
  proportion to the number of ions present.
• NaCl (s) excess H2O ? Na1(aq) Cl1?(aq)
• The vapor pressure is lower for a 1.0M solution
  of NaCl than for a 1.0 M solution of glucose due
  to the number of ions.

37
Lowering of Vapor pressure
38
SAMPLE PROBLEM 13.6
Using Raoults Law to Find the Vapor Pressure
Lowering
SOLUTION
10.0 mL C3H8O3
0.137 mol C3H8O3
x
27.4 mol H2O
500.0 mL H2O
x
0.137 mol C3H8O3
DP
92.5 torr
x
0.461 torr
0.137 mol C3H8O3 27.4 mol H2O
39
Vapor Pressure Raoult's Law

• Determine the vapor pressure of a solution
  prepared by dissolving 18.3 g of sucrose in 500g
  of water at 70?C. The vapor pressure of water at
  70? C is 233.7 torr. The MW of sucrose is
  342.3g/mole.
• What is the vapor pressure of a mixture that is
  25 by mass acetone in water at 25? C? The vapor
  pressure of water at 25? C is 23.8 torr, and the
  vapor pressure of acetone at that temperature is
  200 torr. The molar mass of acetone is 58.0
  g/mole.

40
(No Transcript)
41
(No Transcript)
42
The steps in a typical municipal water treatment
plant.
Figure B13.1
43
Figure B13.2
Ion exchange for removal of hard-water cations.
44
Reverse osmosis for the removal of ions.
Figure B13.3