Daniel L. Reger
Scott R. Goode
David W. Ball
http://academic.cengage.com/chemistry/reger
Chapter 12
Solutions
Solution Concentration
• There are a number of ways to express
concentration. You have seen:
• molarity;
• mole fraction;
• mass percentage:
• for expressing the composition of a compound;
• and can be used for solutions, as well.
• normality
Solution Concentration
• All concentration units are fractions.
• The numerator contains the quantity of
solute.
• The denominator is the quantity of either
solution or solvent.
• They differ in the units used to
express these two quantities.
Units of Concentration Used Earlier
Molarity (Chapter 4)
moles of solute
M
liters of solution
Mole f raction(Chapter 6)
mol A
χA 
mol A  mol B  mol C...
Mass Percent Composition
grams solute
mass percent 
 100%
grams solution
Example: Percent Composition
• A solution is prepared by dissolving 3.00 g
of NaCl (molar mass = 58.44 g/mol) in 150
g of water. Express its concentration as
mass percent.
Molality
• Molality (m or molal) is defined as
moles of solute
molality 
kilograms of solvent
Example: Calculate Molality
• What is the molality of a solution prepared
by dissolving 3.00 g NaCl (molar mass =
58.44 g/mol) in 150 g of water?
Example: Concentration Conversion
• Express the concentration of a 3.00%
H2O2 solution as
(a) molality;
(b) mole fraction.
Test Your Skill
• Calculate (a) the molality, and (b) the
mole fraction of alcohol (C2H5OH; molar
mass = 46.07 g/mol) in a wine that has
an alcohol concentration of 7.50 mass
percent.
Example: Conversion to Molarity
• Conversion of most concentration
units to molarity usually involve using
the density of the solution to convert
units of mass to units of volume.
• The density of a 12.0% sulfuric acid
(H2SO4; molar mass = 98.08 g/mol) is
1.080 g/mL. What is the molarity of
this solution?
Principles of Solubility
• For most substances, there is a limit to
the quantity of solute that dissolves in a
specific quantity of solvent.
• A dynamic equilibrium exists between the
solute particles in solution and the
undissolved solute.
Normality
• Normality, (N) is defined as the number of equivalents per
liter of solution.
• Problem – what are equivalents – depends on reaction
• Not used very often
• One place that normality is sometimes encountered is with
acid-base chemistry.
• How many protons are release by an acid defines the
equivalents
• EX:
• HCl – releases 1 H+ so…
1M = 1N
• H2SO4 – releases 2H+ so… 1M = 2N
• We will not be using normality, but you might encounter it in
other chemistry classes!!
Definitions
• Solubility is the concentration of
solute that exists in equilibrium with an
excess of that substance.
• A saturated solution has a
concentration of solute equal to its
solubility.
Definitions (continued)
• An unsaturated solution is one that has
a solute concentration less than the
solubility.
• A supersaturated solution is one with a
solute concentration that is greater than
the solubility.
• Supersaturation is an unstable condition.
Solute-Solvent Interactions
• Many spontaneous processes are
exothermic.
• Enthalpy of solution: the DH that
accompanies the dissolution of one
mole of solute.
• When a solid and a liquid form a
solution, the enthalpy change arises
mainly from changes in the
intermolecular attractions.
The Solution Process
• Steps 1 and 2 are endothermic; step 3 is
exothermic.
Spontaneity
• A decrease in enthalpy is an
important factor in causing
spontaneous change.
• However, many endothermic processes
are spontaneous, suggesting another
contribution to spontaneity.
• In increase in disorder also favors
spontaneous change.
Spontaneous Mixing of Gases
• An example of increasing disorder as a
driving force is illustrated by the mixing
of gases.
(a) separated gases
(b) spontaneously mixed
Disorder and Spontaneity
• An increase in disorder generally
accompanies the mixing of molecules in
the formation of a solution.
• Ammonium nitrate is very soluble in water
because of the increase in disorder upon
mixing, even though the process is quite
exothermic (DHsoln = +26.4 kJ/mol).
Solubility of Molecular Compounds
• Relative solubilities can often be
predicted by comparing the relative
strengths of the intermolecular
attractions of solute-solute, solventsolvent, and solute-solvent interactions.
Like Dissolves Like
• In general, substances that have similar
intermolecular forces have strong solutesolvent interactions and tend to form
solution.
Example: Relative Solubility
• (a) Is iodine (I2) more soluble in water
or in hexane (C6H14)?
• (b) Is methanol (CH3OH) more soluble
in water or in octane (C8H18)?
Interaction of Ions with Water
• Hydration is the
interaction of
water molecules
with ions, and is
very exothermic.
Ionic Compounds in Water
• When an ionic compound dissolves in
water, disorder changes because:
• separating the ions increases disorder;
• separating the water molecules increases
disorder;
• hydrating the ions, which restricts some water
molecules, decreases disorder.
• A few examples are known where disorder
decreases on dissolving ionic compounds.
Pressure and Solubility
• Pressure has very little effect on the
solubilities of liquids and solids.
• The solubility of gases in a liquid
depends on the pressure of the gas.
• Henry’s Law: The solubility of a gas
is directly proportional to its partial
pressure at any given temperature:
C = kP
Henry’s Law Constants in Water for Various
Gases (molal/atm)
Gas
0°C
20°C
40°C
60°C
CO2
7.60 x 10-2 3.91 x 10-2 2.44 x 10-2 1.63 x 10-2
C2H4
1.14 x 10-2 5.60 x 10-3 3.43 x 10-3
He
4.22 x 10-4 3.87 x 10-4 3.87 x 10-4 4.10 x 10-4
N2
1.03 x 10-3 7.34 x 10-4 5.55 x 10-4 4.85 x 10-4
O2
2.21 x 10-3 1.43 x 10-3 1.02 x 10-3 8.71 x 10-4
---
Henry’s Law Calculation
• Water at 20C is saturated with air
that contains CO2 at a partial
pressure of 8.0 torr. What is the
molal concentration of CO2 in the
solution?
Solubility and Temperature
• Experiments show that the way solubility
changes with temperature depends on
the sign of the enthalpy of solution.
• Solubility increases with increasing
temperature if DHsoln is positive
(endothermic).
• Solubility decreases with increasing
temperature if DHsoln is negative
(exothermic).
Solubility and DHsoln
K2Cr2O7(s) → K2Cr2O7(aq) DH = +66.5 kJ/mol
The solubility increases with increasing
temperature when DHsoln is positive.
Temperature Dependence on Solubility
Colligative Properties of Solutions
• Colligative property: Any property of a
solution that changes in proportion to
the concentration of solute particles.
• Many colligative properties are directly
related to the lowering of solvent vapor
pressure by the presence of solute
particles.
Effect of Solute on Evaporation
• The rate of evaporation of solvent in a
solution is lower than that of the pure
solvent. Solute particles block
opportunities for solvent particles to
enter the vapor phase.
Raoult’s Law
• Raoult’s law: The vapor pressure of
solvent above a dilute solution equals the
mole fraction of the solvent times the
vapor pressure of the pure solvent.
Psolv = csolvPsolv
• Another form of this equation gives the
lowering of the vapor pressure.
DPsolv = csolutePsolv
Example: Raoult’s Law
• At 27C, the vapor pressure of benzene
is 104 torr. What is the vapor pressure
of a solution that has 0.100 mol of
naphthalene in 9.90 mol of benzene?
Boiling Point Elevation
• Because a solute lowers the vapor
pressure of the solvent, it raises the
boiling point of the solution. Below, the
concentration of the solution is increasing
from (a) to (e).
Boiling Point Elevation
• The boiling point elevation is
DTb = mkb
where m is the molal concentration and
kb is the boiling point constant for the
solvent.
Solvent
B.P. (°C)
kb (°C/m)
Acetic acid
117.90
3.07
Benzene
80.10
2.53
Water
100.0
0.512
Freezing Point Depression
• Solute particles interfere with the ability
of solvent particles to form a crystal
and freeze. Thus, it takes a lower
temperature to freeze solvent from a
solution than from the pure solvent.
This is freezing point depression.
Freezing Point Depression
• The freezing point depression is
DTf = mkf
where m is the molal concentration and
kf is the freezing point constant for the
solvent.
Acetic acid
Freezing Pt.
(°C)
16.60
3.90
Benzene
5.51
4.90
Naphthalene
80.2
6.8
Water
0.00
1.86
Solvent
kf (°C/m)
Example: Calculate kf
• Benzophenone freezes at 48.1C. A
solution of 1.05 g urea ((NH2)2CO,
molar mass = 60.06 g/mol) in 30.0 g of
benzophenone freezes at 42.4C.
What is kf for benzophenone?
Test Your Skill
• Benzophenone freezes at 48.1C and
has a kf of 9.8C/molal. A 2.50-g
sample of solute whose molar mass is
130.0 g/mol is dissolved in 32.0 g of
benzophenone. What is the freezing
point of the solution?
Osmosis
• Semipermeable membranes allow
water and small molecules to pass
through them.
• Osmosis is the diffusion of a fluid
through a semipermeable membrane.
Osmosis (continued)
• When a semipermeable membrane separates a
solution from the pure solvent, the net effect is
for pure solvent to move through the membrane
into the solution.
• The higher level of liquid produces an additional
pressure, called osmotic pressure.
Osmotic Pressure
• Osmotic pressure is a colligative
property, and can be calculated by the
equation
P = MRT
where:
P = osmotic pressure
M = molar concentration of solute
R = ideal gas law constant
T = temperature in Kelvin
Example: Molar Mass by Osmotic Pressure
• A 5.70 mg sample of protein is
dissolved in water to give 1.00 mL of
solution. Calculate the molar mass of
the protein if the solution has an
osmotic pressure of 6.52 torr at 20C.
Colligative Properties - Summary
Property
Symbol
Conc. Unit
Constant
Vapor
pressure
∆P
Mole fraction
P°
Boiling Point
∆Tb
Molal
Kb
Freezing
point
∆Tf
Molal
Kf
Osmotic
pressure
Π
Molar
RT
Electrolyte Solutions
• The colligative properties of electrolyte
solutions are more pronounced because
electrolytes separate into ions in solution.
• The van’t Hoff factor, i, is defined by the
equation
measured colligativ e property
i
expectedvalue for nonelectrolyte
The van’t Hoff Factor
• In dilute solution, the van’t Hoff factor for
salts approaches the number of ions
produced by one formula unit of the
substance.
NaCl → Na+(aq) + Cl-(aq)
i=2
MgBr2 → Mg2+(aq) + 2Br-(aq) i = 3
• The van’t Hoff factor generally decreases
as the concentration increases.
Example: the van’t Hoff Factor
• Arrange the following aqueous solutions
in order of increasing boiling points: 0.03
m urea (a nonelectrolyte), 0.01 m NaOH,
0.02 m BaCl2, 0.01 m Fe(NO3)3.
Mixtures of Volatile Substances
• In a solution of two or more volatile
compounds, all components of the mixture
are in equilibrium with their vapors.
• An ideal solution is one in which all
volatile components obey Raoult’s law for
all compositions.
PA = cAPA, PB = cBPB, PC = cCPC, etc.
Ideal Solutions
• Mixtures of toluene and benzene form
nearly ideal solutions.
Example: Vapor Pressure of Solutions
• At 27C, the vapor pressure of carbon
tetrachloride (CCl4) is 127 torr and that of
chloroform (CHCl3) is 212 torr. What is
the partial pressure of each substance,
and the total vapor pressure of the
solution, of a solution that contains 0.40
mol of CCl4 and 0.60 mol of CHCl3?
Distillation
• Distillation is the separation of a mixture
of components based on differences in
volatility (vapor pressure) by repeated
evaporation and condensation of the
mixture.
• The vapor always contains a larger mole
fraction of the more volatile component.
Distillation Apparatus
Deviations from Raoult’s Law
• Most liquid-liquid solutions deviate from
the ideal behavior predicted by Raoult’s
law.
• Solutions have positive deviations if the
vapor pressure is higher than predicted.
• Solutions have negative deviations if the
vapor pressure is lower than predicted.