Solutions
A homogeneous mixture of two or more substances.
The Solution Process
We will focus on solid or liquid solutes
dissolved in a liquid solvent. Since all particles
are in contact with each other, the solute-solute
and solvent-solvent forces of attraction are
disrupted, and new, solute-solvent forces of
attraction are created.
The Solution Process
The disruption of solute-solute and solventsolvent forces of attraction requires energy, and
is endothermic. The interaction of solvent and
solute usually releases energy. The sum of the
energy of all three steps is called the enthalpy of
solution, ΔHosoln.
Note that solutions may form whether the
net process is endothermic or exothermic.
The Solution Process
The Solution Process
In addition to the enthalpy of solution, we
must also consider the entropy of mixing. Entropy
is a measure of randomness or disorder. An
increase in entropy makes a process more likely
to occur.
Since mixing pure substances increases
entropy, this factor makes processes that are
slightly endothermic favorable.
Entropy of Mixing
The Solution Process
The general rule on solution formation is:
Like dissolves like.
Polar and ionic compounds dissolve in polar
solvents. Non-polar compounds dissolve in
non-polar solvents.
Like Dissolves Like
Vitamin A consists
almost entirely of
carbon and hydrogen,
and is non-polar. As
a result, vitamin A is
fat-soluble, and can
be stored in the body.
Like Dissolves Like
C-O bond
O-H bonds
Vitamin C contains
polar C-O and O-H
bonds. It is water
soluble, and must be
consumed often, as it
is excreted easily.
Like Dissolves Like
Ionic Compounds
Like Dissolves Like
The Solution Process
Disrupt- Disrupt- Solute/
Solvent
ion of
ion of
solute
solvent interact
-ion
Ionic Aqueous Solutions
When an ionic compound is dissolved in
water, the energy required to separate the ions
of the solute is equal to –(lattice energy), or
-ΔHlattice.
The energy released as the gaseous ions
dissolve in water is called the hydration energy,
ΔHhydration.
The net energy change is ΔHsoln.
Heat of Hydration
Factors Affecting Solubility



Molecular Structure
Pressure (for gaseous solutes)
Temperature
Pressure Effects
Gases dissolved in a liquid solute obey Henry’s
Law:
C = kP
where C is the concentration, k is a constant
specific to solute and solvent, and P is the
pressure of the gas above the solution
Pressure Effects
Gases dissolved in a liquid solute obey Henry’s
Law:
C = kP
The amount of a gas dissolved in a solution
is directly proportional to the pressure of the gas
above the solution.
Henry’s Law
Pressure Effects
Temperature Effects
For gases dissolved
in liquids, the solubility
decreases as
temperature increases.
That is, gases dissolve
better in cold liquids
than in warmer liquids.
Temperature Effects
For solid solutes
dissolved in water, the
effect of temperature
on solubility is difficult
to predict, although
many solids dissolve
more as temperature
increases.
Solution Concentration
Although molarity (M) is used for
stoichiometry calculations, there are many other
ways to express the concentration of a solution.
Molarity will vary slightly with changes in
temperature as the volume of the solution
expands or contracts. Units such as mass
percent, mole fraction, or molality remain
constant as temperature changes.
Solution Concentration
Mass percent = (mass of solute) (100%)
(mass of solution)
Mole fraction (XA) = (moles of A)
total # of moles
Molality (m) = moles of solute
kg of solvent
Very Dilute Solutions
The concentration of very dilute solutions
are expressed in parts per million (ppm) or parts
per billion (ppb).
ppm = [(mass solute) x 106 ] ÷(mass soln)
ppb = [(mass solute) x 109 ] ÷(mass soln)
The Colligative Properties
The colligative properties are properties that
depend upon the concentration of particles
(molecules or ions) dissolved in a volatile
solvent, and not on the nature of the particles.
They include:
 vapor pressure
 freezing point
 boiling point
 osmotic pressure
The Colligative Properties
Relatively simple mathematical relationships
can be used to predict the changes in vapor
pressure, freezing and boiling point, etc.
The properties can be predicted for dilute
solutions (<0.1M) of non-volatile solute (usually
solids) dissolved in a volatile solvent (usually a
liquid).
Vapor Pressure
The addition
of a non-volatile
solute to a
volatile solvent
lowers the vapor
pressure of the
solvent.
Vapor Pressure
The decrease in vapor pressure can be
understood by looking at the evaporation
process. We need to compare the enthalpy
change (ΔHvap) and entropy change of
evaporation.
Vapor Pressure
The vapor pressure of the pure solvent or
the solution is the result of solvent molecules
escaping the liquid surface and becoming
gaseous. Since the solute is non-volatile, it does
not evaporate.
Since only solvent molecules evaporate, the
enthalpy change for pure solvent or the solution
is the same.
Vapor Pressure
The decrease in
vapor pressure of
the solution is the
result of changes
in entropy. The
vapor in either
container is
disordered, due to
the random
motion of gaseous
solvent.
Vapor Pressure
The liquid phases
differ in entropy.
The pure solvent is
relatively ordered
since all of the
molecules are the
same (solvent).
Vapor Pressure
The liquid phase
of the solution is
much more
random, since it
is a mixture.
Vapor Pressure
Upon evaporation,
the pure solvent
undergoes a
greater increase in
entropy than the
solution.
Vapor Pressure
Systems tend to
maximize entropy.
The pure solvent
evaporates more
readily, because it
undergoes a
greater increase in
entropy.
Boiling Point Elevation
Vapor Pressure Lowering
The change in vapor pressure can be
calculated as follows:
o
∆vp = -Xsolute Psolvent
where X is the mole fraction of solute particles
Posolvent is the vapor pressure of the pure solvent
Vapor Pressure Lowering
∆vp = -Xsolute Posolvent
The sign is negative because the vapor
pressure decreases.
Vapor Pressure Lowering
Psoln = Xsolvent Posolvent
The mole fraction of solvent, Xsolvent , =
moles of solvent/total moles of particles and
solvent.
Problem – Vapor Pressure
Water has a vapor pressure of 92.6 mmHg at 50oC.
a) Compare the vapor pressure of two aqueous
solutions at 50oC. One contains .100 mole of
sucrose dissolved in 1.00 mol of water. The
other contains .100 moles of CaCl2 dissolved in
1.00 mol of water.
b) Calculate the vapor pressure of the CaCl2
solution.
Solution Phase Diagrams
The lowering of the vapor pressure due to the
presence of a non-volatile solute affects several
properties. The phase diagram for the solution
will be shifted, due to the lower vapor pressure
of the solution.
Solution Phase Diagrams
Solution Phase Diagrams
As a result of
the lower vapor
pressure, the
boiling point of
the solution is
greater than that
of pure solvent.
Solution Phase Diagrams
Since the liquidsolid line is shifted
to a lower
temperature, the
freezing point of
the solution is
lowered.
Properties of Solutions
Solutions of non-volatile solutes in a volatile
solvent have
- higher boiling points and
- lower freezing points
than the pure solvent.
Boiling Point Elevation
The size of the increase in boiling point depends
upon the concentration of solute particles.
∆Tb = Kbm(i)
where Kb is the solvent dependent boiling
point elevation constant,
m = molality of the solute
i = van’t Hoff factor
The van’t Hoff Factor, i
The van’t Hoff factor is the number of
particles in solution compared to the number
dissolved. If an ionic compound forms two ions
per formula unit, its i value = 2.
The van’t Hoff Factor, i
If a molecule “pairs up” in solution, with
two molecules uniting to form one molecule,
then the i factor will be 0.5.
For non-electrolytes, the i factor is usually 1,
and is often ignored.
Freezing Point Depression
The size of the decrease in freezing point depends
upon the concentration of solute particles.
∆Tf = -Kfm(i)
where Kf is the solvent dependent freezing
point depression constant,
m = molality of the solute
i = van’t Hoff factor
Constants for Common Solvents
Applications
Solutions of sugar
in water or maple
syrup (sap) have
boiling points that are
higher than 100oC.
Applications
Salt is spread on
roads to lower the
freezing point of ice
and keep the roads
from icing up at
temperatures below
0oC.
Applications
Antifreeze keeps
the radiators in cars
from freezing during
the winter and
overheating in the
summer.
Problem

Which of the following aqueous solutions will
have the lowest freezing point?
0.015m calcium nitrate
0.040m sodium chloride
0.040m sucrose
0.020m hydrochloric acid
Problem

The solubility of NaNO3 in water at 0oC is 75
grams per 100g of water. Calculate the freezing
point of the solution. Kf for water = 1.86oC/m
(or oC-kg/mol).
Applications – Molar Mass
Since boiling point or freezing point changes
are proportional to concentration (molality), it is
possible to calculate molar masses of unknown
solutes using a measured temperature change.
Solvents with greater values of Kf or Kb will
provide the largest change in temperature for a
given concentration.
Constants for Common Solvents
Applications – Molar Mass
∆Tb = Kbm(i)
where m = molality = moles of solute/kg of solvent
∆Tb = Kbm(i) = Kb(moles solute/kg solvent)(i)
or
∆Tf = -Kfm(i) = Kf(moles solute/kg solvent)(i)
Applications – Molar Mass
∆Tb = Kbm(i) = Kb(moles solute/kg solvent)(i)
or
∆Tf = -Kfm(i) = Kf(moles solute/kg solvent)(i)
Using either relationship, moles of solute can
be calculated. If the mass of the solute is also
known, the molar mass is easily calculated.
Problem – Molar Mass

A solution of 2.50g of a compound with an
empirical formula of C6H5P in 25.0 g of benzene
has a freezing point of 4.3oC. Calculate the
molar mass of the solute and its molecular
formula. [The normal freezing point of benzene
is 5.5oC, and Kf for benzene = 5.12 oC/m.
Assume i =1]
Osmotic Pressure
Osmosis is the flow of solvent across a
semipermeable membrane. The membrane allows
solvent molecules to pass through, but not
solute particles.
Osmotic Pressure
Osmotic Pressure
The minimum
pressure needed to
just stop osmosis is
called the osmotic
pressure.
Osmotic Pressure
Π = MRT(i)
where Π is the osmotic pressure
M is molarity (mol solute/L of soln)
R = 0.08206 L-atm/mol-K
T is temperature in Kelvins
Osmotic Pressure - Applications
A relatively dilute solution provides a fairly
large osmotic pressure. As a result, osmotic
pressure is an excellent way to obtain molar
masses of very dilute solutes such a proteins.
Problem

0.8750 g of a protein is dissolved in enough
water to make 100. ml of solution. The solution
has an osmotic pressure of 3.8 mm Hg at
25oC. Calculate the molar mass of the protein.
Osmotic Pressure - Applications
Renal dialysis uses
osmosis to rid the
blood of waste
products in people
with kidney failure.
Osmotic Pressure - Applications
Isotonic saline is a salt
solution with the
same osmotic
pressure as blood
cells. This maintains
a fluid balance within
the cell.
Osmotic Pressure - Applications
If a solution of saline
is too concentrated,
the cell will become
dehydrated and shrink
(crenate).
Osmotic Pressure - Applications
If a solution of saline
is too dilute, the red
blood cells become
swollen with excess
water and eventually
burst (hemolysis).
Osmotic Pressure - Applications
In reverse osmosis, a
pressure greater than
the osmotic pressure is
applied to a solution.
Pure solvent can be
obtained on the other
side of the membrane.
Osmotic Pressure - Applications
Behavior of Electrolytes
The van’t Hoff factor, i, represents the
number of particles formed in solution for each
solute particle dissolved.
i = moles of particles in solution
moles of solute dissolved
Behavior of Electrolytes
For ionic solutes, we expect the value of i to
be 2 for NaCl, 3 for MgCl2, and 4 for FeCl3, etc.
In extremely dilute solutions, the observed value
of i is very close to these expected values.
Behavior of Electrolytes
However, as
solutions become more
concentrated, ion pairing
occurs, and some of the
ions formed in solution
pair up and behave like
a single particle.
Behavior of Electrolytes
Liquid-Liquid Solutions
When two volatile liquids mix, they form a
solution. An ideal solution, similar to an ideal gas,
will exert a vapor pressure which is related to the
vapor pressures of the pure liquids and their
relative abundance in the mixture.
Liquid-Liquid Solutions
The solution obeys Raoult’s law:
PA = χAPoA
PB = χBPoB
where χA is the mole fraction of component A
and PoA is the vapor pressure of pure A
Liquid-Liquid Solutions
Raoult’s law is
best seen graphically.
The vapor pressure of
the mixture is the
sum of the vapor
pressures of each
component.
Liquid-Liquid Solutions
Ideal solutions
typically involve nonpolar molecules with
similar structures.
Mixtures of liquid
hydrocarbons often
form ideal solutions.
Liquid-Liquid Solutions
If the two components of the mixture
are strongly attracted to each other, such as
two polar molecules, the vapor pressure of
the mixture is often less than that predicted
by Raoult’s law.
Liquid-Liquid Solutions
This is known as a
negative deviation from
Raoult’s law. It
occurs with mixtures
of liquid acids and
water. As the acid
ionizes, the forces of
attraction in the
mixture increase.
Liquid-Liquid Solutions
If a mixture contains liquids that have
stronger attractive forces when pure than
when mixed, the mixture will exert a vapor
pressure that is greater than that predicted
by Raoult’s law. This is called a positive
deviation from Raoult’s law.
Liquid-Liquid Solutions
A mixture of ethanol
and water exhibits a
positive deviation
from Raoult’s law.
The hydrogen bonding
of each pure liquid is
disrupted when the
two liquids are mixed.