Chapter
2 SOLUTIONS
Solutions
are homogeneous
mixtures
of two or
more than two components. The component that is
present in
the largest quantity is known as solvent.
Solvent determines the physical state in which
solution exists. One
or more components present in
the solution other than solvent are
called solutes.
In
this Unit we shall consider only binary
solutions.
Expressing
Concentration of Solutions
(i)
Mass
percentage
(w/w):
The mass percentage of
a component of a solution is defined as:
Mass
% of a component =
Mass
of the component in the solution
X 100
Total
mass of the solution
For
example, if a solution is described by 10%
glucose in water by mass,
it means that 10 g of
glucose is dissolved in 90 g of water resulting
in a
100 g solution.
(ii)
Volume
percentage
(v/v):
The volume
percentage is defined as:
Volume %
of a component =
Volume
of the component X 100
Total
volume of solution
For
example, 10% ethanol solution in water means
that 10 mL of ethanol is
dissolved in water such that
the total volume of the solution is 100
mL.
Mass
by volume percentage
(w/v):
Anotherunit
which is commonly used in medicine and
pharmacy is mass
by volume percentage. It is the
mass of solute dissolved in 100 mL
of the
solution.
Parts
per million:
When a solute is present in
trace
quantities,
it is convenient to express
concentration in parts
per million (ppm)
and is
defined as: Parts per million =
Number
of parts of the component X 106
Total number of
parts of all components of the solution
Mole
fraction:
It is defined as: Mole fraction of a
component =
Number
of moles of the component
Total number of
moles of all the components
For
example, in a binary mixture, if the number of
moles of A and B are
nA
and nB
respectively,
the mole fraction of A
will be xA
=
nA
nA
+ nB
In
a given solution sum of all the mole fractions is
unity.
(vi)
Molarity:
Molarity (M)
is defined as number of
moles of solute dissolved in one litre (or
one cubic
decimetre) of solution,
Molarity
= Moles
of solute
Volume
of solution in litre
For
example, 0.25 mol L–1 (or 0.25 M) solution of
NaOH means that 0.25
mol of NaOH has been
dissolved in one litre (or one cubic decimetre).
Molality:
Molality (m)
is defined as the number
of moles of the solute per kilogram (kg) of
the
solvent and is expressed as:
Molality (m) =
Moles
of solute
Mass
of solvent in kg
For
example, 1.00 mol kg–1 (or 1.00 m) solution of
KCl means that 1 mol
(74.5 g) of KCl is dissolved in 1
kg of water.
2.
Solubility
Solubility
of a substance is its maximum amount
that can be dissolved in a
specified amount of
solvent. It depends upon the nature of solute and
solvent as well as temperature and pressure.
Solubility
of a Solid in a Liquid
When
a solid solute is added to the solvent, some
solute dissolves and its
concentration increases in
solution. This process is known as
dissolution. Some
solute particles in solution collide with the solid
solute particles
and get separated out of solution.
This process is known as
crystallisation.
Effect
of temperature
If
in a nearly
saturated solution, the
dissolution
process is endothermic (∆sol
H > 0), the solubility
should increase with rise in temperature
and if it is
exothermic (∆sol
H > 0) the solubility should
decrease.
Effect
of pressure
Pressure
does not have any significant effect on
solubility of solids in
liquids. It is so because solids
and liquids are highly
incompressible and practically
remain unaffected by changes in
pressure.
Solubility
of a Gas in a Liquid
Many
gases dissolve in water. Oxygen dissolves only
to a small extent in
water. It is this dissolved oxygen
which sustains all aquatic life.
Henry was the
first to give a quantitative relation
between pressure and solubility
of a gas in a solvent
which is known as Henry’s
law.
The
law states that
at a constant temperature, the
solubility
of a gas
in a liquid
is
directly proportional to the
pressure
of the gas.
The
most commonly used form of Henry’s law states
that “the
partial
pressure of the gas in vapour
phase (p)
is
proportional
to the mole fraction of
the gas (x)
in
the
solution” and
is expressed as:
p
=
KH
x
Here
KH
is the Henry’s law constant.
Different
gases have different KH
values at the same temperature. This suggests that KH
is a function of the nature of the gas.
The
solubility of gases increases with decrease of
temperature. It is due
to this reason that aquatic
species are more comfortable in cold
waters rather
than in warm waters.
Vapour
Pressure of Liquid Solutions
The
liquid solvent is volatile. The solute may or may
not be volatile. We
shall discuss the properties
of
only binary solutions, that is, the solutions
containing two
components, namely, the solutions of
(i) liquids in liquids and (ii)
solids in liquids.
Vapour
Pressure of Liquid- Liquid Solutions
Let
us consider a binary solution of two volatile
liquids and denote the
two components as 1 and 2.
When taken in a closed vessel, both the
components
would evaporate and eventually an equilibrium would
be
established between vapour phase and the liquid
phase. Let the total
vapour pressure at this stage be
ptotal
and p1
and p2
be the partial vapour
pressures of the two components 1 and 2
respectively. These partial pressures are related to
the mole
fractions x1
and x2
of the two components 1
and 2 respectively.
Raoult’s
law which
states that for
a solution of
volatile liquids, the partial vapour pressure of
each
component in the solution is directly
proportional to its mole
fraction.
Thus,
for component 1 p1
αx1
and
p1
=p
01x1
where
p
01
is
the vapour pressure of pure component 1 at the same
temperature.
Similarly,
for component 2, p2
=p
02x2
where
p
02
represents the vapour pressure of the pure component 2.
According
to Dalton’s
law of partial pressures,
ptotal
= p1
+ p2
Substituting
the values of p1
and p2,
we get, P total
= P10
+ ( P20
– P10
) X2
Raoult’s
Law as a special case of Henry’s Law
If
we compare the equations for Raoult’s law and
Henry’s law, it can
be seen that the partial pressure
of the volatile component or gas is
directly
proportional to its mole fraction in solution. Only the
proportionality constant KH
differs from p10.
Thus, Raoult’s law becomes a special case of Henry’s law in which
KH
becomes equal to p10.
4.
Vapour
Pressure of Solutions of Solids in
Liquids
Liquids
at a given temperature vapourise and under
equilibrium conditions the
pressure exerted by the
vapours of the liquid over the liquid phase
is called
vapour pressure . In a pure liquid the entire surface
is occupied
by the molecules of the liquid. If a
non-volatile solute is added to
a solvent to give a
solution , vapour pressure of the solution at a
given
temperature is found to be lower than the vapour
pressure of
the pure
solvent at the same
temperature. In the solution, the surface has
both
solute and solvent molecules; thereby the fraction of
the
surface covered by the solvent molecules gets
reduced.
Raoult’s
law in its general form can be stated as, for
any solution the partial vapour pressure of each volatile component
in
the solution is directly proportional to its mole fraction.
Ideal
and Nonideal Solutions
Liquid-liquid
solutions can be classified into ideal and
non-ideal solutions on the
basis of Raoult’s law.
Ideal
Solutions
The
solutions which obey Raoult’s law over the
entire range of
concentration are known as ideal
solutions.
∆Hmix
=
0, ∆Vmix
=
0
The
intermolecular attractive forces between the A-A
and B-B are nearly
equal to those between A-B, this
leads to the formation of ideal
solution. Solution of
n-hexane and n-heptane, bromoethane and
chloroethane, benzene and toluene, etc. fall into this
category.
Non-ideal
Solutions
When
a solution does not obey Raoult’s law over the
entire range of
concentration, then it is called
non-ideal
solution.
The
vapour pressure of such a solution is either
higher or lower than
that predicted by Raoult’s law
.If it is higher, the solution
exhibits positive
deviation
and
if it is lower, it exhibits negative
deviation from
Raoult’s law.
In case of
positive
deviation
from Raoult’s law, A-B interactions are
weaker than those between
A-A or B-B, i.e., in this case the intermolecular
attractive forces
between the solute-solvent molecules are weaker than those
between
the solute-solute and solvent-solvent molecules.
Mixtures of
ethanol and acetone behave in this
manner. In pure ethanol, molecules
are hydrogen
bonded. On adding acetone, its molecules get in
between
the host molecules and break some of the
hydrogen bonds between them.
Due to weakening of
interactions, the solution shows positive
deviation
from Raoult’s law.
In case of
negative
deviations
from Raoult’s law, the intermolecular
attractive forces between A-A
and B-B are weaker than those between A-B and
leads to decrease in
vapour pressure resulting in
negative deviations.
A mixture of
chloroform and acetone forms a solution
with negative deviation from
Raoult’s law. This is
because chloroform molecule is able to form
hydrogen bond with acetone molecule.
Some liquids
on mixing, form azeotropes
which
are binary
mixtures having the same composition in liquid and vapour
phase and boil at a
constant temperature.
There are two
types of azeotropes called minimum
boiling azeotrope and maximum boiling
azeotrope.
The solutions which
show a large positive deviation from Raoult’s
law form minimum boiling
azeotrope at a specific composition. The
solutions that show large negative
deviation from Raoult’s law form
maximum boiling azeotrope at a specific
composition.
Colligative
Properties and Determination of
Molar Mass
Properties
depend on the number of solute
particles irrespective of their nature
relative to
the total number of particles present in the
solution.
Such properties are called colligative
properties.
These
are: (1) relative lowering of vapour pressure
of the solvent (2)
depression of freezing point the
solvent (3) elevation of boiling
point of the solvent
and (4) osmotic pressure of the solution.
Relative
Lowering of Vapour Pressure
Raoult
established that the lowering of vapour
pressure depends only on the
concentration of the
solute particles and it is independent of their
identity.
p1
= x1
p10
∆p1
= p10
–
p1
= p10
– x1
p10
= p10
(1 – x1)
p10
–
p1
= W2
X M1
p10
M2
X W1
Elevation
of Boiling Point
The
vapour pressure of a liquid increases with
increase of temperature.
It boils at the temperature
at which its vapour pressure is equal to
the
atmospheric pressure.
The vapour pressure
of the solvent decreases in the
presence of non-volatile solute. The
boiling point of a
solution is always higher than that of the boiling
point of the pure solvent.
Let T
0
b
be
the boiling point of pure solvent and
T
b
be
the boiling point of
solution. The increase in the
boiling point
∆T = Tb0
–
Tb
is
known as
elevation
of boiling po
int.
Experiments
have shown that for dilute
solutions
the
elevation of boiling point (∆Tb)
is
directly
proportional to the molal concentration of
the
solute
in a solution. Thus
∆Tb
α m
or
∆Tb
= Kb
m
Here
m
(molality)
is the number of moles of solute
dissolved in 1 kg of solvent and the
constant of
proportionality, Kb
is called Boiling
Point
Elevation
Constant or Molal Elevation Constant
(EbullioscopicConstant).
The unit of Kb
is K kg
mol-1.
M2
= 1000
X W2
X
Kb
∆Tb
X W2
Depression
of Freezing Point
The
freezing point of a substance, the solid phase is
in dynamic
equilibrium with the liquid phase. The
lowering of vapour pressure of
a solution causes a
lowering of the freezing point compared to that
of
the pure solvent. Thus, the freezing point of a
substance may be
defined as the temperature at
which the vapour pressure of the
substance in its
liquid phase is equal to its vapour pressure in the
solid phase.
Let
T
0
f be
the freezing point of pure solvent
and
T
f
be
its freezing point when non-volatile
solute
is dissolved in it. The decrease in freezing
point.
∆Tf = Tf0
–
Tf
is
known as
depression
in
freezing
point.
∆Tf
α m
or
∆Tf
= Kf
m
Here
m
(molality)
is the number of moles of solute
dissolved in 1 kg of solvent and the
constant of
proportionality, Kf
is called Freezing
Point
Depression Constant or Molal Depression
Constant or Cryoscopic
Constant.
The
unit of Kf
is K kg mol-1.
M2
= 1000
X W2
X
Kf
∆Tf
X W2
Osmosis
and Osmotic Pressure
The flow of
solvent through a semi permeable
membrane from pure solvent to the
solution is
called osmosis.
The osmotic
pressure of a solution is the excess
pressure that must be applied on
the solution to
prevent osmosis.
π
=
C
R T
π=
n2RT
V
M2
= W2RT
π
V
Two
solutions having same osmotic pressure at
a given temperature are
called isotonic
solutions.
Reverse
Osmosis and Water Purification
The
direction of osmosis can be reversed if a
pressure larger than the
osmotic pressure is applied
to the solution side. That is, now the
pure solvent
flows out of the solution through the semi permeable
membrane. This phenomenon is called reverse
osmosis. Reverse
osmosis is used in desalination of
sea water.
6.
Abnormal
Molar Masses
A molar
mass is either lower or higher than the
expected or normal value is
called as abnormal mass.
Ionic
compounds when dissolved in water dissociate
into cations and anions.
When there is dissociation of
solute into ions, the experimentally
determined
molar mass is always lower than the true value.
Molecules
of acetic acid dimerise in benene due to
hydrogen bonding. This
normaly happens in solvents
of low dielectric constant. Here the
number of
particles is reduce due to dimerisation. When there
is
association of solute, the experimentally
determined molar mass is
always higher than the
true value.
In
1880 van’t Hoff introduced a factor i,
known as the
van’t Hoff factor, to account for the extent of
dissociation or association. This factor i
is
defined as:
i = Normal
molar mass
Abnormal
molar mass
= Observed
colligative property
Calculated
colligative property
= Total
number of moles of particles after association/dissociation
Number
of moles of particles before
association/dissociation
