CHAPTER 8
LIQUID SOLUTION
8.1 Concentration Units
There are several methods to express the concentration of
solution. We are going to describe some very important terms used to represent
the concentration of solution.
(a) Percent by weight
(b) Percent by volume
(c) Percent by
weight/volume
(d) Mole fraction
(e) Molarity
(f) Molality
(g) Normality
(h) ppm
8.1.1 Percent by Weight (w/w)
It is the weight of the solute as a per cent of the total weight
of the solution. That is,
%by weight of solute 
For example, if a solution of HCI contains 36 % HCI by weight, it
has 36 g of HCI in 100 g of solution.
8.1.2 Percent by Volume (v/v)
% by volume =
For example, it we have 35% C2H5OH solution
by volume means 25 ml C2H5OH is present per 100 ml
of the solution.
8.1.3 Percent by weight/volume (w/v)
% = 
i.e.30% HCl solution, means 30 g of HCl is present per 100 ml of
solution
8.1.4 Mole Fraction (X)
A simple solution is made of two substances; one is the solute and
the other is solvent. Mole fraction, X, of solute is defined as the ratio of
the number of moles of solute and the total number of moles of solute and
solvent. Thus,
If n represents moles of solute and N number of moles of solvent,
Notice that mole fraction of solvent would be
Mole fraction is unit less and 
8.1.5 Molarity (M)
In current practice, concentration is most often expressed as
molarity. Molarity is defined as the number of moles of solute per litre of
solution.
Molarity
or 
It’s unit is mol/L.
8.1.6 Molality (m)
Molality of a solution is defined as the number of moles of solute
per kilogram of solvent:
Molality 
8.1.7 Normality (N)
Normality of a solution is defined as number of equivalents of
solute per litre of the solution:
Normality 
or 
E = equivalent wt of solute
8.1.8 ppm (parts per million)
It is the mass of solute in grams present per 106 grams
of solution.
and also 
8.2 Vapour Pressure
The molecules of the liquid which possess high kinetic energy have
a tendency to change to vapour state. When a liquid is placed in a closed
container then due to evaporation, vapours of liquid are produced which
ultimately leads to an equilibrium state due to the tendency of the vapours to
convert back to liquid. The pressure
exerted by the vapours of the liquid which are in equilibrium with the liquid
phase at the given temperature, is known as vapour pressure.
The vapour pressure of liquid depends upon following points:
Nature of Liquid
When the intermolecular forces of attractions are stronger then
the vapour pressure will be low because less number of molecules can leave the
liquid.
Out of C2H5OH,
CH3OCH3, CH3CHO the one
with highest vapour pressure is CH3OCH3 and the
one with lowest vapour pressure is C2H5OH because in C2H5OH there is hydrogen bonding leading
to strongest intermolecular forces where as in CH3OCH3 there is Vander Waals forces leading to
weakest intermolecular forces.
Temperature
Higher the temperature, greater would be the vapour pressure. This
is because when temperature is raised, kinetic energy of the molecules increase
and therefore the number of molecules leaving surface of liquid, is large. The
Clausius Clapeyron equation tells very clearly that as temperature increases
the right hand side remains highly and thereby vapours pressure increases.
Mixing of two volatile liquids
Let two volatile liquids A and B dissolve each other to form an
ideal solution. Then the vapours above the solution will contain the vapours of
A and B.
Applying
Psolution = PA + PB
Where PA and PB are the partial vapour pressures of A and B.
Solution being dilute (Condition for ideality) Raoult’s law can
be applied.
Raoult’s
law for binary solutions state that “the vapour pressure of any volatile
constituent of a binary solution at any given temperature is equal to the
product of the vapour pressure of pure constituent and its mole fraction”.
PA =
PºA XA
PB =
PºB XB
PºA and PºB are vapour pressures of pure A and B
respectively.
cA and
cB are
mole fraction of A and B in liquid solution respectively
Hence
Ps = 
Hence,
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Ps = Ps = This equation is of the form y = mx + c The value of m (slope) may be (+ve) or
(–ve) depending upon whether PB0 > PA0 (m = + ve) or PB0 < PA0 (m = –ve). Hence a plot of a graph of Ps versus XB will be a straight line with an intercept on
y-axis equal to pA and slope equal to |
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Vapour composition
Vapour composition means to find out the mole fraction of A and B
in vapour.
Partial pressure =
mole fraction × total pressure
PA = 
or 
Similarly for B
where 
and 
are mole fraction of ‘A’ and ‘B’ in vapour
phase and 
Mixing of Two Immiscible Liquid
Let us consider the case of mixing of two
volatile but immiscible liquids A and B. In the mixture of two liquids, if P0A
and P0B are vapour pressures, of two liquids in pure
state, then according to
PT = PA + PB
Where PA and PB are
the partial vapour pressures of liquids A and B. If XA and XB
are mole fractions of A and B in the mixture (actually they as immiscible) then
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or similarly or |
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Vapour composition
It
X’A and X’B denotes the mole fractions of A and B in
vapour face, then.
Partial
vapour pressure = Mole fraction x Total vapour pressure
PA = X’A ´ PT
or 
similarly
Also
or 
where 
or 
= mass of A
= molecular
mass of A
= mass of B
= molecular
mass of B
8.3 Binary ideal solution
A solution for whichD
H = 0 and DV = 0, is known as ideal solution for
example
Such systems are called nearly ideal or ideal solutions.
Such solutions obey Raoult’s law and comply to the equation
Ps = 
.
To comply to this condition for ideality the two liquids A and B
should fulfill the under mentioned conditions
1. The attractive forces between the particles
A and B (i.e. A–B interactions) should be equal to the attractive forces between A and A (i.e.
A–A interaction) and between B and B (i.e. B–B interaction)
2. Such an interaction can be equal if the
structure and polarity are almost same. e.g. CH3–OH and C2H5–OH. In such
solutions
(1) DVmix = 0 (2) DSmix > 0 (3) DHmix =
0.
8.4 Binary Non Ideal Solutions
Non-Ideal Solutions with Positive
Deviation
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Set-A solution shows a relationship
where the vapour pressure of the solution observed is greater than the vapour
pressure of solution under ideal conditions i.e. Ps (obs) > Ps(actual) or Ps > Pi where
Pi =
i.e.
Ps > Such
solutions are said to have a +ve deviation from ideality. The graph obtained
resembles as given below |
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The reasons for such a
+ve deviations could be linked to the fact that after mixing the interactions
between the liquid A and B is less than the interaction between A–A system and
B–B system.
i.e. A–B
interactions < A–A interactions and B–B interactions.
Non-Ideal
Solution with Negative Deviation
The B set of solutions show a relationship where the vapour
pressure of solution observed is lesser than the vapour pressure of the
solution under ideal conditions i.e.
Ps (obs) < Psolution (ideal)
Ps < Pi.
Þ Ps < 
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A–B
interaction > A–A interaction and B–B interactions. Then
the heat energy released when A–B interaction take place will be more than
compared to the heat energy required for breaking the A–A interaction or B–B
interactions. Hence the net result is DHmix < 0 Þ DHmix = –ve and also DVmix < 0 Þ DVmix = –ve |
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8.5 Colligative Properties of Solution
Colligative properties are those which depend entirely upon the
number of particles of the solute contained in a known volume of a given
solvent and not at all upon mass and the nature (i.e., chemical composition or
constitution) of the solute. Here we shall consider four properties of solution
containing non volatile solutes.
8.5.1 Lowering in Vapour Pressure
When a non volatile
solute is present in the solution, the vapour pressure of the solution will be
less than vapour pressure of pure solvent.
Lowering in
vapour pressure is directly proportional to the mole fraction of solute.
The relative lowering in vapour pressure is equal to the mole
fraction of solute
= XB.
In
above discussion B is a non volatile solute and A is pure liquid. Let us
consider
(where ‘n’ and ‘N’ are moles of solute and
solvent respectively).
For
dilute solutions n << N, hence 
\ 
= Vapour
pressure of pure solvent
PS = Vapour pressure of
solutions
n = Moles of solute
N = Moles of solvent
W = Mass of solvent in grams
m = Molecular mass of solute
w = Mass of solute in grams
M = Molecular mass of solvent
8.5.2
Elevation in Boiling Point
When a liquid is heated then due to rise in temperature the liquid
vapourises and the vapour pressure increases. When the vapour pressure of the
liquid becomes equal to the atmospheric pressure, the liquid begins to boil.
The temperature at which the equilibrium vapour pressure of the liquid becomes
equal to the atmospheric pressure is called boiling point.
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When a non volatile solute is added to
the solvent the vapour pressure of the solvent in the solution decreases.
Consequently the solution has to be heated to a higher temperature to have its
vapour pressure equal to atmospheric pressure. Consider the graph of vapour pressure
verses temperature in Kelvin scale. |
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If
T0 is the boiling point of solvent and T1 is the boiling
point of solution, then
DTb
= Elevation in boiling point
= T1 - T0
DTb = Kb × m
Kb = Molal elevation constant
8.5.3 Depression in Freezing Point
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When a solvent is cooled, a temperature
is eventually reached at which solid begins to separate from the solution.
The temperature at which this separation begins is called freezing point of
solvent. At freezing point liquid and solid are
in equilibrium. At the freezing point the vapour
pressure of liquid and solid will be
same. |
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Additions of a
non-volatile solute, decreases the vapour pressure of pure liquid. Therefore
for a solid to have the same vapour pressure as the solution, the temperature
would lower down.
DTf = Kf × m
Kf = 
8.5.4 Osmotic Pressure
The
osmotic pressure may be defined as the excess pressure which must be applied to
a solution in order to prevent flow of solvent into the solution through the
semi permeable membrane.
Osmotic pressure is represented by p
pV = nRT
p = CRT
C = Concentration of the solution in moles
per litre
T = Temperature in K
R or S
= 0.0821 l atm deg–1 mole–1
8.6 Abnormal Behaviour of Solutions
Since the colligative properties of solutions, viz. lowering of
vapour pressure, elevation in boiling point, depression in freezing point and
osmotic pressure, depends solely on the number of solute particles present in
solution and not on their nature. Colligative properties of the solutes which
undergo dissociation (electrolytes) in solution would be higher than expected
for the normal substances (non-electrolytes).
8.6.1 Van’t Hoff Factor,
i
To account for the above anomalies, Van’t Hoff introduced a factor
‘i’ in the Van’t Hoff equation
(p V = RT) of osmotic pressure. The modified equation
may thus be written as pV = iRT
The factor ‘i’ was defined by the expression
\ 
Because colligative properties directly µ n
\ 
As we know, colligative properties µ
Hence ‘i' can also be defined as
When the Van’t Hoff factor is included then the colligative
properties get modified as follows:
(a) Relative Lowering in Vapour Pressure
= i ´ Xsolute
Where i = van’t Hoff factor
(b) Elevation in Boiling point
DTb = iKb m
(c) Depression in Freezing Point
DTf = iKf m.
(d) Osmotic Pressure
p = i CRT