NCERT Textbook - Solutions | NCERT Textbooks (Class 6 to Class 12) - CTET & State TET PDF Download

 Page 1


After studying this Unit, you will be
able to
• describe the formation of different
types of solutions;
• express concentration of solution
in different units;
• state and explain Henry’s law and
Raoult’s law;
• distinguish between ideal and
non-ideal solutions;
• explain deviations of real solutions
from Raoult’s law;
• describe colligative properties of
solutions and correlate these with
molar masses of the solutes;
• explain abnormal colligative
properties exhibited by some
solutes in solutions.
In normal life we rarely come across pure substances.
Most of these are mixtures containing two or more pure
substances. Their utility or importance in life depends
on their composition. For example, the properties of
brass (mixture of copper and zinc) are quite different
from those of German silver (mixture of copper, zinc
and nickel) or bronze (mixture of copper and tin);
1 part per million (ppm) of fluoride ions in water
prevents tooth decay, while 1.5 ppm causes the tooth
to become mottled and high concentrations of fluoride
ions can be poisonous (for example, sodium fluoride is
used in rat poison); intravenous injections are always
dissolved in water containing salts at particular ionic
concentrations that match with blood plasma
concentrations and so on.
In this Unit, we will consider mostly liquid
solutions and their formation. This will be followed by
studying the properties of the solutions, like vapour
pressure and colligative properties. We will begin with
types of solutions and then various alternatives in
which concentrations of a solute can be expressed in
liquid solution.
Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions
Almost all processes in body occur in some kind of liquid solutions.
Objectives
2.1 2.1 2.1 2.1 2.1 Types of Types of Types of Types of Types of
Solutions Solutions Solutions Solutions Solutions
2
Unit Unit Unit Unit Unit
2
Solutions are homogeneous mixtures of two or more than two
components. By homogenous mixture we mean that its composition
and properties are uniform throughout the mixture. Generally, 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 (i.e.,
Page 2


After studying this Unit, you will be
able to
• describe the formation of different
types of solutions;
• express concentration of solution
in different units;
• state and explain Henry’s law and
Raoult’s law;
• distinguish between ideal and
non-ideal solutions;
• explain deviations of real solutions
from Raoult’s law;
• describe colligative properties of
solutions and correlate these with
molar masses of the solutes;
• explain abnormal colligative
properties exhibited by some
solutes in solutions.
In normal life we rarely come across pure substances.
Most of these are mixtures containing two or more pure
substances. Their utility or importance in life depends
on their composition. For example, the properties of
brass (mixture of copper and zinc) are quite different
from those of German silver (mixture of copper, zinc
and nickel) or bronze (mixture of copper and tin);
1 part per million (ppm) of fluoride ions in water
prevents tooth decay, while 1.5 ppm causes the tooth
to become mottled and high concentrations of fluoride
ions can be poisonous (for example, sodium fluoride is
used in rat poison); intravenous injections are always
dissolved in water containing salts at particular ionic
concentrations that match with blood plasma
concentrations and so on.
In this Unit, we will consider mostly liquid
solutions and their formation. This will be followed by
studying the properties of the solutions, like vapour
pressure and colligative properties. We will begin with
types of solutions and then various alternatives in
which concentrations of a solute can be expressed in
liquid solution.
Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions
Almost all processes in body occur in some kind of liquid solutions.
Objectives
2.1 2.1 2.1 2.1 2.1 Types of Types of Types of Types of Types of
Solutions Solutions Solutions Solutions Solutions
2
Unit Unit Unit Unit Unit
2
Solutions are homogeneous mixtures of two or more than two
components. By homogenous mixture we mean that its composition
and properties are uniform throughout the mixture. Generally, 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 (i.e.,
34 Chemistry
Type of Solution Solute Solvent Common Examples
Gaseous Solutions Gas Gas Mixture of oxygen and nitrogen gases
Liquid Gas Chloroform mixed with nitrogen gas
Solid Gas Camphor in nitrogen gas
Liquid Solutions Gas Liquid Oxygen dissolved in water
Liquid Liquid Ethanol dissolved in water
Solid Liquid Glucose dissolved in water
Solid Solutions Gas Solid Solution of hydrogen in palladium
Liquid Solid Amalgam of mercury with sodium
Solid Solid Copper dissolved in gold
Table 2.1: Types of Solutions
consisting of two components). Here each component may be solid,
liquid or in gaseous state and are summarised in Table 2.1.
Composition of a solution can be described by expressing its
concentration. The latter can be expressed either qualitatively or
quantitatively. For example, qualitatively we can say that the solution
is dilute (i.e., relatively very small quantity of solute) or it is concentrated
(i.e., relatively very large quantity of solute). But in real life these kinds
of description can add to lot of confusion and thus the need for a
quantitative description of the solution.
There are several ways by which we can describe the concentration
of the solution quantitatively.
(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 
100
Total mass of the solution
(2.1)
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. Concentration described by
mass percentage is commonly used in industrial chemical
applications. For example, commercial bleaching solution contains
3.62 mass percentage of sodium hypochlorite in water.
(ii) Volume percentage (V/V): The volume percentage is defined as:
Volume % of a component = 
?
Volume of the component
100
Total volume of solution
(2.2)
2.2 2.2 2.2 2.2 2.2 Expressing Expressing Expressing Expressing Expressing
Concentration Concentration Concentration Concentration Concentration
of Solutions of Solutions of Solutions of Solutions of Solutions
Page 3


After studying this Unit, you will be
able to
• describe the formation of different
types of solutions;
• express concentration of solution
in different units;
• state and explain Henry’s law and
Raoult’s law;
• distinguish between ideal and
non-ideal solutions;
• explain deviations of real solutions
from Raoult’s law;
• describe colligative properties of
solutions and correlate these with
molar masses of the solutes;
• explain abnormal colligative
properties exhibited by some
solutes in solutions.
In normal life we rarely come across pure substances.
Most of these are mixtures containing two or more pure
substances. Their utility or importance in life depends
on their composition. For example, the properties of
brass (mixture of copper and zinc) are quite different
from those of German silver (mixture of copper, zinc
and nickel) or bronze (mixture of copper and tin);
1 part per million (ppm) of fluoride ions in water
prevents tooth decay, while 1.5 ppm causes the tooth
to become mottled and high concentrations of fluoride
ions can be poisonous (for example, sodium fluoride is
used in rat poison); intravenous injections are always
dissolved in water containing salts at particular ionic
concentrations that match with blood plasma
concentrations and so on.
In this Unit, we will consider mostly liquid
solutions and their formation. This will be followed by
studying the properties of the solutions, like vapour
pressure and colligative properties. We will begin with
types of solutions and then various alternatives in
which concentrations of a solute can be expressed in
liquid solution.
Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions
Almost all processes in body occur in some kind of liquid solutions.
Objectives
2.1 2.1 2.1 2.1 2.1 Types of Types of Types of Types of Types of
Solutions Solutions Solutions Solutions Solutions
2
Unit Unit Unit Unit Unit
2
Solutions are homogeneous mixtures of two or more than two
components. By homogenous mixture we mean that its composition
and properties are uniform throughout the mixture. Generally, 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 (i.e.,
34 Chemistry
Type of Solution Solute Solvent Common Examples
Gaseous Solutions Gas Gas Mixture of oxygen and nitrogen gases
Liquid Gas Chloroform mixed with nitrogen gas
Solid Gas Camphor in nitrogen gas
Liquid Solutions Gas Liquid Oxygen dissolved in water
Liquid Liquid Ethanol dissolved in water
Solid Liquid Glucose dissolved in water
Solid Solutions Gas Solid Solution of hydrogen in palladium
Liquid Solid Amalgam of mercury with sodium
Solid Solid Copper dissolved in gold
Table 2.1: Types of Solutions
consisting of two components). Here each component may be solid,
liquid or in gaseous state and are summarised in Table 2.1.
Composition of a solution can be described by expressing its
concentration. The latter can be expressed either qualitatively or
quantitatively. For example, qualitatively we can say that the solution
is dilute (i.e., relatively very small quantity of solute) or it is concentrated
(i.e., relatively very large quantity of solute). But in real life these kinds
of description can add to lot of confusion and thus the need for a
quantitative description of the solution.
There are several ways by which we can describe the concentration
of the solution quantitatively.
(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 
100
Total mass of the solution
(2.1)
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. Concentration described by
mass percentage is commonly used in industrial chemical
applications. For example, commercial bleaching solution contains
3.62 mass percentage of sodium hypochlorite in water.
(ii) Volume percentage (V/V): The volume percentage is defined as:
Volume % of a component = 
?
Volume of the component
100
Total volume of solution
(2.2)
2.2 2.2 2.2 2.2 2.2 Expressing Expressing Expressing Expressing Expressing
Concentration Concentration Concentration Concentration Concentration
of Solutions of Solutions of Solutions of Solutions of Solutions
35 Solutions
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. Solutions coxntaining liquids are commonly
expressed in this unit. For example, a 35% (v/v) solution of
ethylene glycol, an antifreeze, is used in cars for cooling the engine.
At this concentration the antifreeze lowers the freezing point of
water to 255.4K (–17.6°C).
(iii) Mass by volume percentage (w/V): Another unit 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.
(iv) 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 =
= 
6
Number of parts of the component
×10
Total number of parts of all components of the solution
(2.3)
As in the case of percentage, concentration in parts per million
can also be expressed as mass to mass, volume to volume and
mass to volume. A litre of sea water (which weighs 1030 g) contains
about 6 × 10
–3
 g of dissolved oxygen (O
2
). Such a small
concentration is also expressed as 5.8 g per 10
6
 g (5.8 ppm) of sea
water. The concentration of pollutants in water or atmosphere is
often expressed in terms of µg mL
–1
 or ppm.
(v) Mole fraction: Commonly used symbol for mole fraction is x and
subscript used on the right hand side of x denotes the component.
It is defined as:
Mole fraction of a component =
Number of moles of the component
Total number of moles of all the components
(2.4)
For example, in a binary mixture, if the number of moles of A and
B are n
A
 and n
B
 respectively, the mole fraction of A will be
x
A
 =
?
A
A B
 
n
nn
(2.5)
For a solution containing i number of components, we have:
x
i
 = 
?? ?
i
12 i
  
  .......
n
nn n
 = 
?
i
i
n
n
(2.6)
It can be shown that in a given solution sum of all the mole
fractions is unity, i.e.
x
1
 + x
2
 + .................. + x
i
 = 1 (2.7)
Mole fraction unit is very useful in relating some physical properties
of solutions, say vapour pressure with the concentration of the
solution and quite useful in describing the calculations involving
gas mixtures.
Page 4


After studying this Unit, you will be
able to
• describe the formation of different
types of solutions;
• express concentration of solution
in different units;
• state and explain Henry’s law and
Raoult’s law;
• distinguish between ideal and
non-ideal solutions;
• explain deviations of real solutions
from Raoult’s law;
• describe colligative properties of
solutions and correlate these with
molar masses of the solutes;
• explain abnormal colligative
properties exhibited by some
solutes in solutions.
In normal life we rarely come across pure substances.
Most of these are mixtures containing two or more pure
substances. Their utility or importance in life depends
on their composition. For example, the properties of
brass (mixture of copper and zinc) are quite different
from those of German silver (mixture of copper, zinc
and nickel) or bronze (mixture of copper and tin);
1 part per million (ppm) of fluoride ions in water
prevents tooth decay, while 1.5 ppm causes the tooth
to become mottled and high concentrations of fluoride
ions can be poisonous (for example, sodium fluoride is
used in rat poison); intravenous injections are always
dissolved in water containing salts at particular ionic
concentrations that match with blood plasma
concentrations and so on.
In this Unit, we will consider mostly liquid
solutions and their formation. This will be followed by
studying the properties of the solutions, like vapour
pressure and colligative properties. We will begin with
types of solutions and then various alternatives in
which concentrations of a solute can be expressed in
liquid solution.
Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions
Almost all processes in body occur in some kind of liquid solutions.
Objectives
2.1 2.1 2.1 2.1 2.1 Types of Types of Types of Types of Types of
Solutions Solutions Solutions Solutions Solutions
2
Unit Unit Unit Unit Unit
2
Solutions are homogeneous mixtures of two or more than two
components. By homogenous mixture we mean that its composition
and properties are uniform throughout the mixture. Generally, 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 (i.e.,
34 Chemistry
Type of Solution Solute Solvent Common Examples
Gaseous Solutions Gas Gas Mixture of oxygen and nitrogen gases
Liquid Gas Chloroform mixed with nitrogen gas
Solid Gas Camphor in nitrogen gas
Liquid Solutions Gas Liquid Oxygen dissolved in water
Liquid Liquid Ethanol dissolved in water
Solid Liquid Glucose dissolved in water
Solid Solutions Gas Solid Solution of hydrogen in palladium
Liquid Solid Amalgam of mercury with sodium
Solid Solid Copper dissolved in gold
Table 2.1: Types of Solutions
consisting of two components). Here each component may be solid,
liquid or in gaseous state and are summarised in Table 2.1.
Composition of a solution can be described by expressing its
concentration. The latter can be expressed either qualitatively or
quantitatively. For example, qualitatively we can say that the solution
is dilute (i.e., relatively very small quantity of solute) or it is concentrated
(i.e., relatively very large quantity of solute). But in real life these kinds
of description can add to lot of confusion and thus the need for a
quantitative description of the solution.
There are several ways by which we can describe the concentration
of the solution quantitatively.
(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 
100
Total mass of the solution
(2.1)
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. Concentration described by
mass percentage is commonly used in industrial chemical
applications. For example, commercial bleaching solution contains
3.62 mass percentage of sodium hypochlorite in water.
(ii) Volume percentage (V/V): The volume percentage is defined as:
Volume % of a component = 
?
Volume of the component
100
Total volume of solution
(2.2)
2.2 2.2 2.2 2.2 2.2 Expressing Expressing Expressing Expressing Expressing
Concentration Concentration Concentration Concentration Concentration
of Solutions of Solutions of Solutions of Solutions of Solutions
35 Solutions
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. Solutions coxntaining liquids are commonly
expressed in this unit. For example, a 35% (v/v) solution of
ethylene glycol, an antifreeze, is used in cars for cooling the engine.
At this concentration the antifreeze lowers the freezing point of
water to 255.4K (–17.6°C).
(iii) Mass by volume percentage (w/V): Another unit 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.
(iv) 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 =
= 
6
Number of parts of the component
×10
Total number of parts of all components of the solution
(2.3)
As in the case of percentage, concentration in parts per million
can also be expressed as mass to mass, volume to volume and
mass to volume. A litre of sea water (which weighs 1030 g) contains
about 6 × 10
–3
 g of dissolved oxygen (O
2
). Such a small
concentration is also expressed as 5.8 g per 10
6
 g (5.8 ppm) of sea
water. The concentration of pollutants in water or atmosphere is
often expressed in terms of µg mL
–1
 or ppm.
(v) Mole fraction: Commonly used symbol for mole fraction is x and
subscript used on the right hand side of x denotes the component.
It is defined as:
Mole fraction of a component =
Number of moles of the component
Total number of moles of all the components
(2.4)
For example, in a binary mixture, if the number of moles of A and
B are n
A
 and n
B
 respectively, the mole fraction of A will be
x
A
 =
?
A
A B
 
n
nn
(2.5)
For a solution containing i number of components, we have:
x
i
 = 
?? ?
i
12 i
  
  .......
n
nn n
 = 
?
i
i
n
n
(2.6)
It can be shown that in a given solution sum of all the mole
fractions is unity, i.e.
x
1
 + x
2
 + .................. + x
i
 = 1 (2.7)
Mole fraction unit is very useful in relating some physical properties
of solutions, say vapour pressure with the concentration of the
solution and quite useful in describing the calculations involving
gas mixtures.
36 Chemistry
Calculate the mole fraction of ethylene glycol (C
2
H
6
O
2
) in a solution
containing 20% of C
2
H
6
O
2
 by mass.
Assume that we have 100 g of solution (one can start with any amount of
solution because the results obtained will be the same). Solution will
contain 20 g of ethylene glycol and 80 g of water.
Molar mass of C
2
H
6
O
2
 = 12 × 2 + 1 × 6 + 16 × 2 = 62 g mol
–1
.
Moles of C
2
H
6
O
2
 = 
?1
20 g
62 g mol
= 0.322 mol
Moles of water = 
-1
80 g
18 g mol
 = 4.444 mol
?
?
262
glycol
262 2
moles of C H O
x
moles of C H O moles of H O
          
?
?
0.322mol
0.322mol 4.444 mol
 =  0.068
Similarly, 
??
?
water
4.444 mol 
0.932
0.322 mol  4.444 mol
x
Mole fraction of water can also be calculated as: 1 – 0.068 = 0.932
Example 2.1 Example 2.1 Example 2.1 Example 2.1 Example 2.1
(vi) Molarity: Molarity (M) is defined as number of moles of solute
dissolved in one litre (or one cubic decimetre) of solution,
?
Moles of solute
Molarity
Volume of solution in litre
(2.8)
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).
Example 2.2 Example 2.2 Example 2.2 Example 2.2 Example 2.2
Calculate the molarity of a solution containing 5 g of NaOH in 450 mL
solution.
Moles of NaOH = 
-1
5 g
40 g mol
 = 0.125 mol
Volume of the solution in litres = 450 mL / 1000 mL L
-1
Using equation (2.8),
Molarity = 
–1
0.125 mol × 1000 mL L
450 mL
 = 0.278 M
= 0.278 mol L
–1
= 0.278 mol dm
–3
Solution Solution Solution Solution Solution
Solution Solution Solution Solution Solution
Page 5


After studying this Unit, you will be
able to
• describe the formation of different
types of solutions;
• express concentration of solution
in different units;
• state and explain Henry’s law and
Raoult’s law;
• distinguish between ideal and
non-ideal solutions;
• explain deviations of real solutions
from Raoult’s law;
• describe colligative properties of
solutions and correlate these with
molar masses of the solutes;
• explain abnormal colligative
properties exhibited by some
solutes in solutions.
In normal life we rarely come across pure substances.
Most of these are mixtures containing two or more pure
substances. Their utility or importance in life depends
on their composition. For example, the properties of
brass (mixture of copper and zinc) are quite different
from those of German silver (mixture of copper, zinc
and nickel) or bronze (mixture of copper and tin);
1 part per million (ppm) of fluoride ions in water
prevents tooth decay, while 1.5 ppm causes the tooth
to become mottled and high concentrations of fluoride
ions can be poisonous (for example, sodium fluoride is
used in rat poison); intravenous injections are always
dissolved in water containing salts at particular ionic
concentrations that match with blood plasma
concentrations and so on.
In this Unit, we will consider mostly liquid
solutions and their formation. This will be followed by
studying the properties of the solutions, like vapour
pressure and colligative properties. We will begin with
types of solutions and then various alternatives in
which concentrations of a solute can be expressed in
liquid solution.
Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions Solutions
Almost all processes in body occur in some kind of liquid solutions.
Objectives
2.1 2.1 2.1 2.1 2.1 Types of Types of Types of Types of Types of
Solutions Solutions Solutions Solutions Solutions
2
Unit Unit Unit Unit Unit
2
Solutions are homogeneous mixtures of two or more than two
components. By homogenous mixture we mean that its composition
and properties are uniform throughout the mixture. Generally, 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 (i.e.,
34 Chemistry
Type of Solution Solute Solvent Common Examples
Gaseous Solutions Gas Gas Mixture of oxygen and nitrogen gases
Liquid Gas Chloroform mixed with nitrogen gas
Solid Gas Camphor in nitrogen gas
Liquid Solutions Gas Liquid Oxygen dissolved in water
Liquid Liquid Ethanol dissolved in water
Solid Liquid Glucose dissolved in water
Solid Solutions Gas Solid Solution of hydrogen in palladium
Liquid Solid Amalgam of mercury with sodium
Solid Solid Copper dissolved in gold
Table 2.1: Types of Solutions
consisting of two components). Here each component may be solid,
liquid or in gaseous state and are summarised in Table 2.1.
Composition of a solution can be described by expressing its
concentration. The latter can be expressed either qualitatively or
quantitatively. For example, qualitatively we can say that the solution
is dilute (i.e., relatively very small quantity of solute) or it is concentrated
(i.e., relatively very large quantity of solute). But in real life these kinds
of description can add to lot of confusion and thus the need for a
quantitative description of the solution.
There are several ways by which we can describe the concentration
of the solution quantitatively.
(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 
100
Total mass of the solution
(2.1)
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. Concentration described by
mass percentage is commonly used in industrial chemical
applications. For example, commercial bleaching solution contains
3.62 mass percentage of sodium hypochlorite in water.
(ii) Volume percentage (V/V): The volume percentage is defined as:
Volume % of a component = 
?
Volume of the component
100
Total volume of solution
(2.2)
2.2 2.2 2.2 2.2 2.2 Expressing Expressing Expressing Expressing Expressing
Concentration Concentration Concentration Concentration Concentration
of Solutions of Solutions of Solutions of Solutions of Solutions
35 Solutions
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. Solutions coxntaining liquids are commonly
expressed in this unit. For example, a 35% (v/v) solution of
ethylene glycol, an antifreeze, is used in cars for cooling the engine.
At this concentration the antifreeze lowers the freezing point of
water to 255.4K (–17.6°C).
(iii) Mass by volume percentage (w/V): Another unit 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.
(iv) 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 =
= 
6
Number of parts of the component
×10
Total number of parts of all components of the solution
(2.3)
As in the case of percentage, concentration in parts per million
can also be expressed as mass to mass, volume to volume and
mass to volume. A litre of sea water (which weighs 1030 g) contains
about 6 × 10
–3
 g of dissolved oxygen (O
2
). Such a small
concentration is also expressed as 5.8 g per 10
6
 g (5.8 ppm) of sea
water. The concentration of pollutants in water or atmosphere is
often expressed in terms of µg mL
–1
 or ppm.
(v) Mole fraction: Commonly used symbol for mole fraction is x and
subscript used on the right hand side of x denotes the component.
It is defined as:
Mole fraction of a component =
Number of moles of the component
Total number of moles of all the components
(2.4)
For example, in a binary mixture, if the number of moles of A and
B are n
A
 and n
B
 respectively, the mole fraction of A will be
x
A
 =
?
A
A B
 
n
nn
(2.5)
For a solution containing i number of components, we have:
x
i
 = 
?? ?
i
12 i
  
  .......
n
nn n
 = 
?
i
i
n
n
(2.6)
It can be shown that in a given solution sum of all the mole
fractions is unity, i.e.
x
1
 + x
2
 + .................. + x
i
 = 1 (2.7)
Mole fraction unit is very useful in relating some physical properties
of solutions, say vapour pressure with the concentration of the
solution and quite useful in describing the calculations involving
gas mixtures.
36 Chemistry
Calculate the mole fraction of ethylene glycol (C
2
H
6
O
2
) in a solution
containing 20% of C
2
H
6
O
2
 by mass.
Assume that we have 100 g of solution (one can start with any amount of
solution because the results obtained will be the same). Solution will
contain 20 g of ethylene glycol and 80 g of water.
Molar mass of C
2
H
6
O
2
 = 12 × 2 + 1 × 6 + 16 × 2 = 62 g mol
–1
.
Moles of C
2
H
6
O
2
 = 
?1
20 g
62 g mol
= 0.322 mol
Moles of water = 
-1
80 g
18 g mol
 = 4.444 mol
?
?
262
glycol
262 2
moles of C H O
x
moles of C H O moles of H O
          
?
?
0.322mol
0.322mol 4.444 mol
 =  0.068
Similarly, 
??
?
water
4.444 mol 
0.932
0.322 mol  4.444 mol
x
Mole fraction of water can also be calculated as: 1 – 0.068 = 0.932
Example 2.1 Example 2.1 Example 2.1 Example 2.1 Example 2.1
(vi) Molarity: Molarity (M) is defined as number of moles of solute
dissolved in one litre (or one cubic decimetre) of solution,
?
Moles of solute
Molarity
Volume of solution in litre
(2.8)
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).
Example 2.2 Example 2.2 Example 2.2 Example 2.2 Example 2.2
Calculate the molarity of a solution containing 5 g of NaOH in 450 mL
solution.
Moles of NaOH = 
-1
5 g
40 g mol
 = 0.125 mol
Volume of the solution in litres = 450 mL / 1000 mL L
-1
Using equation (2.8),
Molarity = 
–1
0.125 mol × 1000 mL L
450 mL
 = 0.278 M
= 0.278 mol L
–1
= 0.278 mol dm
–3
Solution Solution Solution Solution Solution
Solution Solution Solution Solution Solution
37 Solutions
Example 2.3 Example 2.3 Example 2.3 Example 2.3 Example 2.3
Solution Solution Solution Solution Solution
(vii) 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
(2.9)
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.
Each method of expressing concentration of the solutions has its
own merits and demerits. Mass %, ppm, mole fraction and molality
are independent of temperature, whereas molarity is a function of
temperature. This is because volume depends on temperature
and the mass does not.
Solubility of a substance is its maximum amount that can be dissolved
in a specified amount of solvent at a specified temperature. It depends
upon the nature of solute and solvent as well as temperature and
pressure. Let us consider the effect of these factors in solution of a solid
or a gas in a liquid.
2.3 Solubility 2.3 Solubility 2.3 Solubility 2.3 Solubility 2.3 Solubility
Calculate molality of 2.5 g of ethanoic acid (CH
3
COOH) in 75 g of benzene.
Molar mass of C
2
H
4
O
2
: 12 × 2 + 1 × 4 + 16 × 2 = 60 g mol
–1
Moles of C
2
H
4
O
2
 = 
1
2.5 g
60 g mol
 
 =  0.0417 mol
Mass of benzene in kg = 75 g/1000 g kg
–1
 = 75 × 10
–3
 kg
Molality of C
2
H
4
O
2 
= 
24 2
Moles of C H O
kg of benzene
 = 
1
0.0417 mol 1000 g kg 
75 g 
 
 
                            = 0.556 mol kg
–1
Intext Questions Intext Questions Intext Questions Intext Questions Intext Questions
2.1 Calculate the mass percentage of benzene (C
6
H
6
) and carbon tetrachloride
(CCl
4
) if 22 g of benzene is dissolved in 122 g of carbon tetrachloride.
2.2 Calculate the mole fraction of benzene in solution containing 30% by
mass in carbon tetrachloride.
2.3 Calculate the molarity of each of the following solutions: (a) 30 g of
Co(NO
3
)
2
. 6H
2
O in 4.3 L of solution (b) 30 mL of 0.5 M H
2
SO
4
 diluted to
500 mL.
2.4 Calculate the mass of urea (NH
2
CONH
2
) required in making 2.5 kg of
0.25 molal aqueous solution.
2.5 Calculate (a) molality (b) molarity and (c) mole fraction of KI if the density
of 20% (mass/mass) aqueous KI is 1.202 g mL
-1
.