136 CHEMISTRY
UNIT 5
After studying this unit you will be
able to
•
explain the existence of differ
ent
states of matter in terms of
balance between intermolecular
forces and thermal energy of
particles;
•
explain the laws governing
behaviour of ideal gases;
•
apply gas laws in various r
eal life
situations;
•
explain the behaviour of real
gases;
•
describe the conditions required
for liquifaction of gases;
•
realise that there is continuity in
gaseous and liquid state;
•
differentiate between gaseous
state and vapours; and
•
explain properties of liquids in
terms of intermolecular
attractions.
STATES OF MATTER
INTRODUCTION
In previous units we have learnt about the properties
related to single particle of matter, such as atomic size,
ionization enthalpy, electronic charge density, molecular
shape and polarity, etc. Most of the observable
characteristics of chemical systems with which we are
familiar represent bulk properties of matter, i.e., the
properties associated with a collection of a large number
of atoms, ions or molecules. For example, an individual
molecule of a liquid does not boil but the bulk boils.
Collection of water molecules have wetting properties;
individual molecules do not wet. Water can exist as ice,
which is a solid; it can exist as liquid; or it can exist in
the gaseous state as water vapour or steam. Physical
properties of ice, water and steam ar
e very different. In
all the three states of water chemical composition of water
remains the same i.e., H
2
O. Characteristics of the three
states of water depend on the energies of molecules and
on the manner in which water molecules aggregate. Same
is true for other substances also.
Chemical properties of a substance do not change with
the change of its physical state; but rate of chemical
reactions do depend upon the physical state. Many times
in calculations while dealing with data of experiments we
require knowledge of the state of matter. Therefore, it
becomes necessary for a chemist to know the physical
The snowflake falls, yet lays not long
Its feath’ry grasp on Mother Earth
Ere Sun returns it to the vapors Whence it came,
Or to waters tumbling down the rocky slope.
Rod O’ Connor
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137STATES OF MATTER
laws which govern the behaviour of matter in
different states. In this unit, we will learn
more about these three physical states of
matter particularly liquid and gaseous states.
To begin with, it is necessary to understand
the nature of intermolecular forces, molecular
interactions and effect of thermal energy on
the motion of particles because a balance
between these determines the state of a
substance.
5.1 INTERMOLECULAR FORCES
Intermolecular forces are the forces of
attraction and repulsion between interacting
particles (atoms and molecules). This term
does not include the electr
ostatic forces that
exist between the two oppositely charged ions
and the forces that hold atoms of a molecule
together i.e., covalent bonds.
Attractive intermolecular forces are known
as van der Waals forces, in honour of Dutch
scientist Johannes van der Waals (1837-
1923), who explained the deviation of real
gases from the ideal behaviour through these
forces. We will learn about this later in this
unit. van der Waals forces vary considerably
in magnitude and include dispersion forces
or London forces, dipole-dipole forces, and
dipole-induced dipole forces. A particularly
strong type of dipole-dipole interaction is
hydrogen bonding. Only a few elements can
participate in hydrogen bond formation,
therefore it is treated as a separate
category. We have already learnt about this
interaction in Unit 4.
At this point, it is important to note that
attractive forces between an ion and a dipole
are known as ion-dipole forces and these are
not van der Waals forces. We will now learn
about different types of van der Waals forces.
5.1.1 Dispersion Forces or London Forces
Atoms and nonpolar molecules are electrically
symmetrical and have no dipole moment
because their electronic charge cloud is
symmetrically distributed. But a dipole may
develop momentarily even in such atoms and
molecules. This can be understood as follows.
Suppose we have two atoms ‘A’ and ‘B’ in the
close vicinity of each other (Fig. 5.1a). It may
so happen that momentarily electronic charge
distribution in one of the atoms, say ‘A’,
becomes unsymmetrical i.e., the charge cloud
is more on one side than the other (Fig. 5.1 b
and c). This results in the development of
instantaneous dipole on the atom ‘A’ for a very
short time. This instantaneous or transient
dipole distorts the electron density of the
other atom ‘B’, which is close to it and as a
consequence a dipole is induced in the
atom ‘B’.
The temporary dipoles of atom ‘A’ and ‘B’
attract each other. Similarly temporary dipoles
are induced in molecules also. This force of
attraction was first proposed by the German
physicist Fritz London, and for this reason
force of attraction between two temporary
Fig. 5.1 Dispersion forces or London forces
between atoms.
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138 CHEMISTRY
dipoles is known as London force. Another
name for this force is dispersion force. These
forces are always attractive and interaction
energy is inversely proportional to the sixth
power of the distance between two interacting
particles (i.e., 1/r
6
where r is the distance
between two particles). These forces are
important only at short distances (~500 pm)
and their magnitude depends on the
polarisability of the particle.
5.1.2 Dipole - Dipole Forces
Dipole-dipole forces act between the molecules
possessing permanent dipole. Ends of the
dipoles possess “partial charges” and these
charges are shown by Greek letter delta (δ).
Partial char
ges are always less than the unit
electronic charge (1.6×10
–19
C). The polar
molecules interact with neighbouring
molecules. Fig 5.2 (a) shows electron cloud
distribution in the dipole of hydrogen chloride
and Fig. 5.2 (b) shows dipole-dipole interaction
between two HCl molecules. This interaction
is stronger than the London forces but is
weaker than ion-ion interaction because only
partial charges are involved. The attractive
force decreases with the increase of distance
between the dipoles. As in the above case here
also, the interaction energy is inversely
proportional to distance between polar
molecules. Dipole-dipole interaction energy
between stationary polar molecules (as in
solids) is proportional to 1/r
3
and that
between rotating polar molecules is
proportional to 1/r
6
, where r is the distance
between polar molecules. Besides dipole-
dipole interaction, polar molecules can
interact by London forces also. Thus
cumulative effect is that the total of
intermolecular forces in polar molecules
increase.
5.1.3 Dipole–Induced Dipole Forces
This type of attractive forces operate between
the polar molecules having permanent dipole
and the molecules lacking permanent dipole.
Permanent dipole of the polar molecule
induces dipole on the electrically neutral
molecule by deforming its electronic cloud
(Fig. 5.3). Thus an induced dipole is developed
in the other molecule. In this case also
interaction energy is proportional to 1/r
6
where r is the distance between two
molecules. Induced dipole moment depends
upon the dipole moment present in the
permanent dipole and the polarisability of the
electrically neutral molecule. We have already
learnt in Unit 4 that molecules of lar
ger size
can be easily polarized. High polarisability
increases the strength of attractive
interactions.
Fig. 5.2 (a) Distribution of electron cloud in HCl –
a polar molecule, (b) Dipole-dipole
interaction between two HCl molecules
Fig. 5.3 Dipole - induced dipole interaction
between permanent dipole and induced
dipole
In this case also cumulative effect of
dispersion forces and dipole-induced dipole
interactions exists.
5.1.4 Hydrogen bond
As already mentioned in section (5.1); this is
special case of dipole-dipole interaction. We
have already learnt about this in Unit 4. This
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139STATES OF MATTER
is found in the molecules in which highly polar
N–H, O–H or H–F bonds are present. Although
hydrogen bonding is regarded as being limited
to N, O and F; but species such as
Cl
may
also participate in hydrogen bonding. Energy
of hydrogen bond varies between 10 to 100
kJ mol
–1
. This is quite a significant amount of
energy; therefore, hydrogen bonds are
powerful force in determining the structure and
properties of many compounds, for example
proteins and nucleic acids. Strength of the
hydrogen bond is determined by the coulombic
interaction between the lone-pair electrons of
the electronegative atom of one molecule and
the hydrogen atom of other molecule.
Following diagram shows the formation of
hydrogen bond.
H F H F
δ δ δ δ+ − + −
− ⋅⋅⋅ −
Intermolecular forces discussed so far are
all attractive. Molecules also exert repulsive
forces on one another. When two molecules
are brought into close contact with each other,
the repulsion between the electron clouds and
that between the nuclei of two molecules comes
into play. Magnitude of the repulsion rises very
rapidly as the distance separating the
molecules decreases. This is the reason that
liquids and solids are hard to compress. In
these states molecules are already in close
contact; therefore they resist further
compression; as that would result in the
increase of repulsive interactions.
5.2 THERMAL ENERGY
Thermal energy is the energy of a body arising
from motion of its atoms or molecules. It is
directly proportional to the temperature of the
substance. It is the measure of average
kinetic energy of the particles of the matter
and is thus responsible for movement of
particles. This movement of particles is called
thermal motion.
5.3 INTERMOLECULAR FORCES vs
THERMAL INTERACTIONS
We have already learnt that intermolecular
forces tend to keep the molecules together but
thermal energy of the molecules tends to keep
them apart. Three states of matter are the result
of balance between intermolecular forces and
the thermal energy of the molecules.
When molecular interactions are very
weak, molecules do not cling together to make
liquid or solid unless thermal energy is
reduced by lowering the temperature. Gases
do not liquify on compression only, although
molecules come very close to each other and
intermolecular forces operate to the maximum.
However, when thermal energy of molecules
is reduced by lowering the temperature; the
gases can be very easily liquified.
Predominance of thermal energy and the
molecular interaction ener
gy of a substance
in three states is depicted as follows :
We have already learnt the cause for the
existence of the three states of matter. Now
we will learn more about gaseous and liquid
states and the laws which govern the
behaviour of matter in these states. We shall
deal with the solid state in class XII.
5.4 THE GASEOUS STATE
This is the simplest state of matter.
Throughout our life we remain immersed in
the ocean of air which is a mixture of gases.
We spend our life in the lowermost layer of
the atmosphere called troposphere, which is
held to the surface of the earth by gravitational
force. The thin layer of atmosphere is vital to
our life. It shields us from harmful radiations
and contains substances like dioxygen,
dinitrogen, carbon dioxide, water vapour, etc.
Let us now focus our attention on the
behaviour of substances which exist in the
gaseous state under normal conditions of
temperature and pressure. A look at the
periodic table shows that only eleven elements
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140 CHEMISTRY
exist as gases under normal conditions
(Fig 5.4).
The gaseous state is characterized by the
following physical properties.
• Gases are highly compressible.
• Gases exert pr
essure equally in all
directions.
• Gases have much lower density than the
solids and liquids.
• The volume and the shape of gases are
not fixed. These assume volume and shape
of the container.
• Gases mix evenly and completely in all
proportions without any mechanical aid.
Simplicity of gases is due to the fact that
the forces of interaction between their
molecules are negligible. Their behaviour is
governed by same general laws, which were
discovered as a result of their experimental
studies. These laws are relationships between
measurable properties of gases. Some of these
properties like pressure, volume, temperature
and mass are very important because
relationships between these variables describe
state of the gas. Interdependence of these
variables leads to the formulation of gas laws.
In the next section we will learn about gas
laws.
5.5 THE GAS LAWS
The gas laws which we will study now are the
result of research carried on for several
centuries on the physical properties of gases.
The first reliable measurement on properties
of gases was made by Anglo-Irish scientist
Robert Boyle in 1662. The law which he
formulated is known as Boyle’s Law. Later
on attempts to fly in air with the help of hot
air balloons motivated Jaccques Charles and
Joseph Lewis Gay Lussac to discover
additional gas laws. Contribution from
Avogadro and others provided lot of
information about gaseous state.
5.5.1 Boyle’s Law (Pressure - Volume
Relationship)
On the basis of his experiments, Robert Boyle
reached to the conclusion that at constant
temperature, the pressure of a fixed
amount (i.e., number of moles n) of gas
varies inversely with its volume. This is
known as Boyle’s law. Mathematically, it can
be written as
p
V
1
∝
( at constant T and n) (5.1)
⇒ p
V
= k
1
1
(5.2)
where k
1
is the proportionality constant. The
value of constant k
1
depends upon the
amount of the gas, temperature of the gas
and the units in which p and V are expressed.
On rearranging equation (5.2) we obtain
pV = k
1
(5.3)
It means that at constant temperatur
e,
product of pressure and volume of a fixed
amount of gas is constant.
If a fixed amount of gas at constant
temperature T occupying volume V
1
at
pressure p
1
undergoes expansion, so that
volume becomes V
2
and pressure becomes p
2
,
then according to Boyle’s law :
p
1
V
1
= p
2
V
2
= constant (5.4)
⇒
p
p
V
V
1
2
2
1
=
(5.5)
Fig. 5.4 Eleven elements that exist as gases
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141STATES OF MATTER
Figure 5.5 shows two conventional ways
of graphically presenting Boyle’s law.
Fig. 5.5 (a) is the graph of equation (5.3) at
different temperatures. The value of k
1
for each
curve is different because for a given mass of
gas, it varies only with temperature. Each
curve corresponds to a different constant
temperature and is known as an isotherm
(constant temperature plot). Higher curves
correspond to higher temperature. It should
be noted that volume of the gas doubles if
pressure is halved. Table 5.1 gives effect of
pressure on volume of 0.09 mol of CO
2
at
300 K.
Fig 5.5 (b) represents the graph between p
and
1
V
. It is a straight line passing through
origin. However at high pressures, gases
deviate from Boyle’s law and under such
conditions a straight line is not obtained in the
graph.
Experiments of Boyle, in a quantitative
manner prove that gases are highly
compressible because when a given mass of a
gas is compressed, the same number of
molecules occupy a smaller space. This means
that gases become denser at high pressure. A
relationship can be obtained between density
and pressure of a gas by using Boyle’s law:
By definition, density ‘d’ is related to the
mass ‘m’ and the volume ‘
V’ by the relation
d
V
=
m
. If we put value of V in this equation
from Boyle’s law equation, we obtain the
relationship.
Pressure/10
4
Pa Volume/10
–3
m
3
(1/V )/m
–3
pV/10
2
Pa m
3
2.0 112.0 8.90 22.40
2.5 89.2 11.2 22.30
3.5 64.2 15.6 22.47
4.0 56.3 17.7 22.50
6.0 37.4 26.7 22.44
8.0 28.1 35.6 22.48
10.0 22.4 44.6 22.40
Table 5.1 Effect of Pressure on the Volume of 0.09 mol CO
2
Gas at 300 K.
Fig. 5.5 (b) Graph of pressure of a gas, p vs.
1
V
Fig. 5.5(a) Graph of pressure, p vs. Volume, V of
a gas at different temperatures.
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142 CHEMISTRY
d =
m
k
1
p = k
′
p
This shows that at a constant temperature,
pressure is directly proportional to the density
of a fixed mass of the gas.
Problem 5.1
A balloon is filled with hydrogen at room
temperature. It will burst if pressure
exceeds 0.2 bar. If at 1 bar pressure the
gas occupies 2.27 L volume, upto what
volume can the balloon be expanded ?
Solution
According to Boyle’s Law p
1
V
1
= p
2
V
2
If p
1
is 1 bar, V
1
will be 2.27 L
If p
2
= 0.2 bar, then
V
p V
p
2
1 1
2
=
⇒ =
×
V
2
1 2 27
0 2
bar L
bar
.
.
=11.35 L
Since balloon bursts at 0.2 bar pressure,
the volume of balloon should be less than
11.35 L.
5.5.2 Charles’ Law (Temperature - Volume
Relationship)
Charles and Gay Lussac performed several
experiments on gases independently to
improve upon hot air balloon technology.
Their investigations showed that for a fixed
mass of a gas at constant pressure, volume
of a gas increases on increasing temperature
and decreases on cooling. They found that
for each degree rise in temperature, volume
of a gas increases by
1
273.15
of the original
volume of the gas at 0
°
C. Thus if volumes of
the gas at 0
°
C and at t
°
C are V
0
and V
t
respectively, then
V V V
V V
t 0 0
t 0
= +
t
273.15
=
t
273.15
⇒ +
1
⇒
V V
t 0
=
273.15+ t
273.15
(5.6)
At this stage, we define a new scale of
temperature such that t
°
C on new scale is given
by T = 273.15 + t and 0
°
C will be given by
T
0
= 273.15. This new temperature scale is
called the Kelvin temperature scale or
Absolute temperature scale.
Thus 0
°
C on the celsius scale is equal to
273.15 K at the absolute scale. Note that
degree sign is not used while writing the
temperature in absolute temperatur
e scale,
i.e., Kelvin scale. Kelvin scale of temperatur
e
is also called Thermodynamic scale of
temperature and is used in all scientific
works.
Thus we add 273 (mor
e precisely 273.15)
to the celsius temperature to obtain
temperature at Kelvin scale.
If we write T
t
= 273.15 + t and T
0
= 273.15
in the equation (5.6) we obtain the
relationship
V V
T
T
t 0
t
0
=
⇒
V
V
T
T
t
0
t
=
0
(5.7)
Thus we can write a general equation as
follows.
V
V
T
T
2
1
2
1
=
(5.8)
⇒ =
V
T
V
T
1
1
2
2
⇒
V
T
= =constant k
2
(5.9)
Thus V = k
2
T (5.10)
The value of constant k
2
is determined by
the pressure of the gas, its amount and the
units in which volume V is expressed.
Equation (5.10) is the mathematical
expression for Charles’ law, which states that
pressure remaining constant, the volume
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143STATES OF MATTER
of a fixed mass of a gas is directly
proportional to its absolute temperature.
Charles found that for all gases, at any given
pressure, graph of volume vs temperature (in
celsius) is a straight line and on extending to
zero volume, each line intercepts the
temperature axis at – 273.15
°
C. Slopes of
lines obtained at different pressure are
differ
ent but at zero volume all the lines meet
the temperature axis at – 273.15
°
C (Fig. 5.6).
Each line of the volume vs temperature
graph is called isobar.
Observations of Charles can be interpreted
if we put the value of t in equation (5.6) as
– 273.15
°
C. We can see that the volume of
the gas at – 273.15
°
C will be zero. This means
that gas will not exist. In fact all the gases get
liquified before this temperature is reached.
The lowest hypothetical or imaginary
temperature at which gases are supposed to
occupy zero volume is called Absolute zero.
All gases obey Charles’ law at very low
pressures and high temperatures.
Problem 5.2
On a ship sailing in Pacific Ocean where
temperature is 23.4
°
C, a balloon is filled
with 2 L air. What will be the volume of
the balloon when the ship reaches Indian
ocean, where temperature is 26.1
°
C ?
Solution
V
1
= 2 L T
2
= 26.1 + 273
T
1
= (23.4 + 273) K = 299.1 K
= 296.4 K
From Charles law
V
V
1
1
2
2
2
1 2
1
2
2 299 1
296 4
T
V
T
V
V T
T
=
⇒ =
⇒ =
×L K
K
.
.
= 2L × 1.009
= 2.018L
Fig. 5.6 Volume vs Temperature (
°
C) graph
5.5.3 Gay Lussac’s Law (Pressure-
Temperature Relationship)
Pressure in well inflated tyres of automobiles
is almost constant, but on a hot summer day
this increases considerably and tyre may
burst if pressure is not adjusted properly.
During winters, on a cold morning one may
find the pressure in the tyres of a vehicle
decreased considerably. The mathematical
relationship between pressure and
temperature was given by Joseph Gay Lussac
and is known as Gay Lussac’s law. It states
that at constant volume, pressure of a fixed
amount of a gas varies directly with the
temperature. Mathematically,
p T
p
T
∝
⇒ = constant = k
3
This relationship can be derived from
Boyle’s law and Charles’ Law. Pressure vs
temperature (Kelvin) graph at constant molar
volume is shown in Fig. 5.7. Each line of this
graph is called isochore.
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144 CHEMISTRY
5.5.4 Avogadro Law (Volume - Amount
Relationship)
In 1811 Italian scientist Amedeo Avogadro
tried to combine conclusions of Dalton’s atomic
theory and Gay Lussac’s law of combining
volumes (Unit 1) which is now known as
Avogadro law. It states that equal volumes
of all gases under the same conditions of
temperature and pressure contain equal
number of molecules. This means that as
long as the temperature and pressure remain
constant, the volume depends upon number
of molecules of the gas or in other words
amount of the gas. Mathematically we can write
V n∝
where n is the number of moles
of the gas.
⇒ =V nk
4
(5.11)
The number of molecules in one mole of a
gas has been determined to be 6.022 ×10
23
and
is known as Avogadro constant. You
will find that this is the same number which
Fig. 5.7 Pressure vs temperature (K) graph
(Isochores) of a gas.
we came across while discussing definition of
a ‘mole’ (Unit 1).
Since volume of a gas is directly
proportional to the number of moles; one mole
of each gas at standard temperature and
pressure (STP)* will have same volume.
Standard temperature and pressure means
273.15 K (0°C) temperature and 1 bar (i.e.,
exactly 10
5
pascal) pressure. These
values approximate freezing temperature
of water and atmospheric pressure at sea
level. At STP molar volume of an ideal gas
or a combination of ideal gases is
22.71098 L mol
–1
.
Molar volume of some gases is given in
(Table 5.2).
Argon 22.37
Carbon dioxide 22.54
Dinitrogen 22.69
Dioxygen 22.69
Dihydrogen 22.72
Ideal gas 22.71
Table 5.2 Molar volume in litres per mole of
some gases at 273.15 K and 1 bar
(STP).
Number of moles of a gas can be calculated
as follows
n =
m
M
(5.12)
Where m = mass of the gas under
investigation and M = molar mass
Thus,
V = k
4
m
M
(5.13)
Equation (5.13) can be rearranged as
follows :
M = k
4
m
M
= k
4
d (5.14)
The previous standard is still often used, and applies to all chemistry data more than decade old. In this definition STP
denotes the same temperature of 0°C (273.15 K), but a slightly higher pressure of 1 atm (101.325 kPa). One mole of any gas
of a combination of gases occupies 22.413996 L of volume at STP.
Standard ambient temperature and pressure (SATP), conditions are also used in some scientific works. SATP conditions
means 298.15 K and 1 bar (i.e., exactly 10
5
Pa). At SATP (1 bar and 298.15 K), the molar volume of an ideal gas is
24.789 L mol
–1
.
*
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145STATES OF MATTER
Here ‘d’ is the density of the gas. We can conclude
from equation (5.14) that the density of a gas is
directly proportional to its molar mass.
A gas that follows Boyle’s law, Charles’ law
and Avogadro law strictly is called an ideal
gas. Such a gas is hypothetical. It is assumed
that intermolecular forces are not present
between the molecules of an ideal gas. Real
gases follow these laws only under certain
specific conditions when forces of interaction
are practically negligible. In all other situations
these deviate from ideal behaviour. You will
learn about the deviations later in this unit.
5.6 IDEAL GAS EQUATION
The three laws wh
ich we have learnt till now
can be combined together in a single equation
which is known as ideal gas equation.
At constant T and n; V
∝
1
p
Boyle’s Law
At constant p and n; V
∝
T Charles’ Law
At constant p and T ; V
∝
n Avogadro Law
Thus,
V
n
∝
T
p
(5.15)
⇒ V
n
= R
T
p
(5.16)
where R is proportionality constant. On
rearranging the equation (5.16) we obtain
pV = n RT (5.17)
⇒ R =
pV
Tn
(5.18)
R is called gas constant. It is same for all gases.
Therefore it is also called Universal Gas
Constant. Equation (5.17) is called ideal gas
equation.
Equation (5.18) shows that the value of
R depends upon units in which p, V and T
are measured. If three variables in this
equation are known, fourth can be
calculated. From this equation we can see
that at constant temperature and pressure
n moles of any gas will have the same volume
because
V
n T
=
R
p
and n,R,T and p are
constant. This equation will be applicable to
any gas, under those conditions when
behaviour of the gas approaches ideal
behaviour. V
olume of one mole of an ideal
gas under STP conditions (273.15 K and 1
bar pressure) is 22.710981 L mol
–1
. Value
of R for one mole of an ideal gas can be
calculated under these conditions
as follows :
= 8.314 Pa m
3
K
–1
mol
–1
= 8.314 × 10
–2
bar L K
–1
mol
–1
= 8.314 J K
–1
mol
–1
At STP conditions used earlier
(0
°
C and 1 atm pressure), value of R is
8.20578 × 10
–2
L atm K
–1
mol
–1
.
Ideal gas equation is a relation between
four variables and it describes the state of
any gas, therefore, it is also called
equation
of state.
Let us now go back to the ideal gas
equation. This is the relationship for the
simultaneous variation of the variables. If
temperature, volume and pressure of a fixed
amount of gas vary from T
1
, V
1
and p
1
to T
2
,
V
2
and p
2
then we can write
p V
T
n
p V
T
n
1 1
1
2 2
2
= R and = R
⇒
p V
T
p V
T
1 1
1
2 2
2
=
(5.19)
Equation (5.19) is a very useful equation.
If out of six, values of five variables are known,
the value of unknown variable can be
calculated from the equation (5.19). This
equation is also known as Combined gas law.
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146 CHEMISTRY
Problem 5.3
At 25°C and 760 mm of Hg pressure a
gas occupies 600 mL volume. What will
be its pressure at a height where
temperature is 10°C and volume of the
gas is 640 mL.
Solution
p
1
= 760 mm Hg, V
1
= 600 mL
T
1
= 25 + 273 = 298 K
V
2
= 640 mL and T
2
= 10 + 273 = 283 K
According to Combined gas law
p V
T
p V
T
p
1 1
1
2 2
2
2
1 1 2
1 2
2
760 600 283
64
=
⇒ =
⇒ =
(
)
×
(
)
×
(
)
p
p V
T V
mm mL K
T
Hg
00 298
676 6
mL K
mm Hg
(
)
×
(
)
= .
by the mixture of non-reactive gases is
equal to the sum of the partial pressures
of individual gases i.e., the pressures which
these gases would exert if they were enclosed
separately in the same volume and under the
same conditions of temperature. In a mixture
of gases, the pressure exerted by the individual
gas is called partial pressure. Mathematically,
p
Total
= p
1
+p
2
+p
3
+......(at constant T, V) (5.23)
where p
Total
is the total pressure exerted by
the mixture of gases and p
1
, p
2
, p
3
etc. are
partial pressures of gases.
Gases are generally collected over water
and therefore are moist. Pressure of dry gas
can be calculated by subtracting vapour
pressure of water from the total pressure of
the moist gas which contains water vapours
also. Pressure exerted by saturated water
vapour is called aqueous tension
. Aqueous
tension of water at different temperatures is
given in Table 5.3.
p
Dry gas
= p
Total
– Aqueous tension (5.24)
Table 5.3 Aqueous Tension of Water (Vapour
Pressure) as a Function of
Temperature
Partial pressure in terms of mole fraction
Suppose at the temperature T, three gases,
enclosed in the volume V, exert partial
pressure p
1
, p
2
and p
3
respectively, then,
p
n T
V
1
=
1
R
(5.25)
p
n T
V
2
=
2
R
(5.26)
5.6.1 Density and Molar Mass of a
Gaseous Substance
Ideal gas equation can be rearranged as follows:
n
V
p
T
=
R
Replacing n by
m
M
, we get
m
M
=
RV
p
T
(5.20)
d
M
=
R
p
T
(where d is the density) (5.21)
On rearranging equation (5.21) we get the
relationship for calculating molar mass of a gas.
M =
d T
p
R
(5.22)
5.6.2 Dalton’s Law of Partial Pressures
The law was formulated by John Dalton in
1801. It states that the total pressure exerted
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147STATES OF MATTER
p
n T
V
3
=
3
R
(5.27)
where n
1
n
2
and n
3
are number of moles of these
gases. Thus, expression for total pressure will be
p
Total
= p
1
+ p
2
+ p
3
=
R R R
1 2 3
n
T
V
n
T
V
n
T
V
+ +
= (n
1
+ n
2
+ n
3
)
RT
V
(5.28)
On dividing
p
1
by
p
total
we get
p
p
n
n n n
TV
TV
1
total
1
1 2 3
=
+ +
R
R
=
+ +
= =
1
1 2 3
1
n
n n n
n
n
1
x
where n = n
1
+n
2
+n
3
x
1
is called mole fraction of first gas.
Thus, p
1
= x
1
p
total
Similarly for other two gases we can write
p
2
= x
2
p
total
and p
3
= x
3
p
total
Thus a general equation can be written as
p
i
= x
i
p
total
(5.29)
where p
i
and x
i
are partial pressure and mole
fraction of i
th
gas respectively. If total pressure
of a mixture of gases is known, the equation
(5.29) can be used to find out pressure exerted
by individual gases.
Number of moles of neon
=
167 5
20
1
. g
g mol
−
= 8.375 mol
Mole fraction of dioxygen
=
=
=
2 21
2 21 8 375
2 21
10 585
0 21
.
. .
.
.
.
+
5.7 KINETIC ENERGY AND MOLECULAR
SPEEDS
Molecules of gases remain in continuous
motion. While moving they collide with each
other and with the walls of the container. This
results in change of their speed and
redistribution of energy. So the speed and
energy of all the molecules of the gas at any
instant are not the same. Thus, we can obtain
only average value of speed of molecules. If
there are n number of molecules in a sample
and their individual speeds are u
1
, u
2
, …….u
n
,
then average speed of molecules u
av
can be
calculated as follows:
u
u u u
n
av
n
=
+ +1 2 .........
Problem 5.4
A neon-dioxygen mixture contains
70.6 g dioxygen and 167.5 g neon. If
pressure of the mixture of gases in the
cylinder is 25 bar. What is the partial
pressure of dioxygen and neon in the
mixture ?
Number of moles of dioxygen
=
70 6
32
1
. g
g mol
−
= 2.21 mol
Mole fraction of neon
=
8 375
2 21 8 375
.
. .+
= 0.79
Alternatively,
mole fraction of neon = 1– 0.21 = 0.79
Partial pressure = mole fraction ×
of a gas total pressure
⇒ Partial pressure = 0.21 × (25 bar)
of oxygen = 5.25 bar
Partial pressure = 0.79 × (25 bar)
of neon = 19.75 bar
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148 CHEMISTRY
Maxwell and Boltzmann have shown that
actual distribution of molecular speeds
depends on temperature and molecular mass
of a gas. Maxwell derived a formula for
calculating the number of molecules
possessing a particular speed. Fig. 5.8 shows
schematic plot of number of molecules vs.
molecular speed at two different temperatures
T
1
and T
2
(T
2
is higher than
T
1
). The
distribution of speeds shown in the plot is
called Maxwell-Boltzmann distribution
of speeds.
the molecular speed distribution curve of
chlorine and nitrogen given in Fig. 5.9.
Though at a particular temperature the
individual speed of molecules keeps
changing, the distribution of speeds remains
same.
The graph shows that number of molecules
possessing very high and very low speed is very
small. The maximum in the curve represents
speed possessed by maximum number of
molecules. This speed is called most
probable speed, u
mp
.
This is very close to the
average speed of the molecules. On
increasing the temperature most probable
speed increases. Also, speed distribution
curve broadens at higher temperature.
Broadening of the curve shows that number
of molecules moving at higher speed
increases. Speed distribution also depends
upon mass of molecules. At the same
temperature, gas molecules with heavier
mass have slower speed than lighter gas
molecules. For example, at the same
temperature lighter nitrogen molecules move
faster than heavier chlorine molecules.
Hence, at any given temperature, nitrogen
molecules have higher value of most probable
speed than the chlorine molecules. Look at
Fig. 5.8: Maxwell-Boltzmann distribution of speeds
Fig. 5.9: Distribution of molecular speeds for chlorine
and nitrogen at 300 K
We know that kinetic energy of a particle is
given by the expression:
Kinetic Energy mu =
1
2
2
Therefore, if we want to know average
translational kinetic energy,
1
2
2
mu
, for the
movement of a gas particle in a straight line,
we require the value of mean of square of
speeds,
u
2
, of all molecules. This is
represented as follows:
u
2
1
2
2
2 2
=
u +u +..........u
n
n
The mean square speed is the direct
measure of the average kinetic energy of gas
molecules. If we take the square root of the
mean of the square of speeds then we get a
value of speed which is different from most
probable speed and average speed. This speed
is called root mean square speed and is given
by the expression as follows:
u
rms
= u
2
Root mean square speed, average speed
and the most probable speed have following
relationship:
u
rms
>
u
av
> u
mp
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149STATES OF MATTER
The ratio between the three speeds is given
below :
u
mp
: u
av
: u
rms
: : 1 : 1.128 : 1.224
5.8 KINETIC MOLECULAR THEORY OF
GASES
So far we have learnt the laws (e.g., Boyle’s law,
Charles’ law etc.) which are concise statements
of experimental facts observed in the laboratory
by the scientists. Conducting careful
experiments is an important aspect of scientific
method and it tells us how the particular
system is behaving under different conditions.
However, once the experimental facts are
established, a scientist is curious to know why
the system is behaving in that way. For
example, gas laws help us to predict that
pressure increases when we compress gases
but we would like to know what happens at
molecular level when a gas is compressed ? A
theory is constructed to answer such
questions. A theory is a model (i.e., a mental
picture) that enables us to better understand
our observations. The theory that attempts to
elucidate the behaviour of gases is known as
kinetic molecular theory.
Assumptions or postulates of the kinetic-
molecular theory of gases are given below.
These postulates are related to atoms and
molecules which cannot be seen, hence it is
said to provide a microscopic model of gases.
• Gases consist of large number of identical
particles (atoms or molecules) that are so
small and so far apart on the average that
the actual volume of the molecules is
negligible in comparison to the empty space
between them. They are considered as point
masses. This assumption explains the
great compressibility of gases.
• There is no force of attraction between the
particles of a gas at ordinary temperature and
pressure. The support for this assumption
comes from the fact that gases expand and
occupy all the space available to them.
• Particles of a gas are always in constant and
random motion. If the particles were at rest
and occupied fixed positions, then a gas would
have had a fixed shape which is not observed.
• Particles of a gas move in all possible
directions in straight lines. During their
random motion, they collide with each
other and with the walls of the container.
Pressure is exerted by the gas as a result
of collision of the particles with the walls of
the container.
• Collisions of gas molecules are perfectly
elastic. This means that total energy of
molecules before and after the collision
remains same. There may be exchange of
energy between colliding molecules, their
individual energies may change, but the
sum of their energies remains constant. If
there were loss of kinetic energy, the motion
of molecules will stop and gases will settle
down. This is contrary to what is actually
observed.
• At any particular time, different particles
in the gas have different speeds and hence
different kinetic energies. This assumption
is reasonable because as the particles
collide, we expect their speed to change.
Even if initial speed of all the particles was
same, the molecular collisions will disrupt
this uniformity. Consequently, the particles
must have different speeds, which go on
changing constantly. It is possible to show
that though the individual speeds are
changing, the distribution of speeds
remains constant at a particular
temperature.
• If a molecule has variable speed, then it
must have a variable kinetic energy. Under
these circumstances, we can talk only
about average kinetic energy. In kinetic
theory, it is assumed that average kinetic
energy of the gas molecules is directly
proportional to the absolute temperature.
It is seen that on heating a gas at constant
volume, the pressure increases. On heating
the gas, kinetic energy of the particles
increases and these strike the walls of the
container more frequently, thus, exerting
more pressure.
Kinetic theory of gases allows us to derive
theoretically, all the gas laws studied in the
previous sections. Calculations and predictions
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150 CHEMISTRY
based on kinetic theory of gases agree very well
with the experimental observations and thus
establish the correctness of this model.
5.9 BEHAVIOUR OF REAL GASES:
DEVIATION FROM IDEAL GAS
BEHAVIOUR
Our theoritical model of gases corresponds
very well with the experimental observations.
Difficulty arises when we try to test how far
the relation pV = nRT reproduce actual
pressure-volume-temperature relationship
of gases. To test this point we plot pV vs p plot
of gases because at constant temperature, pV
will be constant (Boyle’s law) and
pV vs p
graph at all pressures will be a straight line
parallel to x-axis. Fig. 5.10 shows such a plot
constructed from actual data for several gases
at 273 K.
negative deviation from ideal behaviour, the pV
value decreases with increase in pressure and
reaches to a minimum value characteristic of
a gas. After that pV value starts increasing. The
curve then crosses the line for ideal gas and
after that shows positive deviation
continuously. It is thus, found that real gases
do not follow ideal gas equation perfectly under
all conditions.
Deviation from ideal behaviour also
becomes apparent when pressure vs volume
plot is drawn. The pressure vs volume plot of
experimental data (real gas) and that
theoretically calculated from Boyle’s law (ideal
gas) should coincide. Fig 5.11 shows these
plots. It is apparent that at very high pressure
the measured volume is more than the
calculated volume. At low pressures, measured
and calculated volumes approach each other.
Fig. 5.10 Plot of pV vs p for real gas and
ideal gas
Fig. 5.11 Plot of pressure vs volume for real gas
and ideal gas
It can be seen easily that at constant
temperature pV vs p plot for real gases is not a
straight line. There is a significant deviation
from ideal behaviour. Two types of curves are
seen. In the curves for dihydrogen and helium,
as the pressure increases the value of pV
also
increases. The second type of plot is seen in
the case of other gases like carbon monoxide
and methane. In these plots first there is a
It is found that real gases do not follow,
Boyle’s law, Charles law and Avogadro law
perfectly under all conditions. Now two
questions arise.
(i) Why do gases deviate from the ideal
behaviour?
(ii) What are the conditions under which gases
deviate from ideality?
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151STATES OF MATTER
We get the answer of the first question if we
look into postulates of kinetic theory once
again. We find that two assumptions of the
kinetic theory do not hold good. These are
(a) There is no force of attraction between the
molecules of a gas.
(b) Volume of the molecules of a gas is
negligibly small in comparison to the space
occupied by the gas.
If assumption (a) is correct, the gas will
never liquify. However, we know that gases do
liquify when cooled and compressed. Also,
liquids formed are very difficult to compress.
This means that forces of repulsion are
powerful enough and prevent squashing of
molecules in tiny volume. If assumption (b) is
correct, the pressure vs volume graph of
experimental data (real gas) and that
theoritically calculated from Boyles law (ideal
gas) should coincide.
Real gases show deviations from ideal gas
law because molecules interact with each other.
At high pressures molecules of gases are very
close to each other. Molecular interactions start
operating. At high pressure, molecules do not
strike the walls of the container with full impact
because these are dragged back by other
molecules due to molecular attractive forces.
This affects the pressure exerted by the
molecules on the walls of the container. Thus,
the pressure exerted by the gas is lower than
the pressure exerted by the ideal gas.
p p
n
V
ideal real
= +
a
2
2
(5.30)
Here, a is a constant.
Repulsive forces also become significant.
Repulsive interactions are short-range
interactions and are significant when
molecules are almost in contact. This is the
situation at high pressure. The repulsive forces
cause the molecules to behave as small but
impenetrable spheres. The volume occupied
by the molecules also becomes significant
because instead of moving in volume V, these
are now restricted to volume (V–nb) where nb
is approximately the total volume occupied by
the molecules themselves. Here, b is a constant.
Having taken into account the corrections for
pressure and volume, we can rewrite equation
(5.17) as
p
n
V
V n n T+
−
(
)
=
a
b R
2
2
(5.31)
Equation (5.31) is known as van der Waals
equation. In this equation n is number of moles
of the gas. Constants a and b are called van
der Waals constants and their value depends
on the characteristic of a gas. Value of ‘a’ is
measure of magnitude of intermolecular
attractive forces within the gas and is
independent of temperature and pressure.
Also, at very low temperature,
intermolecular forces become significant. As
the molecules travel with low average speed,
these can be captured by one another due to
attractive forces. Real gases show ideal
behaviour when conditions of temperature and
pressure are such that the intermolecular
forces are practically negligible. The real gases
show ideal behaviour when pressure
approaches zero.
The deviation from ideal behaviour can be
measured in terms of compressibility factor
Z, which is the ratio of product pV
and
nRT.
Mathematically
Z
pV
n T
=
R
(5.32)
For ideal gas Z = 1 at all temperatures and
pressures because pV = n RT. The graph of Z
vs p will be a straight line parallel to pressure
axis (Fig. 5.12, page 152). For gases which
deviate from ideality, value of Z deviates from
unity. At very low pressures all gases shown
have Z
≈1 and behave as ideal gas. At high
pressure all the gases have Z > 1. These are
more difficult to compress. At intermediate
pressures, most gases have Z < 1. Thus gases
show ideal behaviour when the volume
correction
term
observed
pressure
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152 CHEMISTRY
occupied is large so that the volume of the
molecules can be neglected in comparison
to it. In other words, the behaviour of the gas
becomes more ideal when pressure is very low.
Upto what pressure a gas will follow the ideal
gas law, depends upon nature of the gas and
its temperature. The temperature at which a real
gas obeys ideal gas law over an appreciable
range of pressure is called Boyle temperature
or Boyle point. Boyle point of a gas depends
upon its nature. Above their Boyle point, real
gases show positive deviations from ideality and
Z values are greater than one. The forces of
attraction between the molecules are very feeble.
Below Boyle temperature real gases first show
decrease in Z value with increasing pressure,
which reaches a minimum value. On further
increase in pressure, the value of Z increases
continuously. Above explanation shows that at
low pressure and high temperature gases show
ideal behaviour. These conditions are different
for different gases.
More insight is obtained in the significance
of Z if we note the following derivation
Z
pV
T
=
R
real
n
(5.33)
If the gas shows ideal behaviour then
V
n T
p
ideal
R
=
. On putting this value of
n T
p
R
in equation (5.33) we have
Z
V
V
=
real
ideal
(5.34)
From equation (5.34) we can see that
compressibility factor is the ratio of actual
molar volume of a gas to the molar volume of
it, if it were an ideal gas at that temperature
and pressure.
In the following sections we will see that it
is not possible to distinguish between gaseous
state and liquid state and that liquids may be
considered as continuation of gas phase into a
region of small volumes and very high
molecular attraction. We will also see how we
can use isotherms of gases for predicting the
conditions for liquifaction of gases.
5.10 LIQUIFACTION OF GASES
First complete data on pressure-volume-
temperature relations of a substance in both
gaseous and liquid state was obtained by
Thomas Andrews on Carbon dioxide. He plotted
isotherms of carbon dioxide at various
temperatures (Fig. 5.13). Later on it was found
that real gases behave in the same manner as
carbon dioxide. Andrews noticed that at high
temperatures isotherms look like that of an
ideal gas and the gas cannot be liquified even at
very high pressure. As the temperature is
lowered, shape of the curve changes and data
show considerable deviation from ideal
behaviour. At 30.98
°
C carbon dioxide remains
gas upto 73 atmospheric pressure. (Point E in
Fig. 5.13). At 73 atmospheric pressure, liquid
carbon dioxide appears for the first time. The
temperature 30.98
°
C is called critical
temperature (T
C
) of carbon dioxide. This is the
highest temperature at which liquid carbon
dioxide is observed. Above this temperature it
is gas. Volume of one mole of the gas at critical
temperature is called critical volume (V
C
) and
pressure at this temperature is called critical
pressure (p
C
). The critical temperature, pressure
and volume are called critical constants. Further
increase in pressure simply compresses the
Fig. 5.12 Variation of compressibility factor for
some gases
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153STATES OF MATTER
Thus we see that a point like A in the Fig. 5.13
represents gaseous state. A point like D
represents liquid state and a point under the
dome shaped area represents existence of liquid
and gaseous carbon dioxide in equilibrium. All
the gases upon compression at constant
temperature (isothermal compression) show the
same behaviour as shown by carbon dioxide.
Also above discussion shows that gases should
be cooled below their critical temperature for
liquification. Critical temperature of a gas is
highest temperature at which liquifaction of the
gas first occurs. Liquifaction of so called
permanent gases (i.e., gases which show
continuous positive deviation in Z value)
requires cooling as well as considerable
compression. Compression brings the
molecules in close vicinity and cooling slows
down the movement of molecules therefore,
intermolecular interactions may hold the closely
and slowly moving molecules together and the
gas liquifies.
It is possible to change a gas into liquid or
a liquid into gas by a process in which always
a single phase is present. For example in
Fig. 5.13 we can move from point A to F
vertically by increasing the temperature, then
we can reach the point G by compressing the
gas at the constant temperature along this
isotherm (isotherm at 31.1°C). The pressure
will increase. Now we can move vertically down
towards D by lowering the temperature. As
soon as we cross the point H on the critical
isotherm we get liquid. We end up with liquid
but in this series of changes we do not pass
through two-phase region. If process is carried
out at the critical temperature, substance
always remains in one phase.
Thus there is continuity between the
gaseous and liquid state. The term fluid is used
for either a liquid or a gas to recognise this
continuity. Thus a liquid can be viewed as a
very dense gas. Liquid and gas can be
distinguished only when the fluid is below its
critical temperature and its pressure and
volume lie under the dome, since in that
situation liquid and gas are in equilibrium and
a surface separating the two phases is visible.
In the absence of this surface there is no
liquid carbon dioxide and the curve represents
the compressibility of the liquid. The steep line
represents the isotherm of liquid. Even a slight
compression results in steep rise in pressure
indicating very low compressibility of the liquid.
Below 30.98
°
C, the behaviour of the gas on
compression is quite different. At 21.5
°
C,
carbon dioxide remains as a gas only upto
point B. At point B, liquid of a particular volume
appears. Further compression does not change
the pressure. Liquid and gaseous carbon
dioxide coexist and further application of
pressure results in the condensation of more
gas until the point C is reached. At point C, all
the gas has been condensed and further
application of pressure merely compresses the
liquid as shown by steep line. A slight
compression from volume V
2
to V
3
results in
steep rise in pressure from p
2
to p
3
(Fig. 5.13).
Below 30.98
°
C (critical temperature) each
curve shows the similar trend. Only length of
the horizontal line increases at lower
temperatures. At critical point horizontal
portion of the isotherm merges into one point.
Fig. 5.13 Isotherms of carbon dioxide at various
temperatures
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154 CHEMISTRY
fundamental way of distinguishing between
two states. At critical temperature, liquid
passes into gaseous state imperceptibly and
continuously; the surface separating two
phases disappears (Section 5.11.1). A gas
below the critical temperature can be liquified
by applying pressure, and is called vapour of
the substance. Carbon dioxide gas below its
critical temperature is called carbon dioxide
vapour. Critical constants for some common
substances are given in Table 5.4.
between them and under normal conditions
liquids are denser than gases.
Molecules of liquids are held together by
attractive intermolecular forces. Liquids have
definite volume because molecules do not
separate from each other. However, molecules
of liquids can move past one another freely,
therefore, liquids can flow, can be poured and
can assume the shape of the container in which
these are stored. In the following sections we
will look into some of the physical properties
of the liquids such as vapour pressure, surface
tension and viscosity.
5.11.1 Vapour Pressure
If an evacuated container is partially filled with
a liquid, a portion of liquid evaporates to fill
the remaining volume of the container with
vapour. Initially the liquid evaporates and
pressure exerted by vapours on the walls of
the container (vapour pressure) increases. After
some time it becomes constant, an equilibrium
is established between liquid phase and
vapour phase. Vapour pressure at this stage
is known as equilibrium vapour pressure or
saturated vapour pressure.. Since process of
vapourisation is temperature dependent; the
temperature must be mentioned while
reporting the vapour pressure of a liquid.
When a liquid is heated in an open vessel,
the liquid vapourises from the surface. At the
temperature at which vapour pressure of the
liquid becomes equal to the external pressure,
vapourisation can occur throughout the bulk
of the liquid and vapours expand freely into
the surroundings. The condition of free
vapourisation throughout the liquid is called
boiling. The temperature at which vapour
pressure of liquid is equal to the external
pressure is called boiling temperature at that
pressure. Vapour pr
essure of some common
liquids at various temperatures is given in
(Fig. 5.14, page 155). At 1 atm pressure boiling
temperature is called normal boiling point.
If pressure is 1 bar then the boiling point is
called standard boiling point of the liquid.
Standard boiling point of the liquid is slightly
lower than the normal boiling point because
Table 5.4 Critical Constants for Some
Substances
Problem 5.5
Gases possess characteristic critical
temperature which depends upon the
magnitude of intermolecular forces
between the gas particles. Critical
temperatures of ammonia and carbon
dioxide are 405.5 K and 304.10 K
respectively. Which of these gases will
liquify first when you start cooling from
500 K to their critical temperature ?
Solution
Ammonia will liquify first because its
critical temperature will be reached first.
Liquifaction of CO
2
will require more
cooling.
5.11 LIQUID STATE
Intermolecular forces are stronger in liquid
state than in gaseous state. Molecules in liquids
are so close that there is very little empty space
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155STATES OF MATTER
1 bar pressure is slightly less than 1 atm
pressure. The normal boiling point of water is
100 °C (373 K), its standard boiling point is
99.6 °C (372.6 K).
At high altitudes atmospheric pressure is
low. Therefore liquids at high altitudes boil at
lower temperatures in comparison to that at
sea level. Since water boils at low temperature
on hills, the pressure cooker is used for
cooking food. In hospitals surgical instruments
are sterilized in autoclaves in which boiling
point of water is increased by increasing the
pressure above the atmospheric pressure by
using a weight covering the vent.
Boiling does not occur when liquid is
heated in a closed vessel. On heating
continuously vapour pressure increases. At
first a clear boundary is visible between liquid
and vapour phase because liquid is more dense
than vapour. As the temperature increases
more and more molecules go to vapour phase
and density of vapours rises. At the same time
liquid becomes less dense. It expands because
molecules move apart. When density of liquid
and vapours becomes the same; the clear
boundary between liquid and vapours
disappears. This temperature is called critical
temperature about which we have already
discussed in section 5.10.
5.11.2 Surface Tension
It is well known fact that liquids assume the
shape of the container. Why is it then small
drops of mercury form spherical bead instead
of spreading on the surface. Why do particles
of soil at the bottom of river remain separated
but they stick together when taken out ? Why
does a liquid rise (or fall) in a thin capillary as
soon as the capillary touches the surface of
the liquid ? All these phenomena are caused
due to the characteristic property of liquids,
called surface tension. A molecule in the bulk
of liquid experiences equal intermolecular
forces from all sides. The molecule, therefore
does not experience any net force. But for the
molecule on the surface of liquid, net attractive
force is towards the interior of the liquid (Fig.
5.15), due to the molecules below it. Since there
are no molecules above it.
Liquids tend to minimize their surface area.
The molecules on the surface experience a net
downward force and have more energy than
Fig. 5.14 Vapour pressure vs temperature curve
of some common liquids.
Fig. 5.15 Forces acting on a molecule on liquid
surface and on a molecule inside the
liquid
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156 CHEMISTRY
the molecules in the bulk, which do not
experience any net force. Therefore, liquids tend
to have minimum number of molecules at their
surface. If surface of the liquid is increased by
pulling a molecule from the bulk, attractive
forces will have to be overcome. This will
require expenditure of energy. The energy
required to increase the surface area of the
liquid by one unit is defined as surface energy.
Its dimensions are J m
–2
. Surface tension is
defined as the force acting per unit length
perpendicular to the line drawn on the surface
of liquid. It is denoted by Greek letter γ
(Gamma). It has dimensions of kg s
–2
and in SI
unit it is expressed as N m
–1
.
The lowest energy
state of the liquid will be when surface area is
minimum. Spherical shape satisfies this
condition, that is why mercury drops are
spherical in shape. This is the reason that sharp
glass edges are heated for making them
smooth. On heating, the glass melts and the
surface of the liquid tends to take the rounded
shape at the edges, which makes the edges
smooth. This is called fire polishing of glass.
Liquid tends to rise (or fall) in the capillary
because of surface tension. Liquids wet the
things because they spread across their surfaces
as thin film. Moist soil grains are pulled together
because surface area of thin film of water is
reduced. It is surface tension which gives
stretching property to the surface of a liquid.
On flat surface, droplets are slightly flattened
by the effect of gravity; but in the gravity free
environments drops are perfectly spherical.
The magnitude of surface tension of a liquid
depends on the attractive forces between the
molecules. When the attractive forces are large,
the surface tension is large. Increase in
temperature increases the kinetic energy of the
molecules and effectiveness of intermolecular
attraction decreases, so surface tension
decreases as the temperature is raised.
5.11.3 Viscosity
It is one of the characteristic properties of
liquids. Viscosity is a measure of resistance to
flow which arises due to the internal friction
between layers of fluid as they slip past one
another while liquid flows. Strong
intermolecular forces between molecules hold
them together and resist movement of layers
past one another.
When a liquid flows over a fixed surface,
the layer of molecules in the immediate contact
of surface is stationary. The velocity of upper
layers increases as the distance of layers from
the fixed layer increases. This type of flow in
which there is a regular gradation of velocity
in passing from one layer to the next is called
laminar flow. If we choose any layer in the
flowing liquid (Fig.5.16), the layer above it
accelerates its flow and the layer below this
Fig. 5.16 Gradation of velocity in the laminar
flow
retards its flow.
If the velocity of the layer at a distance dz
is changed by a value du then velocity gradient
is given by the amount .
du
dz
A force is required
to maintain the flow of layers. This force is
proportional to the area of contact of layers
and velocity gradient i.e.
F A∝
(A is the area of contact)
F ∝ A
du
dz
.
(where,
du
dz
is velocity gradient;
the change in velocity with distance)
F ∝ A
du
dz
.
⇒ =F ηA
du
dz
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157STATES OF MATTER
SUMMARY
Intermolecular forces operate between the particles of matter. These forces differ from
pure electrostatic forces that exist between two oppositely charged ions. Also, these do
not include forces that hold atoms of a covalent molecule together through covalent
bond. Competition between thermal energy and intermolecular interactions determines
the state of matter. “Bulk” properties of matter such as behaviour of gases, characteristics
of solids and liquids and change of state depend upon energy of constituent particles
and the type of interaction between them. Chemical properties of a substance do not
change with change of state, but the reactivity depends upon the physical state.
Forces of interaction between gas molecules are negligible and are almost independent
of their chemical nature. Interdependence of some observable properties namely
pressure, volume, temperature and mass leads to different gas laws obtained from
experimental studies on gases. Boyle’s law states that under isothermal condition,
pressure of a fixed amount of a gas is inversely proportional to its volume. Charles’ law
is a relationship between volume and absolute temperature under isobaric condition. It
states that volume of a fixed amount of gas is directly proportional to its absolute
temperature
V T∝
( )
. If state of a gas is represented by p
1
, V
1
and T
1
and it changes to
state at p
2
, V
2
and T
2
, then relationship between these two states is given by combined
gas law according to which
p V
T
p V
T
1 1
1
2 2
2
=
. Any one of the variables of this gas can be
found out if other five variables are known. Avogadro law states that equal volumes of
all gases under same conditions of temperature and pressure contain equal number of
molecules. Dalton’s law of partial pressure states that total pressure exerted by a
mixture of non-reacting gases is equal to the sum of partial pressures exerted by them.
Thus p = p
1
+p
2
+p
3
+ ... . Relationship between pressure, volume, temperature and number
of moles of a gas describes its state and is called equation of state of the gas. Equation
of state for ideal gas is pV=nRT, where R is a gas constant and its value depends upon
units chosen for pressure, volume and temperature.
At high pressure and low temperature intermolecular forces start operating strongly
between the molecules of gases because they come close to each other. Under suitable
temperature and pressure conditions gases can be liquified. Liquids may be considered
as continuation of gas phase into a region of small volume and very strong molecular
attractions. Some properties of liquids e.g., surface tension and viscosity are due to
strong intermolecular attractive forces.
‘
η
’ is proportionality constant and is called
coefficient of viscosity. Viscosity coefficient
is the force when velocity gradient is unity and
the area of contact is unit area. Thus ‘
η
’ is
measure of viscosity. SI unit of viscosity
coefficient is 1 newton second per square metre
(N s m
–2
) = pascal second (Pa s = 1kg m
–1
s
–1
). In
cgs system the unit of coefficient of viscosity is
poise (named after great scientist Jean Louise
Poiseuille).
1 poise = 1 g cm
–1
s
–1
= 10
–1
kg m
–1
s
–1
Greater the viscosity, the more slowly the
liquid flows. Hydrogen bonding and van der
Waals forces are strong enough to cause high
viscosity. Glass is an extremely viscous liquid.
It is so viscous that many of its properties
resemble solids.
Viscosity of liquids decreases as the
temperature rises because at high temperature
molecules have high kinetic energy and can
overcome the intermolecular forces to slip past
one another between the layers.
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158 CHEMISTRY
EXERCISES
5.1 What will be the minimum pressure required to compress 500 dm
3
of air at 1 bar to
200 dm
3
at 30°C?
5.2 A vessel of 120 mL capacity contains a certain amount of gas at 35 °C and 1.2 bar
pressure. The gas is transferred to another vessel of volume 180 mL at 35 °C. What
would be its pressure?
5.3 Using the equation of state pV=nRT; show that at a given temperature density of a
gas is proportional to gas pressure p.
5.4 At 0°C, the density of a certain oxide of a gas at 2 bar is same as that of dinitrogen
at 5 bar. What is the molecular mass of the oxide?
5.5 Pressure of 1 g of an ideal gas A at 27 °C is found to be 2 bar. When 2 g of another
ideal gas B is introduced in the same flask at same temperature the pressure
becomes 3 bar. Find a relationship between their molecular masses.
5.6 The drain cleaner, Drainex contains small bits of aluminum which react with caustic
soda to produce dihydrogen. What volume of dihydrogen at 20 °C and one bar will
be released when 0.15g of aluminum reacts?
5.7 What will be the pressure exerted by a mixture of 3.2 g of methane and 4.4 g of
carbon dioxide contained in a 9 dm
3
flask at 27 °C ?
5.8 What will be the pressure of the gaseous mixture when 0.5 L of H
2
at 0.8 bar and
2.0 L of dioxygen at 0.7 bar are introduced in a 1L vessel at 27°C?
5.9 Density of a gas is found to be 5.46 g/dm
3
at 27 °C at 2 bar pressure. What will be
its density at STP?
5.10 34.05 mL of phosphorus vapour weighs 0.0625 g at 546 °C and 0.1 bar pressure.
What is the molar mass of phosphorus?
5.11 A student forgot to add the reaction mixture to the round bottomed flask at 27 °C
but instead he/she placed the flask on the flame. After a lapse of time, he realized
his mistake, and using a pyrometer he found the temperature of the flask was 477
°C. What fraction of air would have been expelled out?
5.12 Calculate the temperature of 4.0 mol of a gas occupying 5 dm
3
at 3.32 bar.
(R = 0.083 bar dm
3
K
–1
mol
–1
).
5.13 Calculate the total number of electrons present in 1.4 g of dinitrogen gas.
5.14 How much time would it take to distribute one Avogadro number of wheat grains, if
10
10
grains are distributed each second ?
5.15 Calculate the total pressure in a mixture of 8 g of dioxygen and 4 g of dihydrogen
confined in a vessel of 1 dm
3
at 27°C. R = 0.083 bar dm
3
K
–
1
mol
–1
.
5.16 Pay load is defined as the difference between the mass of displaced air and the
mass of the balloon. Calculate the pay load when a balloon of radius 10 m, mass
100 kg is filled with helium at 1.66 bar at 27°C. (Density of air = 1.2 kg m
–
3
and
R = 0.083 bar dm
3
K
–
1
mol
–
1
).
5.17 Calculate the volume occupied by 8.8 g of CO
2
at 31.1°C and 1 bar pressure.
R = 0.083 bar L K
–1
mol
–1
.
5.18 2.9 g of a gas at 95 °C occupied the same volume as 0.184 g of dihydrogen at 17 °C,
at the same pressure. What is the molar mass of the gas?
5.19 A mixture of dihydrogen and dioxygen at one bar pressure contains 20% by weight
of dihydrogen. Calculate the partial pressure of dihydrogen.
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159STATES OF MATTER
5.20 What would be the SI unit for the quantity pV
2
T
2
/n ?
5.21 In terms of Charles’ law explain why –273 °C is the lowest possible temperature.
5.22 Critical temperature for carbon dioxide and methane are 31.1 °C and –81.9 °C
respectively. Which of these has stronger intermolecular forces and why?
5.23 Explain the physical significance of van der Waals parameters.
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