S STATES OF MATTER Y
UNIT: 05
STATES OF MATTER
Introduction:
Anything that has mass and occupies space is called matter, based on the strength of
intermolecular forces operating between the constituent particles, matter exists in
three states - solid, liquid and gas. All the three states contain particles (atoms/molecules).
However, the force of attraction between particles is strongest in the solid state; weak in liquid
state and weaker in the gaseous state.
Physical properties of molecules in the microstate appear different from
those in the bulk state.
 A single molecule does not boil, but a liquid (containing millions of molecules) boils.
 A single molecule does not wet the surface; but a liquid wets the surface of a solid. This
difference arises due to the nature of forces acting between the molecules in bulk.
INTERMOLECULAR FORCES:
Forces of attraction (attractive forces) and repulsion (repulsive forces) that exist between the
atoms or molecules, in all the three physical states of matter is called inter molecular forces.
I. VANDER WAALS FORCES:
An electrostatic force of attraction that exists between any two particles
(atoms/molecules) when bought to sufficient closeness is called Vander Waal's forces.
However, these do not include ion-ion interactions, ion-dipole interactions and
hydrogen bonds.
Types of Vander Waal's forces: There are three types,
i) Dipole - dipole interactions / Kesom forces
ii) Dipole-induced dipole interactions
iii) Induced dipole - induced dipole interactions / Dispersion forces/ London forces
Note: Vander Waals forces may be a cumulative effect of all the three forces.
i) DIPOLE - DIPOLE INTERACTIONS / KESOM FORCES:
Vanderwaal’s forces operating between any two molecules possessing permanent
dipole is called dipole-dipole forces.
OR
Vanderwaal’s forces operating between any two polar molecules is called dipole-dipole
forces of attractions.
Example: Between any two HCl, HBr, HF, CH3Cl… etc. molecules.
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Explanation for dipole-dipole Vanderwaal’s forces operating between two HCl
molecules:
Consider a molecule like H-CI that has a permanent
dipole moment. One end of the molecule has a partial
positive charge, δ+ (It is less than 1.6x 10-19C). The other
end has a partial negative charge, δ – (δ +H-CIδ –). These
charges are developed due to unequal sharing of the
electron pair in a covalent bond. The force of attraction
between the opposite ends (dipole) of neighbouring
molecules is called dipole-dipole interaction.
Characteristics of dipole-dipole Vanderwaal’s forces:
 dipole-dipole Vanderwaal’s forces of attraction decreases as the distance between the
dipole increases to the extent, interaction energy  1 for stationary molecules and
3
d
interaction energy  16 where ‘d’ is the distance between the polar molecules.
d

‘d’ increases as the magnitude of δ + and δ - increases.
ii) DIPOLE-INDUCED DIPOLE INTERACTIONS:
Vanderwaal’s forces operating between the molecules possessing permanent dipole
and the atoms/molecules lacking permanent dipole.
OR
Vanderwaal’s forces operating between a polar molecule and a non-polar molecule is
called dipole-induced dipole forces of attractions.
Examples: Between HCl and He, HBr and H2, HF and Cl2, CH3Cl and F2… etc. molecules.
For example: Between HCl molecules and He atom dipole-induces dipole Vanderwaal’s
forces operates.
Consider a non-polar atom like neon approaches
another molecule having a permanent dipole moment (like
H-Cl), the negative end of the permanent dipolar molecule
repels electron cloud of the non-polar particle and distorts it.
Thus, a temporary polarity is developed in the non-polar
particle i.e. induced dipole is developed. The induced dipole
moment depends upon the dipole moment of the permanent
dipole molecule and the extent of polarisability of the nonpolar particle (i.e. it depends on its size). In this case the
interaction energy 
1
where‘d’ is the distance between
d6
the interacting particles.
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iii) INDUCED DIPOLE - INDUCED DIPOLE INTERACTIONS / DISPERSION FORCES/
LONDON FORCES:
Vanderwaal’s forces operating between any two molecules or atoms not possessing
permanent dipole is called induced dipole - induced dipole forces.
OR
Vanderwaal’s forces operating between any two non-polar molecules or atoms is called
induced dipole - induced dipole forces of attractions.
Examples: Between any two F2, Cl2, Br2, CH3Cl… etc. molecules.
For example: Between any two H2 molecules dipole-dipole Vanderwaal’s forces operates.
Consider a non-polar molecule like H2 ,which is
electrically symmetrical and do not have any dipole
moment approaches another H2 molecule at a very close
distance of ≈500pm then the electron cloud of one
molecule repels the electron cloud of the other. As a result,
the charge distribution in the molecule becomes
unsymmetrical momentarily. Thus the molecule becomes
temporarily polar (i.e polarity is induced). Simultaneously,
this molecule induces polarity in the other molecule so that
their oppositely charged ends attract each other. This
attraction is called 'induced dipole-induced dipole
interaction.' It is also known as 'London forces', named
after a German physicist Fritz London. London forces are
much weaker compared to the earlier two. They do not
exist when the molecules are away from each other by
more than 500 pm. Even here, interaction energy 
1
d6
where‘d’ is the distance between the interacting particles.
II.
HYDROGEN BONDS:
Electrostatic force of attraction that exists between hydrogen atom of one molecule and
electronegative atom such as F, O and N of the same molecule or another molecule is
called hydrogen bond.
H- bond is represented by dotted/ dashed lines (……….)
Hydrogen bond is weak and has bond energy of the order of 10-40 kJ per mole. So
it is about 5 to 10% strong compared to a covalent bond which has bond energy or the
order of 300 - 400 kJ per mole.
Types of hydrogen bonds:
Hydrogen bonding is of two types namely:
1. Intermolecular hydrogen bonding.
2. Intramolecular hydrogen bonding.
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1. INTERMOLECULAR HYDROGEN BONDING:
Hydrogen bond formed between the hydrogen atom of one molecule and the
electronegative atom of the neighboring molecule is called intermolecular hydrogen
bonding.
Note: Because of intermolecular hydrogen bonding association of molecules takes place and
melting and boiling points also increases.
Example: H2O, HF, NH3 m - and p - nitrophenols etc.
O
.........HO
O
N
O ......... HO
N
O .........
p-Nitrophenol
Inter molecular H-bonding
Explanation of hydrogen bonding in HF:
In HF, fluorine is more electronegative than hydrogen. Hence the shared pair of electrons lies
closer to fluorine atom. As a result, fluorine atom gets a partial negative charge while hydrogen
atom acquires a partial positive charge. This results in a dipole in HF molecule. The charged
hydrogen atom exerts electrostatic attraction on the charged fluorine atom of another
molecule. Thus a hydrogen bond is formed between hydrogen atom of one molecule and
fluorine atom of another molecule as shown in Fig.
........ H-F........ H-F........ H-F........
The solid lines between H and F represent covalent bonds and the dotted lines represent
hydrogen bonds. In HF, the covalent bond length is 100 pm and hydrogen bond length
is 155 pm.
2. INTRAMOLECULAR HYDROGEN BONDING:
Hydrogen bonding formed between the hydrogen atom and an electronegative atom
present in the same molecule is called intramolecular hydrogen bonding.
In compounds with Intramolecular hydrogen bonding only Vander Waal’s forces exists.
Example: o-nitrophenol, Salicylic acid, salicylaldehyde.
O
N
O...
...
H
O
o-Nitrophenol
Intra molecular H-bonding
Note:
 Relative strength of intermolecular forces:
Ion - ion interaction (ionic bond) > H-bonding > Vanderwaal’s forces.
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 Relative strength of Vanderwaal’s forces:
Dipole - dipole > dipole-induced dipole > induced dipole- induced dipole.
REPULSIVE FORCES:
At very close distances molecules start repelling each other. When they are extremely close
to each other electron clouds of the two neighbouring molecules repel each other and do not
permit the molecules coming closer. In the liquid and solid states, the distance between the
molecules is extremely small. Due to repulsion between the molecules, it is difficult to
compress a liquid or solid, by applying pressure.
THERMAL ENERGY:
Energy of a body arising from motion of its atoms or molecules is called thermal
energy.
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.
Note: greater thermal energy results in more vigorous movement in the system.
INTERMOLECULAR FORCES V/S THERMAL ENERGY:
 Intermolecular forces tend to keep the molecules together but thermal energy of the molecules
tends to keep the molecules apart.
 Three states of matter is a result of balance between intermolecular forces and the thermal
energy of the molecules.
Intermolecular forces 
1
thermal energy
 Intermolecular forces are most powerful in the solid state, less in the liquid state and
the least in the gaseous state.
 Thermal energy is the least in the solid state, more in the liquid state and highest in
the gaseous state.
INTERMOLECULAR FORCES PREDOMINATES
heat
SOLID
cool
LIQUID
heat
GAS
cool
THERMAL ENERGY PREDOMINATES
DIFFERENCES BETWEEN INTERMOLECULAR FORCES AND THERMAL ENERGY:
Sl.
No.
1.
Intermolecular forces
Thermal energy
Attractive forces
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2.
Strength: Solids>liquids> gases.
Strength: gases >liquids> Solids.
3.
Decreases with temperature.
Increases with temperature.
4.
Increases with decrease in kinetic energy.
Increases with Increases in kinetic energy.
GASES:
Gaseous state has more thermal energy than solid and liquid states. Intermolecular forces
are weaker. Due to this, the molecules move randomly in the gaseous state.
Characteristics of gases:
1. Gases do not have definite shapes, definite boundaries hence they occupy the volume of
entire vessel.
2. Gases have low densities.
3. Gases are highly compressible and liquefiable.
4. Gases exert pressure. Pressure of the gas increases with increase in temperature.
5. Gases freely intermix with each other (diffusion).
6. Gas molecules have three types of movement’s viz. translational, vibrational and rotational
movements.
GAS LAWS:
Properties are explained using the gas laws.
1) BOYLE'S LAW: (Pressure-Volume relationship)
It states that “the volume of a given mass of a gas is inversely proportional to its
pressure at constant temperature”.
Mathematically, V
1
or V
P
k
1
P
or PV
k at constant temperature.
Where ‘k’ is the proportionality constant,
When a fixed mass of a gas is compressed from a pressure P1 to a pressure P2 then its volume
decreases from V1 to V2 Hence P1V1 = P2V2 = constant, at constant temperature.
Graphical representation:
Boyle's law is represented graphically by plotting pressure along y-axis and volume along
x-axis.
It is to be noted that ‘V’ decreases as ‘P’ increases. However, the product of
pressure and volume (P x V) remains constant at a given temperature.
ISOTHERMS:
The graphs of ‘P’ versus ‘V’ plotted at constant temperature are called 'isotherms'.
The two conventional ways of graphically presenting Boyle’s law is as shown in the
above graph.
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At different temperatures the value of k 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.
Note:
 The volume of the gas doubles if pressure is halved.
 The graph between P and 1/V which 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.
CONCLUSION: Experiments of Boyle, in a quantitative manner proves that gases are highly
compressible because when a given mass of a gas is compressed, the same numbers of
molecules occupy a smaller space. This means that gases become denser at high
pressure.
Note: Pressure of a gas can be expressed in various units.
105Pa = I bar; 1 atm = 101325 Pa = 1.01325 bar = 760 mm of Hg.
CHARLE’S LAW:
It states that “The volume of a given mass of gas is directly proportional to its absolute
temperature at constant pressure”.
Mathematically,
V
T or V
kT
or
V
T
k at constant pressure.
Where ‘k’ is the proportionality constant,
Let the volume of the gas be V1 when the temperature is T1 , if the temperature changes to
T2 then its volume changes to V2
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V1
V
 2 at constant pressure.
T1
T2
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Graphical representation: At any given
pressure, graph of volume v/s 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 different but at zero volume all the lines
meet the temperature axis at – 273.15 °C as shown
in the graph.
Each line of the volume v/s temperature graph is
called isobar.
The graphs of ‘V’ versus ‘T’ plotted at
constant Pressure are called ‘isobars’.
ISOBARS:
The graphs of ‘V’ versus ‘T’ plotted at constant pressure are called ' isobars’.
Conclusion: It is seen 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 liquefied before this temperature is reached.
ABSOLUTE ZERO:
The lowest hypothetical or imaginary temperature at which gases are supposed to
occupy zero volume is called Absolute zero.
Note: All gases obey Charles’ law at very low pressures and high temperatures.
GAY LUSSAC'S LAW:
It states that “Pressure of a given mass of a gas is directly proportional to its absolute
temperature at constant volume”.
Mathematically,
P
T or P
kT
or
P
T
k at constant volume.
Where ‘k’ is the proportionality constant,
Let the pressure of the gas be P1 when the temperature is T1 , if the temperature changes to
T2 then its pressure changes to P2
.
P1
P
 2 at constant
T1 T2
volume.
This relationship can be derived from Boyle’s law and Charles’
Law.
Graphical representation:
Pressure v/s temperature (Kelvin) graph at constant
molar volume is shown in graph. Each line/plot of this graph is
called isochore.
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ISOCHORE:
The graphs of ‘P’ versus ‘T’ plotted at constant volume are called ‘isochore’.
AVOGADRO’S LAW:
It states that “Equal volume of all gases contain equal number of particles (atoms /
molecules) under similar conditions of temperature and pressure”
Mathematically,
V
n
V = kn
where, n = number of moles=
n=
m
M
mass of the substance
molecular mass
substituting the value of 'n' in the above equation and rearranging,
we get, M = k
m
V
but, density (d) =
m
V
Where ‘k’ is the proportionality constant,
‘d’ is the density of the gas.
Hence we can conclude from the above equation that the density of a gas is directly
proportional to its molar mass.
i.e. M d
M=kd
M1
d1
M2
d2
Note:
 The number of molecules in one mole of a gas has been determined to be
×1023 and is known as Avogadro constant.
6.022
 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 0C) temperature and 1 bar
(i.e. exactly 105 Pascal) pressure (These values approximate freezing temperature
water and atmospheric pressure at sea level).
 At STP molar volume of an ideal gas is 22.71098 L mol-1.
 *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 00C (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 105 Pa). At SATP
(1 bar and 298.15 K), the molar volume of an ideal gas is24.789 L mol-1.
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IDEAL GAS:
A gas that obeys Boyle’s law, Charles’ law and Avogadro law strictly under all
conditions of temperature and pressure is called an ideal gas.
Note:
 Ideal 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 (at low T and high P). In all other situations these
deviate from ideal behaviour.
COMBINED GAS EQUATION/ IDEAL GAS EQUATION:
1
at constant T
P
According to Charles law V T at constant P
According to Avogadro's law, V n at constant T and P
According to Boyle's law,
Combining them, we get
V
V
nT
nT
OR V = R
OR PV = nRT
P
P
where ‘R’ is Universal gas constant.
This equation is called Ideal gas equation OR combined gas equation for ‘n’ moles of a
gas.
Ideal gas equation for 1 mole of a gas is PV = RT
IDEAL GAS EQUATION AT TWO DIFFERENT STATES:
Let the pressure of the gas be P1 when the temperature is T1 and its volume is V1, if its
pressure changes to P2 then the temperature changes to T2 and the volume changes to V2
P1V1 P2 V2
=
T1
T2
TO CALCULATE THE VALUE OF ‘R’ IN S.I UNITS:
According to ideal gas equation;
PV = nRT
PV
R=
nT
At S.T.P. conditions,
T = 273.15K,
P = 1 bar = 105 N m-2,
n = 1 mole,
V = 22.71 dm3 = 22.71x10-3 m3.
Substituting these values in the above equation
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R=
105 Nm-2 x 0.02271m 3
= 8.314 N m mol -1K -1
1 mol x 273.15 K
Nm = J
R = 8.314 J K -1mol -1
Value of ‘R’ in other units:
Pressure
Temperature
Volume
Value of ‘R’
Litre atmosphere
Kelvin
Mole
0.0821 L atm K-1 mol-1
Litre bar
Kelvin
Mole
0.0831 L bar K-1 mol-1
EXPRESSION FOR RELATIONSHIP BETWEEN DENSITY OF THE GAS,
PRESSURE AND MOLAR MASS:
According to ideal gas equation PV = nRT
mass of the substance m
=
molecular mass
M
substituting the value of 'n' in the ideal gas equation
m
we get, PV =
RT
M
n = number of moles=
by rearranging we get
m RT
m
but, density (d) =
V M
V
RT
P=d
M
PM
d=
RT
At two different states
P=
d1 d 2
=
M1 M1
DALTON’S LAW OF PARTIAL PRESSURES:
This law was stated by John Dalton in order to explain the partial pressures of non - reacting
gases in a mixture.
It states that “Total pressure of the mixture of gases that do not react with each other,
is equal to the sum of the partial pressures of the individual gases.”
Mathematically, it is given by
PTotal = P1 + P2 + P3 + ……
Where,
P = Total pressure of the mixture,
P1, P2, P3 etc. are partial pressures of individual gases.
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NOTE: The pressure exerted by an individual gas in a mixture in its partial pressure.
Partial pressure = Mole fraction x Total pressure
p = x x PTotal
KINETIC THEORY OF GASES:
This theory was proposed first by Bernoulli and the later it was developed by Maxwell,
Boltzmann and others
POSTULATES OF KINETIC THEORY OF GASES:
1. All gases consist of large number of small minute particles called molecules.
2. The gas molecules are in random motion and move in all possible direction with different
velocities in straight lines. They change their direction when they collide with each other
or with the walls of the container.
3. The collisions of gas molecules with each other or with the walls of the container are
perfectly elastic in nature. Hence there is no loss of kinetic energy.
4. Pressure of the gas is due to collisions of gas molecules with the walls of the container.
5. The volume occupied by the gas molecules is negligible when compared to the total
volume of the gas, since they are very small.
6. There is no intermolecular forces attraction or repulsions between the gas molecules
7. The average kinetic energy of the molecules is directly proportional to the absolute
temperature.
REAL GASES:
The gases like H2, CO2, N2 etc. which deviate from the gas laws and gas equation PV =
nRT are called real gases.
Note: In Real gases there exists a weak force of attraction between the gas molecules. All
known gases are real gases.
CAUSES FOR THE DEVIATION OF REAL GASES FROM IDEAL BEHAVIOR:
In nature none of the gases obey the following two postulates of kinetic theory of gases.
They are
1. There is no force of attraction or repulsion between the gas molecules
2. The gas molecules are so small that their actual volume is negligible compared to
the total volume of the gas.
Due to the above facts, the real gases deviate from ideal behavior. Because, in real gases.
1. There exist a force of attraction between the gas molecules
2. The gas molecules occupies a definite volume
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BEHAVIOUR OF REAL GASES:
DEVIATION OF REAL GASES FROM IDEAL BEHAVIOUR:
Our theoretical model of gases corresponds very well with the experimental observations.
Difficulty arises when we try to test how far the relation PV = nRT holds well with actual
pressure-volume-temperature relationship of gases.
The following graph shows such a plot constructed from actual data for several gases.
Experiment-1: To test this point it is required to plot PV v/s P plot of gases because at
constant temperature, PV will be constant according to Boyle’s law (PV=k). Therefore PV v/s
P graph at all pressures should be a straight line parallel to x-axis.
OBSERVATIONS:
From the above graph, It is seen that at constant temperature PV v/s 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 above graph.
 Type-1: The curves of dihydrogen and helium, with increase in pressure the value of
PV also increases, hence there is a steep raise in their plots with increase in temperature
 Type-2: The curves of other gases like carbon monoxide and methane the value of the
PV value decreases with increase in pressure and reaches to a minimum value
characteristic of a gas hence in the curve of PV first there is a negative deviation(dip) from
ideal behaviour,. After that PV value starts increasing as a result the curve then crosses
the line for ideal gas and after that shows positive deviation continuously with steep
increase.
CONCLUSION: It is thus, found that real gases do not follow ideal gas equation perfectly
under all conditions.
Experiment-2: Deviation from ideal behaviour also becomes apparent when pressure v/s
volume plot is drawn. The pressure v/s volume plot of experimental data (real gas) and that
theoretically calculated from Boyle’s law (ideal gas) should coincide. The following graph
shows these plots.
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OBSERVATIONS:
From the graph,
 It is seen that at very high pressure the measured volume is more than the calculated
volume.
 At low pressures, measured and calculated volumes approach each other.
CONCLUSION: Therefore it is found that real gases do not follow Boyle’s law, Charles law
and Avogadro law perfectly under all conditions.
Now two questions arises.
(i) Why do gases deviate from the ideal behaviour?
(ii) What are the conditions under which gases deviate from ideality?
We get the answer for 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. They 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 liquefy. 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 v/s volume graph of experimental data (real
gas) and that theoretically calculated from Boyles law (ideal gas) should coincide.
VANDERWALLS’ EQUATION FOR REAL GASES:
INTRODUCTION OF CORRECTION FACTOR FOR IDEAL GAS EQUATION:
Real gases show deviations from ideal gas law because molecules interact with each other.
PRESSURE CORRECTION:
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 real gas is lower than the pressure exerted by the ideal gas.
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
Pideal
Pr eal
observed
pressure
an 2

V2
correction
pressure
Where ‘a ’= constant.
VOLUME CORRECTION:
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 as

an2 
 P  2  V  nb   nRT
V 

This equation is known as Van der Waals equation.
Where,
n = number of moles of the gas.
‘a’ and ‘b’ = 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.
APPROACH OF REAL GASES TO IDEAL BEHAVIOUR:
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.
Therefore real gases show ideal behaviour when pressure approaches zero.
The deviation from ideal behaviour can be measured in terms of compressibility factor Z,
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COMPRESSIBILITY FACTOR (Z):
Ratio of product PV and nRT is called compressibility factor.
Mathematically, Z 
PV
nRT
For, ideal gas Z = 1 at all temperatures and pressures because PV = n RT.
Therefore, the graph of Z v/s P will be a straight line parallel to pressure axis. For gases
which deviate from ideality, value of Z deviates from unity.
Significance:
1) It represents the ratio of volume of 1 mole of a real gas to the volume of 1 mole of an ideal
gas, under similar conditions.
2) For an ideal gas, Z is always 1
3) For a real gas, the compressibility factor is less than 1 at low pressure and is greater
than 1 at high pressures. (i.e. that the volume of a real gas is less than the corresponding
volume of an ideal gas at low pressure. However, volume of real gas is more than the
corresponding volume of the ideal gas at high pressures.)
4) Gases (like CO2) that deviate more from ideal behaviour can be easily liquefied. For
easily liquefiable gases the depression in the graph of Z versus P is more, at low
pressures.
Suppose volume of 1 mole of a real gas at a temperature T and pressure P is Vreal
and the volume of 1 mole of an ideal gas under same conditions is Videal.
Relationship between Z real and Z ideal:
PVreal
PVideal
and Zideal =
RT
RT
Zreal
V
 real
Z ideal Videal
Zreal =
But, Zideal = 1
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 Zreal 
Vreal
for any real gas.
Videal
BOYLE TEMPERATURE:
The temperature at which a real gas obeys ideal gas laws over an appreciable range of
pressure is called Boyle temperature (Tb).
Note: Above Boyle temperature, the real gas does not show negative deviation at all i.e. Z ≥ 1.
LIQUEFACTION OF GASES:
Molecules of a real gas like CO2 attract each other. On increasing pressure, the molecules
come closer, force of attraction becomes stronger, further upon cooling, molecules lose kinetic
energy and become unable to resist the force of attraction, Thus gas turns into liquid.
Note: a real gas becomes a liquid on compression and cooling. An ideal gas cannot be
liquefied because there is no intermolecular force of attraction.
ANDREWS EXPERIMENTS ON CO2: CRITICAL PHENOMENA:
Thomas Andrew studied the effect of pressure on CO2 gas at different temperatures. He took
a definite mass of CO2 and went on increasing the, pressure, at constant temperature
(isotherm). The volume decreased. He plotted a graph of pressure (y-axis) versus volume (xaxis) at 13.10C, 21.50C, 30.90C, 31.10C, 500C etc.
These plots are called Andrew's isotherms.
OBSERVATIONS:
 The volume of the gas went on decreasing on increasing the pressure. At a certain
pressure the gas started becoming a liquid. Then, the volume suddenly dropped until all
the gas got converted into liquid without applying more pressure. Further, pressure had
not much effect on the volume of liquid CO2,
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 In the isotherm at 13.10C, ‘AB’ shows the effect of pressure on the volume of CO2 gas. At
'B', the liquefaction starts. The volume sharply decreases along ‘BC’. At 'C' liquefaction is
complete. Along ‘CD’, the volume hardly decreases inspite of applying pressure. Liquid
and gas coexist along ‘BC’.
 The isotherm at 21.50C is similar except that the horizontal portion where gas and liquid
coexist ‘FG’ is smaller.
 In the isotherm at 30.980C, this portion where gas and liquid coexist reduces to a point ‘J’.
The gas and the liquid become indistinguishable at this point. This state is called
critical point of the gas.
 At temperatures above 30.90C, CO2 gas could not be liquefied even on applying very high
pressures. Volume of the gas reduces on increasing pressure along ‘LM’.
In the case of easily liquefiable gases like CO2 and NH3 intermolecular force of attraction is
strong. 'a' has a large value. Critical temperature is high.
 Inside the region CJB, gas and liquid coexist. This curve is called 'coexistence curve.'
 It is possible to convert a gas into liquid without having more than one state in the system
throughout the process. Pressure of the gas in the isotherm at 13.10C is increased without
changing volume (by increasing temperature) until the point 'X' is reached. Then, both
pressure and volume are varied along ‘XY’ in the isotherm at 31.1 0C. After reaching 'Y',
pressure is kept constant and volume is decreased (by decreasing temperature) until the
point 'Z' is reached in the critical isotherm. Now the gas becomes a liquid. Since a single
state continues to be present in the whole process, it is called 'continuity of state' during
liquefaction.
CRITICAL TEMPERATURE (Tc):
The maximum temperature at which a gas can be converted into liquid by applying
pressure is called critical temperature.
Example: Tc for CO2 gas is 30.980C
CRITICAL PRESSURE (Pc):
The minimum pressure required to convert a gas into liquid at the critical temperature
is called critical pressure.
Example: Pc for CO2 gas is 73.9 bar = 73 atm.
CRITICAL VOLUME (Vc):
The volume occupied by one mole of the gas at the critical temperature and pressure
is called critical volume.
Example: Vc for CO2 gas is 95 cm3 mol-1.
CRITICAL ISOTHERM:
The isotherm passing through the critical temperature is called critical isotherm.
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CRITICAL CONSTANTS:
Tc, Pc, Vc of a gas are called critical constants of the gas.
FLUID:
It is the term used to indicate either for liquid or gas, to recognize their continuity.
VAPOUR:
A gas below Tc that can be liquefied upon applying pressure is called as vapour of a
substance.
Note:
 Any gas Below Tc exists as vapour and above Tc exists as a gas.
 Greater the value of Tc easier is the liquefaction of the gas.
LIQUID STATE:
In the liquid state, the molecules are closer to each other compared to gaseous state. The
molecules attract each other to a greater extent than gases. There is less empty space
between the molecules. As a result volume of a liquid does not decrease much on
compression by increasing pressure.
Gases occupy the entire volume of the vessel due to rapid diffusion. Liquids have a
definite volume. Their volume is far less compared to that of gases. However, due to weak
intermolecular attractions when compared to solids, they do not have definite shapes. The
molecules move slowly and the liquid has the shape of the container. Volume of a liquid
increases on heating.
On mixing two liquids, the molecules slowly diffuse into each other. Due to a strong
intermolecular force of attraction, the liquid molecules move slowly compared to gas
molecules. Thus, the rates of diffusion of liquids are much less.
In a liquid, the molecules move randomly. Sometimes, they even escape out of the surface. If
a liquid is taken in an open vessel, some molecules escape out to the region above the liquid
surface. This process is called evaporation and only the molecules which have sufficiently
high kinetic energy to overcome the intermolecular force of attraction escape out.
EVAPORATION:
The phenomenon of escape of liquid molecules from the surface of the liquid is called
evaporation.
Factors influencing evaporation of a liquid:
a) Nature of liquid: Liquids in which Vander Waal's forces of attraction are weak (Eg.: Ether,
petrol etc.) evaporate more rapidly.
b) Temperature: On heating, molecules acquire more kinetic energy. They escape out more
rapidly.
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c) Surface area of the liquid: Evaporation takes place on the surface. The larger the surface
area the more rapid is the evaporation.
In addition, if the vapours of the liquid above the surface are removed by blowing air more
liquid vaporises (LeChatelier's principle).
Note: Wet clothes become dry faster, if wind blows.
 Evaporation  Temperature
 Evaporation  surface area
1
 Evaporation 
Intermolecular forces
ENTHALPY OF VAPOURISATION (∆Hvap):
The amount of heat (enthalpy) required to convert one mole of a liquid into vapour at
the boiling point is called enthalpy of vapourisation (∆Hvap).
Example: latent heat of vapourisation for water is 2.246 kJ/g.
Thus. 1 mole (18 g) of water will absorb 18 x 2.246 = 40.43 kJ of heat for evaporation.
SATURATED VAPOUR PRESSURE:
Pressure exerted by the vapour of the liquid when it is in equilibrium with the liquid at
constant temperature is called saturated vapour pressure of the liquid.
When a liquid is taken in a closed vessel, the molecules try to escape out to the region
above the surface. Gradually, these molecules in the vapour state try to condense back into
liquid state. After sometime an equilibrium state is reached. At this state the rate of evaporation
of the liquid is equal to rate of condensation of the vapour.
Vapour pressure of a liquid under constant external pressure depends on
(a) Nature of the liquid
and (b) temperature
Volatile liquids like ether have a high vapour pressure. On heating, vapour pressure of the
liquid increases.
BOILING POINT:
It is the temperature at which its vapour pressure of the liquid becomes equal to
atmospheric pressure.
Why a liquid boils?
If a liquid is taken in an open vessel, the liquid molecules try to escape out due to their
kinetic energy. However, air molecules try to push them back into liquid state. At room
temperature, vapour pressure of the liquid is much less than the atmospheric pressure. On
heating, vapour pressure of the liquid gradually increases. At a certain temperature, vapour
pressure of the liquid becomes equal to atmospheric pressure. Then, the vapour molecules
spontaneously escape into air. More liquid evaporates and escapes into air. This is called
boiling.
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Atmospheric pressure: Pressure excreted by atmospheric gasses on any matter is called
atmospheric pressure.
FACTORS AFFECTING BOILING POINT:
a) Nature of the liquid: Liquids in which the intermolecular forces are weak have a high
vapour pressure even at room temperature hence they have low boiling points. Eg.: Ether,
ethanol etc.
b) External pressure: If the external pressure is high vapour pressure of the liquid becomes
equal to atmospheric pressure only on strong heating. Therefore boiling point of a liquid
increases with increase in external pressure. If the external pressure is low boiling point is low.
 b.p  Molecular mass
 b.p  Attractive forces
 b.p  atmospheric pressure (or) external pessure
Note:
 In the purification of organic liquids distillation is done under reduced pressure. This
requires a low temperature for evaporation of the liquid so that the compound does not
decompose during distillation.
 Boiling point of water is 1000C at sea level where the atmospheric pressure is 1
atmosphere. In elevated places (much above the sea level), the atmospheric pressure is
less than 1 atm. Then, vapour pressure of water becomes equal to atmospheric pressure
at a much lower temperature. Hence, boiling point of water is less than 1000C in such
places.
Example:
1. Boiling point of water in Mysore is 970C because it is 2,500 feet above sea level.
2. Water does not remain in liquid state above 1000C, if the external pressure is 1 atm. inside
a closed vessel like a pressure cooker, pressure becomes much higher than 1 atmosphere
on heating. Hence, boiling point of water is more than 1000C .Water remains in the liquid
state even above 1000C inside a pressure cooker. This explains why vegetables get
cooked faster inside a pressure cooker.
NORMAL BOILING POINT:
Boiling point of the liquid measured at one atmosphere (101.3 kPa) is called normal
boiling point of the liquid.
STANDARD BOILING POINT:
Boiling point of the liquid measured at one bar (105 Pa) is called standard boiling point
of the liquid.
Note: Since 1 bar pressure is less than 1 atmosphere pressure, standard boiling point of liquid
is always less than its normal boiling point.
Example: For water, the normal boiling point is 1000C whereas the standard boiling point is
99.60C.
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SURFACE TENSION (γ):
It is the tangential force acting along the surface of the liquid at right angles to the
surface along unit length of the surface is called surface tension.
Surface tension is expressed in Nm-1
Example:
Surface tension of water = 7.3 x 10-2 Nm-1 at room temperature.
Mercury has a very high surface tension of 46 x 10-2 Nm -1
SURFACE ENERGY:
The amount of energy required to increase the surface area of the liquid by a unit
amount is called 'Surface energy.'
Cause for surface tension:
Molecules of liquid attract each other. A molecule at the centre of the liquid is attracted
equally by molecules around it in all directions. The net force acting on this molecule
becomes zero. However, a molecule on the surface of the liquid is attracted inwards by
molecules beneath it. This inward pull tends to contract the surface of the liquid. Due to the
inward pull the surface tends to become spherical so that the surface area becomes
minimum.
FACTORS AFFECTING SURFACE TENSION:
1) Nature of the liquid: Liquids in which the intermolecular forces of attraction are stronger
have a high surface tension. Water has a higher surface tension than many liquids due to
intermolecular hydrogen bonding.
2) Temperature: On increasing temperature, thermal agitation of the molecules increases,
therefore Intermolecular forces of attraction decreases hence Surface tension of a liquid
decreases.
Importance of surface tension:
a) Liquid drops have spherical shape: Due to surface tension, the molecules on the
surface of a liquid experience an inward pull. They tend to minimise the surface area. They
get reduced to a spherical shape. This can be seen by allowing a liquid drop to freely fall
down in air from a dropper.
b) Capillary action: When a liquid is taken in a vessel two types of intermolecular forces
are present. The force of attraction between the molecules of the same liquid is called
'cohesive force'. The force of attraction between the molecules of the liquid and the
molecules of the vessel is called 'adhesive force'. When water is taken in a glass vessel
like burette, the adhesive force is greater than the cohesive force. This results in a concave
miniscus on the surface. When mercury is taken in a glass vessel the cohesive force is
greater than the adhesive force. This produces a convex meniscus on the surface.
γ  Attractive forces
1
γ
T
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VISCOSITY:
The property by virtue of which the molecules of liquid retard the movement of
molecules of the neighbouring layer is viscosity.
OR
It is the measure of resistance offered to the flow of the liquid, which arises due to the
internal friction b/w the layers of the fluid as they slip past one another while the liquid
flows.
Example: Liquids like honey, castor oil flow slowly while liquids like water flow faster inside a
tube.
LAMINAR FLOW:
It is flow of the liquids where there is a regular gradation in the velocity of the liquid on
passing from one layer to the next is called laminar flow.
VISCOSITY COEFFICIENT (η):
The force acting per unit area between two parallel layers which are unit distance apart
in order to maintain a unit velocity gradient is called coefficient of viscosity of the liquid.
OR
It is the force required to maintain the flow of the layers of liquid when the velocity
gradient and area of contact of the liquid are unity.
S.I unit of viscosity coefficient is N s m-2 = Pa s = Kgm-1s-1
Note: It is also expressed in poise (P): 1 P = 1gcm-1s-1.
FACTORS AFFECTING VISCOSITY:
1. Temperature: On increasing temperature, intermolecular forces decrease. Hence
viscosity decreases.
2. Nature of liquid: Liquid in which intermolecular forces are stronger (due to hydrogen bonds
or dipole-dipole interaction etc.) has a high viscosity. E.g.: Egg albumin, honey etc.
3. Molecular mass: If the molecules are heavy, intermolecular forces are stronger. Viscosity
is generally high in such liquids.
 Viscosity  Attractive forces
 Viscosity  Molecular mass
1
 Viscosity 
T
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