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• Intermolecular forces are the forces of attraction and repulsion
between interacting particles.
• Attractive intermolecular forces are known as van der waals
• Only a few elements can participate in hydrogen bond
• Intermolecular forces are further divided into 3 forces.
dispersion or London forces
dipole-induced dipole forces
Dispersion forces or London forces
CHARECTERISTICS OF DISPERSION OR LONDON FORCES.
• London forces are exhibited by non polar molecules because of
temporarily correlated movements of electrons in interacting
• This force is a temporary force.
• These forces are always attractive.
• The interaction energy is inversely proportional to the sixth
power of the distance between two interacting particles.
• These forces are important at only very short distances.
• Their magnitude depends upon the polarisability of the particle.
• Dipole dipole forces act between the molecules possessing
• Ends of dipole possess "partial charges”.
• Partial charges are always less then the unit electronic charge.
• This interaction is stronger than London forces but is weaker
than ion-ion interaction only because partial charges are
• The attractive forces decrease with the increase of distance
between the dipoles.
• Interaction energy between stationary polar molecules is
interaction energy between rotating polar molecules is double of
stationary polar molecules where r is the distance between the
Dipole induced dipole forces
CHARECTERISTICS OF DIPOLE-INDUCED DIPOLE FORCES.
• This type of attractive forces operate between polar
molecules having permanent dipole and the molecules
lacking permanent dipole.
• The interaction energy is inversely proportional to the sixth
power of the distance between two interacting particles.
• Induced dipole moment depends upon the dipole moment
present in the permanent dipole and the polarisability of
the electrically neutral molecule.
• Molecules of larger size can be easily polarised.
• High polarisability increases the strength of attractive
• Thermal energy is the energy of the body arising from the
motion of its atoms and molecules.
• It is directly proportional to the temperature of a substance.
• It is the measure of the average kinetic energy of the particles
of matter and is thus responsible for the movement of particles.
• The movement of particles is called thermal motion.
• Intermolecular forces tend to keep the molecules together but
thermal energy of the molecules tends to keep them apart.
• The three states of matter are a result of balance between the
intermolecular forces and the thermal energy of the molecules.
THE GAS LAWS
• There are 4 gas laws we are going to study about :-
Dalton's law of partial pressures
• At constant temperature , the pressure of a fixed amount of
gas varies inversely with its volume
• That is
On rearranging we get :
we know that :
Charles law relationship
• For a fixed mass at constant pressure , volume of a gas
increases on increasing temperature and decreases on cooling.
• They found out that for each degree rise in temperature
volume of a gas increased by of the original volume of the
gas at 0 degree Celsius . Thus if the volume of the gas at 0
degree and at “t” degree Celsius are VO and Vt
• At this stage we can define a new scale of temperature such that t
degree Celsius on new scale is given by
and 0 degree Celsius will be given by
This new temperature scale is called the Kelvin temperature scale
or absolute temperature scale.
This scale is also called the thermodynamic scale of temperature.
If we write = 273.15+t and =273.15 in the equation we get
Thus we can write this equation as :-
= constant =
thus we can write that
Thus the value of is determined by the pressure of the gas, its
amount and the units in which volume V is expressed.
• This is the mathematical representation of Charles law which
states that pressure remaining constant , the volume of a fixed
mass of a gas is directly proportional to its absolute
• Each line in the volume vs.
temperature graph is called an
• The lowest hypothetical or imaginary
temperature at which all gas are
supposed to occupy
zero volume is called absolute zero.
Gay lussac’s law(pressure temperature
According to lussac:- At constant volume, pressure of a fixed
amount of a gas varies directly with the temperature. That is:-
This relationship can be derived from
both boyle’s law and Charle’s law.
Each line in this graph is called an
• It states that equal volumes of all gases under the same
condition of temperature and pressure contain equal number of
• We can say that the volume of the gas depends directly to the
number of molecules in it.
• We know that:-
• We know that one mole is equal to molecules and
is called the Avogadro's constant.
How to calculate the number of moles in a
• Number of moles of a gas can be calculated as :-
• Where ‘m’ is equal to the mass of the gas under investigation
and ‘M’ is the molar mass.
This equation can be rearranged as :-
Here ‘d’ is the density of the gas. Density is directly proportional to
its molar mass
Hence this law that follows boyle’s law charles law and
Avogadro's law is called an ideal gas
THE IDEAL GAS EQUATION
• The three laws combined in one single formula is called the
ideal gas equation
• According to this:- boyle’s law =
Combining the equation we get a equation which is called the
ideal gas equation.
• Where R is called the proportionality constant and hence we
• Where R is called the gas constant and therefore also called
the universal gas constant
• At STP the value of R is 8.314 K/mol and this equation is
called equation of state.
• Now we know that
and hence we get :-
This equation is called the combined gas law.
As it is containing 5 variables and it is also known as the special
equation of quartz Lassaigne's.
Density and molar mass of a gaseous
• Ideal gas can be arranged as follows:-
• Replacing ‘n’ by we get :-
• Now m/V=d so we can replace it.⇒
• So for calculating molar mass of a gas we use the formula:-
Dalton’s law of partial pressures
• It states that that the total pressure exerted by a mixture of non
reactive gases is equal to the sum of the partial pressures of
• In a mixture of gases, the pressure exerted by an individual gas
is called its partial pressure
• Pressure of a dry gas can be calculated by subtracting vapour
pressure of water from the total pressure of the moist gas which
contains water vapour too.
Pressure exerted by a saturated water vapour is called aqueous
Partial pressure in terms of mole fraction.
• Suppose at temperature T 3 gases enclosed in the volume in
the volume V exert partial pressures then
Where are the number of moles of these gases
and the expression will be:-
• On dividing by we get
Where and are the partial pressures of the gases., we
can use these useful formulae to find out partial pressures of
Behaviour of real gases : deviation from
ideal gas behaviour
• pV value decreases after an increase in pressure and reaches
to a minimum value characteristic of gas. After the 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 the 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. It is apparent that
at a very high pressure the measured volume is more than the
calculated volume. At low pressures, measured and calculated
volumes approach each other.
• Real gases show deviations from ideal gas law because
molecules interact with each other. At very 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 the other molecules due to molecular
• Thus the pressure exerted by the gas is lower than the
pressure exerted by the ideal gas.
observed correction term.
Here ‘a’ is a constant term.
• Repulsive forces also become significant. The volume occupied
by the molecules because instead of moving in volume ‘V’
these are now restricted to (V-nb) where ‘nb’ is approximately
the total volume occupied by the molecules themselves. Here
‘b’ is a constant term. Having taken into account the corrections
for pressure and volume , we can rewrite the equation as :-
• This equation is known as the van de Waals equation. Where
‘n’ is number of moles of the gas. Constants a and b are called
van der Waals constants and their value depends upon the
characteristic of the individual gases.
• The value of ‘a’ is a measure of magnitude of intermoleculer
attractive forces within the gas and is independent of
temperature and pressure.
• The deviation from ideal behaviour can be measured in terms
of compressibility factor ‘Z’, which is the ratio of the ideal gas
that is :-
For an ideal gas Z = 1 at all temperatures and pressures because
of the ideal gas relationship, the graph Z vs p will be a straight
line parallel to the pressure axis. For gases which deviate from
ideality, value of Z deviates from unity.
• At very low pressures all gases have Z=1 and behave as an
ideal gas. At high pressures Z>1, these gases are difficultt to
compress, whereas Z<1 at intermediate pressures.
• Thus gases show ideal behaviour when the volume
occupied is large so that the volume of the molecules can
be neglected in comparison to it.
• The temperature at which a real gas obeys all ideal gas
laws over an appreciable range of pressure is called boyle
temperature or boyle’s point.
• Boyle’s point depends upon its nature , above boyle’s point real
gases show positive deviations from their ideality and Z values
are greater than 1. 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.
if the gas shows an ideal behaviour then, , On putting
this value of in the equation we get an equation :-
• We can see that compressibility factor is actually 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.
Liquifaction of gases
• The following figure shows the isotherms of carbon dioxide .he
plotted the isotherms of carbon dioxide on various temperatures
, later it was found that all real as behaved like carbon dioxide.
• it was noticed that at very high
temperatures the gases could not be
• At 30.98C carbon dioxide remains
a gas upto 73 degree Celsius.
At 73 atmospheric pressure liquid
carbon dioxide appears for the
first time .
The temperature 30.98o
C is called critical temperature.( ) of
This is the highest temperature at which a liquid carbon dioxide
can be observed.
Volume of one mole of a gas at critical temperature is called
critical volume.( )
The pressure at this temperature is called the critical pressure.
The critical temperature, pressure , and volume are called critical
A gas below the critical temperature can be liquified by applying
pressure and is called vapour of the substance.
The liquid state
• Vapour pressure:-
Vapour pressure at the stage where an equilibrium is established
between liquid phase and vapour phase is known as
equilibrium vapour pressure or saturated vapour pressure.
The temperature at which vapour pressure of a liquid is equal to
the external pressure is called the boiling temperature at that
At 1 atm pressure boiling temperature is called normal boiling
If pressure is 1 bar then the boiling point is called standard
The temperature when the density of a liquid and vapours
become the same that is the boundary between liquid and
vapour disappears is called critical temperature.
• When a molecule experiences equal intermolecular forces from
all sides ,the molecule itself does not experience a net force
and this phenomenon is called surface tension.
• Liquids tend to minimize their surface area.
• The molecules on the surface experience a net downward force
and thus have more energy than the molecules in the bulk.
• If surface of the liquid is increased by pulling a molecule from
the bulk attractive forces will have to be overcome.
• The energy required to increase the surface area of the
liquid by one unit is defined as the surface energy.
• Its SI unit is J/
• Surface tension is defined as the force acting per unit
length perpendicular to the line drawn on the surface of the
• It is denoted by a Greek letter (ᵞ)
It has the dimensions as kg s-2
and in the S.I units it can be
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
the glass smooth.
On heating the glass melts and the surface melts and
the surface of the liquid tends to take the rounded
shape at the edges , which make the glass edges
• Viscosity is the 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.
• 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 the layers from the
fixed layer increases.
• The type of flow in which there is regular gradation of velocity in
passing from one layer to another is called laminar flow.
• If the velocity of the layer at a distance dz is changed by a
value du then velocity gradient is given by du/dz. A force is
required to maintain the flow of layers. This force is proportional
to the area of contact of layers and the velocity gradient i.e
• We know that
(since A= du/dz)
And we know that ;-
Therefore we can write the following equation as combined as:-
WHERE THE PORPORTIONALITY CONSTANT IS CALLED THE
COEFFICIENT OF VISOCSITY.