UNIT –III
MOLECULAR PHENOMENON OF SOLIDS,
LIQUIDS & GASES
Kinetic Theory of Matter
The Kinetic Theory of Matter states that matter is composed of a large number of small
particles individual atoms or molecules that are in constant motion. This theory is also
called the Kinetic Molecular Theory of Matter and the Kinetic Theory.
By making some simple assumptions, such as the idea that matter is made of widely
spaced particles in constant motion, the theory helps to explain the behavior of matter.
Two important areas explained are the flow or transfer of heat and the relationship
between pressure, temperature, and volume properties of gases.
Assumptions of theory
The Kinetic Theory of Matter is a prediction of how matter should behave, based on
certain assumptions and approximations. The assumptions are made from observations
and experiments, such as the fact that materials consist of small molecules or atoms.
Approximations are made to keep the theory from being too complex. One assumption
is that the size of the particles is so small that it can be considered a point.
Matter consists of small particles
The first assumption in this theory is that matter consists of a large number a very small
particles—either individual atoms or molecules.
Large separation between particles
The next assumption concerns the separation of the particles.
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In a gas, the separation between particles is very large compared to their size, such that
there are no attractive or repulsive forces between the molecules.
In a liquid, the particles are still far apart, but now they are close enough that attractive
forces confine the material to the shape of its container.
In a solid, the particles are so close that the forces of attraction confine the material to a
specific shape.
Particles in constant motion
Another assumption is that each particle is in constant motion.
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DEPTT. PHYSICS, LNCT JABALPUR
In gases, the movement of the particles is assumed to be random and free. In liquids, the
movement is somewhat constrained by the volume of the liquid. In solids, the motion of
the particles is severely constrained to a small area, in order for the solid to maintain its
shape.
The velocity of each particle determines its kinetic energy.
Collisions transfer energy
The numerous particles often collide with each other. Also, if a gas or liquid is confined
in a container, the particles collide with the particles that make up the walls of a
container.
Kinetic Theory of Matter
The Kinetic Theory explains the differences between the three states of matter. It states
that all matter is made up of moving particles which are molecules or atoms. In solids,
the particles are so tightly bound to each another that they can only vibrate but not
move to another location.
In liquids, the particles have enough free space to move about, but they still attract one
another. In gases, the particles are far apart and can move about freely since there is
much free space. Solids change into liquids, and liquids into gases, when the particles
gain more kinetic energy, like when being heated and are able to move apart from one
another. When the molecules vibrate more quickly upon heating, some of it escapes
from the matter. This is what the Kinetic Theory is about.
 All matter is composed of small particles.
 The particles of matter are in constant motion.

All collisions between the particles of matter are perfectly elastic
The kinetic theory can be used to describe the
physical states of matter:

Solid - a substance whose particles have a low kinetic
energy. The particles of a solid are held close together by
intermolecular forces of attraction. Because the particles are so close
together, they appear to vibrate around a fixed point.
When the temperature of a solid is raised, the velocity of the particles increases. The
collisions between the particles occur with greater force, causing the particles to more
farther apart. The ordered arrangement of the solid breaks down and a c hange in physical
state occurs.
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DEPTT. PHYSICS, LNCT JABALPUR

Liquid - a substance whose particles have
enough kinetic energy to stretch the intermolecular forces
of attraction. Collisions between the particles a strong
enough to force the particles apart. The particles appear to
have a moving vibration because they are still under the
influence of the intermolecular forces of attraction.
As the temperature of a liquid is raised, the v elocity of the particles
increases. The collisions eventually become so great that the particles
break all intermolecular forces, begin mov ing independently between
collisions, and a change in physical state occurs.

Gas - a substance whose particles have enough
kinetic energy to break all intermolecular forces of
attraction. The particles of a gas move independently of
each other. The particles move at random because they
have overcome the intermolecular forces of attraction.
When a gas is raised to ex treme temperatures, over 5000 oC, they
hav e so much kinetic energy that their collisions will break electrons
out of the atoms, and a change in physical state occurs.
Brownian motion
the random motion of small colloidal particles suspended in a liquid or gas medium,
caused by the collision of the medium's molecules with the particles. Also called
Brown′ian move′ment.
Brownian motion, also called Brownian movement, any of various physical
phenomena in which some quantity is constantly undergoing small, random
fluctuations.
If a number of particles subject to Brownian motion are present in a
given medium and there is no preferred direction for the random oscillations, then over
a period of time the particles will tend to be spread evenly throughout t he medium.
Thus, if A and B are two adjacent regions and, at time t, A contains twice as many
particles as B, at that instant the probability of a particle‟s leaving A to enter B is twice
as great as the probability that a particle will leave B to enter A. The physical process in
which a substance tends to spread steadily from regions of high concentration to regions
of lower concentration is called diffusion. Diffusion can therefore be considered a
macroscopic manifestation of Brownian motion on the microscopic level. Thus, it is
possible to study diffusion by simulating the motion of a Brownian particle and
computing its average behaviour. A few examples of the countless diffusion processes
that are studied in terms of Brownian motion include the diffusion of pollutants through
the atmosphere, the diffusion of “holes” (minute regions in which the electrical charge
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DEPTT. PHYSICS, LNCT JABALPUR
potential is positive) through a semiconductor, and the diffusion of calcium through
bone tissue in living organisms.
Early investigations
The term “classical Brownian motion” describes the random movement of microscopic
particles suspended in a liquid or gas. Brown was investigating the fertilization process
in Clarkia pulchella, then a newly discovered species of flowering plant, when he
noticed a “rapid oscillatory motion” of the microscopic particles within the pollen grains
suspended in water under the microscope. Other researchers had noticed this
phenomenon earlier, but Brown was the first to study it. Initially he believed that such
motion was a vital activity peculiar to the male sex cells of plants, but he then checked to
see if the pollen of plants dead for over a century showed the same movement. Brown
called this a “very unexpected fact of seeming vitality being retained by these „molecules‟
so long after the death of the plant.”
Early explanations attributed the motion to thermal convection currents in the fluid.
When observation showed that nearby particles exhibited totally uncorrelated activity,
however, this simple explanation was abandoned. By the 1860s theoretical physicists
had become interested in Brownian motion and were searching for a consistent
explanation of its various characteristics: a given particle appeared equally likely to
move in any direction; further motion seemed totally unrelated to past motion; and the
motion never stopped. An experiment (1865) in which a suspension was sealed in glass
for a year showed that the Brownian motion persisted. More systematic investigation in
1889 determined that small particle size and low viscosity of the surrounding fluid
resulted in faster motion.
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DEPTT. PHYSICS, LNCT JABALPUR
DERIVATION OF GAS LAWs FROM KINETIC EQUATION
(i) Boyle’s law: According to it, at constant temperature, the volume of a given mass of
a gas is inversely proportional to pressure, i.e.,
V
or
1/p
PV = constant, at constant T
At constant temperature, the kinetic energy (E) of the gas is constant. Therefore, at
constant temperature
PV = constant
[This is Boyle‟s law.]
(ii) Charles’ law: According to it, at constant pressure, the volume of a given mass of a
gas is directly proportional to its absolute temperature, i.e.,
v
T
However, we know that E ∝ T, where T is absolute temperature.
(iii) Avogadro’s hypothesis: According to it, equal volumes of all gases under similar
conditions of temperature and pressure contain equal number of molecules. For any two
gases, the kinetic equation can be written as:
V
n
When pressures and volumes of the gases are the same, i.e., P1 = P2 and V1 = V2 , it
follows that
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DEPTT. PHYSICS, LNCT JABALPUR
When the temperatures of the gases are the same, their mean kinetic energy will also be
the same,
(vi) Derivation of ideal gas equation: let pressure of the definit mass of the
gas is p, and volume is v then according to boyle’s law
1/p
V
…………(1)
And according to Charles‟s law
v
T
…………………..(2)
Combined above both equation we get,
V
T/p
V =k T/p
If
k = R, (gas constant),
then
PV = RT (for one mole of gas)
PV = n RT (for n moles of gas)
which is the required ideal gas equation.
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DEPTT. PHYSICS, LNCT JABALPUR
Derivation of the kinetic theory
formula
Remember that what follows applies to ideal gases only; the assumptions that we make
certainly do not all apply to solids and liquids.
This proof was originally proposed by Maxwell in 1860. He considered a gas to be a
collection of molecules and made the following assumptions
about these molecules:
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molecules behave as if they were hard, smooth, elastic
spheres
molecules are in continuous random motion
the average kinetic energy of the molecules is
proportional to the absolute temperature of the gas
the molecules do not exert any appreciable attraction
on each other
the volume of the molecules is infinitesimal when
compared with the volume of the gas
the time spent in collisions is small compared with the time between collisions
Consider a volume of gas V enclosed by a cubical box of sides L. Let the box contain N
molecules of gas each of mass m, and let the density of the gas be . Let the velocities of
the molecules be u1 , u2 , u3 . . . uN . (Figure 2)
Consider a molecule moving in the x-direction towards
face A with velocity u1 . On collision with face A the
molecule will experience a change of momentum equal to
2mu1 . (Figure 3)
It will then travel back across the box, collide with the
opposite face and hit face A again after a time t, where t =
2L/u1 .
The number of impacts per second on face A will
therefore be 1/t = u1 /2L.
Therefore rate of change of momentum = [mu1 2 ]/L = force on face A due to one
molecule.
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DEPTT. PHYSICS, LNCT JABALPUR
But the area of face A = L2 , so pressure on face A = [mu1 2 ]/L3
But there are N molecules in the box and if they were all travelling along the x -direction
then
Total pressure on face A = [m/L3 ](u12 + u22 +...+ uN2 )
But on average only one-third of the molecules will be travelling along the x -direction.
Therefore: pressure = 1/3 [m/L3 ](u12 + u22 +...+ uN2 )
If we rewrite Nc2 = [u12 + u2 2 + …+ uN2 ] where c is the mean square velocity of the
molecules:
pressure = 1/3 [m/L3 ]Nc2 But L3 is the volume of the gas and therefore:
Pressure (P) = 1/3 [m/V]Nc 2 and so PV = 1/3 [mNc 2 ]
and this is the kinetic theory equation.
Now the total mass of the gas M = mN, and since  = M/V we can write
Pressure (P) = 1/3 [ρc 2 ]
The root mean square velocity or r.m.s. velocity is written as c r.m.s. and is given by the
equation:
r.m.s. velocity = c r.m .s. = [c2 ]1 /2 = [u12 + u2 2 + …+ uN2 ]1 /2 /N
We can use this equation to calculate the root mean square velocity of gas molecules at
any given temperature and pressure.
Mr. INDRAPAL PATEL, ASST. PROF.
DEPTT. PHYSICS, LNCT JABALPUR