This presentation includes: (i) Gas laws (ii) Maxwell Distribution of velocities

1. Dr. Jayeeta Chattopadhyay, Amity University Jharkhand
C H E M 1 0 4 – B . S C . ( H )
C H E M I S T RY ( S E M I I )
Kinetic Theory of Gases

2. What is Kinetic Theory of
Gases?
Describes the molecular composition of the gas in terms of a large
number of submicroscopic particles which include atoms and molecules
Explains that gas pressure arises due to particles colliding with each
other and the walls of the container.
Defines properties such as temperature, volume, pressure s well as
transport properties such as viscosity and thermal conductivity as well
as mass diffusivity.
Explains all the properties that are related to the microscopic
phenomenon.

3. Significance of the theory:
It helps in developing a correlation between the macroscopic
properties and the microscopic phenomenon. In simple terms,
the kinetic theory of gases also helps us study the action of the
molecules. Generally, the molecules of gases are always in
motion and they tend to collide with each other and the walls of
the containers. In addition, the model also helps in
understanding the related phenomena such as the Brownian
motion.

4. Implications:
i) Particles: Gas is a collection of a large number of atoms or molecules.
ii) Point Masses: Atoms or molecules making up the gas are very small particles like a point(dot) on a
paper with a small mass.
iii) Negligible Volume Particles: Particles are generally far apart such that their inter-particle distance
is much larger than the particle size and there is large free unoccupied space in the container.
Compared to the volume of the container, the volume of the particle is negligible (zero volume).
iv) Nil Force of Interaction: Particles are independent. They do not have any (attractive or repulsive)
interactions among them.

5. v) Particles in Motion: The particles are always in constant motion. Because of the lack of interactions and the
free space available, the particles randomly move in all directions but in a straight line.
vi) Volume of Gas: Because of motion, gas particles, occupy the total volume of the container whether it is small
or big and hence the volume of the container to be treated as the volume of the gases.
vi) Mean Free Path: This is the average distance a particle travels to meet another particle.
vii) Kinetic Energy of the Particle: Since the particles are always in motion, they have average kinetic energy
proportional to the temperature of the gas.
viii) Constancy of Energy / Momentum: Moving particles may collide with other particles or containers. But the
collisions are perfectly elastic. Collisions do not change the energy or momentum of the particle.
ix) Pressure of Gas: The collision of the particles on the walls of the container exerts a force on the walls of the
container. Force per unit area is the pressure. The pressure of the gas is thus proportional to the number of
particles colliding (frequency of collisions) in unit time per unit area on the wall of the container.

6. Postulates
• Gases consist of a large number of tiny particles (atoms and molecules). These particles are
extremely small compared to the distance between the particles. The size of the individual
particle is considered negligible and most of the volume occupied by the gas is empty space.
• These molecules are in constant random motion which results in colliding with each other and
with the walls of the container. As the gas molecules collide with the walls of a container, the
molecules impart some momentum to the walls. Basically, this results in the production of a
force that can be measured. So, if we divide this force by the area it is defined to be the
pressure.
• The collisions between the molecules and the walls are perfectly elastic. That means when the
molecules collide they do not lose kinetic energy. Molecules never slow down and will stay at
the same speed.
• The average kinetic energy of the gas particles changes with temperature. i.e., The higher the
temperature, the higher the average kinetic energy of the gas.
• The molecules do not exert any force of attraction or repulsion on one another except during

7. Gas Laws of Ideal Gases:
• i) Pressure α Amount or Number of Particles at Constant Volume:
• The collision of the particles on the walls of the container creates pressure. Larger the
number of the particle (amount) of the gas, the more the number of particles colliding
with the walls of the container.
• At constant temperature and volume, larger the amount (or the number of particles) of
the gas higher will be the pressure.

8. Gas Laws of Ideal Gases:
• Avogadro’s Law – N α V at Constant Pressure:
• When there is a greater number of particles it increases the collisions and the pressure. If
the pressure is to remain constant, the number of collisions can be reduced only by
increasing the volume.
• At constant pressure, the volume is proportional to the amount of gas.

9. Gas Laws of Ideal Gases:
• Boyle’s Law – Pressure α 1/Volume, at Constant Temperature:
• At a constant temperature, the kinetic energy of particles remains the same. If the
volume is reduced at a constant temperature, then the number of particles in unit volume
or area increases. If there is an increased number of particles in the unit area then it
increases the frequency of collisions per unit area.
• At constant temperature, the smaller the volume of the container, the larger the pressure.

10. Gas Laws of Ideal Gases:
Amonton’s Law: P α T at Constant Volume:
• The kinetic energy of the particle increases with temperature. When the volume is
constant, with increased energy, particles move fast and increase the frequency of
collisions per unit time on the walls of the container and hence the pressure.
• At constant volume, the higher the temperature higher will be the pressure of the gas.

11. Gas Laws of Ideal Gases:
• Charles’s Law – V α T at Constant Pressure:
• Change of temperature changes proportionately to the pressure. If the pressure also has
to remain constant, then the number of collisions has to be changed proportionately. At
constant pressure and a constant amount of substance, collisions can be changed only
by changing the area or volume.
• At constant pressure, volume changes proportionally to temperature.

12. Gas Laws of Ideal Gases: Graham’s Law

13. Maxwell Distribution of Velocities
• The Maxwell-Boltzmann distribution (also known as the Maxwell distribution) is a
statistical representation of the energy of molecules in a classical gas. The
distribution of velocities among the molecules of gas was initially proposed by
Scottish physicist James Clerk Maxwell in 1859, based on probabilistic reasons.
German scientist Ludwig Boltzmann expanded Maxwell's result in 1871 to express
the distribution of energy among molecules.

14. Maxwell Distribution of Velocities
• As a result, the fraction of molecules with a specific speed remains
constant. As they were the first to formulate it, it is known as the
distribution of speeds as well as the Maxwell-Boltzmann distribution law or
Maxwell law. Maxwell and Boltzmann plotted the fraction of molecules that
move at different speeds (along the y-axis), against the speeds of the
molecules (along the x-axis). The resulting curve is known as ‘Maxwell's
distribution curve’.

16. Gas is made up of thousands of microscopic particles (atoms or
molecules) separated by enormous empty gaps. These particles move in
all directions all of the time. They collide with each other as well as the
container's walls while in motion. The molecules' speed and directions
are constantly changing as a result of these collisions. As a result, the
speed of all the molecules in a particular gas sample is not the same.
Individual molecule speeds vary and are distributed over a broad range.
Even if all of the particles started at the same speed, molecular
collisions will cause them to move at different speeds. The speeds of
various molecules are also changing. However, at a given temperature,
the distribution of speeds among different molecules remains constant,
despite changes in individual speeds.

17. Key characteristics of the Maxwell
distribution of velocities:
• (i) The fraction of molecules with extremely low or extremely high velocities is
extremely small.
• (ii) The fraction of molecules with higher velocities increases until it reaches a plateau,
at which point it begins to decline.
• (iii) The maximum fraction of molecules has a velocity, which corresponds to the
curve's peak. This is referred to as the most likely velocity.
Thus, the most likely speed of a gas is the speed of the greatest fraction of gas
molecules at a given temperature.

18. The Effect of Temperature on Speed
Distribution
• The increase in molecular motion occurs as the temperature of the gas rises. As the
temperature rises, so does the value of the most likely speed (up). In fact, as the
temperature rises, the entire distribution curve shifts to the right. In other words, as
temperatures rise, the curve broadens. It should be noted, however, that if the
temperature remains constant, the distribution of speeds among molecules does not
change.
• The speed distribution at a given temperature is also affected by the mass of the
molecules. At the same temperature, heavier gas molecules move slower than lighter
gas molecules. Lighter nitrogen molecules, for example, move faster than heavier
chlorine molecules. As a result, at any given temperature, nitrogen molecules are more
likely to move than chlorine molecules.