Kinetic Theory of Gases: Postulates & Assumptions

The kinetic theory of gases is defined as the thermodynamic behavior of gases. The theory explains the macroscopic properties of a gas in terms of the microscopic nature of atoms and molecules present in its composition. 

• In the case of solids and liquids, their physical nature can be described by their shape, size, mass, and volume.
• However, the kinetic theory of gases can be applied in the case of gases. 
• According to the theory, the atoms and molecules are in constant, random motion, frequently colliding with each other and the walls of the container.
• It is used to explain the theory of ideal gas treating the collisions as perfectly elastic.
• The kinetic theory of gases explains the connection between Brownian motion and the Onsager reciprocal relations.

Key Terms: Kinetic Theory of Gases, Ideal Gases, Non-Ideal Gas Behaviour, Avogadro’s Law, Boyle’s Law, Charles’s Law, Graham’s Law of Diffusion, Pressure, Volume, Temperature

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What is the Kinetic Theory of Gases?

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The Kinetic Theory of Gases describes mainly the three properties of gases: volume, pressure, and temperature. It can also explain some transport properties, such as viscosity, thermal conductivity, and mass diffusivity. 

• This theory is based on the molecular composition of the gas in terms of a large number of submicroscopic particles.
• It attempts to develop a correlation between the macroscopic properties and the microscopic phenomenon. 
• According to the kinetic theory of gases, particles undergo random elastic collisions with each other and with the enclosing walls of the container.
• The theory assumes a huge inter-particle distance and that the particles are rather small.

Equation of Kinetic Theory of Gases

The kinetic theory of gases if equation are as follows:

Kinetic gas equation: \(PV = \frac{1}{3}Nm(C_{rms})^2\)

• Where, P = pressure of the gas
• V = volume of the gas
• M = mass of each molecule of the gas
• N = total no. of molecules present in that volume
• C = root mean square speed of the gas

Kinetic Theory of Gase

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Kinetic Theory of Gases Assumptions

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Some important assumptions of Kinetic Theory of Gases are as follows:

Particles

A gas is a collection of large number of loosely-bonded molecules and atoms,

Point Masses

The particles making up the gas are rather small just like a dot on the paper.

Negligible Volume Particles

The distance between the particles is usually much greater than the actual size of the molecules of the gas and there is a large free unoccupied space in the container. Thus the actual volume of the particles is almost negligible compared to the volume of the container.

Nil Force of Interaction

The theory takes into account an ideal gas where the particles are independent and they do not have any (attractive or repulsive) interactions among them.

Particles in Motion

Due to the availability of huge free space and the absence of interactions, the particles move freely around the container constantly but in a straight line.

Volume of Gas

Due to the motion of the gas molecules it can be considered that the gas occupies the whole of a container and thus the volume of the container is the volume of gas as well.

Mean Free Path

Mean Free Path is the average distance a particle travels to meet or collide with another particle in the container.

Kinetic Energy of the Particle

The particles are always in motion which generates the energy and they have an average kinetic energy proportional to the temperature of the gas.

Constancy of Energy / Momentum

Though the particles have a constant collision with other particles or the wall of the container the energy or the momentum does not change. It remains the same due to the collision being totally elastic in nature.

Pressure of Gas

The constant collision of particles on the wall of the container exerts pressure. Thus, the force per unit area is the pressure and it is proportional to the number of particles colliding (frequency of collisions) in unit time per unit area on the wall of the container.

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Kinetic Molecular Theory of Gases Postulates

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The important postulates of the Kinetic Theory of Gases are as follows:

• The gases, though they have a large number of molecules, are small compared to the distance between them. 
• Thus most of the volume occupied by the gas is empty space.
• The average kinetic energy of the gas particles is directly proportional to the temperature of the container or the surroundings.
• The force of gravitation between the molecules is also supposed to be negligible.
• The molecules generally move in different directions with different velocities. 
• Hence, each molecule has a different kinetic energy, but the average energy remains the same.
• The molecules are perfectly elastic hard spheres, and no energy is wasted during collisions with each other or the walls of the containing vessel.
• In the process of striking, some energy from one molecule may be transferred to the other, but the total energy of the gas remains the same.

(A) Understanding Gas Laws of Ideal Gases

Below are some terminologies to understand the gas laws of Ideal Gases 

Number of Particles at Constant Volume: Pressure α Amount 

The force exerted by the collision of the particles on the surrounding wall is the pressure of the gas. It depends on the number of particles of the gas contained. At constant temperature and volume thus the pressure is directly proportionally related to the number of gas molecules.

Avogadro’s Law: At a fixed pressure N\(\alpha\)V

The greater number of particles of a gas increases the collisions and the pressure. If the number of collisions can be reduced only by increasing the volume of the gas it can make the pressure remain constant. Thus at a fixed pressure the volume is proportional to the amount of gas.

Boyle’s Law: At a fixed temperature pressure is \(\alpha\)(1/v)

According to Boyle’s law when the temperature is constant and the volume of the container is reduced then there is an increased number of particles in the unit area and it increases the frequency of collisions per unit area. At constant temperature thus the volume of the container is inversely proportional to the pressure.

Amonton’s Law: At a fixed volume P\(\alpha\)T

When the volume is constant and the kinetic energy of the gas is increased by increasing the temperature, then the particles move more rapidly resulting in more collisions with the container walls, thereby increasing the overall pressure. At constant volume the temperature of the gas is proportional to the pressure.

Charles’s Law: At a fixed pressure V\(\alpha\)T

According to Charles’s law pressure increases along with an increase in the temperature. It can be reduced only by expanding the volume of the gas or the container. At a fixed pressure, the gas’s volume is in direct proportion with the temperature.

Graham’s Law of Diffusion: v\(\alpha\)\(\sqrt{1/M}\)

If it is assumed that two gases with different molecular weights have the same kinetic energy at the same temperature then at constant temperature the velocity of the molecules of the gas are inversely proportional to their molecular weights.

(B) Maxwell – Boltzmann Molecular Distribution of Energy and Velocity

Maxwell – Boltzmann Molecular Distribution of Energy and Velocity helped to calculate the particles' most probable, average and root mean square velocity and find the distribution of gaseous particles between energy zero to infinity. It is found that at constant temperature, the kinetic energy of the gas also remains the same. 

(C) Understanding Non-ideal Gas Behaviour

It is seen that all gas molecules obey the ideal gas laws under conditions of low pressures and high temperatures. There is some fundamental difference between real gas and ideal gas properties. The deviation is traced mainly to wrong or incorrect assumptions in the postulates, which are as follows:

• It is assumed that the volume of a gas is so negligible that it is almost zero. 
• In theory, a gas can be compressed to zero, but it is not possible, indicating that particles have small volume and cannot be neglected.
• The gas molecules are supposed not to interact, but they do interact with each other as well as other molecules of a gas or the container itself.
• All the particles of a real gas do not have the same energy. 
• In practice, the exchange and distribution of energy amongst each other.

Kinetic Theory of Gases

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