Kinetic Theory of Gases

The kinetic theory of gases is a simple, classical model of the thermodynamic behaviour of gases. It has established many fundamental thermodynamic concepts and is also historically significant. 

We use this theoretical model to study the action and reaction of gas molecules and the thermodynamic behaviour of gases. The model describes the composition of gas in terms of submicroscopic particles (atoms or molecules). It assumes that the size of the gas molecules is very small as compared to the distance between them. The gas molecules are constantly in a random motion and hence collide either among themselves or with the walls of the container. This creates pressure among the gas molecules.

These gas molecules contain all the standard physical quantities like mass, momentum, and energy and hence, also possess density, momentum, and pressure. The basic version of the model describes the ideal gas and takes into account no other particle interactions. The model also takes into account related phenomena like Brownian motion.

Basic Important Formulae

Density (ρ): Sum of mass of gas molecules/ The total volume of gas molecules

Pressure (P): Force/ Area

Definition

In the nineteenth century, the British scientist James Clerk Maxwell and the Austrian physicist Ludwig Boltzmann pioneered the theory, which became one of the most important concepts in modern science. The kinetic theory of gases connects macroscopic properties of gases like pressure and temperature to macroscopic properties of gas molecules like speed and kinetic energy.

Kinetic Theory of Ideal Gases

The atoms in an ideal gas do not exert any type of force on each other, but instead, they clash with the container’s walls. Experiments prove that ideal gas law can thus relate the pressure, volume, temperature, and the number of moles of an ideal gas:

PV = nRT,

In which R is a constant also known as the universal gas constant.

It is important to:

1. Ensure that all quantities follow the same unit system!
2. The temperature, T, must be expressed in Kelvin.
3. n denotes the number of moles of the gas, where

n = mass of sample/Molecular mass of gas

Assumptions in the Kinetic Theory of Gases

• Composition: Gas consists of a large number of atoms and molecules.
• Point masses: Atoms and molecules are almost point-sized with a very small mass and hence a small volume.
• Nil force of attraction: Gas particles are independent and have no force of attraction in between them.
• The volume of gas: The gas takes up the shape of the container, whether big or small and is hence assumed to have the volume of the container.
• Kinetic energy: Since the gas particles are in constant random motion, they have some kinetic energy. The kinetic energy is found to be proportional to temperature.
•  Conservation of energy/momentum: The collisions that take place within a gas molecule are completely elastic; that is, there is no loss of energy. Hence, the energy and the momentum always remain conserved.
• The pressure exerted: The collisions that take place inside the molecule also tend to exert pressure on the walls of the container. This pressure equals force per unit area.
• Mean free path: The average distance covered by a particle to meet another particle is called the mean free path. Mathematically, the mean free path can be represented as:

                    λ   =     m /√2πd²P           

Postulates of Kinetic Theory of Gases:

The following are the characteristics of the kinetic theory of gases postulates:

1- A gas’s molecules are small and remain far apart. The majority of a gas’s volume is space.

2- Gas molecules are constantly moving at random. There are just as many molecules moving in one direction as there are in the other.

3- Molecules can collide with the container’s walls and with one another. The pressure of the gas is determined by collisions with the walls.

4- When molecules collide, they lose no kinetic energy; thus, the collisions are said to be perfectly elastic. Unless there is some outside interference with the molecules, the total kinetic energy remains constant.

5- Except during the collision process, the molecules have no attractive or repulsive forces on one another. Between the collisions, they move in straight lines.

Since real gases do not follow ideal gas laws, a new equation had to be made to correct the deviations made by real gases that were caused by molecular interactions and molecules. This equation was called the Van der Waals equation.

P = RT/  V-b – a²/ V²     

Where P = Pressure

           R = Universal gas constant

           T = Absolute Temperature

           V = Molar volume

           b = Gas constant b

           a = Gas constant a

Conclusion

The kinetic theory of gases explains a gas’s microscopic features in terms of its molecules’ mobility. A molecule is the smallest unit with the same chemical properties as the substance, and the gas is thought to be made up of a huge number of similar, discrete particles called molecules. The pressure is exerted by the gas’s continuous collision with any surface; the higher the density of a gas, the more frequent the number of collisions between molecules and the surface, and the greater the pressure exerted.

Between the 1860s and the 1880s, Maxwell, Boltzmann, and Clausius created elements of kinetic theory. There are kinetic theories for gases, solids, and liquids. The kinetic theory of gases is vital for understanding how the diffusion mechanism captures particles.