What is the Kinetic Theory of Gases?

Kinetic theory of gases is the model or method which was developed in the 19th century by Maxwell and Boltzmann. This is possible as the interatomic force which is of short-range forces that are important for solids and liquids can be neglected for gases. This theory or gas law gives a molecular interpretation of the pressure and temperature of a gas and is consistent with gas laws and Avogadro’s hypothesis. This theory is very helpful to correctly explain the specific heat capacities of many gases, kinetic energy and it also explains the transport qualities such as viscosity, thermal conductivity, and diffusion with molecular parameters. As stated in the kinetic-molecular theory, the temperature of a substance or gas particle is related to the average kinetic energy of the particles of that substance. When a substance is heated, some of the absorbed energy is stored within the particles, while some of the energy increases the motion of the particles, called average kinetic energy.

Important characteristics of Gases

Gases have some important characteristics which are described in brief given below:

Gases are highly compressible

An outside pressure compresses the fuel line pattern and reduces its extent, disposing of the outside pressure permits the fuel line extent to increase.

Gases are thermally expendable

When a fuel line pattern is heated, its extent will increase and while it's far cooled then, its extent decreases.

Gases have high viscosity

Gases go with the drift a great deal less difficult than beverages or solids.

Most gases have low densities

Gas densities are in order of gram in keeping with liter whereas, beverages and solids are gram in keeping with cubic cm. a thousand instances greater.

Gases are infinitely miscible

Gases blend in any percentage including in air, a combination of many gases.

Kinetic Theory of Gases

Postulates

There are some points or observations are observed in the reference of the kinetic theory of gases are given following-

• Molecules of the same gases are identical in all respects. (mass, shape & size)
• Molecules or gas particles are constantly in random motion along straight lines.
• All the collisions of gas molecules among themselves & with the container wall are elastic in nature and in random motion. According to this, there will be no loss in the presence of momentum or kinetic energy.
• The pressure of a gas is due to the collision of molecules with the container wall.
• P ∝ No. of collision of molecules per unit area(where P = Pressure of the gas)
• The kinetic energy of gas depends only & only upon temperature (absolute)
• The volume occupied by gas molecules is negligible when compared to the volume of gas.
• There is no intermolecular force of attraction between molecules.
• Gravity is neglected because molecules of gases are so and so light and in this condition, gravity does not pull the molecules and neglected.

Assumptions

There are some useful assumptions of the kinetic theory of gases are given the following:

• A gas is composed of a large number of very small particles called molecules.
• These all particles or molecules have the same mass.
• The molecules are always in a state of motion with varying velocities in all possible directions.
• The hastily transferring debris continuously collides among them and with the partitions of the box and a lot of these collisions are flawlessly elastic. I.e. there's no lack of kinetic electricity inside the collision.
• Expect during collisions, the interaction between the molecules is totally negligible.
• The distance among any consecutive collisions is referred to as loose direction and the common distance is referred to as suggest loose direction.
• The common kinetic electricity of the fuel line debris relies upon simplest at the absolute temperature of the system.
• The time of collisions is negligible as compared with the time taken to cover the free path because having mass, gravity will accelerate molecules.
• The volume of the molecule is negligible in comparison to the volume of the gas.   

Derivation: Pressure exerted by the Gas

As we know that, the pressure is equal to the force exerted by the atoms or molecules hitting and rebounding from a unit area of the gas container surface.

Let us consider, a gas of 'n' molecules each of mass 'm' in closed in a cube of volume ${\text{V = L}}^{\text{3}}$

Now, consider a molecule 'P' moving in a random direction with velocity 'V'. Let us take ${\text{V}}_{\text{x}},{\text{V}}_y, {\text{V}}_z$, be the components of ' $\text{V}$ ' along three mutually perpendicular X, Y, Z-axis respectively.

$$P=m{V}_x$$

$$\Delta \text{P}={\text{mV}}_{\text{x}}-\left(-{\text{mV}}_{\text{X}}\right)$$

$$\Delta \text{P}=2{\text{mV}}_x$$

Now, $\text{F}=\Delta \text{P}/\Delta \text{T}$ (According to Newton's second law)

Now, need to find $\Delta T=2L$ Now, $\text{F}=2{\text{mV}}_{\text{x}}/2 \text{L}/{\text{V}}_{\text{x}}$$\text{F}={\text{mV}}_{\text{x}}^2/\text{L}$............ Equation 1

Now, we consider the components of velocity equal ${\text{V}}^2={\text{V}}_{\text{x}}^2{\text{+V}}_{\text{y}}^2{\text{+V}}_{\text{z}}^2$$V_x=V_y=V_2$${\text{v}}^2=3 {\text{V}}_{\text{x}}^2$$v_x^2=1/3v^2$

Now, put this value in equation $1, {\text{F}}_{\text{P}}=1/3{\text{mV}}^2/\text{L}$

$$\begin{array}{l}\text{F}={\text{mnV}}^2/\text{L}(\text{For n particles})\hfill \\ \text{ Now, Pressure of the gas, }\hfill \\ P=\text{F}/\text{A}\hfill \\ P=mn{V}^2/L^{2}L\hfill \\ \text{ Hence P}=1/3\text{mn}/{\text{Vv}}^2\hfill \end{array}$$

Difference between Real Gas and Ideal Gas

There are some differences between real gases & ideal gases are given following in table.

Context and Applications

• Topic is useful for Bachelors and Masters in Chemistry.