Learn What is Molecular Motion and Gas Behaviour?
The Kinetic Theory of Gases explains gas behaviour by treating molecules as constantly moving particles. It helps derive laws like Boyle’s Law and Charles’s Law, showing how pressure, volume, and temperature are related. The theory assumes random molecular motion, elastic collisions, and pressure exerted on container walls.
This page aims to simplify these concepts and highlight their real-world applications in thermodynamics, engineering, and atmospheric science.
Behaviour of Gas Molecules
Gas molecules move randomly in all directions and follow Newton's laws. The main assumptions of the kinetic theory are:
A gas consists of a large number of tiny molecules in continuous motion.
These molecules undergo elastic collisions with each other and with the container walls.
The actual volume of gas molecules is negligible compared to the container volume.
Intermolecular forces are absent, except during collisions.
The average kinetic energy of the molecules is directly proportional to the temperature of the gas.
These assumptions explain why gases expand to fill their containers and exert pressure on the walls.
Ideal Gas Equation
The Ideal Gas Law relates the pressure, volume, temperature, and number of moles of a gas:
$ PV = nRT $
where:
$ P $ = Pressure of the gas
$ V $ = Volume of the gas
$ n $ = Number of moles
$ R $ = Universal gas constant ($ 8.314 , J mol^{-1}K^{-1} $)
$ T $ = Temperature in Kelvin
This equation applies to ideal gases, which perfectly follow the kinetic theory assumptions.
Kinetic Theory of an Ideal Gas
The pressure exerted by a gas on the walls of its container is derived from the molecular motion. According to kinetic theory:
$ P = \frac{1}{3} \frac{mN}{V} v_{\text{rms}}^2 $
where:
$ m $ = Mass of a single gas molecule
$ N $ = Number of molecules in the gas
$ V $ = Volume of the gas
$ v_{\text{rms}} $ = Root mean square (rms) speed of gas molecules
This equation shows that pressure is directly related to the average kinetic energy of the gas molecules, meaning that higher temperature results in higher pressure.
Kinetic Interpretation of Temperature
Temperature is a direct measure of the average kinetic energy of gas molecules. The relation between kinetic energy and temperature is:
$ KE_{\text{avg}} = \frac{3}{2} k_B T $
where:
$ KE_{\text{avg}} $ = Average kinetic energy per molecule
$ k_B $ = Boltzmann’s constant ($ 1.38 \times 10^{-23} J/K $)
$ T $ = Temperature in Kelvin
This equation explains that:
As temperature increases, molecular motion becomes faster.
As temperature decreases, molecular motion slows down.
This interpretation confirms that temperature determines the energy of molecules rather than the other way around.
Degrees of Freedom
The degree of freedom of a gas molecule is the number of independent ways it can store energy. The number of degrees of freedom depends on the type of molecular motion:
Monatomic gases (e.g., He, Ar) → 3 degrees of freedom (motion in x, y, and z directions).
Diatomic gases (e.g., O₂, N₂) → 5 degrees of freedom (3 translational + 2 rotational).
Polyatomic gases (e.g., CO₂, CH₄) → 6 or more degrees of freedom (translational, rotational, and vibrational).
Degrees of freedom help in energy distribution calculations.
Law of Equipartition of Energy
The Law of Equipartition of Energy states that energy is equally distributed among all degrees of freedom. The energy per degree of freedom is:
$ E = \frac{1}{2} k_B T $
The total average energy per molecule is:
$ KE_{\text{total}} = \frac{f}{2} k_B T $
For one mole of gas, the total kinetic energy is:
$ KE_{\text{mole}} = \frac{f}{2} nRT $
where $ f $ is the number of degrees of freedom.
For different gases:
Monatomic gas (f = 3) → $ KE = \frac{3}{2} nRT$
Diatomic gas (f = 5) → $ KE = \frac{5}{2} nRT $
Polyatomic gas (f = 6 or more) → $ KE = \frac{6}{2} nRT$
List of Important Formulas
Conclusion
The Kinetic Theory of Gases provides a fundamental understanding of gas behaviour through molecular motion. It explains key gas laws and their role in thermodynamics, engineering, and atmospheric science. By grasping this theory, we better understand how gases interact, helping in advancements like engine efficiency, weather predictions, and industrial applications.
Essential Study Materials for NEET 2025
FAQs on Understanding the Kinetic Theory of Gases
1. What is the Kinetic Theory of Gases?
The Kinetic Theory of Gases explains the behaviour of gases by assuming that gas molecules are in constant random motion and undergo elastic collisions. It helps in understanding gas properties like pressure, temperature, and volume at a molecular level.
2. What are the main assumptions of the Kinetic Theory of Gases?
Gas molecules are in continuous random motion. Collisions between gas molecules and container walls are elastic (no loss of kinetic energy). The volume of individual gas molecules is negligible compared to the total gas volume.
3 .What is the relation between temperature and kinetic energy of gas molecules?
The average kinetic energy of gas molecules is given by:
$ KE_{\text{avg}} = \frac{3}{2} k_B T $
This shows that as temperature increases, the kinetic energy of gas molecules also increases.
4. What is the ideal gas equation?
The ideal gas equation is:
$ PV = nRT $
5 . What is the significance of degrees of freedom in gases?
The degree of freedom refers to the number of independent ways a molecule can store energy. It depends on the type of gas:
Monatomic gas (e.g., He, Ar) → 3 degrees of freedom (translational motion only).
Diatomic gas (e.g., O₂, N₂) → 5 degrees of freedom (translational + rotational).
Polyatomic gas (e.g., CO₂, CH₄) → 6 or more degrees of freedom.
6. What is the Law of Equipartition of Energy?
The Law of Equipartition of Energy states that energy is equally distributed among all degrees of freedom. The energy per degree of freedom is:
$ E = \frac{1}{2} k_B T $
The total energy per molecule is:
$ KE_{\text{total}} = \frac{f}{2} k_B T $
where $ f $ is the degrees of freedom.
7. What are the different types of speeds in Kinetic Theory?
Most probable speed: $ v_p = 1.41 \sqrt{\frac{k_B T}{m}} $
Average speed: $ v_a = 1.59 \sqrt{\frac{k_B T}{m}} $
Root mean square (RMS) speed: $ v_{\text{rms}} = 1.73 \sqrt{\frac{k_B T}{M}} $
These speeds help describe how gas molecules move at different temperatures.
8. What is meant by mean free path?
The mean free path is the average distance a gas molecule travels before colliding with another molecule. It is given by:
$ \lambda = \frac{1}{\sqrt{2} \pi n d^2} $
where $ n $ is the number of molecules per unit volume and $ d $ is the diameter of the molecules.
9. Why do gases exert pressure?
Gas molecules are in continuous motion and collide with the walls of the container. These collisions exert force per unit area, which we perceive as gas pressure.
10 . Why do real gases deviate from ideal gas behaviour?
The kinetic theory assumes that gas molecules have no volume and no intermolecular forces, but real gases have both. At high pressures and low temperatures, gas molecules experience intermolecular forces and occupy volume, causing deviations from the ideal gas law.
