Chapter 12 - Kinetic Theory

A gas exerts pressure even though its molecules are too small to see individually. Its temperature rises when the average molecular kinetic energy increases.

Kinetic Theory Class 11 connects the large-scale properties of gases with the microscopic motion of their molecules.

Ideal gas and equation of state

An ideal gas is a simplified model in which molecules are treated as point particles with negligible intermolecular forces except during collisions.

The pressure, volume, temperature and amount of an ideal gas are related through its equation of state.

Students should use absolute temperature in kelvin while applying gas equations.

Assumptions of kinetic theory

The kinetic theory model assumes that:

• A gas contains a very large number of molecules

• Molecules move randomly

• Their size is negligible compared with their separation

• Intermolecular forces are negligible except during collisions

• Collisions are perfectly elastic

• Collision duration is very small

• Molecules follow Newton’s laws between collisions

These assumptions create an idealised model. Real gases behave approximately like ideal gases under suitable conditions.

Molecular explanation of pressure

Gas molecules repeatedly collide with the walls of their container.

During each collision, molecular momentum changes. The total rate of momentum transfer to the walls produces pressure.

This connects a macroscopic property—pressure—with microscopic molecular motion.

Temperature and kinetic energy

Absolute temperature is related to the average translational kinetic energy of gas molecules.

At the same temperature, different ideal gases have the same average translational kinetic energy per molecule.

However, their molecular speeds need not be the same. Lighter molecules generally move faster than heavier molecules at the same temperature.

Root mean square speed

Because gas molecules have a range of speeds, a representative value called root mean square speed is used.

RMS speed increases with temperature and decreases with molar mass.

Students must distinguish between molecular mass, molar mass and total gas mass.

Degrees of freedom

Degrees of freedom are independent ways in which a molecule can store energy.

Depending on molecular structure and conditions, energy may be stored through translational, rotational and vibrational motion.

Equipartition of energy

The law of equipartition distributes thermal energy among active quadratic degrees of freedom.

It helps explain the molar heat capacities of different gases and the relationship between heat capacities at constant pressure and constant volume.

Mean free path

The mean free path is the average distance travelled by a molecule between successive collisions.

It depends on molecular size and the number density of molecules.

Common student difficulties

Students often:

• Use Celsius instead of kelvin

• Confuse average speed with RMS speed

• Assume all molecules have the same speed

• Mix molecular mass and molar mass

• Memorise degrees of freedom without understanding molecular structure

• Treat ideal-gas assumptions as exact properties of all real gases

Learning with Teachoo

Teachoo provides model explanations, derivations, formulae, NCERT solutions, RMS-speed questions, heat-capacity numericals and MCQs.

The derivations show how pressure and temperature emerge from the motion of many molecules.

Frequently Asked Questions

What is kinetic theory?

Kinetic theory explains the macroscopic behaviour of gases using the random motion and collisions of their molecules.

Do all gas molecules have the same speed?

No. Molecules have a distribution of speeds. RMS speed is one useful measure of this molecular motion.

Do different gases have the same RMS speed at the same temperature?

No. RMS speed also depends on molar mass. Lighter gas molecules have a higher RMS speed at the same temperature.

Why must temperature be used in kelvin?

Gas-law and kinetic-theory relationships use absolute temperature, whose zero corresponds to the lower limit of thermal energy in the idealised model.

What is mean free path?

It is the average distance a gas molecule travels between successive collisions.