# Kinetic Molecular Theory

## Introduction

This theory was developed to explain the gas behavior, hence called the "theory of moving molecules".

**Assumptions:**

- Gases consist of a large number ofmolecules in constant random motion.
- Volume of individual molecules isnegligible compared to volume of container.
- Intermolecular forces (forces between gas molecules) negligible.
- Energy can be transferred between molecules, but total kinetic energy is constant at constant temperature.
- Average kinetic energy of molecules is proportional to temperature.

The theory of moving molecules helps us understand the following:

**Pressure and temperature** at the molecular level
**Pressure of a gas** results from the number of collisions per unit time on the walls of container.
**Magnitude of pressure** is given by how often and how hard the molecules strike.
- The average kinetic energy of the gas molecules increases as the temperature increases.

### Application to Gas Laws

- As
**volume increases** at __constant temperature__, the average kinetic of the gas (*u*) __remains constant__.

However, as **volume increases**, gas molecules will have to travel further to hit the walls of the container.

Therefore, **pressure decreases**.
- If
**temperature increases** at __constant volume__, the average kinetic energy of the gas molecules (*u*) __increases__.

__Therefore__, there are __more collisions with the container__ walls and the **pressure increases**.

The **average kinetic energy (ε)** is related to the root mean square speed (*u*) via the relation:

ε = ½*mu*^{2}

Hence, as *u* __increases__, (ε) will also __increase__

**Remark:**

The average kinetic energy (ε) depends on the mass of the molecules (*m*) and their speed (*u*)

Where the speed (*u*) is related to the molar mass of the gas molecule and the temperature through the relation:

*u* =
√ 3RT/M
Therefore, the speed of a gas molecule **increases with temperature and decreases with its molar mass:**

### Exercises on Kinetic Molecular Theory

*Exercise on Finding the RMS Speed of He atom*

Check your answers here:
*Solution to the Exercise on Finding the RMS Speed of He atom*

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Date of last modification: 2024