2.4.1 Boyle's Law

Introduction

Boyle's Law describes what happens to the volume of a gas when its pressure changes, while the temperature and the amount of gas stay the same. It is one of the oldest and simplest gas laws.

Definition

Boyle's Law: It states that for a fixed amount of gas at a constant temperature, the volume of a gas is inversely proportional to its pressure.

In simple words: If you increase the pressure on a gas, its volume decreases. If you decrease the pressure, its volume increases — as long as the temperature and the amount of gas stay the same.

Main Idea

• Inverse relationship: When pressure goes up, volume goes down.
• When pressure goes down, volume goes up.
• The product of pressure and volume is constant (at constant temperature and fixed amount of gas).

Core Concept

The relationship can be written mathematically as:

V ∝ 1P

This means:

V = k · 1P

Rearranging:

PV = constant

Where:

• V = volume of the gas
• P = pressure of the gas
• k = a constant (for a fixed amount of gas at constant temperature)

Key point: If the pressure is doubled, the volume is halved. If the pressure is halved, the volume is doubled.

Mathematical Form

The mathematical statement of Boyle's Law is:

V ∝ 1P

V = k · 1P

PV = constant

For two different sets of conditions (with the same amount of gas at constant temperature):

P₁ V₁ = P₂ V₂

Where:

• P₁ = initial pressure
• V₁ = initial volume
• P₂ = final pressure
• V₂ = final volume

Units:

• Pressure is usually measured in atm, kPa, or Pa.
• Volume is usually measured in dm³, cm³, or m³.

Kinetic Particle Theory Interpretation

Effect of Volume on Pressure

What happens when volume decreases:

• When the volume of a gas decreases, the gas particles have less space to move around.
• This results in more frequent collisions with the walls of the container.
• More frequent collisions → increased pressure.

What happens when volume increases:

• If the volume increases, the particles collide with the walls less often.
• Less frequent collisions → decreased pressure.

Simple explanation: Imagine a room full of people bouncing around. If you make the room smaller, the people hit the walls more often. If you make the room bigger, they hit the walls less often. The same idea applies to gas particles.

Constant Temperature

• The average kinetic energy of the particles remains constant since the temperature does not change.
• The speed of the particles does not change.
• But the frequency of collisions with the container walls changes due to the volume change.

Key point: At constant temperature, the particles move at the same average speed. Only the number of collisions per unit area changes when the volume changes.

Formula / Mathematical Form

V ∝ 1P

V = k · 1P

PV = constant

P₁ V₁ = P₂ V₂

Solved Example

Example: A gas occupies a volume of 500\ cm³ at a pressure of 1\ atm. If the pressure is increased to 2\ atm at constant temperature, what will be the new volume?

Given: P₁ = 1\ atm V₁ = 500\ cm³ P₂ = 2\ atm

Required: V₂ = ?

Formula: P₁ V₁ = P₂ V₂

Substitution: (1)(500) = (2)(V₂)

Calculation: V₂ = 5002 V₂ = 250\ cm³

Final Answer: The new volume is 250\ cm³.

Check: Pressure doubled → volume halved. ✓

Important Points

• - Boyle's Law applies to a fixed amount of gas at constant temperature.
• - Volume is inversely proportional to pressure.
• - PV = constant.
• - The formula for two sets of conditions is P₁ V₁ = P₂ V₂.
• - When volume decreases, pressure increases (more frequent collisions).
• - When volume increases, pressure decreases (less frequent collisions).
• - At constant temperature, the average kinetic energy of the particles remains constant.

Remember

• - Boyle's Law → pressure and volume are inversely related.
• - PV = constant.
• - P₁ V₁ = P₂ V₂.
• - Pressure up → volume down.
• - Pressure down → volume up.
• - Temperature must be constant.
• - Amount of gas must be fixed.
• - More collisions → higher pressure.
• - Fewer collisions → lower pressure.

Common Mistakes

Quick Revision

Boyle's Law states that for a fixed amount of gas at constant temperature, the volume of a gas is inversely proportional to its pressure.

• Mathematically:
• V ∝ 1P
• V = k · 1P
• PV = constant
• P₁ V₁ = P₂ V₂

Kinetic Particle Theory Interpretation:

• Effect of Volume on Pressure: When volume decreases, particles have less space → more frequent collisions with walls → increased pressure. When volume increases, particles collide less often → decreased pressure.
• Constant Temperature: The average kinetic energy of particles remains constant. The speed of particles does not change, but the frequency of collisions with the container walls changes due to the volume change.

60-Second Revision

• Boyle's Law: V ∝ 1P at constant temperature and fixed amount of gas.
• PV = constant
• P₁ V₁ = P₂ V₂
• Pressure ↑ → Volume ↓
• Pressure ↓ → Volume ↑
• More collisions → higher pressure.
• Particle speed unchanged at constant temperature.
• ⚠️ Warning: Boyle's Law only applies when temperature and amount of gas are constant.