2.5 Diffusion of Gases

Introduction

Have you ever smelled perfume from across a room? Or noticed the smell of food cooking in another part of the house? These are examples of diffusion — the process by which gas particles spread from an area of high concentration to an area of low concentration.

Diffusion is one of the most important properties of gases. It explains how gases mix, how smells travel, and how substances move in the air we breathe.

Definition

Diffusion: Diffusion is the process by which gas particles spread from an area of high concentration to an area of low concentration due to their random motion.

In simple words: Diffusion is the spreading out of gas particles until they are evenly mixed.

Main Idea

• Gas particles are in constant random motion.
• They move from areas of high concentration to areas of low concentration.
• Eventually, the particles spread out evenly throughout the available space.
• This even spreading is called equilibrium.
• The rate of diffusion depends on molecular mass and temperature.

Core Concept

Diffusion happens because gas particles have kinetic energy and move randomly in all directions. When two different gases come into contact, their particles move into each other's space, and over time, they mix completely.

Simple explanation: Imagine a room with two groups of people — one group on the left and one on the right. If they start walking randomly, after some time, people from both groups will be spread evenly across the room. That is diffusion.

Detailed Explanation

Diffusion Process Explained by Kinetic Particle Theory

What happens:

• When two different gases come into contact, their particles begin to move together.
• Because of their kinetic energy, each type of gas particle moves randomly in all directions.
• The random motion of these particles ensures that the particles from each of the two gases move into the other gas's space.
• This random and constant motion causes the gases to spread and mix up.
• The gas particles change direction as they move and collide with each other.
• As they change direction, they spread out and move through the space available to them.
• As time goes on, this random motion causes the particles to spread out evenly across the space.
• Eventually, the concentration of both types of gas particles is uniform across the entire space, and equilibrium is achieved.

Key point: Diffusion is driven by the random motion of particles. It is a passive process — it does not require any external force.

Factors Affecting Diffusion

The rate of diffusion — the process by which molecules spread from areas of high concentration — is affected by several factors, including molecular weight and temperature.

1. Molecular Weight

According to Graham's law of diffusion:

The rate of diffusion is inversely proportional to the square root of the molar mass of the gas particles.

Mathematically:

Rate of diffusion, r ∝ 1√m at constant T and P

This means that lighter molecules diffuse faster than heavier ones.

According to kinetic particle theory:

• All molecules at the same temperature have the same average kinetic energy.
• Since kinetic energy (K.E) = 12mv², where m is the molecular mass and v is the velocity, lighter molecules (smaller m) have a greater velocity (v) than heavier molecules with the same kinetic energy.
• Because lighter molecules move faster, they can travel greater distances in a given time than heavier molecules, resulting in a higher rate of diffusion.

Simple explanation: Light molecules are like small, fast runners. Heavy molecules are like big, slow runners. At the same energy, the small ones move faster.

Example: Hydrogen gas (H₂, molar mass = 2 g/mol) diffuses much faster than oxygen gas (O₂, molar mass = 32 g/mol).

2. Temperature

What happens:

• Diffusion rate increases with temperature.
• Higher temperatures give molecules more energy, which increases their kinetic energy.
• As the temperature increases, the average kinetic energy of the molecules increases.
• Since kinetic energy is proportional to the square of the velocity, this results in a higher molecular velocity.
• Higher molecular velocities at higher temperatures cause more frequent and energetic collisions between molecules, facilitating faster diffusion.

Simple explanation: When you heat a gas, its particles move faster. Faster particles spread out more quickly. So diffusion is faster at higher temperatures.

Example: Smell of food spreads faster when the food is hot than when it is cold.

Summary Table

Intermediate Level

Diffusion explained by kinetic particle theory:

• Gas particles are in constant random motion.
• They move from high concentration to low concentration.
• Eventually, they spread evenly (equilibrium).

Factors affecting diffusion:

Graham's Law: r ∝ 1√m

Key insight: At the same temperature, all gas molecules have the same average kinetic energy. Since KE = 12mv², lighter molecules must have higher velocities.

Formula / Mathematical Form

Graham's Law of Diffusion:

r ∝ 1√m

Where:

• r = rate of diffusion
• m = molar mass of the gas

For two gases at the same temperature and pressure:

r₁r₂ = √m₂m₁

Where:

• r₁ = rate of diffusion of gas 1
• r₂ = rate of diffusion of gas 2
• m₁ = molar mass of gas 1
• m₂ = molar mass of gas 2

Key point: The lighter the gas, the faster it diffuses.

Solved Example

Example: Compare the rates of diffusion of hydrogen gas (H₂, molar mass = 2 g/mol) and oxygen gas (O₂, molar mass = 32 g/mol) at the same temperature and pressure.

Given: m₁ = 2\ g/mol (H₂) m₂ = 32\ g/mol (O₂)

Required: r₁r₂ = ?

Formula: r₁r₂ = √m₂m₁

Substitution: r₁r₂ = √322

Calculation: r₁r₂ = √16 = 4

Final Answer: Hydrogen diffuses 4 times faster than oxygen.

Check: Hydrogen is lighter → diffuses faster. ✓

Important Points

• - Diffusion is the spreading of gas particles from high concentration to low concentration.
• - It is driven by the random motion of particles.
• - Eventually, particles spread evenly (equilibrium).
• - Molecular weight affects diffusion rate: lighter gases diffuse faster.
• - Temperature affects diffusion rate: higher temperature → faster diffusion.
• - Graham's Law: r ∝ 1√m.
• - At the same temperature, all gas molecules have the same average kinetic energy.
• - Lighter molecules have higher velocities → faster diffusion.
• - Diffusion is faster at higher temperatures.

Remember

• - Diffusion = spreading of gas particles.
• - High concentration → low concentration.
• - Driven by random motion.
• - Equilibrium = even spreading.
• - Lighter gases diffuse faster.
• - Higher temperature → faster diffusion.
• - Graham's Law: r ∝ 1√m.
• - At same T, all gases have same average KE.
• - Lighter molecules → higher velocity.

Common Mistakes

Quick Revision

Diffusion is the process by which gas particles spread from an area of high concentration to an area of low concentration due to their random motion.

Diffusion Process Explained by Kinetic Particle Theory:

• When two different gases come into contact, their particles begin to move together.
• Because of their kinetic energy, each type of gas particle moves randomly in all directions.
• The random motion causes the gases to spread and mix up.
• Eventually, the concentration of both types of gas particles is uniform across the entire space, and equilibrium is achieved.

Factors Affecting Diffusion:

• Molecular Weight: According to Graham's law of diffusion, the rate of diffusion is inversely proportional to the square root of the molar mass of the gas particles. Lighter molecules diffuse faster than heavier ones.
• Temperature: Diffusion rate increases with temperature. Higher temperatures give molecules more energy, which increases their kinetic energy. Higher molecular velocities at higher temperatures cause more frequent and energetic collisions between molecules, facilitating faster diffusion.

• Graham's Law:
• r ∝ 1√m

60-Second Revision

• Diffusion = spreading of gas particles from high to low concentration.
• Driven by random motion.
• Equilibrium = even spreading.
• Lighter gases diffuse faster (Graham's Law: r ∝ 1√m).
• Higher temperature → faster diffusion.
• At same T, all gases have same average KE.
• Lighter molecules → higher velocity → faster diffusion.
• ⚠️ Warning: diffusion is driven by random motion, not by a force.