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Ideal Gas Molecules

Kinetic Theory of Gases

Learning Outcomes

  • 5.15: Explain how molecules in a gas have random motion and exert force and pressure on container walls
  • 5.18: Understand why increased temperature increases the average speed of gas molecules
  • 5.19: Know that Kelvin temperature is proportional to average kinetic energy

Interactive Gas Simulation

Average Speed
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Pressure
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Average KE
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Maxwell-Boltzmann Speed Distribution

Random Motion

Gas molecules move in random directions with varying speeds, constantly colliding with each other and container walls.

Pressure

Pressure results from the force of molecular collisions against container walls. More collisions or faster molecules means higher pressure.

Temperature and Speed

Higher temperature means molecules move faster on average. The color coding shows this: blue (cold/slow) to red (hot/fast).

Temperature and KE

Temperature (in Kelvin) is directly proportional to average kinetic energy: T ∝ KE. Double the temperature, double the average KE.

Volume and Collisions

Reducing volume at constant temperature increases collision frequency with walls, raising pressure.

Temperature Scales

Learning Outcomes

  • 5.16: Understand why there is an absolute zero at -273°C
  • 5.17: Describe the Kelvin scale and convert between Kelvin and Celsius

Kinetic Energy vs Temperature (Celsius)

This graph shows how kinetic energy relates to temperature in Celsius. Notice that at -273.15°C (absolute zero), the kinetic energy reaches its minimum.

Kinetic Energy vs Temperature (Kelvin)

When we use the Kelvin scale, we see a beautiful direct proportionality between temperature and kinetic energy, starting from absolute zero at 0 K.

What is Absolute Zero?

Absolute zero (-273.15°C or 0 K) is the lowest possible temperature. At this point, molecules have minimum kinetic energy (they don't stop completely due to quantum mechanics, but their motion is minimal). It's impossible to reach absolute zero in practice, but it serves as the zero point for the Kelvin scale.

Why Use Kelvin?

The Kelvin scale starts at absolute zero (0 K), making it ideal for scientific calculations. Temperature in Kelvin is directly proportional to average kinetic energy: if you double the Kelvin temperature, you double the average KE. This simple relationship doesn't work with Celsius!

K = °C + 273.15

Temperature Converter

Example Conversions

Water freezes: 0°C = 273.15 K

Water boils: 100°C = 373.15 K

Room temperature: 25°C = 298.15 K

Absolute zero: -273.15°C = 0 K

Gas Laws

Learning Outcomes

  • 5.20: Use the relationship between pressure and volume at constant temperature: P₁V₁ = P₂V₂
  • 5.21: Use the relationship between pressure and temperature at constant volume: P₁/T₁ = P₂/T₂
  • 5.22: Explain the relationships in terms of kinetic theory

Boyle's Law: P ∝ 1/V (at constant T)

At constant temperature, pressure and volume are inversely proportional. When you compress a gas (reduce volume), molecules hit the walls more frequently, increasing pressure.

Visual Piston Simulation

Pressure: 100
P₁V₁ = P₂V₂

Boyle's Law Calculator

Worked Example: Boyle's Law

Problem: A gas has a volume of 250 cm³ at 100 kPa. What is the pressure if the volume is compressed to 100 cm³ at constant temperature?

Solution:

Given: P₁ = 100 kPa, V₁ = 250 cm³, V₂ = 100 cm³

Using P₁V₁ = P₂V₂:

P₂ = (P₁ × V₁) / V₂ = (100 × 250) / 100 = 250 kPa

Answer: The pressure increases to 250 kPa

Gay-Lussac's Law: P ∝ T (at constant V)

At constant volume, pressure is directly proportional to absolute temperature. When you heat a gas, molecules move faster and hit the walls harder and more frequently, increasing pressure.

Visual Temperature Simulation

Pressure: 100
P₁/T₁ = P₂/T₂

Gay-Lussac's Law Calculator

Worked Example: Gay-Lussac's Law

Problem: A gas has a pressure of 150 kPa at 300 K. What is the pressure if heated to 600 K at constant volume?

Solution:

Given: P₁ = 150 kPa, T₁ = 300 K, T₂ = 600 K

Using P₁/T₁ = P₂/T₂:

P₂ = (P₁ × T₂) / T₁ = (150 × 600) / 300 = 300 kPa

Answer: The pressure doubles to 300 kPa (because temperature doubled)

Knowledge Check

0/5 answered

1. What happens to the average speed of gas molecules when temperature increases?

2. Convert 25°C to Kelvin.

3. If the volume of a gas is halved at constant temperature, what happens to the pressure?

4. Absolute zero is the temperature at which...

5. A gas at 300 K has pressure 150 kPa. If heated to 600 K at constant volume, what is the final pressure?