Ideal Gas Laws - Physics A Level Study Notes

Ideal Gas Laws form the foundation for understanding gas behaviour at the molecular level. An ideal gas is a theoretical gas composed of randomly moving point particles that interact only through elastic collisions, with negligible intermolecular forces and volume.

Key Equations:

1. Equation of State: pV = nRT where p = pressure (Pa), V = volume (m³), n = amount of substance (mol), R = molar gas constant (8.31 J mol⁻¹ K⁻¹), T = absolute temperature (K)

2. Alternative form: pV = NkT where N = number of molecules, k = Boltzmann constant (1.38 × 10⁻²³ J K⁻¹)

3. Boyle's Law: p₁V₁ = p₂V₂ (constant T and n)

4. Charles's Law: V₁/T₁ = V₂/T₂ (constant p and n)

5. Pressure Law: p₁/T₁ = p₂/T₂ (constant V and n)

Kinetic Theory Assumptions: Gas molecules are in continuous random motion; collisions are perfectly elastic; intermolecular forces are negligible except during collisions; molecular volume is negligible compared to container volume; collision time is negligible compared to time between collisions.

Key Definitions:

• Absolute zero (0 K = -273°C): The lowest possible temperature where particles have minimum kinetic energy
• Mole: Amount of substance containing 6.02 × 10²³ particles (Avogadro's constant, Nₐ)
• Root mean square (r.m.s.) speed: √(mean of v²) representing average molecular speed

Mnemonic: "Pretty Vivid = New Red Truck" for pV = nRT

Cambridge Note: Always convert temperature to Kelvin and pressure to Pascals in calculations.

Understanding ideal gas behaviour illuminates countless everyday phenomena. Consider a bicycle tyre pump: as you compress the handle, you decrease the volume available to air molecules. With the same number of molecules now confined to a smaller space, they collide with the pump walls more frequently, increasing pressure—Boyle's Law in action.

Hot air balloons demonstrate Charles's Law beautifully. When propane burners heat the air inside the envelope, molecular kinetic energy increases. At constant atmospheric pressure, the gas expands, decreasing its density. The balloon rises because the heated air inside weighs less than the cooler surrounding air it displaces.

Car tyres on hot days exemplify the Pressure Law. Morning tyre pressure might read 32 psi at 15°C, but after motorway driving, internal temperature rises to 45°C. Since volume remains essentially constant (rigid tyre walls), pressure increases proportionally with absolute temperature—potentially reaching 35-36 psi.

Think of gas molecules like dancers at a party: In a small room (low volume), dancers bump into walls frequently (high pressure). Play faster music (higher temperature), and dancers move more energetically, hitting walls harder and more often (increased pressure). Add more guests (more moles), and wall collisions increase proportionally.

Aerosol cans carry warnings against heating because trapped gas obeys pV = nRT. If you heat a sealed can (constant n and V), temperature T rises, forcing pressure p to increase dramatically. This can exceed the container's structural limit, causing explosive failure—a critical safety consideration in consumer products.

Real-world limitation: Real gases deviate from ideal behaviour at high pressures and low temperatures when intermolecular forces and molecular volume become significant.