Gas laws and kinetic theory

Why gases behave as they do

The kinetic molecular theory explains gas behaviour with a few assumptions:

1. Gases are made of tiny particles that are far apart compared with their size.
2. The particles move constantly and randomly in straight lines until they collide.
3. Collisions are perfectly elastic (no kinetic energy is lost overall).
4. There are no attractive or repulsive forces between particles.
5. The average kinetic energy of the particles is proportional to the kelvin temperature.

A gas that follows these rules exactly is an ideal gas. Real gases behave nearly ideally at high temperature and low pressure.

Measuring gases

• 1 atm = 101.325 kPa = 760 mmHg
• K = °C + 273.15 (usually 273)

Always use kelvin in gas law calculations. At absolute zero (0 K or −273.15 °C), particle motion is at its minimum.

Boyle’s law (pressure and volume)

Boyle’s law: at constant temperature, pressure and volume are inversely proportional.

P₁V₁ = P₂V₂

Squeeze a gas into half the volume, and the particles hit the walls twice as often, so pressure doubles.

Example: A balloon holds 4.0 L at 100 kPa. What’s its volume at 50 kPa?
V₂ = (100 × 4.0) ÷ 50 = 8.0 L

This is why balloons expand as they rise and why your ears pop on airplanes.

Charles’s law (volume and temperature)

Charles’s law: at constant pressure, volume is directly proportional to kelvin temperature.

V₁ ÷ T₁ = V₂ ÷ T₂

Hotter particles move faster and push outward more.

Example: 2.0 L of gas at 300 K is heated to 450 K. V₂ = 2.0 × 450 ÷ 300 = 3.0 L

This is why a basketball goes flat in the cold and why hot-air balloons rise.

Gay-Lussac’s law (pressure and temperature)

At constant volume: P₁ ÷ T₁ = P₂ ÷ T₂

This is why aerosol cans warn "do not heat": pressure rises with temperature and can burst the can.

The combined gas law

P₁V₁ ÷ T₁ = P₂V₂ ÷ T₂

Avogadro’s law

At constant temperature and pressure, equal volumes of gases contain equal numbers of particles. At STP (0 °C and 1 atm), one mole of any ideal gas occupies about 22.4 L.

The ideal gas law

The ideal gas law combines all of these:

PV = nRT

R is the gas constant: 8.314 L·kPa/(mol·K) or 0.0821 L·atm/(mol·K).

Example: How many moles of gas are in a 10.0 L tank at 202 kPa and 300 K?
n = PV ÷ RT = (202 × 10.0) ÷ (8.314 × 300) = 0.810 mol

Dalton’s law of partial pressures

In a mixture, each gas exerts its own partial pressure, and the total pressure is the sum:

P(total) = P₁ + P₂ + P₃ + …

Air at sea level (101.3 kPa) is about 78% nitrogen and 21% oxygen, so the partial pressure of oxygen is about 21 kPa. On Mount Everest, total pressure is about one-third of sea level, so climbers get much less oxygen per breath.

Real gases

Real gases deviate from ideal behaviour at:

• high pressure, where particle volume matters
• low temperature, where attractions between particles matter (and gases condense)

Common mistakes

• Using °C instead of K.
• Mixing pressure units with the wrong R value.
• Forgetting that Boyle’s law is inverse: as P goes up, V goes down.

Try it yourself

1. A syringe holds 60 mL of air at 100 kPa. It’s compressed to 20 mL. What is the new pressure?
2. A 1.5 L balloon at 25 °C is put in a freezer at −15 °C. What is its new volume?
3. How many litres does 2.0 mol of gas occupy at STP?
4. Use the kinetic molecular theory to explain why a tire’s pressure rises after a long drive.

(Answers: 300 kPa; 1.5 × 258 ÷ 298 = 1.3 L; 44.8 L; friction heats the air, particles move faster and hit the walls harder and more often)

Quick recap

• Kinetic molecular theory: gas particles move randomly and collide elastically.
• Boyle’s law: P and V are inversely related.
• Charles’s law: V and T (in kelvin) are directly related.
• The ideal gas law PV = nRT connects all four variables.
• Partial pressures add up to the total pressure.