Gas Laws

Grade 11 · Science · Study Guide

Explore the relationships between pressure, volume, temperature, and moles of a gas using the foundational gas laws of chemistry and physics.

Gases behave in predictable ways when conditions change, and scientists have described those behaviors with a set of elegant laws. All of these laws ultimately come together in the Ideal Gas Law, but each individual law isolates one relationship while holding other variables constant. Understanding these laws explains everything from how a tire pump works to why weather balloons expand as they rise.

Boyle's Law states that at constant temperature, pressure and volume are inversely proportional: P₁V₁ = P₂V₂. Squeeze a gas into a smaller space and pressure rises; allow it to expand and pressure drops. Charles's Law describes volume and temperature at constant pressure: V₁/T₁ = V₂/T₂ (temperature always in Kelvin). A gas expands when heated and contracts when cooled — this is why a balloon deflates in the cold.

Gay-Lussac's Law covers pressure and temperature at constant volume: P₁/T₁ = P₂/T₂. This explains why sealed aerosol cans warn against high heat. The Combined Gas Law merges all three: (P₁V₁)/T₁ = (P₂V₂)/T₂, useful when two of the three variables change simultaneously.

The Ideal Gas Law, PV = nRT, is the master equation. It relates pressure (P), volume (V), moles of gas (n), the ideal gas constant R (0.0821 L·atm/mol·K), and absolute temperature (T in Kelvin). An ideal gas has no intermolecular forces and zero molecular volume — real gases approach ideal behavior at low pressure and high temperature.

Dalton's Law of Partial Pressures states that the total pressure of a mixture equals the sum of each component's partial pressure: P_total = P₁ + P₂ + P₃. This is critical in scuba diving gas mixtures and respiratory physiology.

Key terms

Boyle's Law

At constant T, P and V are inversely proportional: P₁V₁ = P₂V₂.

Charles's Law

At constant P, V and T are directly proportional: V₁/T₁ = V₂/T₂ (T in Kelvin).

Gay-Lussac's Law

At constant V, P and T are directly proportional: P₁/T₁ = P₂/T₂ (T in Kelvin).

Ideal Gas Law

PV = nRT; relates pressure, volume, moles, and temperature for an ideal gas.

STP

Standard Temperature and Pressure: 0°C (273.15 K) and 1 atm; 1 mol ideal gas = 22.4 L.

Partial Pressure

The pressure exerted by one component of a gas mixture as if it occupied the container alone.

Ideal Gas Constant (R)

R = 0.0821 L·atm/mol·K (or 8.314 J/mol·K).

Practice questions

1. A gas at 2.0 atm occupies 4.0 L. Pressure increases to 4.0 atm at constant temperature. What is the new volume?

   1. 1.0 L
   2. 2.0 L
   3. 8.0 L
   4. 16.0 L
   Show answer

   Boyle's Law: (2.0)(4.0) = (4.0)(V₂) → V₂ = 2.0 L.

2. A gas occupies 3.0 L at 300 K. What volume at 600 K at constant pressure?

   1. 1.5 L
   2. 3.0 L
   3. 6.0 L
   4. 9.0 L
   Show answer

   Charles's Law: 3.0/300 = V₂/600 → V₂ = 6.0 L.

3. In PV = nRT, the letter 'n' represents the number of ______ of gas.

   Show answer

   n is the number of moles of gas in the sample.

4. How many moles of gas are in a 5.0 L container at 1.0 atm and 273 K? (R = 0.0821 L·atm/mol·K)

   1. 0.22 mol
   2. 0.45 mol
   3. 1.0 mol
   4. 2.2 mol
   Show answer

   n = PV/RT = (1.0 × 5.0)/(0.0821 × 273) = 5.0/22.4 ≈ 0.22 mol.

5. Which gas law explains why a sealed spray can may explode if thrown into a fire?

   1. Boyle's Law
   2. Charles's Law
   3. Gay-Lussac's Law
   4. Dalton's Law
   Show answer

   At constant volume, pressure increases proportionally with temperature. Heating the sealed can raises pressure until it exceeds structural limits.

Fun facts

• Jacques Charles, who formulated Charles's Law, was also one of the first humans to fly in a hydrogen balloon — literally living his own law as his balloon expanded with altitude.
• The atmosphere on Mars is about 0.6% of Earth's surface pressure. A 1-liter container brought from Earth to Mars at the same temperature would need to expand to about 167 liters to equalize — Boyle's Law in action.
• Scuba tanks are filled to 200–300 atm. Gay-Lussac's Law explains why leaving a tank in a hot car is dangerous — heat raises pressure and can cause catastrophic failure.

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