The Gas Laws

Pressure, volume, temperature and amount are locked in a see-saw. Learn the four simple rules that tie them together.

High schoolIntro Gen ChemUni Year 1
⏱️ About 20 min

Push a plunger into a sealed syringe and the trapped air fights back harder. Leave a balloon in a hot car and it strains at its skin. These are not separate mysteries — they are the same handful of relationships between a gas's pressure, volume, temperature and amount, worked out centuries ago and still exactly right.

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The big idea: For a fixed sample of gas, pressure (P), volume (V) and absolute temperature (T) are tied together. Change one and, holding a second fixed, the third must respond in a predictable way. The gas laws are just these paired trade-offs — and they all demand temperature in KELVIN.
🎯 By the end, you'll be able to
  • State Boyle's, Charles's, Gay-Lussac's and Avogadro's laws and what each holds constant
  • Convert temperatures to kelvin before using any gas law
  • Use the combined gas law to handle P, V and T changes at once
  • Solve for an unknown P, V or T from a before/after scenario
📎 Helpful to know first
⚠️ First rule of gas laws: use kelvin
Every law here that involves temperature needs the absolute temperature in kelvin: K = °C + 273.15. Using Celsius will give nonsense (a gas at 0 °C is nowhere near having 'zero' temperature). Convert first, calculate second.

Boyle's law: squeeze it, and pressure climbs

Hold temperature and amount fixed. Now shrink the volume. The particles hit the walls more often, so the pressure rises. Pressure and volume are inversely proportional — halve the volume and you double the pressure.

\[ P \propto \dfrac{1}{V} \qquad\Longrightarrow\qquad P_1 V_1 = P_2 V_2 \]
Boyle's law (constant T, n): the product P*V stays the same before and after.
📝 Worked example: A gas occupies 4.0 L at 1.0 atm. At constant temperature, it is compressed to 1.0 L. What is the new pressure?
  1. Boyle's law: P₁V₁ = P₂V₂.
  2. Solve for P₂: P₂ = P₁V₁ / V₂ = (1.0 atm × 4.0 L) / 1.0 L.
  3. = 4.0 atm. Quartering the volume quadruples the pressure.
✓ 4.0 atm.

Charles's law: heat it, and volume grows

Now hold pressure and amount fixed and heat the gas. The particles move faster, so to keep the pressure the same the gas must expand. Volume is directly proportional to absolute temperature — this is why a balloon puffs up in the heat and shrinks in the cold.

\[ V \propto T \qquad\Longrightarrow\qquad \dfrac{V_1}{T_1} = \dfrac{V_2}{T_2} \]
Charles's law (constant P, n), with T in kelvin.
📝 Worked example: A balloon holds 2.0 L of air at 27 C. It is warmed to 177 C at constant pressure. What is its new volume?
  1. Convert to kelvin: T₁ = 27 + 273.15 ≈ 300 K; T₂ = 177 + 273.15 ≈ 450 K.
  2. Charles's law: V₂ = V₁ × (T₂ / T₁) = 2.0 L × (450 / 300).
  3. = 3.0 L. (Had you wrongly used 27 and 177, the ratio 177/27 ≈ 6.6 would be badly off.)
✓ 3.0 L.

Gay-Lussac's law: seal it and heat it, and pressure spikes

Keep the volume and amount fixed — a rigid, sealed can — and heat it. The particles strike the walls harder and more often, so the pressure climbs. Pressure is directly proportional to absolute temperature. This is exactly why aerosol cans warn against heat.

\[ P \propto T \qquad\Longrightarrow\qquad \dfrac{P_1}{T_1} = \dfrac{P_2}{T_2} \]
Gay-Lussac's law (constant V, n), with T in kelvin.

Avogadro's law: more gas, more room

At fixed temperature and pressure, adding more gas particles means the gas needs more room. Volume is directly proportional to the amount of gas (in moles). Blow more air into a balloon and it grows — no surprise, but it is a genuine law.

A striking consequence: equal volumes of any gases, at the same T and P, contain equal numbers of particles. One mole of any ideal gas fills about 22.4 L at 0 °C and 1 atm (STP).

\[ V \propto n \qquad\Longrightarrow\qquad \dfrac{V_1}{n_1} = \dfrac{V_2}{n_2} \]
Avogadro's law (constant T, P): volume tracks the number of moles n.
🔑 The combined gas law
When P, V and T all change at once for a fixed amount of gas, bundle the three laws into one:
\[ \dfrac{P_1 V_1}{T_1} = \dfrac{P_2 V_2}{T_2} \]
Combined gas law (constant n). Boyle, Charles and Gay-Lussac are each just this equation with one variable held fixed. T in kelvin, always.
📝 Worked example: A gas occupies 2.0 L at 1.0 atm and 300 K. It is changed to 2.0 atm and 600 K. What is its new volume?
  1. Combined gas law, solved for V₂: V₂ = V₁ × (P₁/P₂) × (T₂/T₁).
  2. = 2.0 L × (1.0 / 2.0) × (600 / 300).
  3. = 2.0 L × 0.5 × 2.0 = 2.0 L. The doubled pressure and doubled temperature exactly cancel.
✓ 2.0 L (the two changes offset each other).
✏️ Practice: A gas is held at constant temperature. It occupies 6.0 L at 2.0 atm. If the pressure is lowered to 1.5 atm, what is the new volume (in L)?
L
Solution
  1. Constant temperature and amount → Boyle's law: P₁V₁ = P₂V₂.
  2. V₂ = P₁V₁ / P₂ = (2.0 atm × 6.0 L) / 1.5 atm.
  3. = 12 / 1.5 = 8.0 L. Lower pressure, larger volume — as expected.
✏️ Practice: At constant pressure, a gas occupies 2.0 L at 300 K. It is heated to 450 K. What is its new volume (in L)?
L
Solution
  1. Constant pressure and amount → Charles's law: V₁/T₁ = V₂/T₂.
  2. Both temperatures are already in kelvin.
  3. V₂ = V₁ × (T₂/T₁) = 2.0 L × (450/300) = 3.0 L.
🎮 Interactive: Gas Law Sandbox LIVE
Predict first: If you halve the volume at constant temperature, what happens to the pressure?

An interactive gas simulation with sliders for amount, temperature and volume; pressure is computed from PV=nRT and a particle box shows count, speed and spacing.

Adjust amount (n), temperature (T) and volume (V) — pressure follows PV = nRT while the particle box shows why: more particles or faster particles or a smaller box all mean more wall collisions, and more pressure.

Check your understanding

1. Which temperature scale must you use in the gas laws?
Gas laws are built on absolute temperature. Only kelvin makes ratios like T2/T1 meaningful; a gas at 0 C is not at zero temperature. Convert with K = C + 273.15.
2. You halve the volume of a gas at constant temperature. What happens to the pressure?
Boyle's law: P and V are inversely proportional, so P*V is constant. Halving V doubles P — the particles strike the walls twice as often.
3. A rigid sealed can of gas is heated. Nothing leaks. What happens?
Volume is fixed (rigid can), so this is Gay-Lussac's law: pressure rises with absolute temperature as the particles hit the walls harder and more often.
🔎 Related lessons
Previous: Kinetic-Molecular Theory Next: The Ideal Gas Law
✅ Key takeaways
  • Boyle: P is inversely proportional to V (constant T, n) — P1V1 = P2V2.
  • Charles: V is directly proportional to T (constant P, n) — V1/T1 = V2/T2.
  • Gay-Lussac: P is directly proportional to T (constant V, n) — P1/T1 = P2/T2.
  • Avogadro: V is directly proportional to n (constant T, P); 1 mol fills ~22.4 L at STP.
  • Combined gas law: P1V1/T1 = P2V2/T2. Always use temperature in kelvin.
➡️ Each of these laws holds something constant. What if we could handle pressure, volume, temperature AND amount all in one equation, with no 'before and after' needed? That single master equation is the ideal gas law.
Want to test yourself on this? Try the Chemistry practice test →