Four numbers describe any gas
To pin down a gas you only need four measurements, and the gas laws are the rules that tie them together:
- Pressure (P), how hard the gas pushes on its container, in atmospheres (atm).
- Volume (V), the space it fills, in liters (L).
- Temperature (T), how fast its particles move, in kelvin (K).
- Amount (n), how much gas there is, in moles (see the mole).
Change one and the others respond. The simulator above lets you change exactly one at a time: pick a law and it locks the two quantities that law holds constant, leaving you one slider. Everything you watch (the piston, the graph, the equation) is computed live from the single relationship that contains all the gas laws, the ideal gas law:
P V = n R T
The rest of this page takes that apart one law at a time. Each law just answers “if I hold these two steady and change that one, what happens to the fourth?”
Boyle’s law: squeeze it and pressure climbs
At constant temperature (and a fixed amount of gas), pressure and volume are inversely proportional. Halve the volume and the pressure doubles; the product stays constant.
P₁V₁ = P₂V₂
Boyle’s law in real life: pushing a capped syringe or a bicycle pump gets harder as the trapped air’s pressure climbs; a scuba diver’s lungs and air bubbles are squeezed as the total pressure on them roughly doubles by 10 m depth; and breathing itself works this way, as expanding your chest lowers your lung pressure so air flows in.
Charles’s law: heat it and it expands
At constant pressure, volume is directly proportional to absolute temperature. Heat the gas and it expands; cool it and it shrinks, in lockstep with the kelvin temperature.
V₁ / T₁ = V₂ / T₂
Charles’s law in real life: a hot-air balloon rises because heating the air expands it and lowers its density; a balloon shrinks in a freezing car overnight and re-inflates indoors; and bread and cakes rise as trapped gas pockets expand in the oven.
Gay-Lussac’s law: heat a sealed can and pressure rises
At constant volume (a rigid, sealed container), pressure is directly proportional to absolute temperature.
P₁ / T₁ = P₂ / T₂
Avogadro’s law: more gas, more volume
At constant temperature and pressure, volume is directly proportional to the amount of gas. Add twice the moles and the volume doubles.
V₁ / n₁ = V₂ / n₂
The combined gas law: when everything changes at once
When a fixed amount of gas moves from one set of conditions to another and pressure, volume, and temperature all change together, merge the three single laws into one:
P₁V₁ / T₁ = P₂V₂ / T₂
Worked example. A gas occupies 4.00 L at 1.00 atm and 300 K. The pressure is raised to 2.00 atm and the temperature to 600 K. Solving for V₂:
V₂ = (P₁V₁T₂) / (T₁P₂) = (1.00 × 4.00 × 600) / (300 × 2.00) = 4.00 L
Doubling the temperature alone would double the volume; doubling the pressure alone would halve it. Here the two effects exactly cancel, so the volume is unchanged.
The ideal gas law: PV = nRT
Hold nothing constant and you need the full relationship. The ideal gas law ties all four quantities together with one constant, R:
P V = n R T
| Symbol | Meaning | Unit |
|---|---|---|
| P | pressure | atm |
| V | volume | L |
| n | amount of gas | mol |
| T | temperature (absolute) | K |
| R | universal gas constant | 0.082057 L·atm/(mol·K) |
R is the same physical constant everywhere; in SI units it is 8.314 J/(mol·K). You pick the version of R whose units match your pressure and volume.
Worked example. What volume does 2.00 mol of gas occupy at 3.00 atm and 27 °C? First convert the temperature: T = 27 + 273 = 300 K. Then
V = nRT / P = (2.00 × 0.082057 × 300) / 3.00 = 16.4 L
The gas law formulas at a glance
| Law | Held constant | Formula | Relationship |
|---|---|---|---|
| Boyle’s | T, n | P₁V₁ = P₂V₂ | P inversely proportional to V |
| Charles’s | P, n | V₁/T₁ = V₂/T₂ | V directly proportional to T |
| Gay-Lussac’s | V, n | P₁/T₁ = P₂/T₂ | P directly proportional to T |
| Avogadro’s | P, T | V₁/n₁ = V₂/n₂ | V directly proportional to n |
| Combined | n | P₁V₁/T₁ = P₂V₂/T₂ | merges the three above |
| Ideal | (nothing) | PV = nRT | all four at once |
Always use kelvin
The single most common gas-law mistake is using Celsius. Every temperature in these formulas must be in kelvin. The laws are proportionalities measured from absolute zero: plot the volume of any gas against Celsius temperature, extend the line backward, and every gas reaches zero volume at the same point, −273.15 °C. That point is 0 K. Only on the kelvin scale does “twice the temperature” mean “twice the volume,” because 0 °C is an ordinary, energetic temperature, not zero. Convert with T(K) = T(°C) + 273.15.
Why the gas laws work, and where they bend
These laws are the large-scale shadow of what individual particles are doing. Pressure is countless tiny collisions with the walls; temperature is the particles’ average kinetic energy. Watch that microscopic story directly in the Particle Box, where the same PV ∝ nT emerges from a live box of bouncing atoms. The gas laws describe an ideal gas; real gases drift from them at very high pressure or very low temperature, where the particles’ own volume and their attractions start to matter.
It’s free to embed on your own site or LMS. Next, see the gas laws emerge from moving particles in the Particle Box, or connect amount to mass in the mole.