Ideal Gas Law: PV = nRT
Blow up a balloon, watch a tire warm on a hot day, or feel a deodorant can chill as it sprays — all of these obey a single, elegant relationship. The ideal gas law, PV = nRT, ties together the pressure, volume, temperature, and amount of a gas in one of the most useful equations in all of science.
Meet the four variables
The law connects four measurable properties of a gas:
- P — pressure: the force the gas exerts per unit area on its container, in pascals.
- V — volume: the space the gas occupies, in cubic meters.
- n — amount: the number of moles of gas molecules.
- T — temperature: the absolute temperature, which must be in kelvin.
The constant R, the universal gas constant, is about 8.314 J/(mol·K). It is the same for every ideal gas, which is part of what makes the law so powerful.
The equation
Read it as a single statement of balance: for a fixed amount of gas, the product of pressure and volume is proportional to temperature. Push any one quantity and the others must adjust to keep the equation true. Crucially, T must be absolute (kelvin); using Celsius gives nonsense, because the law assumes that doubling the temperature really does double the molecular energy.
The ideal gas law is the combination of three older “named” laws — Boyle’s (P ∝ 1/V), Charles’s (V ∝ T), and Avogadro’s (V ∝ n). Each is a special case where you hold the other variables fixed. PV = nRT unifies them into one compact rule.
Where the law comes from
The macroscopic equation has a beautifully simple microscopic origin. A gas is a swarm of molecules flying about and bouncing off the container walls. Pressure is the cumulative force of those countless impacts. The kinetic theory of gases shows that temperature is a direct measure of the average kinetic energy of the molecules:
Heat the gas and the molecules move faster, striking the walls harder and more often — so pressure rises. Squeeze the volume and the impacts come more frequently — pressure rises again. The whole law falls out of this picture.
What “ideal” assumes
The model treats gas molecules as point particles that take up no volume and exert no forces on each other except during brief collisions. Real gases violate these assumptions, especially when:
- The pressure is very high, so molecules are crowded and their own volume matters.
- The temperature is very low, so attractions between molecules become significant and the gas nears condensing.
Under everyday conditions, though — room temperature, ordinary pressures — air and most common gases follow PV = nRT remarkably well. The lighter and less reactive the gas, the better it behaves: helium and hydrogen are nearly ideal across a wide range, while water vapour and carbon dioxide, with their stronger intermolecular forces, deviate sooner. Engineers quantify the departure with a “compressibility factor,” Z = PV/(nRT), which equals exactly 1 for an ideal gas and drifts above or below 1 as real behaviour creeps in.
Putting it to work
The law lets you predict how a gas responds to change. A few classic examples:
- A sealed tire heats up as you drive. With V and n fixed, raising T raises P — your tire pressure climbs.
- A balloon shrinks in the cold. With P roughly fixed, lowering T lowers V.
- A diver’s air bubble grows as it rises. As external P falls, V expands.
Because temperature in the law tracks molecular kinetic energy, the ideas here connect closely to specific heat capacity and to the broader role of disorder captured by entropy.
Frequently asked questions
Why must temperature be in kelvin?
Because the law assumes pressure and volume scale in direct proportion to temperature, and only an absolute scale starting at true zero energy makes that proportion meaningful. At 0 K the molecular motion is minimized; Celsius has an arbitrary zero point and would break the math.
When does the ideal gas law fail?
At high pressures and low temperatures, where molecules are close enough that their finite size and mutual attractions matter. The van der Waals equation corrects for these effects, but for ordinary conditions the ideal law is an excellent approximation.
What exactly is a mole?
A mole is simply a count — about 6.022 × 10²³ particles (Avogadro’s number). Using moles lets the same constant R work for any gas, since equal numbers of molecules behave alike regardless of their identity.
