What is an ideal gas?
Gas molecules are almost all empty space, and the ideal gas is the pleasant fiction that takes that literally: point particles with no volume of their own and no attraction between them, whose collisions are perfectly bouncy. For most gases near room conditions the fiction works to a fraction of a percent, and it buys one compact equation — PV = nRT — that ties pressure, volume, amount and temperature together with a single constant R. Every named gas law on this page is that one equation with something held fixed.
The one rule to remember: temperature in gas arithmetic must be kelvin. T(kelvin) is proportional to the molecules' average kinetic energy, and 0 °C is not “no heat” — plug Celsius into Charles' or Gay-Lussac's law and the answer is silently nonsense.
One equation, three shadows
Hold temperature fixed in PV = nRT and PV is constant — that is Boyle's law: squeeze a gas to half the volume and the pressure doubles (the sample: 1 atm·2 L → 2 atm gives 1 L). Hold pressure fixed and V ∝ T — Charles' law: heat 2 L from 0 °C to 100 °C (273 K to 373 K) and it grows to 2.73 L. Hold volume fixed and P ∝ T — Gay-Lussac's law: the reason a sealed aerosol can warns against incineration. Nothing is sacred about which variable is blank: each panel here solves for the one you leave empty, and the combined law P1V1/T1 = P2V2/T2 does all three changes at once.
STP and the 22.4-liter mole
At STP — 0 °C and 1 atm — one mole of any (ideal) gas occupies 22.414 L, a number worth memorizing because it converts directly between moles and volume. The Ideal Gas sample reproduces it exactly: 1 mol at 1 atm and 0 °C solves to V = 22.414 L. Chemists also use NTP (25 °C, 1 atm), where the molar volume grows to about 24.5 L — same moles, warmer gas.
Dalton: gases ignore each other
In a mixture, each gas pushes on the walls as if the others were not there; its share of the total pressure is its partial pressure, and the total is simply the sum. Better yet, partial pressure ÷ total pressure = mole fraction: air is roughly 78% N2 and 21% O2, so at 1 atm oxygen contributes about 0.21 atm. The Dalton sample (0.4 + 0.35 + 0.25 atm) sums to 1.0 atm total with mole fractions 40/35/25%. This is also why scuba tables and deep-sea physiology are done in partial pressures — oxygen toxicity depends on its pressure, not the mixture's.
Graham: lighter molecules fly faster
At the same temperature all molecules carry the same average kinetic energy, so light ones must move faster — and rate of effusion (escape through a pinhole) goes as 1/√M. The sample compares helium (4 g/mol) with oxygen (32 g/mol): He escapes √(32/4) = 2.83 times faster. It is why a helium balloon sags overnight while air-filled ones last for weeks.
When gases stop being ideal
Two assumptions break down at the extremes: molecules do take up space, and they do attract each other. The van der Waals equation (P + an²/V²)(V − nb) = nRT patches both — b removes the volume the molecules themselves occupy, and a adds an inward pull that softens their wall-banging. At high pressure the volume term dominates and real pressure runs above ideal; near condensation the attraction dominates and it runs below. The CO2 sample (1 L, 0.042 mol, 273 K) is the second case: ideal predicts 0.9409 atm, van der Waals 0.9362 atm — a small but real shortfall, growing fast as the gas approaches becoming a liquid. Rule of thumb: switch to van der Waals above a few hundred atmospheres, near the boiling point, or for strongly attracting gases like NH3 and CO2.
Common misconceptions
- Celsius is fine if you're consistent. Only temperature differences agree between °C and K. Ratios like V1/T1 need absolute temperature — Charles' law gives 2 L → 2.73 L in kelvin but an absurd answer in Celsius.
- Every gas occupies 22.4 L at STP. Per mole, yes — the number counts particles, not species. And it is an ideal-gas value; real gases land slightly off.
- Real gases always deviate upward. Deviation direction depends on which term dominates: excluded volume pushes pressure up, attractions pull it down.
- Helium balloons shrink because rubber is porous to chemistry. It is physics: small, fast molecules effuse through tiny gaps — rate ∝ 1/√M.
Related tools: Thermochemistry (heat and work of gases), Chemical Equilibrium (Kp from gas pressures), and Molar Mass (the M in Graham's law).
