Ideal Gas Law Calculator

The ideal gas law ties together the four state variables of a gas sample in one equation:

$PV = nRT$

• $P$ — pressure, in atm (or Pa, or kPa).
• $V$ — volume, in litres (or m³).
• $n$ — amount of gas, in moles.
• $T$ — absolute temperature in kelvin, never °C.
• $R$ — the universal gas constant. Its numerical value depends entirely on the units you chose: $R = 0.082057\ \mathrm{L\,atm\,mol^{-1}K^{-1}}$ with atm and litres, or $R = 8.3145\ \mathrm{J\,mol^{-1}K^{-1}}$ with pascals and cubic metres.

What "ideal" assumes. The molecules are treated as point particles with no volume of their own and no attraction between them, colliding elastically. That is a good description at low pressure and high temperature — roughly, ordinary room conditions for $\mathrm{N_2}$, $\mathrm{O_2}$ or He, with errors under about 1%. Near condensation, or above a few tens of atmospheres, real gases deviate and a correction such as the van der Waals equation is needed.

Standard conditions. At STP (0 °C = 273.15 K and 1 bar) one mole of an ideal gas occupies 22.71 L; under the older 1 atm definition it occupies 22.41 L.

Rearrangements

$P = \frac{nRT}{V} \qquad V = \frac{nRT}{P} \qquad n = \frac{PV}{RT} \qquad T = \frac{PV}{nR}$

Procedure

1. Write down the three known quantities with units.
2. Convert: temperature to kelvin, pressure and volume to units matching your chosen $R$ (mL → L, kPa → atm by dividing by 101.325, mmHg → atm by dividing by 760).
3. Substitute and evaluate, carrying units through so they cancel to the unit you expect.
4. Check plausibility: a mole of gas near room conditions occupies roughly 24 L, so an answer of 0.02 L or 2000 L for one mole signals an arithmetic slip.

The combined gas law

When the amount of gas is fixed and only the conditions change, $n$ and $R$ cancel and you never need $R$ at all:

$\frac{P_1V_1}{T_1} = \frac{P_2V_2}{T_2}$

Boyle's Law ($T$ constant), Charles's Law ($P$ constant) and Gay-Lussac's Law ($V$ constant) are each this equation with one variable held fixed.

Significant figures

The result carries the fewest significant figures of the inputs. Because $R$ is quoted to 5 figures it never limits the answer; a 3-figure pressure does.

• Leaving temperature in Celsius. 27 °C is 300.15 K, and using 27 makes the answer wrong by a factor of about 11.
• Mismatching $R$ with the units. Using $R = 0.082057$ with pressure in kPa, or volume in mL, is the single most common source of wrong answers. Pick the $R$ that matches your units, or convert the units to match $R$.
• Confusing gauge and absolute pressure. $P$ in $PV = nRT$ is absolute. A tyre gauge reading 2.0 atm means 3.0 atm absolute.
• Using the combined gas law when moles change. $P_1V_1/T_1 = P_2V_2/T_2$ is valid only for a sealed, fixed amount of gas; if gas is added, removed or produced by a reaction, go back to $PV = nRT$ for each state.
• Assuming 22.4 L per mole always. That molar volume belongs to one specific temperature and pressure, not to room conditions.