Ideal Gas Law (PV = nRT)
Solve for any variable — fill in the other three.
Want to understand how this works? Study it in the States of Matter & Gas Laws lesson →
Free chemistry formula cheat sheet (PDF)
One page with the formulas you use most — molar mass, grams ⇄ moles, pH and PV = nRT — each with a worked example. Leave your email and we'll send it over.
Worked examples
One mole of any ideal gas at 0 °C (273.15 K) and 1 atm: V = nRT/P = (1 × 0.08206 × 273.15) / 1 = 22.41 L. This "molar volume" is the same for every gas — a consequence of the gas particles being mostly empty space.
2.0 mol of helium at 25 °C and 1.5 atm: V = (2.0 × 0.08206 × 298.15) / 1.5 = 32.6 L. Warm helium expands — that's why balloons deflate faster in a cold room.
0.8 mol of gas in a 10 L container at 2 atm: T = PV/(nR) = (2 × 10) / (0.8 × 0.08206) = 304.7 K ≈ 31.5 °C. Notice temperature must go in and comes out of the formula in kelvin.
How it works
PV = nRT combines Boyle's law (P ∝ 1/V), Charles's law (V ∝ T) and Avogadro's law (V ∝ n) into one equation, with R = 0.08206 L·atm/(mol·K) as the proportionality constant. To solve for any variable, isolate it algebraically and let the calculator handle the units.
Two habits prevent most mistakes: always convert temperature to kelvin (°C + 273.15) before plugging in, and make sure your pressure and volume units match the R you use. "Ideal" assumes negligible particle volume and no intermolecular forces — an excellent approximation at everyday temperatures and pressures.
Take it with you: download the one-page formula cheat sheet (PDF) — print it and keep it on your desk.
Next steps: see where the law comes from in the States of Matter & Gas Laws lesson, and check the whole topic in the practice quiz.