Ideal Gas Law Calculator (PV = nRT)
Use PV = nRT to find any one of pressure, volume, moles or temperature when the other three are known.
How to use this ideal gas law calculator
- Select which variable to solve for (pressure, volume, moles, or temperature).
- Enter the three known values — temperature must be in Kelvin (add 273.15 to Celsius).
- Use R = 0.08206 L·atm/(mol·K) for pressure in atm and volume in litres.
- Check your result against common benchmarks: 1 mol at STP (0°C, 1 atm) occupies 22.414 L.
- For pressure in kPa, multiply the atm result by 101.325; for mmHg, multiply by 760.
Formula
PV = nRT where R = 0.08206 L·atm/(mol·K). T = PV/nR | P = nRT/V | V = nRT/P | n = PV/RT. STP: 0°C, 1 atm → 22.414 L/mol.
About the Ideal Gas Law Calculator
PV = nRT unifies three centuries of gas research into one equation. Boyle's Law (1662), Charles's Law (1787), Gay-Lussac's Law (1809), and Avogadro's Law (1811) are all special cases with one variable held constant. At STP (0°C, 1 atm), 1 mole of any gas — oxygen, hydrogen, methane — occupies the same 22.414 litres. This universality is remarkable and deeply practical for chemistry calculations worldwide.
Real gases approach ideal behaviour at low pressure and high temperature, where molecules are far apart and intermolecular forces are negligible. For most lab work at ambient conditions (20–25°C, 1 atm), the ideal gas law is accurate to within 1–2%. Only near liquefaction — high pressure, low temperature — do significant deviations appear. Carbon dioxide, for instance, behaves non-ideally even at room temperature above ~30 atm, which matters for supercritical CO₂ extraction processes used in coffee decaffeination and pharmaceutical purification.
Industrial applications are vast: chemical engineers use PV = nRT to size reactors, calculate compressor energy requirements, and design gas storage vessels. The Haber process (ammonia synthesis at 400–500°C, 150–300 atm) must account for real gas deviations — at 300 atm, nitrogen's compressibility factor Z = PV/nRT is ~1.4, meaning it behaves as if 40% more molecules are present. Accurate van der Waals corrections are essential to prevent dangerous over-pressurisation or under-production in these high-stakes industrial reactors.
Frequently asked questions
+What is R in PV=nRT?
R is the universal gas constant: 0.08206 L·atm/(mol·K) or equivalently 8.314 J/(mol·K). The value depends on the units chosen for pressure and volume — always check unit consistency before calculating.
+When does the ideal gas law fail?
At high pressures (>10 atm) or low temperatures (near the boiling point of the gas), real gases deviate significantly. Intermolecular forces and molecular volume become important. The van der Waals equation (P + a/V²)(V − b) = nRT adds correction factors a (attraction) and b (volume).
+What is STP and what is the molar volume there?
Standard Temperature and Pressure: 0°C (273.15 K) and 1 atm. At STP, 1 mole of any ideal gas occupies exactly 22.414 L. IUPAC's newer STP definition (0°C, 100 kPa = 1 bar) gives 22.711 L/mol — a 1.3% difference worth noting for precise calculations.
+How is the ideal gas law used in real life?
Airbag deployment calculations, predicting gas volumes in chemical reactions, designing pressure vessels, and weather balloon trajectories all rely on PV = nRT. Medical ventilators use it to deliver precise tidal volumes at different pressures and temperatures in ICU settings.
+What is the difference between PV = nRT and the combined gas law?
PV = nRT includes the amount of gas (n). The combined gas law P₁V₁/T₁ = P₂V₂/T₂ holds when n is constant — it is derived from PV = nRT by setting nR as a constant. Use combined gas law when no gas enters or leaves; use the full ideal gas law when amounts change.