Ideal Gas Law Calculator

The Ideal Gas Law (PV = nRT) is a fundamental equation relating the pressure (P), volume (V), amount in moles (n), and absolute temperature (T) of an ideal gas. R is the universal gas constant. The law combines Boyle's Law (P∝V at constant T), Charles's Law (V∝T at constant P), and Avogadro's Law (V∝n at constant P,T) into one equation.

The gas constant R has different values depending on units: R = 8.314 J/(mol·K) = 8.314 kPa·L/(mol·K) for SI units, R = 0.08206 L·atm/(mol·K) for atmospheres and liters, R = 62.36 L·mmHg/(mol·K) for mmHg and liters. Always match R with your pressure and volume units.

STP (Standard Temperature and Pressure) is defined as 273.15 K (0°C) and exactly 1 atm (101.325 kPa). At STP, one mole of an ideal gas occupies 22.414 liters (the molar volume). Note: IUPAC now defines STP as 273.15 K and 1 bar (100 kPa), giving a molar volume of 22.711 L.

The Combined Gas Law (P₁V₁/T₁ = P₂V₂/T₂) relates initial and final states of a gas when the amount (n) stays constant. It combines Boyle's and Charles's laws. You can solve for any one variable if you know the other five. Temperature must be in Kelvin.

Rearranging PV = nRT and using n = mass/molar mass (M): density = PM/(RT). This shows gas density increases with pressure and molar mass, but decreases with temperature. For air (M ≈ 29 g/mol) at STP: density = (101325 × 0.029)/(8.314 × 273.15) ≈ 1.29 kg/m³.

The Ideal Gas Law assumes gas particles have no volume and no intermolecular forces. It fails for: (1) High pressures - particle volume becomes significant, (2) Low temperatures - intermolecular forces become important, (3) Polar or large molecules - stronger intermolecular forces. Real gas behavior is better described by the van der Waals equation.

To convert Celsius to Kelvin: K = °C + 273.15. To convert Fahrenheit to Kelvin: K = (°F - 32) × 5/9 + 273.15. Kelvin is the absolute temperature scale where 0 K is absolute zero. The Ideal Gas Law requires temperature in Kelvin because volume is directly proportional to absolute temperature.

Avogadro's Law states that equal volumes of gases at the same temperature and pressure contain equal numbers of molecules (V ∝ n at constant P, T). One mole of any gas contains Avogadro's number (6.022 × 10²³) of molecules. At STP, one mole occupies 22.4 L regardless of the gas type.