What the Ideal Gas Law actually says
The Ideal Gas Law relates four quantities that describe a gas: pressure P, volume V, number of moles n, and absolute temperature T. The equation PV = nRT means the product of pressure and volume equals the product of the amount of gas, the gas constant R, and the absolute temperature. It is called ideal because it assumes gas molecules have zero volume and do not attract or repel each other — conditions real gases approach at high temperature and low pressure.
Robert Boyle published the pressure-volume relationship in 1662. Jacques Charles observed the temperature-volume relationship around 1787. Amedeo Avogadro proposed in 1811 that equal volumes of gases at the same temperature and pressure contain equal numbers of particles. The unified law combining all three observations was first stated in its modern form by August Krönig in 1856 and refined by Rudolf Clausius the following year.
For most classroom problems and many laboratory situations, the ideal behavior is close enough that the error is under one percent. The calculator above uses the standard value of R = 0.08205746 L·atm/(mol·K) internally and converts all your inputs to consistent units before computing.
The gas constant R: four values, one physics
The gas constant R appears as the proportionality factor that makes the units work. Its value depends entirely on which units you choose. The most common value in chemistry textbooks is 0.08205746 L·atm/(mol·K), which this calculator uses as its internal base.
In SI units, R equals 8.314462618 J/(mol·K). Because one joule equals one pascal times one cubic meter, this value is equivalent to 8.314462618 Pa·m³/(mol·K). The relationship: 1 L·atm equals 101.325 J exactly, so 0.08205746 × 101.325 = 8.31446.
For pressure in torr or mmHg, use 62.36367 L·torr/(mol·K). For bar, use 0.08314472 L·bar/(mol·K). This calculator handles all four values automatically.
Temperature must be absolute
The most common error in gas law calculations is using Celsius or Fahrenheit instead of Kelvin. The equation requires absolute temperature because the relationship is proportional: doubling the Kelvin temperature doubles the volume, all else equal. Fifty degrees Celsius is not twice as hot as twenty-five.
The conversion: K = °C + 273.15 exactly, by definition since 1954. Room temperature at 25 °C is 298.15 K; boiling water at 100 °C is 373.15 K. This calculator converts Celsius, Fahrenheit, and Kelvin automatically.
If you forget to convert and enter 0 °C as 0 K, you will calculate a volume roughly one-tenth the correct answer. The calculator eliminates this error by performing the conversion internally.
How the calculator works
Select which variable to solve for — P, V, n, or T. The calculator disables that input and shows it is being solved. Enter the three known values with their units. The calculator converts all inputs to consistent units (atmospheres and liters), applies the formula, and converts the result to your chosen output unit.
The step-by-step panel shows every intermediate value: conversions to Kelvin, the value of R used, the arithmetic, and the final unit conversion. Each step is labeled.
Standard conditions: STP and SATP
STP (Standard Temperature and Pressure): 0 °C (273.15 K) and 1 atm. One mole of ideal gas occupies 22.414 L. This value comes from plugging n = 1, T = 273.15 K, P = 1 atm and R = 0.08205746 into V = nRT/P.
SATP (Standard Ambient Temperature and Pressure): 25 °C and 1 bar. Molar volume at SATP is 24.79 L. The 10% difference from STP comes mainly from the 25-degree temperature increase.
When the Ideal Gas Law fails
The Ideal Gas Law works well at low pressure and high temperature. At high pressure or low temperature, real gases deviate measurably. The van der Waals equation corrects for these effects.
Water vapor near its condensation point and any gas above roughly 10 atm show significant deviations. For air at 100 atm the error is approximately five percent.
Worked examples
Example 1: A cylinder contains 2.5 mol of nitrogen at 25 °C and 150 kPa. What volume? Convert 25 °C to 298.15 K, 150 kPa to 1.480 atm. V = nRT/P = (2.5 × 0.08205746 × 298.15) / 1.480 = 41.3 L.
Example 2: A scuba tank rated for 11.1 L holds air at 204 atm. How many moles at 20 °C? n = PV/RT = (204 × 11.1) / (0.08205746 × 293.15) = 94.2 mol. At 28.97 g/mol for air, that is 2.73 kg of air in an 11-liter tank.
Example 3: A balloon with 0.12 mol He at 1.0 atm and 22 °C is cooled to -50 °C at constant pressure. New volume? Using V₁/T₁ = V₂/T₂: V₂ = (0.12 × 0.08205746 × 295.15 / 1.0) × 223.15/295.15 = 2.18 L.
Frequently asked questions
What is the Ideal Gas Law formula? PV = nRT, where P is pressure, V is volume, n is moles, R is the gas constant, and T is absolute temperature in Kelvin.
What value of R should I use? 0.08205746 L·atm/(mol·K) for most chemistry problems. Use 8.31446 J/(mol·K) for SI. This calculator auto-selects based on your units.
Why must temperature be in Kelvin? Because the gas laws are proportional to absolute temperature. 50 °C is not twice as hot as 25 °C, but 323.15 K is proportional to 298.15 K.
What is the molar volume at STP? 22.414 L/mol at 0 °C and 1 atm. This is derived directly from the Ideal Gas Law with n = 1, T = 273.15 K, P = 1 atm.
When does the Ideal Gas Law break down? At high pressures (above about 10 atm) or low temperatures, when intermolecular forces and molecular volume become significant. Use the van der Waals equation instead.