ChemistryStepByStep

Ideal Gas Law Calculator

Enter three of pressure, volume, moles and temperature to solve for the fourth using PV = nRT.

V -- volume (L)
22.4140

PV = nRT, with R = 0.082057 L·atm/(mol·K) (from NIST CODATA), solved for V = 22.4140.

PV = nRT

The ideal gas law connects all four state variables of a gas sample in one equation. Given any three of pressure, volume, moles and temperature, it solves directly for the fourth -- no need to compare a before-and-after state the way the combined gas law does.

This calculator uses R = 0.0820574 L·atm/(mol·K), derived from the exact NIST CODATA value R = 8.314462618 J/(mol·K), so pressure is entered in atmospheres and volume in liters.

Worked example

What volume does 1 mole of an ideal gas occupy at STP (1 atm, 273.15 K)?

V = nRT / P = (1 × 0.082057 × 273.15) / 1 = 22.414 L.

This matches the textbook STP molar volume of 22.414 L/mol -- computed here entirely from the cited gas constant, not typed in as a separate fact.

Common mistake

Mixing unit systems -- using R in J/(mol·K) with pressure in atm and volume in L, instead of L·atm/(mol·K). Always match R's units to the units of every other variable.

Keep going

  • The ideal gas law needs to know the moles of gas present; if you're instead comparing the same fixed amount of gas before and after a change, the combined gas law skips that requirement. Combined Gas Law Calculator
  • Solving the ideal gas law for moles gives you a mole count directly; the mole calculator converts that mole count into a mass if you need to weigh out that much gas. Moles Calculator

Frequently Asked Questions

What is the ideal gas law?

PV = nRT relates a gas's pressure (P), volume (V), moles (n) and temperature (T) all at once, using the gas constant R. It's called "ideal" because it assumes gas particles have no volume of their own and no attraction to each other -- a good approximation for most gases at ordinary pressure and temperature.

Where does the gas constant R come from?

R = 8.314462618 J/(mol·K), an exact value fixed by the 2019 SI redefinition (via NIST's CODATA reference). This calculator uses R converted to L·atm/(mol·K) units (dividing by 101.325 J per L·atm, the exact SI definition of 1 atm) to match pressure in atmospheres and volume in liters.

What is STP and why does it matter here?

Standard Temperature and Pressure (0°C / 273.15 K, 1 atm) is a common reference condition. At STP, one mole of any ideal gas occupies 22.414 L -- a useful check: this calculator reproduces that exact textbook number from R alone.

When does the ideal gas law break down?

At very high pressure or very low temperature, where real gas molecules' own volume and intermolecular attractions actually matter -- that's when the Van der Waals equation (a real-gas correction) is needed instead. For typical classroom and lab conditions, ideal gas law is accurate enough.

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