The ideal-gas law — PV = nRT — relates the pressure, volume, temperature, and amount (in moles) of a gas. The Toolenza calculator solves for whichever variable you don't have, using R = 8.314 J/(mol·K) when inputs are in SI units (Pa, m³, K).

When the ideal-gas law actually works

The law is a near-perfect approximation for most gases at most conditions. It assumes molecules have no volume of their own and don't interact except by collision. In practice the ideal model is within 1% of real behaviour for:

• Air, nitrogen, oxygen, CO₂ at room temperature and atmospheric pressure.
• Any gas well above its boiling point.
• Any gas at low pressure (where molecules are far apart).

It fails when molecules are close together (high pressure, near the liquid-vapour transition) — there you need the van der Waals or Redlich-Kwong equations.

Worked examples

• A bicycle tyre. 0.5 L volume, 700 kPa pressure (about 100 psi), 295 K (room temp). Moles = PV/RT = (700,000 × 0.0005) / (8.314 × 295) ≈ 0.143 mol of air. At 29 g/mol, that's 4.1 g.
• A weather balloon. Released at sea-level (101 kPa) with 5 m³ of helium; ascends to where pressure is 30 kPa. New volume = 5 × (101/30) ≈ 16.8 m³ (assuming temperature stays constant).
• Standard temperature and pressure (STP) — 1 mole of any ideal gas occupies 22.414 L at 0 °C and 101.325 kPa. The reason "22.4 L/mol" is burned into every chemistry student's memory.

Units gotcha

Use kelvins, not Celsius, for T. Pressure in Pa with volume in m³ uses R = 8.314 J/(mol·K). Pressure in atm with volume in L uses R = 0.08206 L·atm/(mol·K). Mixing units is the most common error.