Ideal Gas Law Explained
By the Periodixy Editorial Team · Last reviewed July 10, 2026
The ideal gas law, PV = nRT, packs four properties of a gas — pressure, volume, amount and temperature — into one equation. Know any three and the fourth follows. It works because gases, unlike solids and liquids, behave remarkably alike regardless of what molecules they contain.
Meet the variables
| Symbol | Meaning | Common unit |
|---|---|---|
| P | pressure | atm (or kPa, torr) |
| V | volume | L |
| n | amount of gas | mol |
| R | gas constant | 0.0821 L·atm/mol·K |
| T | temperature | K — always kelvin |
R changes numeric value with your pressure unit: 0.0821 for atm, 8.314 for kPa, 62.4 for torr. Pick the R that matches your units and everything cancels cleanly.
Worked examples
Finding a volume
What volume does 0.50 mol of gas occupy at 25 °C and 1.0 atm?
- Convert temperature: 25 + 273.15 = 298 K.
- V = nRT ÷ P = (0.50 × 0.0821 × 298) ÷ 1.0
Answer: ≈ 12.2 L
Finding moles (and then grams)
A 5.0 L tank holds gas at 3.0 atm and 300 K. How many moles is that?
- n = PV ÷ RT = (3.0 × 5.0) ÷ (0.0821 × 300)
Answer: ≈ 0.61 mol. Multiply by molar mass to get grams if needed.
Where does the law come from?
PV = nRT merges three older laws: Boyle's (P and V inverse at fixed T), Charles's (V grows with T at fixed P) and Avogadro's (V grows with n). Each is a slice of the ideal gas law with something held constant.
When “ideal” fails
The law assumes gas molecules have zero size and no attraction to each other. That approximation cracks at high pressure (molecules crowd) and low temperature (attractions matter — gases eventually condense). For everyday classroom conditions near room temperature and one atmosphere, the ideal gas law is accurate to about 1%.
Solve any arrangement of PV = nRT — with automatic unit conversion — in the Ideal Gas Law Calculator.
Summary
- PV = nRT connects pressure, volume, moles and temperature.
- Match R to your pressure unit; temperature is always kelvin.
- 1 mol of ideal gas ≈ 22.4 L at STP.
- The law weakens at high pressure and low temperature.