The Ideal Gas Law
PV = nRT relates four gas properties: pressure, volume, amount (moles), and temperature. Given any three, calculate the fourth.
The Equation
PV = nRT
P = absolute pressure (Pa or atm)
V = volume (m³ or L)
n = amount (moles)
R = 8.314 J/mol·K (universal gas constant)
T = absolute temperature (K = °C + 273.15)Worked Example
2 mol CO₂ at 300K, 1 atm (101,325 Pa):
V = nRT/P = 2 × 8.314 × 300 / 101325 = 0.0492 m³ = 49.2 LCombined Gas Law (fixed n)
P₁V₁/T₁ = P₂V₂/T₂
Boyle's Law (T const): P₁V₁ = P₂V₂
Charles' Law (P const): V₁/T₁ = V₂/T₂
Gay-Lussac (V const): P₁/T₁ = P₂/T₂Standard Conditions
- STP (IUPAC): 0°C (273.15K), 100 kPa → 1 mol = 22.71 L
- NTP: 20°C, 101.325 kPa → 1 mol ≈ 24.04 L
- SATP: 25°C, 100 kPa → 1 mol = 24.79 L
Calculate gas properties: Free Ideal Gas Law Calculator
Ideal Gas Law Quick-Reference Table
| Scenario | P (Pa) | V (L) | n (mol) | T (K) |
|---|---|---|---|---|
| STP (standard conditions) | 101,325 | 22.4 | 1 | 273 |
| Room temperature, 1 atm | 101,325 | 24.5 | 1 | 298 |
| Car tyre (cold, 2.2 bar) | 220,000 | ~30 | ~2.7 | 293 |
| Scuba tank (200 bar, 12 L) | 20,000,000 | 12 | ~97 | 293 |
How the Ideal Gas Law Works
The ideal gas law PV = nRT relates pressure (P), volume (V), amount of substance (n, in moles), and absolute temperature (T, in kelvin). R = 8.314 J/(mol·K) is the universal gas constant. The law assumes gas molecules have negligible volume and no intermolecular attractions — valid at low pressures and high temperatures for most common gases.
In engineering, the ideal gas law governs pneumatic systems, HVAC design, internal combustion engine modelling, and compressed-gas storage. In chemistry, it allows calculation of molar quantities from pressure-volume-temperature measurements. Real gases deviate from ideal behaviour at high pressures or near their condensation points; the van der Waals equation adds correction terms for these situations.
Common Mistakes
- Using Celsius instead of Kelvin: T must always be in kelvin (K = °C + 273.15). Using 25 instead of 298 is one of the most common errors.
- Inconsistent pressure units: R = 8.314 J/(mol·K) requires P in pascals. If using atm, use R = 0.08206 L·atm/(mol·K) and V in litres.
- Forgetting gauge vs. absolute pressure: Tyre gauges show gauge pressure (above atmospheric). Add 101,325 Pa to convert to absolute pressure for PV = nRT.
Frequently Asked Questions
As temperature rises, gas molecules move faster and hit the tyre walls more frequently and forcefully, increasing pressure. At constant volume, P ∝ T (Gay-Lussac's law). A 10°C rise in a 2.2 bar tyre adds approximately 0.08 bar of pressure — hence the recommendation to check tyre pressure when cold.
Standard Temperature and Pressure (STP) is defined as 0°C (273.15 K) and 1 atm (101,325 Pa). At STP, 1 mole of ideal gas occupies 22.4 litres — a useful reference value for gas density calculations, stoichiometry, and comparing experimental results across laboratories.
At very high pressures (above ~10 atm for most gases) or near the condensation point, intermolecular forces and finite molecular volumes become significant. For example, CO₂ near its critical point (31°C, 74 atm) behaves very differently from an ideal gas, which is why real-gas equations like van der Waals or Peng-Robinson are used in industrial process simulation.