Ideal Gas Equation (PV = nRT)
The ideal gas equation PV = nRT relates pressure, volume, temperature, and amount of gas.
Learn with worked examples.
The Formula
The ideal gas equation combines Boyle's law, Charles' law, and Avogadro's law into a single equation. It describes the behavior of an ideal gas where molecules have no volume and no intermolecular forces.
The equation was first stated by French engineer Emile Clapeyron in 1834. It provides an excellent approximation for real gases at moderate temperatures and low pressures. At high pressures or low temperatures, real gases deviate from ideal behavior and the van der Waals equation is more accurate.
The universal gas constant R has the value 8.314 J/(mol·K) in SI units. It can also be expressed as 0.0821 L·atm/(mol·K) when using liters and atmospheres. The equation shows that if you know any three of the four variables, you can calculate the fourth.
Variables
| Symbol | Meaning |
|---|---|
| P | Pressure (pascals, Pa, or atmospheres, atm) |
| V | Volume (cubic meters, m³, or liters, L) |
| n | Amount of gas (moles) |
| R | Universal gas constant (8.314 J/(mol·K)) |
| T | Absolute temperature (kelvin, K) |
Example 1
What volume does 2 moles of gas occupy at 300 K and 1 atm?
Use R = 0.0821 L·atm/(mol·K) for convenience
Rearrange: V = nRT/P = 2 × 0.0821 × 300 / 1
V = 49.26 L
V ≈ 49.3 liters
Example 2
A sealed container holds 0.5 mol of gas at 200 kPa and 25°C. What is the volume?
Convert temperature: T = 25 + 273 = 298 K
Convert pressure: P = 200,000 Pa
V = nRT/P = 0.5 × 8.314 × 298 / 200,000
V = 1238.8 / 200,000
V ≈ 0.00619 m³ = 6.19 liters
When to Use It
Use the ideal gas equation whenever you need to relate the pressure, volume, temperature, and amount of a gas.
- Calculating gas volumes in chemistry and engineering
- Determining gas pressure in sealed containers
- Predicting how gases behave when heated or compressed
- Finding the number of moles from measured conditions