Ideal Gas Law
The ideal gas law PV = nRT relates pressure, volume, temperature, and amount of gas.
Master gas calculations with worked examples.
The Formula
PV = nRT
The ideal gas law connects four properties of a gas: pressure, volume, amount, and temperature. It works well for most gases at moderate temperatures and pressures.
Variables
| Symbol | Meaning |
|---|---|
| P | Pressure (measured in pascals, Pa, or atmospheres, atm) |
| V | Volume (measured in cubic meters, m³, or liters, L) |
| n | Number of moles of gas (mol) |
| R | Universal gas constant (8.314 J/(mol·K) or 0.0821 L·atm/(mol·K)) |
| T | Temperature (measured in kelvin, K) |
Example 1
What volume does 2 moles of gas occupy at 1 atm and 25°C?
Convert temperature: T = 25 + 273.15 = 298.15 K
Rearrange: V = nRT / P
V = (2 × 0.0821 × 298.15) / 1
V ≈ 48.9 L
Example 2
A 10 L container holds gas at 300 K and 202,650 Pa. How many moles of gas are present?
Convert volume: V = 10 L = 0.01 m³
Rearrange: n = PV / (RT)
n = (202,650 × 0.01) / (8.314 × 300)
n = 2,026.5 / 2,494.2
n ≈ 0.81 mol
When to Use It
Use the ideal gas law when working with gases at known conditions.
- Calculating the volume, pressure, temperature, or amount of a gas
- Problems involving gas reactions and stoichiometry
- Determining molar mass of an unknown gas
- Always convert temperature to kelvin before calculating
Key Notes
- Formula: PV = nRT: P is pressure (Pa), V is volume (m³), n is amount in moles, R = 8.314 J/(mol·K), and T is temperature in Kelvin. All individual gas laws (Boyle's, Charles's, Gay-Lussac's) are special cases of this equation.
- Temperature must be in Kelvin: Always convert: K = °C + 273.15. Using Celsius gives completely wrong answers. At T = 0 K, the ideal gas would have zero volume — a theoretical limit never reached in practice.
- Ideal gas assumptions: Gas molecules have negligible volume, no intermolecular forces, and undergo perfectly elastic collisions. Real gases approximate this well at low pressure and high temperature.
- Real gases deviate at extremes: At high pressures or low temperatures, real gas molecules are close enough that intermolecular attractions and molecular volume matter. Use the van der Waals equation for these conditions: (P + a/V²)(V − b) = nRT.
- Molar volume at STP: At standard temperature and pressure (0°C, 1 atm), one mole of any ideal gas occupies 22.4 L. At standard conditions (25°C, 1 bar), molar volume is 24.8 L. These reference values speed up many calculations.