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