Root Mean Square Speed
Average molecular speed in gases
Formula
vrms = √(3RT / M)
- vrms = root mean square speed (m/s)
- R = gas constant (8.314 J·mol⁻¹·K⁻¹)
- T = absolute temperature (K)
- M = molar mass (kg/mol)
Example: O₂ at 25°C
Given: M(O₂) = 32 g/mol = 0.032 kg/mol, T = 298 K.
vrms = √[(3 × 8.314 × 298) / 0.032]
vrms = √(7434 / 0.032) = √232,312
vrms ≈ 482 m/s
Answer: vrms ≈ 482 m/s
Notes
- Lighter molecules move faster at same temperature.
- Higher temperature = higher vrms.
- Related to kinetic energy: KEavg = ½ m vrms² = (3/2) kBT.