RMS Speed of Gas Molecules (v_rms = √(3kBT/m) = √(3RT/M))
jee-mainjee-advanced
v_rms = √(3kBT/m) = √(3RT/M)
What each symbol means
| Symbol | What it stands for |
|---|---|
| M | Molar mass in kg/mol (NOT g/mol) |
| R | Universal gas constant = 8.314 J mol⁻¹ K⁻¹ |
| T | Absolute temperature (K) |
| m | Mass of one molecule (kg) |
| kB | Boltzmann constant = 1.38 × 10⁻²³ J K⁻¹ |
| v_rms | Root mean square speed (m/s) |
When to use this
Derived from KE = (3/2)kBT. v_rms ∝ √T (at constant M). v_rms ∝ 1/√M (at constant T). Lighter molecules have higher v_rms. M MUST be in kg/mol in SI formula.