Gas Molecule Speed Calculator
Calculate the rms speed, average speed, and most probable speed of gas molecules at any temperature.
Based on the Maxwell-Boltzmann distribution.
The kinetic molecular theory describes gas molecules as point particles in constant random motion. At a given temperature, molecules have a distribution of speeds described by the Maxwell-Boltzmann distribution.
Three characteristic speeds:
Root mean square speed (v_rms):
v_rms = √(3RT/M) = √(3kBT/m)
Average speed (v_avg):
v_avg = √(8RT/πM) = √(8kBT/πm)
Most probable speed (v_mp):
v_mp = √(2RT/M) = √(2kBT/m)
Relationship: v_mp < v_avg < v_rms (approximate ratio: 1 : 1.128 : 1.225)
Where:
- R = 8.314 J/mol·K
- T = temperature (Kelvin)
- M = molar mass (kg/mol)
Gas molecule speeds at 25°C (298 K):
| Gas | M (g/mol) | v_rms (m/s) |
|---|---|---|
| H₂ | 2.016 | 1,920 |
| He | 4.003 | 1,363 |
| H₂O | 18.02 | 645 |
| N₂ | 28.02 | 515 |
| O₂ | 32.00 | 482 |
| CO₂ | 44.01 | 411 |
| Xe | 131.3 | 238 |
| UF₆ | 352.0 | 145 |
Why do lighter molecules move faster?
Kinetic energy is equally distributed among all molecules at the same temperature:
KE_avg = (3/2)kBT (same for all gases at same T)
Since KE = ½mv², lighter molecules must move faster to have the same energy.
Temperature effect: Speed ∝ √T. To double v_rms, temperature must quadruple. Going from 298 K to 1192 K (×4 T) only doubles the speed.
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