Root-Mean-Square Speed
Definition and meaning of Root-Mean-Square Speed in chemistry.
Root-mean-square speed (rms) is the square root of the average of the squared molecular speeds in a gas sample. It is the most representative measure of molecular motion and is derived directly from kinetic molecular theory.
In more detail
The rms speed accounts for the full distribution of molecular velocities and always exceeds the simple arithmetic mean speed because squaring weights faster molecules more heavily. It depends on two variables: absolute temperature (Kelvin) and molar mass. Higher temperatures increase molecular motion and rms speed, while heavier molecules move more slowly at the same temperature. This concept is essential for predicting gas diffusion rates, effusion, and the relationship between molecular motion and macroscopic properties like pressure.
Key facts
| Formula | vrms = √(3RT/M), where R = gas constant, T = absolute temperature in Kelvin, M = molar mass in kg/mol |
|---|---|
| Unit | meters per second (m/s) |
| Field | Physical Chemistry |
| Key Properties | Increases with temperature; decreases with molar mass; independent of pressure |
At 298 K, oxygen (O2) molecules have an rms speed of approximately 482 m/s, while hydrogen (H2) molecules at the same temperature have an rms speed of approximately 1,928 m/s. The dramatic difference reflects H2's much lower molar mass (2 g/mol versus 32 g/mol for O2).
Frequently asked questions
How does rms speed differ from average molecular speed?
Rms speed involves squaring each speed before averaging, which weights faster-moving molecules more heavily. Consequently, rms speed is always greater than the arithmetic mean speed.
Why is rms speed independent of pressure?
Rms speed depends only on the intrinsic properties of temperature and molar mass. Pressure is a macroscopic consequence of molecular collisions but does not alter the individual molecular speeds.