Find the square-root mean of squared molecular speeds in an ideal gas.
Difficulty
Intermediate
Read time
3 min
Prerequisites
Algebra, logarithms, and molar quantities
Source
OpenStax, Chemistry 2e, §9.5Adapted from Teng-Jui Lin’s CHEM 145 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.
Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.
FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example.
The rms speed is the square root of the average squared molecular speed. It rises with the square root of absolute temperature and is lower for gases with larger molar mass at the same temperature.
| Symbol | Meaning | Units |
|---|---|---|
| Root-mean-square molecular speed | ||
| Molar gas constant | ||
| Absolute temperature | ||
| Molar mass, expressed in kilograms per mole |
Estimate the characteristic rms speed of a gas.
Compare speeds for different molar masses at one temperature.
Estimate the rms speed of oxygen at 300 K, taking its molar mass as 0.0320 kg/mol.
Adapted from Teng-Jui Lin’s CHEM 145 equation sheet. The linked textbook reference was used to check the equation and its physical context. Pending editorial review.
Adapted from Teng-Jui Lin, Equation Sheets, under CC BY 4.0.
FormuLab adapted notation and chemical symbols, added variable meanings, units, applicability conditions, and an original worked example.
Assumptions
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