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Root-Mean-Square Molecular Speed — result sheet
Calculate the root-mean-square speed of ideal-gas molecules from temperature and molar mass.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: vᵣₘₛ = √(3RT/M), with M converted from g/mol to kg/mol.
Root-mean-square speed is obtained from the mean square molecular speed in the ideal-gas kinetic model. It is not the same as the arithmetic mean speed or the most probable speed. The calculator converts the entered molar mass into SI units before applying the gas constant.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Absolute temperature — K; minimum 1.0E-6; maximum 10000000
- Molar mass — g/mol; minimum 1.0E-6; maximum 1000000
Worked example
| Input | Value |
|---|---|
| Absolute temperature | 300 |
| Molar mass | 28.97 |
Air-like molar mass at 300 K gives an RMS speed of about 508.23 m/s.
Assumptions and limits
- The gas is treated as ideal and the temperature is absolute Kelvin temperature.
- Molar mass is the average mass for the gas mixture or species being modeled and is converted to kg/mol.
- The output is a statistical molecular-speed measure, not a bulk flow velocity or a measured speed of one selected molecule.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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