RMS speed is the square root of the average of the squared molecular speeds. It gives a measure of the typical speed of molecules in a gas.

How does RMS speed relate to temperature?

RMS speed is proportional to √T. Doubling the absolute temperature increases RMS speed by a factor of √2 ≈ 1.41.

Why use kg/mol for molar mass?

The gas constant R = 8.314 J/(mol·K) uses SI units. Molar mass must be in kg/mol (not g/mol) for the units to work out to m/s.

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Calculate the root-mean-square speed of gas molecules from temperature and molar mass using kinetic molecular theory.

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Temperature (T)

Molar Mass

kg/mol

RMS Speed

515.2 m/s

RMS Speed vs Temperature (T)

View formula & how it works →

Root-Mean-Square Speed

Formula

v_rms = √(3RT / M)

Where:

v_rms = root-mean-square speed (m/s)

R = 8.314 J/(mol·K)

T = temperature (K)

M = molar mass (kg/mol)

RMS speed is slightly higher than the average molecular speed due to the squaring in the averaging.

Example Calculation

Calculate the RMS speed of N₂ molecules (M = 0.028 kg/mol) at 298 K.

01v_rms = √(3RT/M)
02v_rms = √(3 × 8.314 × 298 / 0.028)
03v_rms = √(7434.6 / 0.028)
04v_rms = √(265521)
05v_rms = 515.3 m/s

Frequently Asked Questions

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Understanding Molarity

Learn what molarity is, how to calculate it, and why it matters in chemistry. Covers moles, liters, dilution, and step-by-step examples for preparing solutions.

Free RMS Speed Calculator

Root-Mean-Square Speed

Formula

Example Calculation

Frequently Asked Questions

Understanding Molarity

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