Maxwell-Boltzmann Distribution

Molecules in a gas share a spread of speeds, not one. Heat the gas or lighten the molecule and the whole distribution shifts faster and flatter.

Maxwell–Boltzmann DistributionLive

molecular speeds in a gas

Controls

Gas molecules do not all move at one speed — they spread into this distribution. Heat the gas or lighten the molecule and the curve broadens and shifts faster.

Presets

Temperature (K)

Molar mass (g/mol)

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Data Inspector

Most probable0 m/s

Average0 m/s

RMS0 m/s

Governing equation

f (v) = 4 π (\frac{m}{2 π k T})^{3/2} v^{2} e^{- m v^{2} /2 k T}, v_{p} = \frac{2 k T}{m} = 0 m/s at T = 300 K

Reading this result: The peak (v_mp 0 m/s) sits below the average and RMS speeds because the long high-speed tail pulls those means upward.

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How it works

The Maxwell-Boltzmann distribution gives the probability of molecular speeds in an ideal gas. Its most-probable, average, and root-mean-square speeds all scale with the square root of temperature over mass, connecting the microscopic and thermodynamic pictures of a gas.

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