---
title: "The Maxwell-Boltzmann Distribution of Molecular Speeds"
description: "Molecules in a gas do not share one speed but a distribution with a peak, a mean and a longer tail at high speed. Raising the temperature flattens and widens the curve rather than shifting it rigidly."
canonical: https://lightmysky.com/learn/science/the-maxwell-boltzmann-distribution-of-molecular-speeds-mt_njr5r5YtuT
source: https://lightmysky.com/learn/science/the-maxwell-boltzmann-distribution-of-molecular-speeds-mt_njr5r5YtuT.md
retrieved: 2026-09-12
---

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# The Maxwell-Boltzmann Distribution of Molecular Speeds

Molecules in a gas do not share one speed but a distribution with a peak, a mean and a longer tail at high speed. Raising the temperature flattens and widens the curve rather than shifting it rigidly.

Subject: Science · Area: Thermal & Statistical Physics · Ages 18 to 19
Page: https://lightmysky.com/learn/science/the-maxwell-boltzmann-distribution-of-molecular-speeds-mt_njr5r5YtuT

## Ready when they can

- Sketches the speed distribution at two temperatures and describes how the peak and tail change
- Distinguishes the most probable, mean and root mean square speeds and orders them
- Explains evaporation and reaction rates by appealing to the high-speed tail

## Lesson: Gas molecules and their spread of speeds

Molecules in a gas do not share one speed. At one temperature they spread over a wide range of speeds, and temperature sets only the average kinetic energy. Lighter molecules move faster on average, so their whole curve shifts toward higher speeds.

The Maxwell-Boltzmann curve counts how many molecules sit at each speed. Its peak marks the most probable speed. Heating the gas shifts the peak toward higher speeds and flattens and widens the curve instead of shifting it rigidly.

Three speeds describe the curve, and they always line up the same way. From slowest to fastest they are the most probable speed, then the mean speed, then the root mean square speed.

**Tip.** Only the rare fast molecules in the high speed tail can escape a liquid or clear the bar for a reaction. A small rise in temperature grows that tail fast, so evaporation and reaction rates jump.

**Recap.** One temperature means a spread of speeds, not one speed, and the fast tail runs evaporation and reactions.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Kinetic Theory: Pressure from Molecular Motion](https://lightmysky.com/learn/science/kinetic-theory-pressure-from-molecular-motion-mt_2ARUheICqu)
- [The Normal Distribution and Standardised Scores](https://lightmysky.com/learn/mathematics/the-normal-distribution-and-standardised-scores-mt_Cs32DT9KnA)

## Opens up

- [Equipartition and the Heat Capacities of Gases](https://lightmysky.com/learn/science/equipartition-and-the-heat-capacities-of-gases-mt_3OjJwVWlYD)