How is this lab different from Graham’s law?

This lab focuses on the speed distribution, characteristic speeds and speed-band fractions. The separate Graham’s Law lab connects molecular motion with effusion and diffusion comparisons.

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LIVE LAB 20 • STATES OF MATTER & KINETIC THEORY

Maxwell–Boltzmann 3D Lab

Q: What does the Maxwell–Boltzmann curve show?

It shows the probability density for molecular speeds in a gas at thermal equilibrium. The area between two speeds gives the fraction in that interval; the height at one speed is not itself a fraction.

Q: What happens when absolute temperature doubles?

For the same gas, the most probable, mean and RMS speeds each increase by √2, approximately 1.414. They do not double.

Q: Why is RMS speed greater than mean speed?

Squaring speeds gives larger values more weight. Taking the square root after averaging therefore gives a larger result than the arithmetic mean when the speeds vary.

Explore molecular motion and speed distributions in 3D. Change temperature and gas mass, compare fixed speed bands and practise 20 questions with worked solutions.

Foundation to AdvancedFoundation • Core • AdvancedInteractive 3D molecular-speed laboratoryPersonal study

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Maxwell–Boltzmann 3D Lab — actual simulation with its model and controls

ACTUAL LAB PREVIEW

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COMPLETE CONCEPT GUIDE

Maxwell–Boltzmann distribution: temperature, mass and molecular speeds

Even at one temperature, gas molecules have a range of speeds. Compare the particle view with a normalised speed-distribution curve and connect changes in its shape with temperature and molar mass.

Three characteristic speeds

For an ideal gas, the most probable speed is √(2RT/M), the mean speed is √(8RT/πM), and the RMS speed is √(3RT/M). Their order is most probable < mean < RMS. Use kelvin and kg/mol when R is in SI units.

Heating and cooling

For a fixed gas, characteristic speeds scale with √T. Heating shifts the peak toward higher speeds and broadens the curve. The area under a normalised probability-density curve remains one; the peak height is not the number of molecules.

Worked temperature comparison

For the same gas heated from 300 K to 600 K, every characteristic speed increases by √(600/300) = √2 ≈ 1.414. Average translational kinetic energy doubles, while the normalised area under the speed-distribution curve stays one.

Comparing gases at the same temperature

Characteristic speeds scale as 1/√M. A lighter gas has a distribution shifted toward higher speeds, but ideal gases at the same temperature have the same average translational kinetic energy per molecule.

Fixed speed bands

The fraction of molecules between two speeds is the area under the curve across that interval. Keep the interval boundaries fixed when comparing temperatures. The finite animated sample fluctuates around the theoretical fractions.

MAXWELL–BOLTZMANN FAQ

Questions students ask while mastering this concept.

What does the Maxwell–Boltzmann curve show?

It shows the probability density for molecular speeds in a gas at thermal equilibrium. The area between two speeds gives the fraction in that interval; the height at one speed is not itself a fraction.

What happens when absolute temperature doubles?

For the same gas, the most probable, mean and RMS speeds each increase by √2, approximately 1.414. They do not double.

Why is RMS speed greater than mean speed?

Squaring speeds gives larger values more weight. Taking the square root after averaging therefore gives a larger result than the arithmetic mean when the speeds vary.

Maxwell–Boltzmann 3D Lab

Maxwell–Boltzmann 3D Lab

Start with the concept.