How do we read a gas-speed distribution?
You will be able to: Interpret shifts, spread and area in normalized molecular-speed graphs.
How do we read a gas-speed distribution?
A class can share one average height without everyone having that height. Similarly, a gas can have one temperature while its particles span many speeds.
A useful starting point: Does equal temperature mean equal particle speed? →
Words and symbols before equations
- Distribution
- How particles are spread over possible speeds or energies.
- Probability density
- Curve height whose area over an interval gives a fraction.
- Most probable speed
- Speed at the peak; distinct from mean and rms speed.
- Normalized area
- Total area of one distribution is one, representing the entire sample.
What this picture assumes
Normalized Maxwell–Boltzmann speed probability density for an equilibrium ideal gas. Molar mass is converted from g/mol to kg/mol. Graph shows 0–4000 m/s; a very small high-speed tail can extend beyond it. Orange = selected temperature, navy = 300 K reference for the same species. RMS speed is an explanatory readout, not a required memorized AP equation.
Read the picture in three steps
- Read the species and labels first. Identify what each symbol and line represents. Read the units and fixed conditions before comparing quantities.
- M = 28 g/mol; T = 300 K; rms speed = 516.9 m/s. Average translational energy is 1 times its 300 K value.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the chemistry
On a speed-distribution graph, the horizontal axis is speed. The vertical axis is probability density, not the energy of a single particle. Fractions correspond to areas over intervals.
Heating a fixed gas moves its characteristic speeds higher and broadens its normalized distribution. The peak becomes lower because the same total area spreads over a wider range.
At the same temperature, a lighter gas has a distribution shifted toward higher speeds. These are statistical descriptions: a particular heavy particle can be faster than a particular light one. Equal temperature does not give identical speed distributions for different masses.
A worked example, step by step
Compare normalized N₂ speed distributions at 300 K and 600 K. Predict the characteristic-speed ratio and the direction of the peak-height change.
- The species and mass are fixed; temperature doubled.
- Characteristic speeds scale as √T, giving √(600/300) = √2 ≈ 1.41.
- The hotter curve spreads toward higher speeds and its peak is lower.
- Each complete curve still encloses area one. A lower peak does not mean fewer particles in a normalized sample.
Curve height alone is not a particle fraction. Use area across a speed interval.
Does the tallest point mark the rms speed?
Compare with an explanation
No. The peak marks the most probable speed; rms speed is calculated from the squared-speed average.
Predict. Change one thing. Explain.
Keep the species fixed and change T from 300 K to 600 K. Compare the orange current curve with the 300 K reference. Identify what its normalized area means.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
M = 28 g/mol; T = 300 K; rms speed = 516.9 m/s. Average translational energy is 1 times its 300 K value.
Normalized Maxwell–Boltzmann speed probability density for an equilibrium ideal gas. Molar mass is converted from g/mol to kg/mol. Graph shows 0–4000 m/s; a very small high-speed tail can extend beyond it. Orange = selected temperature, navy = 300 K reference for the same species. RMS speed is an explanatory readout, not a required memorized AP equation.
Explain what you noticed: Answer the investigation prompt above. State one observation and explain it using particle interactions, concentration, gas behavior or energy transfer. Identify what the representation cannot tell you.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionSketch and label normalized speed curves for the same ideal gas at T and 4T. Compare their peak positions, widths and total areas.
This response is not submitted or saved. Copy it before leaving.
Compare with the answer and four-point rubric
- 1 point: Label horizontal speed and vertical probability density.
- 1 point: Place the hotter characteristic speeds at twice the original scale.
- 1 point: Draw the hotter curve broader with a lower peak.
- 1 point: Give both full curves equal total area one; acknowledge that particle speeds vary.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1What does total normalized area mean?
All particles, or total probability one.
RECALL 2Does a distribution describe a single particle trajectory?
No; it describes the statistical spread across a sample.
RECALL 3How are speed and energy distributions different?
Their horizontal variables differ; do not treat the axes as interchangeable.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
How do we read a gas-speed distribution?
- Fraction in an interval = area under its normalized density curve.
- Fixed species: speed scale ∝ √T.
Remember: Curve height alone is not a particle fraction. Use area across a speed interval.
Conditions: Normalized Maxwell–Boltzmann speed probability density for an equilibrium ideal gas. Molar mass is converted from g/mol to kg/mol. Graph shows 0–4000 m/s; a very small high-speed tail can extend beyond it. Orange = selected temperature, navy = 300 K reference for the same species. RMS speed is an explanatory readout, not a required memorized AP equation.
Refresh Kid · AP Chemistry Unit 3 · Objectives 3.5.A · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 3.5, objective 3.5.A. CED effective Fall 2024 and June 2026 clarifications checked September 16, 2026. Unit 3: Properties of Substances and Mixtures, Topics 3.1–3.13. Focused lesson names, examples, models and assessments are original Refresh Kid teaching materials, not additional official topics or official AP questions. Official corrections.
The model states its assumptions beside the diagram. Colligative-property calculations and solution molality/mass-percent/volume-percent calculations are not required here. The optional speed-density model illustrates distributions; it does not require memorizing its mathematical derivation.
Teaching resources: The Organic Chemistry Tutor video titles/descriptions and topic coverage were checked for optional links; no claim is made to have watched every video. No creator scripts, examples, worksheets or artwork were copied. GitHub’s 3D website collection and its Three.js camera-control example informed the idea of controllable spatial inspection. Scientific diagrams, geometry and interactions here are original. The self-hosted Three.js runtime retains its MIT license. Camera rotation changes the view, not the chemistry.
Independent teacher review and observation of students remain pending. Implementation checks do not certify scientific accuracy, accessibility or learning effectiveness. This is a review edition.
Optional official resource: Released AP Chemistry questions and scoring guides. This archive contains questions across units; it is not an assignment of every question to this lesson.
The teaching sequence is informed by the IES learning guide; this exact implementation has not been evaluated with learners.
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