The Maxwell-Boltzmann Distribution of Molecular Speeds · seed 1 · A4, ink-friendly. The answer key prints on its own page for grown-ups.

Gas molecules and their spread of speeds

Science · Thermal & Statistical Physics · ages 18-19
Name ______________________   Date ____________

  1. What does the peak of the speed curve mark?

    • The average bond length
    • The most probable speed
    • The total gas pressure

  2. At one temperature, how do molecular speeds compare?

    • They spread over a wide range
    • They are all exactly equal
    • They split into two fixed values

  3. Heating a gas shifts its speed curve rigidly right with the same shape.

    Circle one:   True   False

  4. Why does evaporation draw only on the tail of the curve?

    • Only the fastest molecules can escape the surface
    • Slow molecules boil more easily
    • The peak molecules carry no energy

  5. Order the three speeds from slowest to fastest.

    • Mean, most probable, root mean square
    • Root mean square, mean, most probable
    • Most probable, mean, root mean square

  6. Two gases share a temperature, but one has lighter molecules. What differs?

    • Both curves match exactly
    • The heavier gas averages faster
    • The lighter gas averages faster

  7. A student sketches the heated curve taller and narrower. What is the error?

    • Heating flattens and widens the curve
    • Heating removes the peak
    • Heating leaves the peak fixed

  8. A student says the mean speed explains why slight heating doubles a reaction rate. What is wrong?

    • Reaction rates ignore temperature
    • Most molecules never react, so the tail count matters, not the mean
    • Heating shrinks the fast tail
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Answer key

For grown-ups. Fold this page away before handing over the rest.

Gas molecules and their spread of speeds W1-mt_njr5r5YtuT-s1

  1. The most probable speed · The tallest point of the curve is the speed most molecules have.
  2. They spread over a wide range · One temperature fixes the average energy, not each single speed.
  3. False · Heating flattens and widens the curve while the peak moves right.
  4. Only the fastest molecules can escape the surface · Escaping the liquid takes rare high energy that only tail molecules hold.
  5. Most probable, mean, root mean square · The peak comes first, then the mean, then the root mean square.
  6. The lighter gas averages faster · Equal temperature means equal average energy, so lighter mass means higher speed.
  7. Heating flattens and widens the curve · Higher temperature spreads molecules wider, so the peak drops and broadens.
  8. Most molecules never react, so the tail count matters, not the mean · Only tail collisions clear the bar, and the tail grows far faster than the mean.
Worksheet · LightMySky