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5.2.7Additional lessons

Maxwell–Boltzmann Distribution Curves — IB Chemistry SL Revision Notes & Topical Questions

5 min read 5 parts Lesson 72 of 98

📚 IB Chemistry SL Hub / Topical Revision
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Part 1 of 5Reading the Curve

5.2.7 Maxwell–Boltzmann Distribution Curves

The curve shows how the particles in a sample are spread across a range of energies.

Axes
  • The horizontal axis shows kinetic energy and the vertical axis shows the number of particles having that energy.
Shape
  • The curve starts at the origin, rises to a peak and then falls gradually without touching the axis at high energies.
Area
  • The total area under the curve is the total number of particles in the sample.
Most probable energy
  • The peak shows the energy possessed by the greatest number of particles, and the mean energy is slightly higher than this.

Part 2 of 5Activation Energy on the Graph

Activation Energy on the Graph
Position
  • Eₐ is marked on the energy axis with a vertical line, and the area to its right represents particles able to react.
Fraction
  • The shaded area to the right of Eₐ divided by the total area is the fraction of particles with sufficient energy.
Small fraction
  • At ordinary temperatures only a small portion of the area lies to the right of Eₐ.
Link to rate
  • A bigger shaded area means more successful collisions and a faster reaction.

Part 3 of 5Effect of Temperature

1
At a higher temperature the peak of the curve moves to the right, as the average kinetic energy is higher.
2
The peak becomes lower and the curve broadens, because the same total number of particles is spread over a wider range of energies.
3
The area under the curve is unchanged since the number of particles is the same.
4
The area to the right of Eₐ increases significantly, so a greater fraction of collisions are successful and the rate rises.
FeatureLower THigher T
Peak positionLeftRight
Peak heightHigherLower
Total areaSameSame
Area beyond EₐSmallLarger

Part 4 of 5Effect of a Catalyst

Effect of a Catalyst
Curve unchanged
  • A catalyst does not alter the temperature, so the shape and position of the curve stay the same.
Eₐ moves left
  • Its lower activation energy is drawn as a second vertical line to the left of the original Eₐ.
Greater fraction
  • The area to the right of the new line is larger, so more particles can react.
Drawing tip
  • Show both Eₐ lines on one curve and label them as uncatalysed and catalysed.

Part 5 of 5Exam Checklist & Tips

5.2.7 – Key Points for the Exam

  • Maxwell–Boltzmann distribution A graph showing the distribution of kinetic energies of the particles in a sample at a given temperature.
  • Most probable energy The energy at the peak of the curve, held by the greatest number of particles.
  • Fraction with E ≥ Eₐ The area under the curve to the right of the activation energy divided by the total area.
  • Kinetic energy The energy a particle has because of its movement.

Common Mistakes

  • Drawing the curve touching the energy axis at high energy; it approaches the axis but never reaches it.
  • Drawing a curve for a higher temperature that has a higher peak.
  • Changing the area under the curve when temperature is raised.
  • Moving the curve instead of the Eₐ line when a catalyst is added.

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