5.2.7Additional lessons
Maxwell–Boltzmann Distribution Curves — IB Chemistry SL Revision Notes & Topical Questions
5 min read 5 parts Lesson 72 of 98
Curriculum Equation Key قوانين الرقم الهيدروجيني والاتزان الأيوني - pH & Acid-Base Equilibrium FormulasFast Exam Solution
pH = -log[H⁺] | pOH = -log[OH⁻] | pH + pOH = 14 | [H⁺][OH⁻] = 10⁻¹⁴
Word Equation & Conditions: الرقم الهيدروجيني = -لوغاريتم تركيز أيون الهيدروجين | pH + pOH = 14
Location & Specifications: الاتزان الأيوني، كيمياء 3 ثانوي، التحصيلي، و AP Chemistry.
Part 1 of 5Reading the Curve
The curve shows how the particles in a sample are spread across a range of energies.
Axes
- Axes The horizontal axis shows kinetic energy and the vertical axis shows the number of particles having that energy.
Shape
- Shape The curve starts at the origin, rises to a peak and then falls gradually without touching the axis at high energies.
Area
- Area The total area under the curve is the total number of particles in the sample.
Most probable energy
- 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
- Position Eₐ is marked on the energy axis with a vertical line, and the area to its right represents particles able to react.
Fraction
- Fraction The shaded area to the right of Eₐ divided by the total area is the fraction of particles with sufficient energy.
Small fraction
- Small fraction At ordinary temperatures only a small portion of the area lies to the right of Eₐ.
Link to rate
- 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.
| Feature | Lower T | Higher T |
|---|---|---|
| Peak position | Left | Right |
| Peak height | Higher | Lower |
| Total area | Same | Same |
| Area beyond Eₐ | Small | Larger |
Part 4 of 5Effect of a Catalyst
Effect of a Catalyst
Curve unchanged
- Curve unchanged A catalyst does not alter the temperature, so the shape and position of the curve stay the same.
Eₐ moves left
- Eₐ moves left Its lower activation energy is drawn as a second vertical line to the left of the original Eₐ.
Greater fraction
- Greater fraction The area to the right of the new line is larger, so more particles can react.
Drawing tip
- 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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