Maxwell–Boltzmann distribution — AQA A-Level Chemistry
Test yourself on Maxwell–Boltzmann distribution with AQA A-Level practice questions.
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Maxwell–Boltzmann distribution explained
The Maxwell–Boltzmann distribution is a graph of the number of molecules against molecular kinetic energy for a gas at a fixed temperature.
Read the full explanation
Its shape is fixed by physics: it starts at the origin, because no molecule has zero energy, rises steeply to a peak at the most probable energy, then falls away with a long tail to the right that never touches the axis, because there is no upper limit to the energy a molecule can have. The mean energy sits slightly to the right of the peak because that tail drags the average up. The area under the whole curve equals the total number of molecules, so it stays constant at a fixed amount of gas, and the area beyond Eₐ represents the molecules able to react.
Students should be able to: draw and interpret distribution curves for different temperatures.
When a gas is heated the total number of molecules is unchanged, so the area under the curve must stay the same, but the molecules are redistributed towards higher energies. The curve for the higher temperature has its peak lower and shifted to the right, and it crosses the original curve exactly once before running above it at all energies past that crossing point. That combination is what examiners look for: a lower, flatter, right shifted maximum, an unchanged total area, and a single crossing. The consequence is read off the tail. Beyond a marked Eₐ the shaded area under the hotter curve is many times larger, so many more molecules have energy greater than or equal to the activation energy and the rate rises sharply.
Your focus
- Sketch a Maxwell–Boltzmann distribution with correctly labelled axes, starting at the origin and with an asymptotic tail.
- Identify the most probable energy and the mean energy on a distribution curve and explain why they differ.
- Interpret the area under a region of the curve in terms of numbers of molecules.
Show all 8 objectives
- Explain what the shaded area beyond Eₐ represents and why it determines the rate.
- Draw two Maxwell–Boltzmann distributions for the same gas at different temperatures on one pair of labelled axes.
- Explain why the two curves must enclose the same total area and cross only once.
- Interpret the change in the shaded area beyond Eₐ when the temperature is raised, and link it to rate.
- Identify errors in a given sketch of two distribution curves and state how each should be corrected.
Maxwell–Boltzmann distribution exam tips
Marking Points
- one mark for a curve starting at the origin, since no molecules have zero energy
- one mark for a single peak at the most probable energy with the curve falling away to the right
- one mark for an asymptotic tail that never meets the energy axis
- one mark for stating that the area under the curve equals the total number of molecules
- one mark for both axes labelled, number of molecules against energy
- one mark for Eₐ marked on the energy axis to the right of the peaks
- one mark for the original curve drawn with the correct shape from the origin
- one mark for the higher temperature curve with a lower peak shifted to the right, crossing the first curve only once
- one mark for stating that at the higher temperature many more molecules have energy greater than or equal to Eₐ
Examiner Tips
- 💡Label the axes number of molecules and energy; an unlabelled sketch usually scores nothing.
- 💡Practise drawing the curve in one stroke from the origin, so the start and the tail both come out right.
- 💡Mark Eₐ well to the right of the peak and shade the area beyond it when explaining rate.
- 💡Draw the lower temperature curve first, then fit the hotter one under and to the right of it, checking there is exactly one crossing.
- 💡Write T₁ and T₂ on the curves themselves, and state which is hotter.
- 💡Finish with the sentence about the area beyond Eₐ; the shape marks and the explanation mark are separate.
Common Mistakes
- drawing a symmetrical, normal distribution rather than a skewed curve with a long tail
- letting the curve start above the origin or cut the energy axis at high energy
- labelling the peak as the mean energy rather than the most probable energy
- labelling the y axis as energy and the x axis as number of molecules
- assuming a molecule at the peak of the curve has enough energy to react
- drawing the hotter curve taller as well as shifted, so the total area is no longer constant
- drawing curves that cross twice or run parallel without crossing
- shifting the peak to the right but keeping it at the same height
- marking Eₐ at the peak instead of far out on the tail
- leaving the axes unlabelled so no shape marks can be awarded