What you will learn

Read particle-energy distributions and use them to explain concentration, temperature and catalysis. Distinguish the fraction of particles with enough energy from the number of particles in a fixed volume. Interpret the activation-energy threshold without confusing it with the energy distribution.

1. Reading a distribution curve

Particles in a gas do not all have the same kinetic energy. Collisions redistribute energy continuously. At a fixed temperature, a Maxwell–Boltzmann curve describes the distribution of translational kinetic energies in a large sample. It describes a population, not the journey of one particle. The same collision-theory ideas help explain many reactions, although real solution reactions can be more complicated than this ideal-gas model.

• The horizontal axis is kinetic energy. It is not time or distance through a reaction.
• The vertical axis gives the number, number density or fraction per energy interval. Read its label before comparing areas.
• The curve starts at the origin, rises to a most probable energy, then has a long tail approaching the axis. The ideal continuous distribution has no finite maximum energy.
• The peak is the most probable energy, not the energy of every particle. The mean energy lies to the right of the peak.
• An area over an energy interval gives the number or fraction in that interval; the height at one energy does not give the total with energy above it.

Activation energy, Eₐ, is the minimum collision energy needed for reaction along a specified pathway. The area to the right of an Eₐ line represents particles with sufficient kinetic energy in this model. An appropriate collision and orientation are also necessary: not every sufficiently energetic particle reacts immediately.

2. Temperature changes the energy distribution

For the same number of particles, increasing temperature makes the energy distribution broader, lowers its peak and moves the peak to higher energy. The total number of particles is unchanged, so total area on a number plot is unchanged; total area on a normalised fraction plot remains one. More particles have energy at least Eₐ, often giving a large increase in rate. Collision frequency can also increase as particles move faster, but the increased energetic fraction is the key distribution explanation.

The Eₐ line remains in the same place if the reaction pathway has not changed. Heating changes particle energies; it does not supply a new pathway or lower the activation energy. Cooling reverses these distribution changes. Two temperature curves cross, so the hotter curve is not higher at every energy.

3. Concentration: first identify the vertical axis

At constant temperature, increasing concentration does not change the normalised kinetic-energy distribution or its peak energy. In the same volume there are more particles and more frequent encounters. If the vertical axis is number of particles per energy interval in that fixed volume, the whole curve scales upwards and its total area increases. Doubling concentration doubles this number-density curve. The fraction above Eₐ is unchanged, but the number above Eₐ per unit volume increases.

If the vertical axis instead shows a fraction per energy interval, the curves overlap at the same temperature. If a fixed total number of gas particles is compressed, its total-number distribution also stays unchanged, even though the concentration and collision frequency rise. Therefore “concentration makes the curve taller” is incomplete without the axis and sample definition.

A higher concentration usually increases the rate of a reaction involving that species, but the exact factor is experimental and depends on the rate equation. Twice as many energetic particles per volume does not alone prove that the overall reaction rate doubles.

4. Catalysis: move the threshold, keep the curve

A catalyst provides an alternative reaction pathway with lower activation energy. At the same temperature and for the same reactant population, the energy distribution is unchanged. Draw one curve and two Eₐ lines, with the catalytic threshold to the left. The larger area above the lower threshold means a greater fraction of collisions can overcome the barrier.

A catalyst does not heat the reactants, increase their mean kinetic energy or shift the Maxwell–Boltzmann peak. It is regenerated overall, and it changes neither the reaction enthalpy nor the equilibrium position. Detailed reaction-profile diagrams belong to the separate energetics lesson.

5. Worked interpretations

Compare the three changes

Common misconceptions

• All particles have the peak energy: the curve shows a range of energies.
• A catalyst shifts the curve right: it lowers the threshold on the same distribution.
• Heating lowers Eₐ: it increases energies; the pathway barrier remains fixed.
• Concentration always makes every curve taller: that depends on whether number density, total number or fraction is plotted.
• Area beyond Eₐ is a rate: it is an energetic number or fraction; reaction also requires encounters and appropriate orientation.
• Concentration raises mean kinetic energy: at the same temperature, it does not.

Exam tips

• Label kinetic energy and state precisely what the vertical axis represents.
• State which quantities stay constant: temperature, number and volume.
• For a temperature comparison, preserve total area when particle number is fixed.
• For a catalyst, use one curve and label both thresholds.
• Describe the area beyond Eₐ and connect it to successful collisions.
• Use number per unit volume when explaining concentration changes.

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