Topic 9 · page 9 of 15

Catalysts and the Maxwell–Boltzmann curve

A catalyst does not change the temperature, so the curve stays exactly the same. It moves the activation energy to the left, so more molecules lie beyond it. Temperature moves the curve; a catalyst moves the line.

9 min read9.8

Read first: Temperature and the curve, Catalysts and reaction profiles

The catalyst moves the activation energy, not the curve 9.8

The Maxwell–Boltzmann curve describes the energies of the molecules at one temperature. A catalyst does not heat anything, so the curve is unchanged. What the catalyst changes is the activation energy: the alternative route has a lower barrier (page 8), so the EaE_\text{a} line moves to the left.

A single Maxwell-Boltzmann curve with two vertical dashed lines. The right line marks the activation energy without a catalyst and the left line, at a lower energy, marks the lower activation energy with a catalyst. An arrow points from the right line to the left line. The area under the curve beyond the left line is larger than the area beyond the right line, so more molecules have enough energy when a catalyst is present. The curve itself is unchanged.
One curve, two activation energies. Moving the line left puts more of the area, so more molecules, beyond it.

The area to the right of the new EaE_\text{a} is bigger than before. More molecules have energy of at least the (lower) activation energy, so a greater proportion of collisions are successful and the rate is higher. The extra area is the strip between the two lines.

Worked exampleExplaining a catalyst with the distribution

Explain, using the Maxwell–Boltzmann distribution, how a catalyst increases the rate at constant temperature.

  1. The catalyst provides an alternative route with a lower activation energy.
  2. The distribution of molecular energies is unchanged (same temperature, same curve).
  3. The EaE_\text{a} line moves to the left, so more molecules have energy greater than or equal to EaE_\text{a}.
  4. A greater proportion of collisions are successful, so the rate increases.

Temperature against catalyst 9.8

The two changes have the same result, more molecules above the line, reached in opposite ways.

Raise the temperature Add a catalyst
The curve changes: flatter, peak to the right stays the same
EaE_\text{a} stays where it is moves to the left
More molecules with E≥EaE \geq E_\text{a} because the curve moves the line moves

Check yourself

  1. Explain, using the Maxwell–Boltzmann distribution, why a catalyst increases the rate at constant temperature.
  2. For each of raising the temperature and adding a catalyst, state whether the curve changes and whether EaE_\text{a} changes.
  3. A student sketches two curves for a reaction, one without and one with a catalyst, at the same temperature. Explain why this is wrong.
  4. State one way in which the effects of a catalyst and a temperature rise are alike, and one way in which they differ.
  5. Does adding a catalyst change the amount of product eventually made? Explain.

Answers cover these until you have tried the questions

  1. The catalyst provides an alternative route with a lower activation energy. The distribution is unchanged, but the EaE_\text{a} line moves to the left, so more molecules have energy greater than or equal to EaE_\text{a}. A greater proportion of collisions are successful, so the rate increases.
  2. Raising the temperature: the curve changes (flatter, peak to the right) and EaE_\text{a} does not change. Adding a catalyst: the curve does not change and EaE_\text{a} moves to a lower value.
  3. The temperature is the same, so the distribution of energies is the same curve. A catalyst changes EaE_\text{a}, not the curve. The sketch should show one curve and two EaE_\text{a} lines.
  4. Alike: both increase the proportion of molecules with energy of at least EaE_\text{a}, so more collisions are successful. Different: a temperature rise changes the curve and keeps EaE_\text{a} fixed, while a catalyst keeps the curve and lowers EaE_\text{a}.
  5. No. The amount of product depends on the amount of limiting reactant (and, for a reversible reaction, on the position of equilibrium). A catalyst only changes how fast the reaction proceeds.