Maxwell-Boltzmann Distribution

What is a Maxwell-Boltzmann distribution curve?

• A graph that shows the distribution of kinetic energies of particles in a sample (usually a gas) at a constant temperature.

What do the x-axis and y-axis represent on a Maxwell-Boltzmann distribution curve?

• X-axis: Kinetic energy (or 'Energy', E)

• Y-axis: Number of particles (or 'Proportion of molecules')

What does the total area under the curve represent?

• The total number of particles in the sample.

Why does the Maxwell-Boltzmann distribution curve start at the origin (0,0)?

• Because no particles have zero kinetic energy (as all particles are in motion, unless at absolute zero).

What is the activation energy (E_a) and how is it shown on the curve?

• E_a is the minimum energy required for a collision to result in a reaction.

• It is shown as a vertical line on the x-axis.

• The area to the right of this line shows the number of particles with E ≥ E_a.

Draw a diagram showing how the curve changes when temperature is increased from T₁ to T₂

• The T₁ curve is lower and broader.

• The T₂ peak is shifted to the right.

• Both curves start at (0,0).

• The total area under both curves is the same.

Explain why increasing temperature increases the rate of reaction, using the Maxwell-Boltzmann distribution.

• Increasing temperature shifts the curve to the right, so particles have more kinetic energy on average.

• The activation energy (E_a) does not change.

• The area under the curve to the right of E_a is much larger at the higher temperature.

• This means a greater proportion of particles have energy ≥ E_a, so the frequency of successful collisions increases.

Draw a diagram showing the effect of a catalyst on a Maxwell-Boltzmann distribution curve.

• The curve itself does not change.

• The catalyst provides a lower activation energy (Ea_(cat)).

• A new line for (Ea_(cat)) is drawn to the left of the original (E_a).

Explain why a catalyst increases the rate of reaction, using the Maxwell-Boltzmann distribution.

• The catalyst provides an alternative reaction pathway with a lower activation energy (Ea_(cat)).

• The distribution curve does not change.

• The area under the curve to the right of Ea_(cat) is larger than the area to the right of the original Ea_(cat).

• This means a greater proportion of particles have sufficient energy to react, increasing the frequency of successful collisions.

(1 mark) What does the peak of the Maxwell-Boltzmann distribution curve represent?

• The most probable energy (E_mp) of the particles. (1)

(2 marks) A Maxwell-Boltzmann distribution curve is shown.

(a) Label the y-axis. (1 mark) (b) Label the x-axis. (1 mark)

• (a) y-axis: Number of particles (or 'Proportion of molecules' / 'Frequency') (1)

• (b) x-axis: Kinetic energy (or 'Energy') (1)

(3 marks)

Draw a Maxwell-Boltzmann distribution curve.

On your diagram:

• Label the activation energy (E_a).

• Shade the area that represents the number of particles with sufficient energy to react.

• Correctly shaped curve starting at (0,0) and approaching the x-axis asymptotically. (1)

• A vertical line correctly labelled E_a (1)

• The area under the curve to the right of the E_a line is shaded. (1)