Maxwell-Boltzmann Distribution Curves (DP IB Chemistry): Revision Note

Caroline Carroll

Written by: Caroline Carroll

Reviewed by: Philippa Platt

Updated on

Maxwell-Boltzmann distribution curves

What is a Maxwell-Boltzmann distribution curve?

  • A Maxwell-Boltzmann distribution curve is a graph that shows the distribution of energies at a certain temperature

  • In a sample of a substance:

    • A few particles will have very low energy

    • A few particles will have very high energy

    • Many particles will have energy in between

Maxwell-Boltzmann distribution curve 

Maxwell-Boltzmann distribution curve showing the activation energy
The Maxwell-Boltzmann distribution curve shows the distribution of energies and the activation energy
  • The graph shows that only a small proportion of particles in the sample have enough energy for an effective or successful collision and for a chemical reaction to take place

  • The most probable energy of a particle is represented by the highest point on the curve's peak

    • This is sometimes written as EMP 

Effect of changes in temperature on the Maxwell-Boltzmann distribution curve

  • When the temperature of a reaction mixture is increased, the particles gain more kinetic energy

  • This causes the particles to move around faster, resulting in more frequent collisions

  • The proportion of successful collisions increases, meaning a higher proportion of the particles possess the Ea to cause a chemical reaction

  • With higher temperatures, the Maxwell-Boltzmann distribution curve flattens and the peak shifts to the right

Graph of the effect of temperature on the Maxwell-Boltzmann distribution curve

The peak of the Maxwell-Boltzmann curve of a higher temperature is lower and to the right of a lower temperature
The Maxwell–Boltzmann curves at two temperatures: note that as temperature increases, the curve flattens and shifts right, showing more particles exceed Ea
  • Therefore, an increase in temperature causes an increased rate of reaction due to:

    • More effective collisions as the particles have more kinetic energy, making them move around faster

    • A greater proportion of the molecules having kinetic energy greater than the Ea

Examiner Tips and Tricks

  • When drawing Maxwell-Boltzmann distribution curves at different temperatures, make sure that:

    • The peak of the curve of the higher temperature is lower and to the right of the peak of the curve of the lower temperature

    • The two curves should only cross each other once

    • The tail of the curve of the higher temperature should be higher than that of the lower temperature

  • Careful: Examiners currently prefer to ask about the effect of reducing the temperature of a reaction, rather than increasing the temperature 

    • The underlying theory is still the same, but you need to apply it in the opposite direction

Effect of a catalyst on the Maxwell-Boltzmann distribution curve

  • A catalyst provides the reactants with another reaction pathway which has a lower activation energy

  • By lowering Ea, a greater proportion of molecules in the reaction mixture will have sufficient energy for a successful collision

  • As a result of this, the rate of the catalysed reaction is increased compared to the uncatalysed reaction

Maxwell-Boltzmann distribution curve with a catalyst

The activation energy of a catalysed reaction shown on a Maxwell-Boltzmann curve is less than the uncatalysed reaction
The total shaded area shows particles with energy ≥ Ea with catalyst. The light purple area shows the extra particles that now have enough energy to react due to the lower Ea.

Examiner Tips and Tricks

  • Make sure you know how to sketch and label the axes in Maxwell-Boltzmann distribution curves

    • The curve must start at the origin, and it approaches, but never touches the x-axis

  • If you are asked to show the area that represents the particles with an energy greater than the activation energy with a catalyst, make sure you highlight the total shaded area, not just the light-shaded area

You've read 0 of your 5 free revision notes this week

Unlock more, it's free!

Join the 100,000+ Students that ❤️ Save My Exams

the (exam) results speak for themselves:

Did this page help you?

Caroline Carroll

Author: Caroline Carroll

Expertise: Physics & Chemistry Subject Lead

Caroline graduated from the University of Nottingham with a degree in Chemistry and Molecular Physics. She spent several years working as an Industrial Chemist in the automotive industry before retraining to teach. Caroline has over 12 years of experience teaching GCSE and A-level chemistry and physics. She is passionate about creating high-quality resources to help students achieve their full potential.

Philippa Platt

Reviewer: Philippa Platt

Expertise: Chemistry Content Creator

Philippa has worked as a GCSE and A level chemistry teacher and tutor for over thirteen years. She studied chemistry and sport science at Loughborough University graduating in 2007 having also completed her PGCE in science. Throughout her time as a teacher she was incharge of a boarding house for five years and coached many teams in a variety of sports. When not producing resources with the chemistry team, Philippa enjoys being active outside with her young family and is a very keen gardener