The Boltzmann Factor 44-45

Question 1

What is the Boltzmann factor?

Answer 1

The Boltzmann factor, e^-E/kT, gives the ratio of the number of particles in energy states in E joules apart.

Question 2

For an activation energy of E, processes start happening quickly when E/kT is between what values?

Answer 2

Between 15 and 30

Question 3

For E/kT = 15 what is the Boltzmann factor and what does this value mean?

Answer 3

For E/kT = 15 the Boltzmann factor is 10^-7, that means that only about one in 10⁷ particles have enough energy to overcome the activation energy.

Question 4

Why do reactions still occur if only one in 10⁷ particles have enough energy to overcome the activation energy?

Answer 4

It might sound like a tiny proportion of gases have enough energy, but the particles are moving very fast. Gases collide 10⁹ times a second, so even with a few particles with the activation energy can allow a reaction to happen in a matter of seconds.

Question 5

Draw the Boltzmann factor vs temperature (log scale ) graph.

Explain what the shape of the graph shows.

Answer 5

• The graph can be found on page 44 of the ocr revision guide.
• At low temperatures, the Boltzmann factor is very low, so few particles will have sufficient energy to react.
• At high temperatures, the Boltzman factor approaches 1, so nearly all the particles will have enough energy to react and the reaction rate will be fast.
• In between, the Boltzmann factor increases rapidly with temperature. So a small increase in temperature can make a big difference to the rate.

Question 6

What is the approximated relationship between the rate of reaction and the Boltzmann factor, e^-E/kT?

Answer 6

The rate of a reaction with activation energy E is proportional to the Boltzmann factor, e^-E/kT.