15: The Boltzmann Factor Flashcards
What is the average thermal energy per particle?
kT
What is the activation energy?
Particles of matter are held together by bonds. The energy needed to break these bonds in a given substance is the activation energy.
Explain what the activation energy is in a change of state
The particles need enough energy to break the forces between them
Explain the activation energy in thermionic emission
If you heat up a conductor, electrons are released from the surface. These electrons need enough energy to escape from the attraction of the positive nuclei
Explain what the activation energy is in the ionisation of a candle flame
The molecules in the air need enough energy to split up into individual atoms and ions.
Explain the activation energy in conduction in a semiconductor
Semiconductors will only start to conduct once there are electrons in a high energy state called the ‘conduction band’, so electrons need enough energy to jump from the ground state to this higher energy state
Explain the activation energy in viscous flow
Viscous fluid have strong attractive forces between the particles, causing the fluid to flow slowly. As you increase the temperature, you increase the kinetic energy of the particles. This means they have more energy to overcome these forces and so the fluid will be able to flow more easily
What does the ratio E/kT of need to get to in order for processes to happen at a fair rate?
Where E is the activation energy
15-30
What is the relationship between activation energy and random thermal energy for a process happened?
kT must be greater than or equal to E
Explain how a particle can have a much higher than average thermal energy
Every time particles collide, there is a chance that one of them will gain extra energy – above and beyond the average kT. If that happens several times in a row, a particle can gain energies much, much higher than the average
If f is the fraction of particles with an extra energy E. What is the fraction of particles with energy NE where N is an integer?
fᴺ
What does the Boltzmann factor tell you?
Gives the ratio of the number of particles in energy states E joules apart, at a temperature T (K)
Also the approximate probability that a particle has an energy of at least E
What is the only variable that will change the Boltzmann factor?
Temperature.
Describe the graph of Boltzmann factor against temperature
At low temperatures, the BF is also very low, so very few particles will have sufficient energy to react and the reaction will be really slow
At high temperatures the BF approaches one, so nearly all the particles will have enough energy to react and the reaction will be really fast
In between, the BF increase rapidly with temperature. So a small increase in temperature can make a big difference to the rate
The Boltzmann Factor and rate of reaction both vary with [ ]
Temperature
