# Boltzmann distribution

### Boltzmann distribution

#### Lessons

In this lesson, we will learn:

• How to draw the Boltzmann kinetic energy distribution and understand its meaning.
• How a change in reaction conditions affects the Boltzmann distribution curves.
• How to explain changes in the Boltzmann distribution in terms of molecules and kinetic energy.
Notes:

• The Boltzmann distribution (AKA kinetic energy distribution) is a distribution that describes the amount of kinetic energy that a proportion of gas particles have in a given sample. See below:
• As with all graphs, read the axes carefully and think about what they mean when put together:
• It is not possible for an atom or molecule to have absolute zero kinetic energy, so the Boltzmann curve never touches the y-axis, starting just to the right of it.
• There is no limit to the amount of energy an atom or molecule can have, so the curve once started never touches the x axis a second time.
• The y-axis is measuring number, or proportion of molecules. Therefore, the x-value marked with the highest y-coordinate the distribution makes is the 'Average energy of molecules' because it is the amount of energy 'most of the molecules' have.
• The activation energy, Ea, is the energy required by a molecule to initiate reaction. Molecules lower energy than this will not react, while the portion of molecules with higher (to the right) energy than this will have energy to react.
• Because the y axis is measuring number of molecules, you can think of the area under the curve as all of the molecules in the reaction – the greater the area under the curve at a certain point, the more molecules there are!
• No values are ever given to the axes of the distribution. The distribution just tells us the proportion of molecules and how much energy they have!
• The Boltzmann curve can be used to show changes in the conditions of the reaction in a number of ways:
• An increase in temperature will increase the average kinetic energy of the molecules in the reaction – remember that for many reactions, a 10°C rise in temperature will double the reaction rate. This will change the graph in a few ways:
• The 'average energy of molecules' will shift to the right.
• The area of the curve beyond the 'activation energy' marker, because now that the average molecule has more energy, more molecules will now also have the required activation energy to react.
• The area under the curve shouldn't change. The curve will look 'shorter' and 'wider' due to the shift to the right. See below:
• Adding a catalyst to a reaction mixture will have an effect on the Boltzmann distribution too:
• A catalyst reduces the activation energy of a reaction, it does not affect the actual kinetic energy of the molecules that are reacting. So a catalyst will shift the activation energy label to the left of the distribution. This will show a greater area of the curve on the right – more molecules having the required energy to react! See below:
• Introduction
The Boltzmann kinetic energy distribution
a)
Introduction to the Boltzmann distribution.

b)
Changes in the Boltzmann distribution.

c)
Explaining curve changes in the Boltzmann distribution.

• 1.
Recall the shape and features of the Boltzmann distribution.
a)
Sketch the Boltzmann distribution for a reaction proceeding slowly at room temperature. Include the axis titles and the labels Ea and average energy of molecules.

b)
The reaction vessel has its temperature raised by 10°C. On the same axes, sketch another Boltzmann curve showing the new distribution of the kinetic energy possessed by the reactant molecules.

c)
A catalyst is added to change the rate of reaction. Sketch the change this catalyst has on the reaction onto your Boltzmann distribution and explain the effect on the rate of reaction.