Maxwell-Boltzmann Distribution

Understandings:

• Activation energy (Ea) is the minimum energy that colliding molecules need in order to have successful collisions leading to a reaction.

• By decreasing Ea, a catalyst increases the rate of a chemical reaction, without itself being permanently chemically changed.

Applications and skills:

• Description of the kinetic theory in terms of the movement of particles whose average kinetic energy is proportional to temperature in Kelvin.

• Explanation of the effects of temperature, pressure/concentration and particle size on rate of reaction.

• Construction of Maxwell–Boltzmann energy distribution curves to account for the probability of successful collisions and factors affecting these, including the effect of a catalyst.

James Clerk Maxwell and Ludwig Boltzmann

Maxwell-Boltzmann Distribution Curves and Temperature

The above diagram shows how the energy is distributed in a given volume of gases at a constant temperature. Here we can observe that:

• Particles found to the right have HIGH ENERGY and are at a high temperature
• Particles found to the left have LOW ENERGY and are at a low temperature
• For most of these diagrams we can see that MOST PARTICLES are found in between these two extremes
• As the X axis represents the energy particles have we can also place the ACTIVATION ENERGY on the Maxwell-Boltzmann Curve - This is represented as a VERTICAL LINE labelled E_A
• Any particles that are found TO THE RIGHT OF THE E_A LINE HAVE THE ACTIVATION ENERGY and will SUCCESSFULLY COLLIDE
• These particles are said to have E>E_A
• Any particles that are found TO THE LEFT OF THE E_A LINE DO NOT HAVE ENOUGH ENERGY TO REACT
• These particles are said to have E<E_A

High Temperatures

Higher Temperature Reaction systems are represented by T2 on the Maxwell-Boltzmann Curve above.

At Higher Temperatures you can observe that:

• the Peak of the curve is lower down and to the right of the cooler temperature curve
• The number of Particles with E>E_A is Greater than at Lower Temperatures and represented by the Blue Shading beyond the E_A Line
• this would result in more particles with E>E_A and thus a higher frequency of successful collisions at higher temperatures

Lower Temperatures

Lower Temperature Reaction systems are represented by T1 on the Maxwell-Boltzmann Curve above.

At Lower Temperatures you can observe that:

• the Peak of the curve is HIGHER and to the LEFT of the higher temperature curve
• The number of Particles with E>E_A is LOWER than at higher Temperatures and represented by the RED Shading beyond the E_A Line
• this would result in LESS particles with E>E_A and thus a LOWER frequency of successful collisions at lower temperatures

Catalysts

When a catalyst is added to a system you should understand that the Activation Energy for the reaction is Reduced.

This would mean that the Activation Energy Line would move to the LEFT on the curve and be labelled as E_CAT

This would increase the number of particles with E>E_A and this is shown by the GREY shaded area on the above Maxwell-Boltzmann Curve

Therefore, as a greater number of particles have E>E_A a greater frequency of successful collisions occurs when using a catalyst