Boltzmann Distribution of Curve

Boltzmann Distribution of Curve

Boltzmann distribution curve is a graph that shows the distribution of energies of the particle in a sample at a given temperature

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History:

• 1857-Rudolf Clausius wrote a paper which discussed calculating the speed of atoms
• 1860-James Maxwell elaborate on Claudius's findings, showing how to obtain the distribution of atoms’ speed within a gas, determining atoms with greater or lesser speed than average
• 1868-Ludwig Boltzmann published a paper proving Maxwell’s then disputed findings. He did this by applying Maxwell’s mathematical forms into differing pressures, proving that they were correct.

Boltzmann distribution curve with change of  Catalyst:

A catalyst is a substance that increase the rate of a reaction but remain chemically unchanged itself at the end of reaction. With the presence of catalyst the activation energy will be decrease, which will result more chance for successful atom to reaction. Just like what we can see from the picture above.

Boltzmann distribution curve with change of Temperature:

Increase in temperature lead to an increase in Kinetic Energy on the molecules. Therefore the collision or impact energy is stronger which then result the graph to shift the molecular energy to the right. And the peak also decrease because the peak shift to the right, but it still maintain the same amount of molecule. That is because temperature did not affect the activation energy. Only catalyst affect the activation energy. Just like what we can see from the illustration above.

Example of Exercise:

QP12 2015 No.11

The Boltzmann distribution below show the distribution below shows the distribution of molecular energies in a sample of a gas at a given temperature.

Which statement correctly describes the change in such a distribution if the temperature increase?

1. Fewer molecules possess the most probable energy value and this value shifts to the left
2. Fewer molecule possess the most probable energy value and this volume shifts to the right
3. More molecules possess the most probable energy value and this value shift to the left
4. The area under the curve to the distribution increases

Answer: B (since the graph will shift to the right)