Question

Statistical Mechanics:

Explain the purpose of a partition function in a way that a general chemistry student would understand. Then, discuss what the translation, vibration, and rotation are in terms of what is happening to a molecule. Finally, say why they are important for a partition function.

Answer 1

The partition function of a system originates from all of the energy terms that are associated with the constituent molecules of the system. It is represented as

As can be seen from the function, the partition function has contribution from all the energy terms in the system. Therefore it gives us a tool to calculate the different thermodynamic quantities such as free energy or entropy of the system.

When a system is kept at a finite temperature, the molecules in the system may undergo translation, rotation or vibratuonal motions. All such motions will give rise to different energy contributions. Hence if we know the energies associated with the translational motions of a molecule, then we can obtain the translational partition function and similarly the rotational and vibrational partition functions can be obtauned. Now the relation between these different partition functions and the overall partition function of the system is

Thus we see that the overall partition function is the product of translational, vibrational and rotational partition function.

Answer 2

The partition function of a system originates from all of the energy terms that are associated with the constituent molecules of the system. It is represented as

As can be seen from the function, the partition function has contribution from all the energy terms in the system. Therefore it gives us a tool to calculate the different thermodynamic quantities such as free energy or entropy of the system.

When a system is kept at a finite temperature, the molecules in the system may undergo translation, rotation or vibratuonal motions. All such motions will give rise to different energy contributions. Hence if we know the energies associated with the translational motions of a molecule, then we can obtain the translational partition function and similarly the rotational and vibrational partition functions can be obtauned. Now the relation between these different partition functions and the overall partition function of the system is

Thus we see that the overall partition function is the product of translational, vibrational and rotational partition function.