Question

4. One of the most important things in science, not often done, is effectively commu- nicating on a subject. Since you all have spent so much time on partition functions, this is a good idea. 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

-purpose of partition function; partitions fuctions are functions of the thermodynamic state variables such as temperature and volume. the thermodynamic variables of a system such as total energy, total entropy, free enery and pressure etc can be expressed in terms of partition function. partition function is a diemensionless quandity. each partition function represents a particular ensemble.the canonical partion functions applied to canonical ensemble in which sysym exchanges heat with the enviornment at constant temperature, volume and number of paarticles. grand canonical partition applied to grand canonical ensemble in which system allowed to transfer both heat and no of particles at fixed temperature, volume and chemical potential.

-tanslational motion; it is the motion by which a molecule changes its position from one point to another in space.

-rotational motion; here the molecule undergo bodily rotation about an axis passes through its centre of gravity.

-vibrational motion; here in the molecules undergo distribution of the electrons of the molecule in its various energy states.

- the molar partition function is written as the product of electronic , vibrational,rotational and translational partition functions.

it is given by q=qel.qvib.qrot.qtrans

the partition function is a sum over state and it is a number. larger the value of q larger the number of states available molecules to occupy. using the standard formulae for translational, rotational and vibrational energy levels we can molecular translational,vibrational,and rotational partition functions for diatomic molecules.