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# Working with partition function and entropy

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1. Given the rotational temperature of HCl is 15.02 K,
a) what is the ratio of the number of particles in the J= 14 to the J=4 level at a temperature of 1900 K?
b) What J level has the highest proportion of particles at the temperature 1900 K?
c) What is the energy, E, of rotation at this temperature?
d) What is the entropy, S, of rotation at this temperature?

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#### Solution Preview

The rotational energy of a linear molecule (neglecting such things as centrifugal distortion) is given by BJ(J+1) and each J level is 2J+1 degenerate.

The rotational temperature is defined as,

T = B/k ......(1)

where k is the Boltzmann constant and B is the rotational constant given by

B = h/(8pi^2I c) cm^-1 ........(2)

From (1), B = kT

B = 1.38*10^-23*15.02 = 20.73*10^-23 J

= (20.73*10^-23/hc) ...

#### Solution Summary

The partition function and entropy are examined. The rotation of the temperature for energy and entropy is found. The solution explains each step and provides all mathematical steps.

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