Maria a gomez, mhc page 1 9 20 07 partition functions of systems

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Partition Functions of Systems of Independent Molecules Consider a system of independent distinguishable molecules a, b, c, .... Suppose each molecule can be in a variety of different energy levels. The total energy of the system is the sum of the energy of each of the N molecules.

The partition function for this system is

If the molecules were not distinguishable, we would not have been able to label them. Then, the partition function would have been more difficult to find. There are two types of indistinguishable particles that chemists are concerned about. You will learn more about these in the second semester of physical chemistry.

In the case of fermions, the restriction that two identical particles can not occupy the same energy state makes the summations above interdependent e.g. in the j summation care must be taken that the value i is not covered. In the case of bosons, two identical particles can have the same energy state. However, since the particles are indistinguishable, care must be taken not to

countas different from . In other words, the order in which indistinguishable particles are written is not important. In either of these case, we can find a general form for the partition function of a system of independent indistinguishable molecules. If the number of states with energy smaller than kT is much larger than the number of particles, likely, each particle is in a different energy state. This is usually true with just translational states for

Maria A. Gomez, MHC

Page 1

9/20/07