Summary of Statistical Mechanical Results for a Gaseous Diatomic Molecule Xy

SUMMARY OF STATISTICAL MECHANICAL RESULTS FOR A GASEOUS DIATOMIC MOLECULE XY

Function Translation3 Rotation2,5 Vibration2 Electronic4

Q

E - E°

Cv

S

A - A°

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1) Contributions to the single-particle partition function q are multiplicative; to the thermodynamic state functions, additive. For the molecule XY, q(XY) = qTqRqVqe. For an atom X, q(X) = qTqe. The results for translation and rotation are at the high-T limit.

2) The spectroscopic parameters Be, we, and D0 are in cm-1. hc/kB = 1.4388 cm-1; x = hcwe/kBT. D0 is the bond dissociation energy for dissociation of the molecule from the ground (v = 0) vibrational state. e here is the base of the natural logarithm.

3) The translational entropy is easily calculated from the Sackur-Tetrode equation: ST = (5/2)Rln(T) - Rln(p) + (3/2)Rln(M) + X.

Values of the additive constant X for various choices of units are given below.

value of X ST(units) p(units) R(units) M(units)

-2.31484 cal/K-mole atm cal/K-mole g/mole

-9.69004 J/K-mole atm J/K-mole g/mole

172.2934 J/K-mole Pa J/K-mole Kg/mole

4) g0 is the electronic degeneracy of the ground electronic state. Contributions from excited electronic states are neglected.

5) s, the rotational symmetry number, is 1 (one) for heteronuclear species and 2 for homonuclear species.