Contribution of Bound, Metastable, and Free Molecules to the Second Virial Coefficient and Some Properties of Double Molecules

The second virial coefficient for molecules interacting with a spherically symmetric potential is divided into three parts: (1) a contribution Bb, related to the equilibrium constant for the formation of bound double molecules; (2) a contribution Bm, related to the equilibrium constant for the formation of metastably-bound double molecules; and (3) a contribution Bf, due to molecules which interact but are free to separate after the interaction. Equations are given for determining each of the three parts of the second virial coefficient. A detailed treatment of these three contributions together with numerical tables on a reduced temperature basis is given for the square-well, Sutherland, and Lennard-Jones (6–12) potentials. The mean lifetimes of metastably bound double molecules are discussed, and numerical values are given for the special case of argon. Tables for computing mean lifetimes in other Lennard-Jones gases are given. It is found that most metastably bound double molecules have mean lifetimes considerably longer than the mean time between collisions at ordinary pressures. Finally, an equation is developed for the number of vibrational levels of a double molecule.