This derivation follows the one provided in [41], and is included here for completeness. Consider an equilibrium of ideal gases . We compute the number of particles , , and by maximizing the total number of available states:

(4.14) |

where , , and are the partition functions of A, B, and C. If we take to be the fraction of dissociated C, we then have

where we have factored out the translational partition functions explicitly to leave , the vibrational-rotational-electronic partition functions. We compute the partition functions from the ``bottom of the well,'' which incurs a factor of , where is the dissociation energy of . Substituting the de Broglie wavelength and the volume per atom we are left with the expression

(4.15) |

For hydrogen atom, electron, and proton, we take ; for hydrogen molecule we use the expression for an ideal diatomic

(4.16) |

where = 85.3 K and = 6215 K.