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Equilibrium Constant for the Gas-Phase Dissociation of a Diatomic Molecule

Equilibrium Constant for the Gas-Phase Dissociation of a Diatomic Molecule

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Question:
Show that the equilibrium constant Kc for the gas-phase dissociation of a diatomic molecule, A2 ⇄ 2A, at temperatures T much higher than the molecule’s Θrot but much lower than its Θvib and too low for significant electronic excitation of either the molecules or the atom, is

where D0 is the energy of dissociation of the molecule from its ground vibrational state, m is the mass of the atom, r is the equilibrium internuclear distance in the molecule, and gA and gA2 are the degeneracies of the ground electronic states of the atom and molecule.

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