The dissociation of molecular hydrogen into atomic

Chapter 6, Problem 53P

(choose chapter or problem)

Problem 53P

The dissociation of molecular hydrogen into atomic hydrogen,

can be treated as an ideal gas reaction using the techniques of Section 5.6. The equilibrium constant K for this reaction is defined as

where P° is a reference pressure conventionally taken to be 1 bar, and the other P’s are the partial pressures of the two species at equilibrium. Now, using the methods of Boltzmann statistics developed in this chapter, you are ready to calculate K from first principles. Do so. That is, derive a formula for K in terms of more basic quantities such as the energy needed to dissociate one molecule (see Problem) and the internal partition function for molecular hydrogen. This internal partition function is a product of rotational and vibrational contributions, which you can estimate using the methods and data in Section 6.2. (An H2 molecule doesn’t have any electronic spin degeneracy, but an H atom does—the electron can be in two different spin states. Neglect electronic excited states, which are important only at very high temperatures. The degeneracy due to nuclear spin alignments cancels, but include it if you wish.) Calculate K numerically at T = 300 K, 1000 K, 3000 K, and 6000 K. Discuss the implications, working out a couple of numerical examples to show when hydrogen is mostly dissociated and when it is not.

Problem:

Look up the enthalpy of formation of atomic hydrogen in the back of this book. This is the enthalpy change when a mole of atomic hydrogen is formed by dissociating 1/2 mole of molecular hydrogen (the more stable State of the element). From this number, determine the energy needed to dissociate a single H2 molecule, in electron-volts.