CALCULATION OF
THE DISSOCIATION ENERGY
OF DIATOMIC MOLECULES
Dissociation energy is the change in energy (usually expressed in kcal per mole) at absolute zero temperature in the ideal gas state for the reaction
the products (atoms A and B) being in their ground states and the reactant (molecule A-B) in the zeroth vibrational level. Note that dissociation energy is slightly different from bond energy, which is defined as the standard enthalpy change at 25º C for the ideal gas reaction given above. Calculating dissociation energy rather than bond energy frees us from having to consider molecular thermal energy. Now let us proceed to the derivation of the expression for bond dissociation energy from the principles of the Reciprocal System. A diatomic molecule, as a unit, exists in the time-space region. However, the two individual atoms of the molecule, relative to one another, exist in the time region because the interatomic distance is less than one space unit; hence, time region expressions apply to the attributes of the bond. To quote Larson,
Thus,
This energy equation gives the proper dimensional form of the expression for dissociation energy. It can be generalized to
In application to the problem at hand, t As it stands, equation (4) expresses the energy in natural units of the time region. We have to convert the equation to an equivalent expression for the time-space region so that we can compare calculated to observed results. First of all we must apply the fourth power of the interregional ratio, 1/156.44, to the equation, just as is done in the atomic force equation.
This is the energy in natural units as would be observed
in the time-space region. To convert this to conventional units
of measurement we multiply by the value of the natural unit of energy
expressed in conventional units, E
The experimental values are expressed as kcal/mole so we must multiply the right side of the equation (6) by a conversion factor, k, and by Avogadro’s number, N.
Next we must append a factor of ½ to the expression to account for the inherent vibrational nature of the time region motions and a factor of 1/3 to the expression to reduce the energy to one dimension. So now we have
I have applied equation (9) to 18 diatomic molecules
of the elements. The theoretical and experimental results are given
in table II. Let t
For electronegative elements, the 8-t
The values of t A future paper will apply equation (9) to diatomic molecules of unlike atoms.
- Dewey B. Larson,
*Nothing But Motion*(Portland, Oregon: North Pacific Publishers, 1979), p. 155. - John A. Dean, ed.,
*Lange’s Handbood of Chemistry,*Eleventh Edition (New York: McGraw-Hill Book Company, 1973), pp. 3-123 to 3-127.
Table I: Allowed Values of Dissociation Energy
Note: the observed values, E |