Page 167 - Chemical equilibria Volume 4

Determination of the Values Associated with Reactions – Equilibrium Calculations 143
4.9.1. Method of evaluating the energies of dissociation by
spectroscopy
We have seen (section 4.2.7.4) the method for determining the bond
energies on the basis of the limit of the continuous absorption spectrum. This
limit, though, is often fairly difficult to observe directly. We shall see,
however, that we can estimate the energy of dissociation by calculation, by
determining the law which gives the position of the successive vibration
bands.

Let us look again at the approximate expression [4.25] for the absorption
energy corresponding to a spectral line for the value v of the level parameter.
We shall apply that relation for the first two lines in the spectral series
characterized by the transitions v = 1→ v = 2 and v = 2→ v = 3. We obtain:

⎡ hν ⎤
Δ E = hν vibr ⎢ 1− vibr ⎥ [4.50]
2
1
⎣ E ∞ ⎦
and:

⎡ hν ⎤
Δ E = hν vibr ⎢ 1 6 vibr ⎥ [4.51]
−
3
2
⎣ E ∞ ⎦
By solving the system composed of these two equations [4.50] and
[4.51], we obtain an estimated value of the energy E ∞ and of the vibration
frequency ν vibr . The energy of dissociation is then calculated by the relation:

hν
D = E − vibr [4.52]
∞
2
In the evaluation of the enthalpy of formation, we can then treat the
energy of dissociation and the bond energy as identical.

4.9.2. Group contribution methods

We have shown how the concept of bond energy could facilitate an
estimation of the standard enthalpies of formation on the basis of the