Page 154 - Chemical equilibria Volume 4

130 Chemical Equilibria
the spectral method is only applicable for molecules whose spectra are
sufficiently well interpreted – i.e. are not overly complex. Hence, we only
have an accurate measurement of the absolute entropy for a limited number
of substances.
NOTE 4.4.– as noted in section 4.2.5.3, we can treat the enthalpy of
formation and the pure-substance enthalpy as one and the same thing, which
is expressed by the following double relation, for a given substance:

0
Δ h = H = h T 0 [4.36]
0
T
T
f
The same is no longer true for the absolute entropies, which are not
entropies of formation. Thus, we have:
Δ s = S ≠ s T 0 [4.37]
0
0
f T
T
The entropy of formation is calculated on the basis of the absolute
entropies of the simple substances and the stoichiometric coefficients of the
formation reaction.

Hence, the same is true for the Gibbs energies:

Δ g = G ≠ g T 0 [4.38]
0
0
T
f
T
4.3.3.3. Residual entropy of crystalline substances
The existence of a residual entropy at the temperature of 0 K means, by
application of Boltzmann’s equation, that the number of complexions Ω is
not necessarily equal to 1 at that temperature. Thus, absolute order is not
always reached, and the value of the number of complexions must be able to
be greater than 1 (never less than 1, of course, which would be absurd. This
explains why the residual entropy value is always positive). By quantitative
study, we have been able to quantify the initial state of disorder and evaluate
the residual entropy. To exhibit the method, we shall consider a crystal of
carbon monoxide, in which the two oxygen and carbon atoms are
differentiated, but are nonetheless very similar. In particular, they have the
same weak electric dipole moment.

If we examine a crystallographic assay of the lattice of crystallized CO,
the molecules may have either the configuration “CO” or the configuration