Page 152 - Chemical equilibria Volume 4

128 Chemical Equilibria
4.3.2. Spectroscopic determination of entropies – absolute
entropies
Statistical thermodynamics enables us to express the entropy as a
function of the canonical partition function Z C (relation [A2.39], see
Appendix 2). This partition function is expressed by relation [A2.36], on the
basis of the molecular partition functions. These molecular partition
functions are expressed, in relation [A2.21], by the partition functions of
translation, vibration and rotation. These are calculated on the basis of the
molecule mass and relation [A2.26] for a perfect gas, the vibration
frequencies (relation [A2.30]) of its bonds and of its moments of inertia
(expression [A2.29]). These data are determined by studying the spectra of
the molecules – particularly the absorption spectra in the infrared. Hence, at
least for simple molecules, we are able to calculate an absolute value for the
entropy – i.e. with no frame of reference, and in particular without the aid of
Planck’s hypothesis.

4.3.3. The third law

We have given an initial approximation of the third law on the basis of
Planck’s hypothesis. We shall come back to this formula after comparing the
values of the calorimetric standard entropies (extracted from relation [4.34])
with the absolute entropies measured with spectroscopic data.

4.3.3.1. Comparison between calorimetric and spectroscopic
sources – residual entropy
Table 4.5, for a number of substances, gives the values found by
calorimetry, calculated using Planck’s hypothesis, and the absolute values
found by spectroscopic measurements, independent of Planck’s hypothesis.
We can see two distinct categories of molecules:
– firstly, we have those, such as nitrogen and oxygen, with which there is
a satisfactory correspondence between the values found by the two
techniques; and
– secondly, there are those, such as the other molecules shown in
Table 4.5, where the spectroscopic value is consistently higher than the
calorimetric value. The fourth column in Table 4.5 expresses these
differences.