Contributions to the Data on Theoretical Metallurgy: [Part] 11. Entropies of Inorganic Substances: Revision (1948) of Data and Methods of Calculation Page: 12
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12 CONTRIBUTIONS TO DATA ON THEORETICAL METALLURGY
=R In ii pie-,/ /k-ln Po+ 1 e-I lkT "(33)
But, as So=R In Po,
SY+.+==R In 7pie-'/'-T+ pce-i 1 (34)
The quantity given by equation (34) is the sum of the rotational,
vibrational, and electronic entropies. This sum must be added to the
result given by the Sackur equation (18) to obtain the total entropy
(excluding that due to nuclear spin). Evaluation of this sum is
possible for gases on which extensive enough spectroscopic measure-
ments have been made to enable an assignment of es and pi values
to all the states occupied by the system at the temperature under
consideration. It is customary to omit nuclear spin from considera-
tion in the values of pi, as Gibson and Heitler (193) have shown that
the resulting entropy contribution balances out in reactions involving
diatomic gases, and it is presumed that it always does so. It will be
noted that if all the molecules are in their lowest energy state of
quantum weight p,, then equation (34) reduces to R In po.
To illustrate this method of calculation, two simple cases will be
considered, nickel gas at 298.160 K., in which only translational and
electronic entropies are concerned, and carbon monoxide at 298.160,
in which only translational and rotational entropies are concerned.
The question may arise as to why the calculation is made for nickel
which does not exist in the gaseous state at any appreciable pressure
at 298.160 K. The answer is that it seems desirable to have a fairly
simple, but not too simple, example for illustration. The common
substances that exist as monatomic gases under measurable pressures
at 298.160 K. have electronic states so separated that calculation
reduces to the mere addition of R In po as mentioned above. More-
over, the entropy of Ni(g) at 298.160 K. may be employed formally
in the thermodynamic calculations in the same manner as the entropy
of H20(g) at 298.160 in the hypothetical state of 1 atmosphere fugacity.
Only a question of degree is involved.
The data to be considered for Ni(g) (364) at 298.160 are shown in
table 2. Column 1 gives the designation of the state, column 2 the
energies in wave numbers (these usually are called term values),
column 3 the quantum weights, and column 4 the energies in ergs per
molecule (E=hCl= 1.98572 X 10-16). The calculated items for comput-
ing the sums in equation (34) are shown in columns 5 and 6.
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Kelley, K. K. Contributions to the Data on Theoretical Metallurgy: [Part] 11. Entropies of Inorganic Substances: Revision (1948) of Data and Methods of Calculation, report, 1950; Washington D.C.. (https://digital.library.unt.edu/ark:/67531/metadc12637/m1/16/: accessed April 21, 2019), University of North Texas Libraries, Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.