Page 187 - Physical Chemistry

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Chapter 5 Group-additivity values for H° have been tabulated for solid, for liquid, and
298
f
Standard Thermodynamic for gaseous C-H-O compounds in N. Cohen, J. Phys. Chem. Ref. Data, 25, 1411
Functions of Reaction
(1996). The average absolute errors are 1.3 kcal/mol for gases, 1.3 kcal/mol for liq-
uids, and 2.2 kcal/mol for solids. (A few compounds with large errors were omitted in
calculating these errors.)
The computer programs CHETAH (www.chetah.usouthal.edu/), NIST Therm/Est
(www.esm-software.com/nist-thermest), and NIST Organic Structures and Properties
(www.esm-software.com/nist-struct-prop) use Benson’s group-additivity method to
estimate thermodynamic properties of organic compounds.

Sign of S°
Now consider S°. Entropies of gases are substantially higher than those of liquids or
solids, and substances with molecules of similar size have similar entropies. Therefore,
for reactions involving only gases, pure liquids, and pure solids, the sign of S° will usu-
ally be determined by the change in total number of moles of gases. If the change in moles
of gases is positive, S° will be positive; if this change is negative, S° will be negative;
if this change is zero, S° will be small. For example, for 2H (g) O (g) → 2H O(l),
2
2
2
the change in moles of gases is 3, and this reaction has S° 327 J/(mol K).
298
Other Estimation Methods
Thermodynamic properties of gas-phase compounds can often be rather accurately
calculated by combining statistical-mechanics formulas with quantum-mechanical
calculations (Secs. 21.6, 21.7, 21.8) or molecular-mechanics calculations (Sec. 19.13).

5.11 THE UNATTAINABILITY OF ABSOLUTE ZERO

Besides the Nernst–Simon formulation of the third law, another formulation of this
law is often given, the unattainability formulation. In 1912, Nernst gave a “derivation”
of the unattainability of absolute zero from the second law of thermodynamics (see
Prob. 3.37). However, Einstein showed that Nernst’s argument was fallacious, so the
unattainability statement cannot be derived from the second law. [For details, see P. S.
Epstein, Textbook of Thermodynamics, Wiley, 1937, pp. 244–245; F. E. Simon, Z.
Naturforsch., 6a, 397 (1951); P. T. Landsberg, Rev. Mod. Phys., 28, 363 (1956); M. L.
Boas, Am. J. Phys., 28, 675 (1960).]
The unattainability of absolute zero is usually regarded as a formulation of the third
law of thermodynamics, equivalent to the entropy formulation (5.25). Supposed proofs of
this equivalence are given in several texts. However, careful studies of the question show
that the unattainability and entropy formulations of the third law are not equivalent [P. T.
Landsberg, Rev. Mod. Phys., 28, 363 (1956); R. Haase, pp. 86–96, in Eyring, Henderson,
and Jost, vol. I]. Haase concluded that the unattainability of absolute zero follows as a
consequence of the first and second laws plus the Nernst–Simon statement of the third
law. However, Landsberg disagreed with this conclusion and work by Wheeler also indi-
cates that the unattainability formulation does not follow from the first and second laws
plus the Nernst–Simon statement [J. C. Wheeler, Phys. Rev. A, 43, 5289 (1991); 45, 2637
(1992)]. Landsberg states that the third law of thermodynamics should be regarded as
consisting of two nonequivalent statements: the Nernst–Simon entropy statement and the
unattainability statement [P. T. Landsberg, Am. J. Phys., 65, 269 (1997)].
Although absolute zero is unattainable, temperatures as low as 2 10 8 K have
been reached. One can use the Joule–Thomson effect to liquefy helium gas. By pump-
ing away the helium vapor above the liquid, thereby causing the liquid helium to evap-
orate rapidly, one can attain temperatures of about 1 K. To reach lower temperatures,
adiabatic demagnetization can be used. For details, see Zemansky and Dittman, chaps.
18 and 19, and P. V. E. McClintock et al., Matter at Low Temperatures, Wiley, 1984.