Revision
of the Thermodynamics of the Proton in Gas
Phase
- Publication date
- Publisher
Abstract
Proton
transfer is ubiquitous in various physical/chemical processes,
and the accurate determination of the thermodynamic parameters of
the proton in the gas phase is useful for understanding and describing
such reactions. However, the thermodynamic parameters of such a proton
are usually determined by assuming the proton as a classical particle
whatever the temperature. The reason for such an assumption is that
the entropy of the quantum proton is not always soluble analytically
at all temperatures. Thereby, we addressed this matter using a robust
and reliable self-consistent iterative procedure based on the Fermi–Dirac
formalism. As a result, the free proton gas can be assumed to be classical
for temperatures higher than 200 K. However, it is worth mentioning
that quantum effects on the gas phase proton motion are really significant
at low temperatures (<i>T</i> ≤ 120 K). Although
the proton behaves as a classical particle at high temperatures, we
strongly recommend the use of quantum results at all temperatures,
for the integrated heat capacity and the Gibbs free energy change.
Therefore, on the basis of the thermochemical convention that ignores
the proton spin, we recommend the following revised values for the
integrated heat capacity and the Gibbs free energy change of the proton
in gas phase and, at the standard pressure (1 bar): Δ<i>H</i><sub>0→<i>T</i></sub> = 6.1398 kJ mol<sup>–1</sup> and Δ<i>G</i><sub>0→<i>T</i></sub> = −26.3424 kJ mol<sup>–1</sup>. Finally,
it is important noting that the little change of the pressure from
1 bar to 1 atm affects notably the entropy and the Gibbs free energy
change of the proton