free energy table

An example 1998 thermodynamic table showing the standard enthalpy of formation ΔHf°, standard Gibbs free energy of formation ΔGf°, and standard entropy S°. [1]

In thermodynamics, a free energy table or “table of standard free energies of formation at 25 °C”, is a set of calculated data for values of free energy, enthalpy, and entropy of various chemical species that is used to determine reaction feasibility among other information.

An example of a basic free energy table for various organic species is shown adjacent. [1]

Affinity tables
The precursor to the free energy tables were the various "affinity tables", the first of which was constructed in 1718 by French physician and chemist Étienne Geoffroy during a translation into French of English physicist Isaac Newton's famous "Query 31" of his Opticks, wherein verbal affinity preferences are enunciated. [2] The largest affinity table built was Bergman's affinity table constructed in 1775 by Swedish chemist Torbern Bergman. It soon thereafter became apparent that each affinity reaction depend on temperature, and that each table would need to be constructed anew for each different temperature. Affinity table construction generally came to a halt, in the years to follow, because of this impediment.

Free energy tables

See main: Thermodynamic data table

In the decades 1775-1840s, it was increasingly becoming apparent that the "affinity table" approach to the quantification of chemical reactions had its limitation. One, Bergman's multi-page map size affinity table was approaching the limit in functionability. Two, and most importantly, it was becoming apparent that that reactions seemed to depend on temperature, meaning that one would have to construct a different affinity table for each temperature, and hence make hundreds of affinity tables. Third, and most importantly, was the puzzling nature of heat, which between 1780s to 1830s, had its roots in the now defunct so-called "caloric theory of heat" which held that heat was a type of fluid-like indestructible particle (caloric).

In the late 1850s and into the 1870s, the so-called "thermal theory of affinity" was proposed, which held that heat release was the measure of affinity and hence the true measure of the driving force of chemical reactions. This theory, however, soon showed limitations: for instance, it could not explain endothermic reactions.

In 1882, German physicist Hermann Helmholtz, in his seminal paper "On the Thermodynamics of Chemical Processes", showed that the true measure of affinity is not "heat" but rather "free energy", which depended on reaction conditions, as shown below:

Thermal theory of affinity
(1854-1864)
Thermodynamic theory of affinity
(1882-1936)

Driving force / Measure of affinity (isochoric-isobaric reactions) Q U – TS
Driving force / Measure of affinity (isothermal-isobaric reactions) Q U + PV – TS

Helmholtz, in short, showed that heat is NOT the driving force of a reaction, but rather "free energy" is and also that the measure of affinity A is free energy change (ΔF or ΔG, depending on the type of process):

A = – ΔF (isochoric-isobaric processes)
A = – ΔG (isothermal-isobaric processes)

Soon thereafter, free energy tables began to be made, listing the standard free energy of formation for various elements, molecules, and compounds. Helmholtz's proof that overthrew the thermal theory of affinity of thermochemistry, updating things with the newly-forming science of chemical thermodynamics. In the decades to follow affinity tables were soon replaced by free energy tables.

The first outlines of which were made by German physical chemist Fritz Haber in regards to gas phase reactions. [1] In more detail, according to Gilbert Lewis (1923), "the first systematic study of all the thermodynamic data necessary for the calculation of the free energy of chemical substances in a group of important reactions was done by Haber", as presented in his 1905 work Thermodynamics of Technical Gas Reactions. [5] Haber, however, did not make actual free energy tables, but rather made tables of equilibrium constants, discussing reaction energies, which is nearly synonymous with free energy, loosely speaking.

Lewis | 1923
The work of Haber gave way to the construction of the first so-called “table of free energies” made in 1914 by American physical chemists Gilbert Lewis and Merle Randall, giving free energies of formation values for oxygen, hydrogen, and a few oxides of hydrogen. [6] This formed the basis for their expanded-followup 1923 “Table of Standard Free Energies of Formation at 25 °C”, giving free energies of formation for 28 cations and a few metallic compounds and 111 non-metallic compounds and anions, as shown below: [5]

Table of Free Energies (a)

Table of Free Energies (b)

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Burton | 1957

The first thermodynamic table for biochemical species, according to Robert Alberty, was the 1957 "Free Energies of Formation from the Elements" table, made by English electrical engineer and physicist Keith Burton, as found the appendix of tables in Hans Krebs and Hans Kornberg's Energy Transformations in Living Matter. [7] Burton's table, which contains about 100 biochemical species, is shown below: [3]

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Chang | 1998
The following is Chinese-born American Raymond Chang's thermodynamic data table, from his 6th edition, 1998 college Chemistry textbook, which in and of itself is nothing unique but is representative of the late 20th century view that the concept of elementary chemical thermodynamic reaction calculations is something that had distilled down, in a generic format, to the level of the general chemistry chemistry student (and possibly high school level chemistry student): [8]

Chang header

Chang (a)

Chang (b)

Chang (c)

Chang (d)

Chang (e)

Chang (f) 500px

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Create a rabbit (free energy diagram)

A semi-cartoonish, semi-realistic rendition of relationship between Gibbs free energy, G, and the “creation” of a rabbit (compare: creation by breath), from American physicist Daniel Schroeder’s 2000 Thermal Physics textbook.

Free energy of formation of an animal
The following 1993 quote by American physical chemist Martin Goldstein, from his chapter section on the “Entropy of a Mouse”, gives idea of what is means for a biochemical species or for that matter a so-called biological entity, such as a mouse (or a human) to have a free energy value in a given state: [9]

“To apply thermodynamics to the problem of how life got started, we must ask what net energy and entropy changes would have been if simple chemical substances, present when the earth was young, were converted into living matter [as in the formation of a mouse] … to answer this question [for each process], we must determine the energies and entropies of everything in the initial state and final state.”

In other words, the above table, showing the Gibbs free energies of formation for different biochemical species, such as Fructose (218 kgcal), molecular formula C6H12O6, gives way to the idea that this logic can be extrapolated upward to calculate the standard Gibbs free energy of formation for different types of proto-life entities, chemicals, or molecules, such as a mouse.

Human free energy tables
The future goal of human chemical thermodynamics, will be to calculate "human free energy tables" for the calculation of reaction feasibilities and spontaneities of different combinations of human chemical species (human molecules); as in different sets of potentials in the process of "love the chemical reaction." [4] The affinity-based beta-stage online pair-matching site ReactionMatch.com has this goal in mind.

References
1. Chang, Raymond. (1998). Chemistry, 6th ed. (Appendix 3). New York: McGraw-Hill.
2. Kim, Mi G. (2003). Affinity , That Elusive Dream: a Genealogy of the Chemical Revolution. Cambridge, Mass.: MIT Press.
3. Krebs, H.A. and Kornberg, H.L. (1957). Energy Transformations in Living Matter (with an Appendix by K. Burton with 21 figures). Berlin: Springer-Verlag.
4. Thims, Libb. (2007). Human Chemistry (Volume Two) (§11: "Affinity and Free Energy", §§: Human affinity - Gibbs free energy - tables, pgs. 464-68). Morrisville, NC: LuLu.
5. Lewis, Gilbert N. and Randall, Merle. (1923). Thermodynamics and the Free Energy of Chemical Substances (pgs. 5-6; Table of Free Energies, pgs. 607-08). McGraw-Hill Book Co., Inc.
6. (a) Lewis, Gilbert and Randall, Merle. (1914). “The Free Energy of Oxygen, Hydrogen, and the Oxides of Hydrogen”, Journal of American Chemical Society, 35:1964.
(b) Randall, Merle and Young, Leona E. (1942). Elementary Physical Chemistry (note, pg. 302). Randall and Sons.
7. Alberty, Robert, A. (2003). Thermodynamic of Biochemical Reactions (pg. 2). Hoboken, New Jersey: John Wiley & Sons, Inc.
8. Chang, Raymond. (1998). Chemistry (Appendix 3: Selected Thermodynamic Data at 1 atm and 25° C). McGraw-Hill.
9. Goldstein, Martin and Goldstein, Inge F. (1993). The Refrigerator and the Universe: Understanding the Laws of Energy (section: Entropy of a mouse, pgs. 297-99). Harvard University Press.

External links
● Thermodynamics tables – URI.edu.
● Thermodynamic tables – GenChem.net.