# ΔG = –nFE

In equations, the following formula:

$\Delta G = - nFE \,$

is called “[name]” and states that Gibbs free energy change ΔG of a Galvanic cell equals the negative of the number of faradays n passing through the cell, when the reaction takes place, times the Faraday constant F times the electromotive force E of the cell. [1]

History
The basics of this equation was first outlined by American engineer Willard Gibbs in his 1876 section "Electromotive Force" of his Equilibrium treatise, in which he derived the following formula for a perfect (reversible) electrochemical apparatus:

$V'' - V' = - \frac{d \zeta}{de} \,$

where V' and V'' denote the electrical potentials in pieces of the same kind of metal connected with the two electrodes, de is a differential quantity of electricity, and dζ (differential of zeta) is the change in the available energy (or isothermal-isobaric free energy, i.e. Gibbs free energy dG). [2]

The work of Gibbs was expanded on further by German physicist Hermann Helmholtz in his 1877 "On Galvanic Currents originated by Differences of Concentration", and followup famous 1882 "On the Thermodynamics of Chemical Processes", in which he is said to have derived the function in terms of the isochoric-isobaric free energy (Helmholtz free energy, dF); although, it is difficult to pin down the exact formulation. [3]

In 1923, American physical chemists Gilbert Lewis and Merle Randall were stating this equation in its essential modern notation, as follows:

$\Delta F = - NFE \,$

albeit, in his characteristic function notation, where ΔF is the Lewis free energy (in place of G or Gibbs free energy), F is the Faraday equivalent, and N (in place of n) is the number of equivalents passing through the cell when the reaction occurs as written. [4]

Here, no note, we see a notation our first instance of notation confusion overlap, i.e. the symbol F, being used for two different quantities (Faraday constant and Free energy); hence the symbol "G" was instilled as the standard symbol for the isothermal-isobaric free energy in honor of Willard Gibbs in 1933 by English chemical thermodynamicist Edward Guggenheim.

References
1. (a) Laidler, Keith. (1993). The World of Physical Chemistry (section: thermodynamics of electrochemical cells, pgs. 220-21). Oxford University Press.
(b) Merle, Randall. (1942). Physical Chemistry (pgs. 325-). Randall and Sons.
2. Gibbs, Willard. (1876). On the Equilibrium of Heterogeneous Substances (section: "Electromotive Force", pgs. 331-49). Dover.
3. (a) Helmholtz, Hermann. (1877). “On Galvanic Currents Originated by Differences of Concentration”, Wiss. Abh. Bd. i. No. xliv.
(b) Helmholtz, Hermann. (1882). “On the Thermodynamics of Chemical Processes” (Die Thermodynamic Chemischer Vorgange), in: Physical Memoirs Selected and Translated from Foreign Sources, 1: 43-97. Physical Society of London, Taylor and Francis, 1888.
4. (a) Lewis, Gilbert and Randall, Merle. (1923). Thermodynamics and the Free Energy of Chemical Substances (pgs. 157). McGraw-Hill.
(b) Merle, Randall. (1942). Physical Chemistry (pgs. 325-). Randall and Sons.