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Gibbs energy

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Gibbs energy

Description

Gibbs energy G [J] is exergy which cannot be created internally (subscript i), but in contrast to internal-energy (diU/dt = 0) is not conserved but is dissipated (diG/dt < 0) in irreversible energy transformations at constant temperature and (barometric) pressure, T,p. Exergy is available as work in reversible energy transformations (100 % efficiency), and can be partially conserved when the exergonic transformation is coupled to an endergonic transformation.

Abbreviation: G [J]

Reference: Energy

Figure 8.5. Gibbs energy as a function of advancement of a transformation (0 = -1 A + 1 B) in a closed isothermal system at constant pressure, for A掳 = B掳 = 0 kJ路mol-1 (modified from Gnaiger 2020 BEC MitoPathways - see Footnote 1).

Gibbs energy as a function of advancement

Communicated by Gnaiger E 2022-10-19
In a transformation tr 0 = -1 A +1 B proceeding in a system with volume V at constant barometric pressure p, the Gibbs energy of reactants A and B is
Eq. 1:  G = AnA + BnB [J] 
A small change dtrG at constant chemical potentials i is due to a small advancement of a transformation tr, in closed or open isothermal systems, exchanging heat in equilibrium with an external thermostat at constant temperature,
Eq. 2:  dtrG = A路dtrnA + B路dtrnB [J] 
where the advancement dtri (i = A or B) is
Eq. 3:  dtri = dtrnAA-1 = dtrnBB-1 [mol] 
The total change of Gibbs energy dG is the sum of all partial transformations, dG = 危dtriG, where tri = 1 to N transformation types 鈥 not to be confused with the internal Gibbs energy change diG due to internal transformations (i) only.
The isomorphic force of transformation 螖trFX is the derivative of exergy per advancement (Gibbs force, compare affinity of reaction),
Eq. 4:  螖trFX = 鈭G/鈭trX [J路mol-1] 
Note that 鈭G 鈮 dtrG. Then inserting Eq. 2 and Eq. 3 into Eq. 4, the force of transformation is expressed as
Eq. 5:  螖trFX = (A路dtrnA + B路dtrnB)/dtri [J路mol-1] 
Using Eq. 3, Eq. 5 can be rewritten as
Eq. 6:  螖trFX = A路dtrnA/(dtrnAA-1) + B路dtrnB/(dtrnBB-1) [J路mol-1] 
This yields the force as the sum of stoichiometric potentials, summarized in Figure 8.5 (Chapter 8; Gnaiger 2020 BEC MitoPathways),
Eq. 7:  螖trFX = AA + BB [J路mol-1] 
In general,
Eq. 8:  螖trFX = 危ii = 危Ftri[J路mol-1] 
It may arouse curiosity, why the sign of difference 螖 is used in the symbol, whereas the equation suggest a sum 危 in contrast to a difference. This is best explained by the fact that in various conventional contexts 鈥 such as the classical formulation of the pmF 鈥 the stoichiometric numbers (-1 and +1) are omitted, which yields a difference 螖 as an equivalence,
Eq. 9:  螖trFXB - A [J路mol-1] 
The conceptual importance of the stoichiometric numbers is emphasized by defining the term stoichiometric potential (Gnaiger 2020), analogous to combining dtrnAA-1 in the expression of advancement (Eq. 3; see Eqs. 7 and 8),
Eq. 10:  Ftri = ii [J路mol-1] 
To get acquainted with the meaning of subscripts such as 'tr' used above, consult 禄Abbreviation of iconic symbols.

References


Footnote 1

The original Figure 8.5 shows 鈭trX = 鈭trnXX-1 instead of dtrX = dtrnXX-1. The formal inconsistency was pointed out by Marin Kuntic during the BEC tutorial-Living Communications: pmF to pmP (Schroecken 2022 Sep 30-Oct 03).



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Units
  • Joule [J]; 1 J = 1 N路m = 1 V路C; 1 cal = 4.184 J
Fundamental relationships
Energy
Exergy
Extensive quantity
Contrast
Force
Pressure
Intensive quantity
Forms of energy
Internal-energy dU
Enthalpy dH
Heat deQ
Bound energy dB
Forms of exergy
Helmholtz energy dA
Gibbs energy dG
Work deW
Dissipated energy diD



MitoPedia concepts: Ergodynamics