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 (d_iU/dt = 0) is not conserved but is dissipated (d_iG/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 μ_A° = μ_B° = 0 kJ·mol^-1 (modified from Gnaiger 2020 BEC MitoPathways).

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 = µA·nA + µB·nB [J] 

A small change d_trG at constant chemical potentials µ_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 = µA·dtrnA + µB·dtrnB [J] 

where the advancement d_trξ_i (i = A or B) is

Eq. 3:  dtrξi = dtrnA·νA-1 = dtrnB·νB-1 [mol] 

The total change of Gibbs energy dG is the sum of all partial transformations, dG = Σd_iG, where i = 1 to N transformation types — not to be confused with the internal Gibbs energy change d_iG due to internal transformations (i) only.

The isomorphic force of transformation Δ_trF_X is the derivative of exergy per advancement (Gibbs force, compare affinity of reaction),

Eq. 4:  ΔtrFX = ∂G/∂trξX [J·mol-1] 

Note that ∂G ≝ d_trG. Then inserting Eq. 2 and Eq. 3 into Eq. 4, the force of transformation is expressed as

Eq. 5:  ΔtrFX = (µA·dtrnA + µB·dtrnB)/(dtrnB·νB-1) [J·mol-1] 

which can be rewritten as

Eq. 6:  ΔtrFX = µA·dtrnA/(dtrnA·νA-1) + µB·dtrnB/(dtrnB·νB-1) [J·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:  ΔtrFX = µA·νA + µB·νB [J·mol-1] 

In general,

Eq. 8:  ΔtrFX = Σµi·νi = ΣFtri[J·mol-1] 

It may arouse curiosity, why the sign of difference Δ is used in the symbol, whereas the equation suggest a sum Σ in contrast to a difference. This is best explained by the fact that in various conventional contexts — such as the classical formulation of the pmF — the stoichiometric numbers (-1 and +1) are omitted, which yields a difference as an equivalence,

Eq. 9:  ΔtrFX ≡ µB - µA [J·mol-1] 

The conceptual importance of the stoichiometric numbers — as in d_trn_A·ν_A^-1 (Eq. 3) — is emphasized by defining the term stoichiometric potential (Gnaiger 2020; see Eqs. 7 and 8),

Eq. 10:  Ftri = µi·νi [J·mol-1] 

To get acquainted with the meaning of subscripts such as 'tr' used above, consult »Abbreviation of iconic symbols.

References

• Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2. https://doi.org/10.26124/bec:2020-0002

»Bioblast links: Energy and exergy - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>

Units

• Joule [J]; 1 J = 1 N·m = 1 V·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 d_eQ

» Bound energy dB

Forms of exergy

» Helmholtz energy dA

» Gibbs energy dG

» Work d_eW

» Dissipated energy d_iD

MitoPedia concepts: Ergodynamics