Difference between revisions of "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, 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 2022-10-18

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 = µ_A·n_A + µ_B·n_B [J]

A small change dG at constant chemical potentials µ_i is due to a small advancement of the transformation, in closed or open isothermal systems, exchanging heat in equilibrium with an external thermostat at constant temperature,

Eq. 2:  d_trG = µ_A·d_trn_A + µ_B·d_trn_B [J]

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

Eq. 3:  d_trξ_i = d_trn_A·ν_A^-1 = d_trn_B·ν_B^-1 [mol]

The isomorphic force of transformation Δ_trF_X is the derivative of exergy per advancement,

Eq. 4:  Δ_trF_X = ∂G/∂_trξ_X [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:  Δ_trF_X = (µ_A·d_trn_A + µ_B·d_trn_B)/(d_trn_B·ν_B^-1) [J·mol^-1]

which can be rewritten as

Eq. 6:  Δ_trF_X = µ_A·d_trn_A/(d_trn_A·ν_A^-1) + µ_B·d_trn_B/(d_trn_B·ν_B^-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:  Δ_trF_X = µ_A·ν_A + µ_B·ν_B [J·mol^-1]

In general,

Eq. 8:  Δ_trF_X = Σµ_i·ν_i = ΣFtr_i[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 the difference,

Eq. 9:  Δ_trF_X ≡ µ_B - µ_A [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:  F_tri = µ_i·ν_i [J·mol^-1]

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

@@ Line 16: / Line 16: @@
   <big>'''Eq. 2''':  d<sub>tr</sub>''G'' = ''µ''<sub>A</sub>·d<sub>tr</sub>''n''<sub>A</sub> + ''µ''<sub>B</sub>·d<sub>tr</sub>''n''<sub>B</sub> [J] </big>
-:::: where the advancement d<sub>tr</sub>''ξ''<sub>''i''</sub> (''i'' = A or B) is
+:::: where the [[advancement]] d<sub>tr</sub>''ξ''<sub>''i''</sub> (''i'' = A or B) is
   <big>'''Eq. 3''':  d<sub>tr</sub>''ξ''<sub>''i''</sub> = d<sub>tr</sub>''n''<sub>A</sub>·''ν''<sub>A</sub><sup>-1</sup> = d<sub>tr</sub>''n''<sub>B</sub>·''ν''<sub>B</sub><sup>-1</sup> [mol] </big>