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 (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 = µ_A·n_A + µ_B·n_B [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:  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 total change of Gibbs energy dG is the sum of all partial transformations, dG = Σd_iG. 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 a difference as an equivalence,

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]

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

@@ Line 1: / Line 1: @@
 {{MitoPedia
 |abbr=''G'' [J]
-|description='''Gibbs energy''' ''G'' [J] is [[exergy]] which cannot be created internally (subscript i), but in contrast to [[internal-energy]] (d<sub>i</sub>''U''/d''t'' = 0) is not conserved but is dissipated (d<sub>i</sub>''G''/d''t'' < 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.
+|description='''Gibbs energy''' ''G'' [J] is [[exergy]] which cannot be created internally (subscript i), but in contrast to [[internal-energy]] (d<sub>i</sub>''U''/d''t'' = 0) is not conserved but is dissipated (d<sub>i</sub>''G''/d''t'' < 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.
 |info=<u>[[Energy]]</u>
 }}
 [[File:Gibbs energy advancement.png|right|330px|link=Gnaiger_2020_BEC_MitoPathways#Chapter_8._Protonmotive_pressure_and_respiratory_control |Gibbs energy and advancement|thumb|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''<sub>A</sub>° = ''μ''<sub>B</sub>° = 0 kJ·mol<sup>-1</sup> (modified from [[Gnaiger 2020 BEC MitoPathways]]).]]
 == Gibbs energy as a function of advancement ==
-  Communicated by [[Gnaiger E]] 2022-10-18
+  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
@@ Line 12: / Line 13: @@
   <big>'''Eq. 1''':  ''G'' = ''µ''<sub>A</sub>·''n''<sub>A</sub> + ''µ''<sub>B</sub>·''n''<sub>B</sub> [J] </big>
-:::: A small change d''G'' at constant chemical potentials ''µ''<sub>''i''</sub> 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,
+:::: A small change d<sub>tr</sub>''G'' at constant chemical potentials ''µ''<sub>''i''</sub> 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,
   <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>
@@ Line 20: / Line 21: @@
   <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>
-:::: The isomorphic force of transformation Δ<sub>tr</sub>''F''<sub>''X''</sub> is the derivative of exergy per advancement,
+:::: The total change of Gibbs energy d''G'' is the sum of all partial transformations, d''G'' = Σd<sub>''i''</sub>''G''. The isomorphic force of transformation Δ<sub>tr</sub>''F''<sub>''X''</sub> is the derivative of exergy per advancement,
   <big>'''Eq. 4''':  Δ<sub>tr</sub>''F''<sub>''X''</sub> = ∂''G''/∂<sub>tr</sub>''ξ''<sub>''X''</sub> [J·mol<sup>-1</sup>] </big>
@@ Line 40: / Line 41: @@
   <big>'''Eq. 8''':  Δ<sub>tr</sub>''F''<sub>''X''</sub> = Σ''µ''<sub>''i''</sub>·''ν''<sub>''i''</sub> = Σ''F''tr<sub>''i''</sub>[J·mol<sup>-1</sup>] </big>
-:::: 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,
+:::: 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]],
   <big>'''Eq. 9''':  Δ<sub>tr</sub>''F''<sub>''X''</sub> ≡ ''µ''<sub>B</sub> - ''µ''<sub>A</sub> [J·mol<sup>-1</sup>] </big>
@@ Line 47: / Line 48: @@
   <big>'''Eq. 10''':  ''F''<sub>tr''i''</sub> = ''µ''<sub>''i''</sub>·''ν''<sub>''i''</sub> [J·mol<sup>-1</sup>] </big>
+:::: To get acquainted with the meaning of subscripts such as 'tr' used above, consult »[[Iconic_symbols#Abbreviation_of_iconic_symbols |Abbreviation of iconic symbols]].
 '''References'''