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. 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 transformation in a closed isothermal system at constant pressure (modified from Gnaiger 2020 BEC MitoPathways).

Gibbs energy as a function of advancement

Communicated by Gnaiger E 2022-10-17

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

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] 

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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