Equivalence: Difference between revisions

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Equivalence

Description

Numerical equivalence (symbol ≡) indicates that two quantities are numerically equal, even if the full meaning may be different. For instance: 1 ≡ 1·1 and 1 ≡ 1/1. In contrast to ≡, the symbol = indicates physicochemical equality.

Abbreviation: ≡

Reference: Gnaiger 2020 BEC MitoPathways

Example

Iconic symbols indicate equality beyond equivalence, for instance in equations for the protonmotive force pmF (Blue Book Eq. 8.1 and 8.2)

Conventional symbols:

The protonmotive force *pmF*
Format	Definition	Units
charge format:	Δp ≡ ∆𝜇_H⁺ ∙ (𝑧_H⁺ ∙ 𝐹)⁻¹ + ∆𝛹_p⁺	[J∙C^-1 = V]
amount format:	Δ𝜇̃ _H⁺ ≡ ∆𝜇_H⁺ + ∆𝛹_p⁺ ∙ (𝑧_H⁺ ∙ 𝐹)	[J∙mol^-1 = Jol]

Iconic symbols: Δ_mF_H⁺ = Δ_dF_H⁺ + Δ_elF_p⁺

Chemical potential, stoichiometry, and metabolic force
Quantity	Symbol	Equation	Units	Blue Book 8.2.2.
potential:	μ_H⁺	= RT∙ln a_H⁺ = -RT∙ln(10)∙pH	[kJ∙mol^-1]	8.18a
difference	Δμ_H⁺	= -RT∙ln(10)∙ΔpH = -RT∙2.303∙(pH_b-pH_a)	[kJ∙mol^-1]	8.18b
force:	Δ_dF_H⁺	= μ_H⁺a∙ν_a + μ_H⁺b∙ν_b =-RT∙2.303∙∆_dpH	[kJ∙mol^-1]	8.18c

MitoPedia concepts: Ergodynamics

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+== Example ==
+:::* [[Iconic symbols]] indicate [[equality]] beyond [[equivalence]], for instance in equations for the [[protonmotive force]] ''pmF'' ([[Blue Book]] Eq. 8.1 and 8.2)
+:::: Conventional symbols:
+:::::::::::: {| class="wikitable"
+|+ The protonmotive force ''pmF''
+|-
+! Format !! Definition !! Units
+|-
+| charge format: || Δp ≡ ∆''𝜇''<sub>H<sup>+</sup></sub> ∙ (''𝑧''<sub>H<sup>+</sup></sub> ∙ ''𝐹'')<sup>−1</sup> + ∆''𝛹''<sub>p<sup>+</sup></sub> || [J∙C<sup>-1</sup> = V]
+|-
+| amount format:  || Δ''𝜇̃  ''<sub>H<sup>+</sup></sub> ≡ ∆''𝜇''<sub>H<sup>+</sup></sub> + ∆''𝛹''<sub>p<sup>+</sup></sub> ∙ (''𝑧''<sub>H<sup>+</sup></sub> ∙ ''𝐹'') || [J∙mol<sup>-1</sup> = Jol]
+|}
+:::: Iconic symbols: Δ<sub>m</sub>''F''<sub>H<sup>+</sup></sub> = Δ<sub>d</sub>''F''<sub>H<sup>+</sup></sub> + Δ<sub>el</sub>''F''<sub>p<sup>+</sup></sub>
+:::::: {| class="wikitable"
+|+ Chemical potential, stoichiometry, and metabolic force
+|-
+! Quantity !! Symbol !! Equation !! Units !! [[Blue Book]] 8.2.2.
+|-
+| potential: || ''μ''<sub>H<sup>+</sup></sub> || = ''RT''∙ln ''a''<sub>H<sup>+</sup></sub> = -''RT''∙ln(10)∙pH || [kJ∙mol<sup>-1</sup>] || 8.18a
+|-
+| difference || Δ''μ''<sub>H<sup>+</sup></sub> || = -''RT''∙ln(10)∙ΔpH = -''RT''∙2.303∙(pH<sub>''b''</sub>-pH<sub>''a''</sub>) || [kJ∙mol<sup>-1</sup>] || 8.18b
+|-
+| force: || Δ<sub>d</sub>''F''<sub>H<sup>+</sup></sub> || = ''μ''<sub>H<sup>+</sup>''a''</sub>∙''ν''<sub>a</sub> + ''μ''<sub>H<sup>+</sup>''b''</sub>∙''ν''<sub>b</sub> =-''RT''∙2.303∙∆<sub>d</sub>pH || [kJ∙mol<sup>-1</sup>] || 8.18c
+|}
 {{MitoPedia concepts
 |mitopedia concept=Ergodynamics
 }}