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Iconic symbols

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Iconic symbols

Description

Iconic symbols are used in ergodynamics to indicate more explicitely than standard SI or IUPAC symbols the quantity represented, particularly in ratios of quantities (normalized quantities). Iconic (or canonical) symbols help to clarify the meaning, are based on SI and IUPAC symbols as far as possible, or may be translated into more commonly used, practical symbols. Several ambiguities in SI and IUPAC symbols are eliminated by the systematic structure of iconic symbols, but it may be impossible to avoid all ambiguities, particulary when long (canonical) symbols are abbreviated in a particular context. Clarity is further improved by showing the unit of a quantity together with the iconic symbol of the quantity.


Reference: Gnaiger 2020 MitoPathways

Communicated by Gnaiger E 2020-11-29

Normalized quantities

Iconic symbols show the quantity, the format of the normalization in the subscript (U, n, e), and the entity specified in the subscript (X). The normalized quantities are per X. In the quantities QelX, NX, nX, VX, mX, the subscript X without attachment to a format indicates the quantity of X.

Canonical comments on IUPAC definitions in the context of charge

Charge of the proton versus charge per proton

Proton charge is the elementary charge e [C·x-1], which is charge per count of protons.
QelQelp+ [C]
eQNp+ = Qel·Np+-1  [C∙x-1]
The distinction of charge of particles versus charge per single particle is not made sufficiently clear by IUPAC, when defining "-e is the charge of an electron" — it must be corrected to "-e is the charge per electron".
For comparison, the name "charge density of electrons" is used by IUPAC with symbol ρ [C·m-3]. Dividing ρ by the count concentration of electrons [x·m-3], we obtain the unit [C·x-1] for the electron charge. Therefore, electron charge (or proton charge) is clearly the charge per particle.

Ambiguity of QB

IUPAC (Cohen 2008 IUPAC Green Book) defines the charge number as
IUPAC:  zB = QB·e-1
Therefore, QB = zBe. The subscript in QB indicates per elementary entity B. This is opposite to the subscript in VB as the symbol for the volume of a substance of type B (e.g. VO2 [L]). For consistency with this convention, the symbol QelB or QelX [C] is used for indicating charge of a substance of type B or X, distinguished from particle charge as the quantity of charge per elementary entity X with symbol QNX [C∙x-1]. To avoid too long and multiple subscript levels, QNX is used instead of QUX, and the ‘el’ is dropped from QelNX. The particle charge QNH+ per hydrogen ion is identical to the definition of the elementary charge e. Therefore, the charge number of the hydrogen ion is zH+ = QNH+/e = 1. In summary:
zB = QNB·e-1
QNB = QelB·NB-1 [C∙x-1]


Keywords

» charge QelX
» charge number zX
» electrochemical constant f
» elementary charge e
» Faraday constant F
» hydrogen ion versus proton
» iconic symbols
» motive entity
» particle charge QNX


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Normalization of charge and iconic symbols
Iconic symbols show the quantity, the format of the normalization in the subscript (N, n, e), and the entity specified in the subscript (X). The normalized quantities are per X. In the quantities QelX, NX, nX, VX, mX, the subscript X without attachment to a format indicates the quantity of X.
Quantity Unit Normalized for quantity Unit Iconic symbol Unit Practical symbol Quantity
charge QelX [C] / count NX [x] = QNX [C·x-1] particle charge (IUPAC: QB)
charge QelX [C] / amount nX [mol] = QnX [C·mol-1] charge number times Faraday constant
charge QelX [C] / volume VX [m3] = QVX [C·m-3] ρel charge density
charge QelX [C] / mass mX [kg] = QmX [C·kg-1] specific charge
count NX [x] / charge QelX [C] = NeX [x·C-1]
amount nX [mol] / charge QelX [C] = neX [mol·C-1]
volume VX [m3] / charge QelX [C] = VeX [m3·C-1] ρel-1
mass mX [kg] / charge QelX [C] = meX [kg·C-1]



References

  1. Gnaiger E (2020) Mitochondrial pathways and respiratory control. An introduction to OXPHOS analysis. 5th ed. Bioenerg Commun 2020.2. - »Bioblast link«
  2. Gnaiger Erich (2020) Canonical reviewer's comments on: Bureau International des Poids et Mesures (2019) The International System of Units (SI) 9th ed. MitoFit Preprint Arch 2020.4 doi:10.26124/mitofit:200004.
  3. Grosholz Emily R (2007) Representation and productive ambiguity in mathematics and the sciences. Oxford Univ Press 312 pp. - »Bioblast link«


MitoPedia concepts: Ergodynamics