Charge number

high-resolution terminology - matching measurements at high-resolution

Charge number

Description

The charge number of an ion X or electrochemical reaction with unit stoichiometric number of X is the particle charge [C·x^-1] divided by the elementary charge [C·x^-1]. The particle charge Q_NX is the charge per count of ions X or per ion X transferred in the reaction as defined in the reaction equation.

Abbreviation: z_X

Reference: Gnaiger 2020 BEC MitoPathways

Communicated by Gnaiger Erich (2020-11-23) last update 2020-12-06

z_X = Q_NX / Q_Np⁺

z_X = Q_elX / (e·N_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.

Q_el ≝ Q_elp⁺ [C]

e ≝ Q_Np⁺ = Q_el·N_p⁺^-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 Q_B

IUPAC (Cohen 2008 IUPAC Green Book) defines the charge number as

IUPAC:  z_B = Q_B·e^-1

Therefore, Q_B = z_B∙e. The subscript in Q_B indicates per elementary entity B. This is opposite to the subscript in V_B as the symbol for the volume of a substance of type B (e.g. V_O₂ [L]). For consistency with this convention, the symbol Q_elB or Q_elX [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 Q_NX [C∙x^-1]. To avoid too long and multiple subscript levels, Q_NX is used instead of Q_{U_X}, and the ‘el’ is dropped from Q_elNX. The particle charge Q_NH⁺ per hydrogen ion is identical to the definition of the elementary charge e. Therefore, the charge number of the hydrogen ion is z_H⁺ = Q_NH⁺/e = 1. In summary:

z_B = Q_NB·e^-1

Q_NB = Q_elB·N_B^-1 [C∙x^-1]

Keywords

» charge Q_elX

» charge number z_X

» electrochemical constant f

» elementary charge e

» Faraday constant F

» hydrogen ion versus proton

» iconic symbols

» motive entity

» particle charge Q_NX

Bioblast links: Charge - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>

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 Q_elX, N_X, n_X, V_X, m_X, 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 Q_elX	[C]	/ count N_X	[x]	= Q_NX	[C·x^-1]		particle charge (IUPAC: Q_B)
charge Q_elX	[C]	/ amount n_X	[mol]	= Q_nX	[C·mol^-1]		charge number times Faraday constant
charge Q_elX	[C]	/ volume V_X	[m³]	= Q_VX	[C·m^-3]	ρ_el	charge density
charge Q_elX	[C]	/ mass m_X	[kg]	= Q_mX	[C·kg^-1]		specific charge
count N_X	[x]	/ charge Q_elX	[C]	= N_eX	[x·C^-1]
amount n_X	[mol]	/ charge Q_elX	[C]	= n_eX	[mol·C^-1]
volume V_X	[m³]	/ charge Q_elX	[C]	= V_eX	[m³·C^-1]	ρ_el^-1
mass m_X	[kg]	/ charge Q_elX	[C]	= m_eX	[kg·C^-1]

Bioblast links: SI base units - >>>>>>> - Click on [Expand] or [Collapse] - >>>>>>>

Entity, count, and number, and SI base quantities / SI base units

Quantity name	Symbol	Unit name	Symbol	Comment
elementary	U_X	elementary unit	[x]	U_X, U_B; [x] not in SI
count	N_X	elementary unit	[x]	N_X, N_B; [x] not in SI
number	N	-	dimensionless	= N_X·U_X^-1
amount of substance	n_B	mole	[mol]	n_X, n_B
electric current	I	ampere	[A]	A = C·s^-1
time	t	second	[s]
length	l	meter	[m]	SI: metre
mass	m	kilogram	[kg]
thermodynamic temperature	T	kelvin	[K]
luminous intensity	I_V	candela	[cd]

Fundamental relationships

» Avogadro constant N_A

» Boltzmann constant k

» elementary charge e

» Faraday constant F

» gas constant R

» electrochemical constant f

SI and related concepts

» International System of Units

» elementary unit x

» SI prefixes

» International Union of Pure and Applied Chemistry, IUPAC

» entity

» quantity

» dimension

» format

» motive unit