= Electrolyte
An <electrolyte> is a conducting medium in which mobile <ions> carry <electric current>, according to https://goldbook.iupac.org/terms/view/09061[IUPAC Gold Book: electrolyte]. In introductory <chemistry>, a substance that yields <ions> when dissolved in <water> is also called an <electrolyte>. Both usages point to the same mechanism: an <electric field> gives mobile <cations> and <anions> directed <drift velocities>.
Mobility matters as much as the presence of <electric charge>. In a simple ideal model of solid <sodium chloride>, <ions> are confined to their sites and do not carry a sustained transport <electric current>. Molten <sodium chloride> has mobile <ions>; dissolved <sodium chloride> gives mobile $\mathrm{Na}^+$ and $\mathrm{Cl}^-$ <ions> in <water>. Real solids can have some ionic transport through imperfections; the immobile-solid picture is an introductory limit, rather than a claim that all solids are perfect insulators.
A <strong electrolyte> yields essentially all <ions> from the dissolved substance, whereas a <weak electrolyte> yields only a fraction under the specified conditions. Dissolved <sodium chloride> is a <strong electrolyte>. <Sucrose> is a <nonelectrolyte>: it dissolves as neutral <molecules>, so dissolving something does not automatically create mobile <ions>. <Water>'s own small population of <hydronium> and <hydroxide> remains possible. See <Chemistry 2e by Paul Flowers and others/11.2 Electrolytes> (§11.2: strong, weak, and nonelectrolytes) and https://openstax.org/books/chemistry-2e/pages/11-4-colligative-properties[Flowers et al., Chemistry 2e, §11.4, Table 11.3: sucrose and sodium chloride].
<Acetic acid> is a <weak electrolyte> and a <weak acid>. In <water>, some neutral <acetic acid> <molecules> transfer a <proton> to <water>, producing <hydronium> and the negatively charged partner:
$$
\mathrm{CH_3COOH}+\mathrm{H_2O}\rightleftharpoons\mathrm{CH_3COO^-}+\mathrm{H_3O^+}.
$$
Both sides have net <electric charge> zero. At <chemical equilibrium>, neutral <acetic acid> coexists with these <ions>; the fraction converted depends on the conditions. <Electrolyte> strength describes this extent of ion production, while <concentration> describes how much substance is present per specified quantity of <chemical solution>. A dilute <strong electrolyte> can contain fewer <ions> per volume than a concentrated <weak electrolyte>. Neither the words strong and weak nor a conductivity comparison alone specifies <concentration>.
Now specify an <electrolytic cell> with a positive <anode> on the left, a negative <cathode> on the right, and an approximately uniform <electric field> pointing right in the bulk <electrolyte>. With a steady external source and neglecting <diffusion> and <convection>, positive <cations> drift right toward the negative <cathode>; negative <anions> drift left toward the positive <anode>. Yet both populations contribute a rightward <conventional current>! For <number densities> $n_+,n_-$ and <drift velocities> $\mathbf v_+,\mathbf v_-$, the transport <current density> is
$$
\mathbf J=n_+(+e)\mathbf v_++n_-(-e)\mathbf v_-.
$$
The product of <electric charge> and <velocity> determines <conventional current>: for the <anion>, both the charge and its rightward velocity component are negative, making its rightward contribution positive. This is the same sign rule used for <electron> <conventional current>. It follows directly from the existing <charge carrier> formula.
\Image[/electrolyte-ion-drift-current.png]
{title=Opposite <ion> <drift velocities> contribute to the same <conventional current> in a specified <electrolytic cell>}
{description=The positive <anode> is left and the negative <cathode> right. The upper arrows show <ion> motion; the lower arrows show the signs of $nqv_x$ for <current density>. A uniform bulk <electric field> is assumed; <diffusion>, <convection>, and <electrode> boundary layers are omitted. Arrow lengths are schematic.}
For an independent numerical example, stipulate $n_+=n_-=10^{25}\,\mathrm{m^{-3}}$, $v_{+,x}=2\times10^{-4}\,\mathrm{m\,s^{-1}}$, and $v_{-,x}=-3\times10^{-4}\,\mathrm{m\,s^{-1}}$. With the exact <elementary charge> $e=1.602176634\times10^{-19}\,\mathrm C$, the contributions are
$$
J_{+,x}=320.4353268\,\mathrm{A\,m^{-2}},\qquad
J_{-,x}=480.6529902\,\mathrm{A\,m^{-2}},\qquad
J_x=801.088317\,\mathrm{A\,m^{-2}}.
$$
Equal <number densities> of singly charged <cations> and <anions> give zero bulk <charge density>, while their motion gives nonzero <current density>. This is why a neutral <electrolyte> can conduct. These numbers are chosen toy inputs, not measurements of <sodium chloride>; maintaining sustained cell <electric current> also requires suitable <electrode> reactions. Blocking <electrodes> can instead lead to charge accumulation and decay of the <electric current>.
An <electrolyte> connects the microscopic motion of <ions> to observable <electrical conductivity>. A counterion-only model keeps just the mobile <counterions> needed to oppose a fixed <electric charge>; <Poisson-Boltzmann equations> use ideal <Boltzmann distributions> to model their equilibrium distributions, rather than the drift example above.
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