Conductance of Electrolytic Solutions

Before we can talk about how well an electrolyte solution conducts electricity, we need a few terms carried over from the physics of resistance.

Resistance and Resistivity

For any conductor, the electrical resistance $R$ is directly proportional to its length $l$ and inversely proportional to its area of cross-section $A$:

$R$ — resistance, measured in ohm ($\Omega$)

$\rho$ (rho) — the proportionality constant, called resistivity (or specific resistance)

$l$ — length of the conductor

$A$ — area of cross-section

Resistivity is a property of the material itself: it is numerically the resistance offered by a piece of that material one metre long with a cross-sectional area of one square metre. Its SI unit is ohm metre ($\Omega$ m), though the submultiple ohm centimetre ($\Omega$ cm) is very commonly used, with

Conductance and Conductivity

The reciprocal of resistance is called conductance, $G$:

$G$ — conductance, in siemens (S), where $1\ \text{S} = 1\ \Omega^{-1}$ (also called mho)

$\kappa$ (kappa) — the reciprocal of resistivity, called conductivity (or specific conductance)

Conductivity is likewise a material property — it is the conductance of a sample that is 1 m long with a cross-sectional area of 1 m². Its SI unit is S m⁻¹, though S cm⁻¹ is frequently used instead, with $1\ \text{S cm}^{-1} = 100\ \text{S m}^{-1}$.

How Conductivity Varies Across Materials

The magnitude of conductivity differs enormously from one substance to another, and it also depends on temperature and pressure. On this basis, materials are grouped into:

• Conductors — metals and alloys, with very high conductivity (movement of electrons)
• Insulators — substances such as glass and ceramics, with extremely low conductivity
• Semiconductors — substances such as silicon and gallium arsenide, with conductivity intermediate between conductors and insulators
• Superconductors — materials with, by definition, zero resistivity (infinite conductivity); once limited to metals/alloys at very low temperatures (0–15 K), but now also seen in certain ceramics and mixed oxides up to around 150 K

A dedicated data table listing representative conductivity values across these classes (metals, aqueous electrolyte solutions, insulators, semiconductors) is provided alongside this section as a reference card — refer to it rather than re-deriving the numbers here.

Electronic (Metallic) Conductance

Conduction through metals is called electronic or metallic conductance, and arises purely from the movement of electrons through the fixed metallic lattice. As electrons enter one end of the conductor and leave from the other, the composition of the metal itself remains unchanged. Electronic conductance depends on:

1. the nature and structure of the metal
2. the number of valence electrons per atom
3. temperature — it decreases as temperature rises

Ionic (Electrolytic) Conductance …