Electrolyte Solutions and Ionic Conduction

Drop a pinch of table salt into water and the light bulb in a simple circuit glows the moment the electrodes touch the solution. Pure water alone barely conducts. The difference is ions: charged particles set free to wander and carry current from one electrode to the other. Electrolyte solutions sit at the foundation of electrochemistry, biology, and industrial chemistry. Nerve signals, batteries, corrosion, and seawater desalination all depend on how ions dissociate and move. Understanding ionic conduction lets chemists predict how well a solution conducts, diagnose whether a compound dissociates fully, and design cells that store or deliver energy. This article builds the picture from the ground up. You will see how electrolytes form ions. You will see how those ions carry charge under an electric field. You will meet the quantities chemists actually measure: conductance, resistivity, and molar conductivity. The article closes by pointing toward strong versus weak electrolytes and the practical measurement of conductivity.

Key takeaways

Electrolytes are substances that dissociate into ions in solution, producing a medium that conducts electricity.
Ionic conduction differs fundamentally from metallic conduction: charge is carried by moving ions, not free electrons.
Conductance depends on ion concentration, ionic charge, and ionic mobility through an applied electric field.
Molar conductivity, $\Lambda_m$ , normalizes conductivity per mole of electrolyte, enabling fair comparisons between salts.
Resistance measurements in a standard cell, combined with the cell constant, give quantitative access to conductivity.
Key idea: dissolved ions, driven by an electric field, migrate through solution and this directed ionic drift is electric current.

The core insight

An electrolyte solution conducts electricity because dissociation liberates mobile, charged ions that drift under an applied electric field, each ion's contribution to the total current set by its charge, concentration, and intrinsic mobility.

The physical picture

Consider a beaker of water into which crystalline sodium chloride is stirred. The strongly polar water molecules surround each $\text{Na}^+$ and $\text{Cl}^-$ ion, stabilizing separated charges that were locked into a rigid lattice. This process, hydration of ions, is the mechanism that pulls the ionic solid apart. The resulting solution contains free-swimming cations and anions, each cloaked in a shell of oriented water dipoles. With no applied field, these ions undergo random thermal motion, colliding with solvent molecules and each other, executing a jittery random walk with zero net displacement over time. This is ordinary diffusion, driven by thermal energy $k_BT$ , and it produces no net current because as many ions drift left as drift right. Apply an electric field, however, by dipping two electrodes into the solution and connecting them to a battery, and the picture changes. The field exerts a force $qE$ on every ion, superimposing a slow net drift on top of the random thermal jostling. Cations drift toward the cathode; anions drift toward the anode. This net, field-driven migration of charge is exactly what we call electric current in an electrolyte solution. Crucially, conduction here is fundamentally different from conduction in a metal wire. In a metal, mobile electrons carry charge through a fixed lattice of positive ions. In an electrolyte, both positive and negative charge carriers are heavy, solvated ions, and both species usually move, contributing to the total current in the same direction (conventional current), even though they physically travel in opposite directions. The drift velocity of an ion is not arbitrary; it is set by a balance between the electric force accelerating the ion and viscous drag from the surrounding solvent, which grows with speed. Very quickly, the ion reaches a terminal drift velocity proportional to the applied field strength. The proportionality constant is called the ionic mobility, and it depends on the ion's size, charge, and the solvent's viscosity.

Figure

Ions drifting under an applied field between two electrodes

The second useful picture is quantitative: how conductance scales with concentration, and why chemists prefer to track molar conductivity rather than raw conductivity when comparing electrolytes of different concentration.

Figure

Conductivity increases with ion concentration in a dilute NaCl solution

The core relations

\kappa = \sum_i z_i F c_i u_i

where $\kappa$ is conductivity, $z_i$ ion charge number, $F$ the Faraday constant, $c_i$ ion concentration, $u_i$ ionic mobility.

\Lambda_m = \frac{\kappa}{c}

where $\Lambda_m$ is molar conductivity, $\kappa$ conductivity, $c$ molar concentration of the electrolyte.

G = \frac{1}{R}

where $G$ is conductance in siemens, $R$ the measured resistance of the solution between electrodes.

\kappa = G\left(\frac{l}{A}\right) = G K_{\text{cell}}

where $l/A = K_{\text{cell}}$ is the cell constant, fixed by electrode geometry, $l$ electrode separation, $A$ electrode area.

v = uE

where $v$ is the terminal ionic drift velocity, $u$ ionic mobility, $E$ the applied electric field strength.

Derivation AFrom ionic drift to solution conductivity

Goal. Show how the microscopic drift of individual ions under an applied field builds up to the macroscopic conductivity $\kappa$ that appears in Ohm's law for the solution.

Step 1: force balance on a single ion. An ion of charge $ze$ in a field $E$ feels an electric force $zeE$ . As it accelerates, viscous drag from the solvent grows with speed, well approximated (for a small sphere in a continuous fluid) by Stokes' law, $f = 6\pi\eta r v$ , with $\eta$ the solvent viscosity and $r$ the ion's effective hydrodynamic radius. Terminal drift velocity is reached when these forces balance:

zeE = 6\pi\eta r v

Step 2: define ionic mobility. Solving for $v$ and writing the constant of proportionality as the ionic mobility $u$ ,

v = \left(\frac{ze}{6\pi\eta r}\right)E = uE

Mobility is an intrinsic property of the ion-solvent pair: bigger, more heavily solvated ions, or more viscous solvents, give smaller $u$ .

Step 3: current carried by one ionic species. Picture a cross-section of area $A$ perpendicular to the field. In time $\Delta t$ , every ion of species $i$ within a slab of length $v_i\Delta t$ reaches the plane, so the flux of ions crossing per unit time is $c_iN_A v_i A$ (using ion number density $c_iN_A$ ). Each carries charge $z_ie$ , so the current contributed is

I_i = z_i e N_A c_i v_i A = z_i F c_i v_i A

using $F = N_Ae$ .

Step 4: substitute the drift velocity. Since $v_i = u_iE$ ,

I_i = z_i F c_i u_i E A

Step 5: sum over all ionic species and define conductivity. Total current is the sum over cations and anions (and any other ions present). Recognizing $\kappa$ as the proportionality constant between current density $I/A$ and field $E$ in the solution's Ohm's-law relation $I/A = \kappa E$ , we identify:

\boxed{\kappa = \sum_i z_i F c_i u_i}

This result shows conductivity is built additively from every ion's charge, concentration, and mobility, exactly the microscopic picture of drifting solvated ions carrying current across the solution.

Worked examples

Example 1 — Converting a resistance measurement into conductivity and molar conductivity. A conductivity cell with electrodes of area $A = 1.00\ \text{cm}^2$ separated by $l = 1.50\ \text{cm}$ is filled with a $0.0500\ \text{mol L}^{-1}$ KCl solution. The measured resistance is $R = 325\ \Omega$ . Step 1 — cell constant.

K_{\text{cell}} = \frac{l}{A} = \frac{1.50\ \text{cm}}{1.00\ \text{cm}^2} = 1.50\ \text{cm}^{-1}

Step 2 — conductance.

G = \frac{1}{R} = \frac{1}{325\ \Omega} = 3.077\times10^{-3}\ \text{S}

Step 3 — conductivity.

\kappa = G K_{\text{cell}} = (3.077\times10^{-3}\ \text{S})(1.50\ \text{cm}^{-1}) = 4.615\times10^{-3}\ \text{S cm}^{-1}

Converting to SI (S m⁻¹), multiply by 100 cm/m:

\kappa = 0.4615\ \text{S m}^{-1}

Step 4 — molar conductivity. Convert concentration to mol m⁻³: $0.0500\ \text{mol L}^{-1} = 50.0\ \text{mol m}^{-3}$ .

\Lambda_m = \frac{\kappa}{c} = \frac{0.4615\ \text{S m}^{-1}}{50.0\ \text{mol m}^{-3}} = 9.23\times10^{-3}\ \text{S m}^2\ \text{mol}^{-1}

Sanity check: this is $92.3\ \text{S cm}^2\ \text{mol}^{-1}$ , squarely in the expected range for a 1:1 strong electrolyte like KCl at moderate concentration (literature values around 100–140 S cm² mol⁻¹ depending on concentration), so the arithmetic is physically reasonable.

Example 2 — Estimating ionic mobility and drift velocity from conductivity data. Suppose a fully dissociated 1:1 electrolyte MX has concentration $c = 0.0100\ \text{mol L}^{-1} = 10.0\ \text{mol m}^{-3}$ , and the measured molar conductivity is $\Lambda_m = 1.26\times10^{-2}\ \text{S m}^2\ \text{mol}^{-1}$ . Assume the cation and anion contribute equally to $\Lambda_m$ (a simplifying assumption for this estimate). Find the mobility of the cation, and its drift velocity in a field of $E = 100\ \text{V m}^{-1}$ . Step 1 — conductivity from $\Lambda_m$ .

\kappa = \Lambda_m c = (1.26\times10^{-2}\ \text{S m}^2\ \text{mol}^{-1})(10.0\ \text{mol m}^{-3}) = 0.126\ \text{S m}^{-1}

Step 2 — split conductivity between the two ionic species (equal contribution assumed).

\kappa_+ = \kappa_- = \tfrac{1}{2}(0.126\ \text{S m}^{-1}) = 0.0630\ \text{S m}^{-1}

Step 3 — solve $\kappa_+ = z_+Fc_+u_+$ for mobility. Here $z_+ = 1$ , $c_+ = c = 10.0\ \text{mol m}^{-3}$ (full dissociation, 1:1 salt), and $F = 96\,485\ \text{C mol}^{-1}$ .

u_+ = \frac{\kappa_+}{z_+Fc_+} = \frac{0.0630\ \text{S m}^{-1}}{(1)(96\,485\ \text{C mol}^{-1})(10.0\ \text{mol m}^{-3})}

u_+ = \frac{0.0630}{9.6485\times10^{5}}\ \text{m}^2\text{V}^{-1}\text{s}^{-1} = 6.53\times10^{-8}\ \text{m}^2\text{V}^{-1}\text{s}^{-1}

Step 4 — drift velocity in the given field.

v_+ = u_+E = (6.53\times10^{-8}\ \text{m}^2\text{V}^{-1}\text{s}^{-1})(100\ \text{V m}^{-1}) = 6.53\times10^{-6}\ \text{m s}^{-1}

Sanity check: this mobility, of order $10^{-7}\ \text{m}^2\text{V}^{-1}\text{s}^{-1}$ , matches the accepted range for small hydrated ions such as $\text{Na}^+$ or $\text{K}^+$ (typically $5$ – $8\times10^{-8}\ \text{m}^2\text{V}^{-1}\text{s}^{-1}$ ), and the resulting drift speed, only micrometers per second, confirms that ions crawl slowly compared to their much faster random thermal motion, exactly as the physical picture predicts.

Limiting cases & common traps

Situation	What actually happens	Common error
Very dilute solution	$\kappa$ nearly proportional to $c$ ; ions rarely interact	Assuming $\Lambda_m$ is constant at all concentrations
Concentrated solution	Ion-ion interactions slow drift; $\Lambda_m$ decreases with $c$	Extrapolating dilute-limit mobility to concentrated solutions
Pure water	Conducts extremely weakly; only trace $\text{H}^+$ / $\text{OH}^-$ present	Thinking water itself is a good conductor
Molten ionic solid or ionic liquid	Also conducts by ion migration, no solvent needed	Believing conduction always requires a solvent
Metal wire vs electrolyte	Electrons carry charge in metal; ions in solution	Treating ionic mobility numerically like electron mobility

The chemist behind it

Svante Arrhenius proposed, in his 1884 doctoral thesis, that salts and acids dissociate into charged ions when dissolved in water, even without an applied current. This was a bold claim at a time when ions were thought to exist only under electrolysis. His dissociation theory explained why electrolyte solutions conduct electricity, why they show colligative properties inconsistent with simple molecular counts, and it eventually earned him the 1903 Nobel Prize in Chemistry.

Origins · 1 minSvante Arrhenius and how this was discovered

Svante Arrhenius

1859–1927 · Proposed that electrolytes spontaneously dissociate into ions in solution, founding modern ionic theory

Ask the tutor: How does molar conductivity behave differently for a strong electrolyte like NaCl versus a weak electrolyte like acetic acid as concentration changes?

Why does pure water conduct electricity so poorly?

Pure water undergoes only slight self-ionization, producing tiny concentrations of $\text{H}^+$ (as $\text{H}_3\text{O}^+$ ) and $\text{OH}^-$ , roughly $10^{-7}\ \text{mol L}^{-1}$ each at 25°C. With so few mobile charge carriers present, the conductivity is extremely low, though not exactly zero. Adding even a small amount of an ionic solute dramatically increases the number of mobile ions, which is why tap water, containing dissolved minerals, conducts far better than laboratory-grade deionized water.

Do both the cation and anion always contribute equally to conductivity?

No. Each ion's contribution depends on its own charge, concentration, and mobility, and these generally differ between cation and anion. Small, singly charged ions like $\text{H}^+$ and $\text{OH}^-$ have unusually high mobility because they move via a special relay mechanism through the hydrogen-bond network of water, so acids and bases often conduct better than similarly concentrated salts of the same charge type.

How is conductance related to conductivity, and why do we need the cell constant?

Conductance $G$ is simply the reciprocal of measured resistance and depends on the specific cell geometry used. Conductivity $\kappa$ is an intrinsic property of the solution, independent of cell shape. The cell constant, $l/A$ , converts the geometry-dependent conductance into the geometry-independent conductivity, which lets chemists compare measurements from cells with different electrode sizes and spacings.

Why does molar conductivity change with concentration instead of staying fixed?

At higher concentrations, ions crowd closer together and their electric fields interfere with each other's motion, slowing the drift velocity per ion. This inter-ionic interaction reduces the effective mobility, so $\Lambda_m$ decreases as concentration rises. The precise mathematical form of this decrease, and how it differs for strong versus weak electrolytes, is the subject of the next article in this sequence.

Does temperature affect ionic conduction, and if so how?

Yes, conductivity generally increases with temperature in electrolyte solutions. Higher temperature lowers the solvent's viscosity, so drag on each ion decreases and mobility rises. Higher temperature can also increase the degree of dissociation for weak electrolytes, adding more mobile ions to the mix, which is the opposite trend from metals, where conductivity typically falls as temperature rises.