10.1 Electrolytes and ionic conductivity

Electrolytes and their properties

Electrolytes are substances that dissociate into ions when dissolved in a solvent, producing solutions that conduct electric current. Understanding how and why they conduct is foundational to electrochemistry, since every electrochemical cell depends on ion transport through an electrolyte to complete its circuit.

Dissociation and conductivity

When an electrolyte dissolves, it breaks apart into cations and anions. These free ions are what carry charge through the solution. The extent of dissociation depends on both the strength of the electrolyte and the nature of the solvent.

• Solubility, conductivity, and ion mobility together determine how well a given electrolyte performs in a specific application.
• Without dissolved ions, a solution cannot conduct appreciable current, which is why pure water is a very poor conductor.

Role in electrochemistry

Electrolytes bridge the gap between electrodes by allowing ionic charge transfer, which sustains the redox reactions that drive electrochemical cells.

• Electrolytes can be acids, bases, or salts. Common examples: HCl, NaOH, NaCl.
• Batteries: The electrolyte enables ion transfer between electrodes during charge and discharge. For instance, Li-ion batteries use $\text{LiPF}_6$ dissolved in organic solvents.
• Fuel cells: The electrolyte transports ions (often $\text{H}^+$ or $\text{OH}^-$) between electrodes, converting chemical energy to electrical energy.
• Electroplating: Electrolyte solutions supply metal ions that deposit as thin layers onto a substrate.

Ionic conductivity in solutions

Measuring and defining conductivity

Conductivity ($\kappa$) quantifies how well an electrolyte solution carries current through ion movement. It has units of S/m (siemens per meter).

Molar conductivity ($\Lambda_m$) normalizes conductivity to the amount of dissolved electrolyte:

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

where $c$ is the molar concentration. This quantity is useful because it lets you compare how effectively different electrolytes conduct on a per-mole basis.

Kohlrausch's law describes how molar conductivity varies with concentration for strong electrolytes:

$\Lambda_m = \Lambda_m^\circ - K\sqrt{c}$

where $\Lambda_m^\circ$ is the limiting molar conductivity (the value at infinite dilution) and $K$ is an empirical constant. The decrease with $\sqrt{c}$ arises because interionic interactions (ion-ion drag, electrophoretic effects) become stronger at higher concentrations.

Ion movement and electric fields

When an external electric field is applied across a solution:

1. Cations (positive ions) migrate toward the cathode (negative electrode).
2. Anions (negative ions) migrate toward the anode (positive electrode).

The overall conductivity depends on three factors: the concentration of ions, their charge, and their mobility (how fast they move under a given field). Ions with higher charge and smaller solvated radius tend to have greater mobility, contributing more to conductivity.

Strong vs. weak electrolytes

Degree of dissociation

Strong electrolytes dissociate completely (or very nearly so) in solution. Every formula unit produces free ions, giving high conductivity.

• Examples: strong acids ($\text{HCl}$, $\text{H}_2\text{SO}_4$), strong bases ($\text{NaOH}$, $\text{KOH}$), soluble salts ($\text{NaCl}$, $\text{KNO}_3$)

Weak electrolytes only partially dissociate, establishing an equilibrium between undissociated molecules and ions. This means fewer charge carriers and lower conductivity at comparable concentrations.

• Examples: weak acids ($\text{CH}_3\text{COOH}$, $\text{H}_2\text{CO}_3$), weak bases ($\text{NH}_3$, amines), sparingly soluble salts ($\text{AgCl}$, $\text{CaCO}_3$)

A practical consequence: the molar conductivity of a strong electrolyte changes only modestly with dilution (following Kohlrausch's law), while the molar conductivity of a weak electrolyte rises sharply upon dilution because the degree of dissociation increases.

Dissociation constants

The equilibrium position for a weak electrolyte is characterized by its dissociation constant ($K_a$ for acids, $K_b$ for bases). For a generic weak acid $\text{HA}$:

$K_a = \frac{[\text{H}^+][\text{A}^-]}{[\text{HA}]}$

A larger $K_a$ means more dissociation at a given concentration, and therefore higher conductivity. You can also connect $K_a$ to the degree of dissociation $\alpha$ using Ostwald's dilution law:

$K_a = \frac{c\alpha^2}{1 - \alpha}$

This relationship is especially useful for relating conductivity measurements to thermodynamic equilibrium data, since $\alpha$ can be estimated from $\Lambda_m / \Lambda_m^\circ$.

Factors influencing conductivity

Concentration effects

• As concentration increases, more ions are available, so conductivity ($\kappa$) generally rises.
• At very high concentrations, ion pairing and increased interionic friction reduce effective mobility, and conductivity can actually decrease.
• For weak electrolytes, the relationship is more complex because the degree of dissociation itself changes with concentration (higher dilution pushes the equilibrium toward more dissociation).

Temperature dependence

Higher temperature increases the kinetic energy of ions and decreases solvent viscosity, both of which boost ionic mobility. The temperature dependence of conductivity often follows an Arrhenius-type expression:

$\kappa = A \, e^{-E_a / RT}$

where $A$ is a pre-exponential factor, $E_a$ is the activation energy for ion transport, $R$ is the gas constant, and $T$ is the absolute temperature.

By plotting $\ln \kappa$ vs. $1/T$, you can extract $E_a$ from the slope. Typical activation energies for aqueous electrolytes are on the order of 10–20 kJ/mol, reflecting the energy needed for ions to push through the solvent structure.

Solvent effects

The solvent influences conductivity through two main properties:

• Dielectric constant ($\varepsilon$): A high dielectric constant stabilizes separated ions by reducing the electrostatic attraction between them. Water ($\varepsilon \approx 80$) strongly favors dissociation; hexane ($\varepsilon \approx 2$) does not.
• Viscosity ($\eta$): Lower viscosity allows ions to move more freely. Water's low viscosity supports fast ion transport, while glycerol's high viscosity slows it considerably.

Choosing the right solvent is a real design decision in electrochemical systems. For example, Li-ion battery electrolytes use organic carbonates that balance a reasonable dielectric constant with electrochemical stability at high voltages.

Applications of electrolytes and ionic conductivity

Electrochemical power sources

• Batteries: Electrolyte conductivity directly affects internal resistance, which in turn controls power output and efficiency. Li-ion cells use $\text{LiPF}_6$ in mixed carbonate solvents to achieve conductivities around 10 mS/cm.
• Fuel cells: Proton exchange membrane (PEM) fuel cells use Nafion, a polymer electrolyte that conducts $\text{H}^+$ ions while blocking electron flow and gas crossover.

Electrolytic processes

• Electroplating: A $\text{CuSO}_4$ electrolyte, for example, supplies $\text{Cu}^{2+}$ ions that are reduced onto the substrate. Higher electrolyte conductivity enables more uniform deposition.
• Electrolysis: Non-spontaneous reactions are driven by applied voltage. Water electrolysis in KOH solution produces $\text{H}_2$ and $\text{O}_2$; the electrolyte's conductivity determines how much voltage is lost to ohmic resistance.

Electrochemical sensors

• pH meters measure the activity of $\text{H}^+$ ions using a glass electrode immersed in an electrolyte solution. The measured potential relates to $\text{H}^+$ activity through the Nernst equation.
• Ion-selective electrodes (ISEs) work on the same principle but are designed to respond selectively to a target ion ($\text{K}^+$, $\text{Ca}^{2+}$, etc.).
• Sensor performance depends on both the electrolyte properties and the electrode materials, since sluggish ion transport in the electrolyte degrades response time and sensitivity.