7.1 Principles of electrochemistry

Fundamentals of Electrochemistry

Electrochemistry deals with the interconversion of electrical and chemical energy. Understanding these principles is essential for electroanalytical methods, where you use electrical measurements to determine the identity and concentration of analytes in solution.

Redox Reactions and Electron Transfer

Every electrochemical process is built on oxidation-reduction (redox) reactions, which involve the transfer of electrons between chemical species.

• Oxidation is the loss of electrons
• Reduction is the gain of electrons

A helpful mnemonic: OIL RIG (Oxidation Is Loss, Reduction Is Gain).

These two processes always occur together. You can't have oxidation without reduction happening somewhere else. In an electrochemical cell, these half-reactions are physically separated at two electrodes:

• The anode is the electrode where oxidation occurs
• The cathode is the electrode where reduction takes place

Electrodes and Electrolytes

Electrodes are conductors that allow electrons to flow to and from the solution in an electrochemical cell. Common electrode materials include metals (platinum, gold, silver) and carbon (graphite, glassy carbon). The choice of material depends on your application and the potential window you need. For instance, platinum works across a wide potential range in many solutions, while carbon electrodes are preferred for certain organic analytes.

Electrolytes are substances that dissociate into ions when dissolved in a solvent, enabling ionic conduction through the solution. Common examples include aqueous solutions of salts (NaCl, KCl), acids (HCl, $H_2SO_4$), and bases (NaOH, KOH). Both the concentration and the composition of the electrolyte affect the solution's conductivity and the electrochemical reactions at the electrodes.

Electrical Potential and Chemical Reactions

Standard Electrode Potential and the Nernst Equation

Electrical potential (voltage) is the driving force that pushes electrons through an electrochemical cell. The standard electrode potential ($E°$) quantifies the tendency of a chemical species to be reduced, measured under standard conditions (25°C, 1 M concentrations, 1 atm).

• More positive $E°$ values mean a greater tendency to be reduced (the species is a stronger oxidizing agent)
• More negative $E°$ values mean a greater tendency to be oxidized

Some reference values to know:

$E = E° - \frac{RT}{nF} \ln \frac{[\text{Red}]}{[\text{Ox}]}$

where $R$ is the gas constant (8.314 J/mol·K), $T$ is the temperature in Kelvin, $n$ is the number of electrons transferred, and $F$ is Faraday's constant (96,485 C/mol). At 25°C, this simplifies to:

$E = E° - \frac{0.05916}{n} \log \frac{[\text{Red}]}{[\text{Ox}]}$

This simplified form shows up constantly in analytical calculations, so it's worth committing to memory.

Cell Potential and Gibbs Free Energy

The cell potential ($E_{cell}$) is the difference in electrode potentials between the cathode and anode:

$E_{cell} = E_{cathode} - E_{anode}$

• A positive $E_{cell}$ indicates a spontaneous reaction (galvanic cell)
• A negative $E_{cell}$ indicates a non-spontaneous reaction (requires external energy)

The cell potential connects directly to thermodynamics through the Gibbs free energy change:

$\Delta G = -nFE_{cell}$

Because of the negative sign, a positive $E_{cell}$ gives a negative $\Delta G$, confirming the reaction is spontaneous. This relationship is what links measurable voltage to the thermodynamic favorability of a reaction.

Electrochemical Cells and Applications

Components and Principles of Electrochemical Cells

An electrochemical cell consists of two half-cells, each containing an electrode immersed in an electrolyte. The half-cells are connected by:

• An external circuit (wire) that carries electrons between electrodes
• A salt bridge or porous membrane that allows ions to migrate between solutions, maintaining charge balance without letting the electrolytes mix

Salt bridges are typically made from agar gel saturated with an inert electrolyte like KCl or $KNO_3$. Porous glass frits serve the same purpose.

Consider the classic Daniell cell as an example:

• Cathode half-reaction: $Cu^{2+} + 2e^- \rightarrow Cu$
• Anode half-reaction: $Zn \rightarrow Zn^{2+} + 2e^-$
• Overall: $Cu^{2+} + Zn \rightarrow Cu + Zn^{2+}$

Zinc is oxidized because it has the more negative $E°$, and copper is reduced because it has the more positive $E°$. The cell potential is $+0.34 - (-0.76) = +1.10$ V.

Applications in Analytical Chemistry

Electrochemical cells are the basis for two major families of analytical methods:

Potentiometric methods measure the potential difference between a reference electrode and an indicator electrode at essentially zero current. The measured voltage relates to analyte concentration through the Nernst equation.

• Ion-selective electrodes (ISEs) are the most common potentiometric tools. The pH glass electrode is the most familiar example, but ISEs also exist for fluoride, potassium, calcium, and many other ions.
• These methods are widely used because they're simple, inexpensive, and work well for field measurements.

Amperometric methods measure the current produced when an analyte is oxidized or reduced at a working electrode under an applied potential.

• Voltammetry varies the applied potential and records the resulting current, producing a current-potential curve that reveals both identity and concentration.
• Coulometry measures the total charge passed during complete electrolysis of an analyte, relating it to the amount of substance through Faraday's law.
• In both cases, the measured current is proportional to analyte concentration, making these methods useful for quantitative analysis.

Galvanic vs. Electrolytic Cells

These are the two fundamental types of electrochemical cells, and distinguishing them is critical.

Galvanic Cells

Galvanic (voltaic) cells convert chemical energy into electrical energy through spontaneous redox reactions. Electrons flow from the anode to the cathode through an external circuit, and this flow can do useful work.

A practical example is the lead-acid battery: the anode is lead (Pb), the cathode is lead dioxide ($PbO_2$), and the electrolyte is sulfuric acid. The overall reaction is:

$Pb + PbO_2 + 2H_2SO_4 \rightarrow 2PbSO_4 + 2H_2O$

In analytical chemistry, galvanic cells underlie potentiometric measurements. For pH determination, a glass electrode (indicator) and a reference electrode (such as Ag/AgCl or saturated calomel) form a galvanic cell. The glass electrode develops a potential that depends on the hydrogen ion activity of the solution, while the reference electrode provides a stable, known potential for comparison.

Electrolytic Cells

Electrolytic cells convert electrical energy into chemical energy by using an external power source to drive a non-spontaneous reaction. The electrode labels stay the same (oxidation at the anode, reduction at the cathode), but the reaction would not proceed without the applied voltage.

A classic example is the electrolysis of water:

• Anode: $2H_2O \rightarrow O_2 + 4H^+ + 4e^-$
• Cathode: $4H^+ + 4e^- \rightarrow 2H_2$
• Overall: $2H_2O \rightarrow 2H_2 + O_2$

In analytical chemistry, electrolytic cells are used for techniques like electrodeposition. For example, $Cu^{2+}$ ions can be reduced to Cu metal at the cathode while a platinum anode completes the circuit. The mass of copper deposited is calculated using Faraday's laws of electrolysis:

$m = \frac{QM}{nF}$

where $Q$ is the total charge passed (in coulombs), $M$ is the molar mass, $n$ is the number of electrons per ion, and $F$ is Faraday's constant. This makes electrogravimetry a highly accurate quantitative method.