Electrochemistry

An electrochemical cell converts chemical energy into electrical energy (galvanic/voltaic cell) or electrical energy into chemical energy (electrolytic cell). In a galvanic cell, a spontaneous redox reaction is split into two half-reactions that occur at physically separated electrodes dipped in their own electrolyte solutions, connected by a metallic wire externally and a salt bridge internally. The salt bridge (a U-tube containing an inert electrolyte like KNO₃ or KCl in agar-agar gel) completes the internal circuit and maintains electrical neutrality in both half-cells by allowing ion migration, without mixing the two solutions.

By convention, oxidation occurs at the anode (negative electrode in a galvanic cell) and reduction occurs at the cathode (positive electrode in a galvanic cell). Electrons flow through the external circuit from anode to cathode, while conventional current flows from cathode to anode. A cell is represented in shorthand notation with the anode written on the left and the cathode on the right, a single vertical line for a phase boundary, and a double vertical line for the salt bridge. For the Daniell cell, the reaction Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s) is written as:

Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s)

The potential difference between the two electrodes of a galvanic cell is called the cell potential or electromotive force (emf), measured in volts. Since the absolute potential of a single electrode cannot be measured, all electrode potentials are measured relative to a reference electrode — the Standard Hydrogen Electrode (SHE), whose standard reduction potential is arbitrarily fixed at exactly 0.00 V at all temperatures. The SHE consists of platinum foil coated with platinum black, dipped in 1 M H⁺ solution with H₂ gas at 1 bar bubbled over it. By measuring the emf of a cell formed with SHE and any other electrode under standard conditions (1 M concentration, 1 bar pressure, 298 K), the standard electrode potential (E°) of that electrode is obtained. Arranging elements in order of increasing standard reduction potential gives the electrochemical series, which predicts relative oxidising/reducing strength, the feasibility of a redox reaction, and displacement reactions.

Worked example: Calculate the standard emf of the Daniell cell, given E°(Cu²⁺/Cu) = +0.34 V and E°(Zn²⁺/Zn) = −0.76 V.

Here Cu²⁺/Cu is the cathode (higher, more positive reduction potential — reduction favoured) and Zn²⁺/Zn is the anode (lower reduction potential — oxidation favoured).

E°_cell = E°_cathode − E°_anode = 0.34 − (−0.76) = +1.10 V

Since E°_cell is positive, the reaction Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s) is spontaneous as written, which matches the observed behaviour of the Daniell cell.

Standard electrode potentials apply only when all species are at 1 M concentration (or 1 bar for gases) at 298 K. For any other concentration, the actual electrode/cell potential is given by the Nernst equation. For a general electrode reaction Mⁿ⁺(aq) + ne⁻ → M(s), the electrode potential is:

E_(Mⁿ⁺/M) = E°_(Mⁿ⁺/M) − (RT/nF) ln [1/[Mⁿ⁺]]

For a full cell reaction, the Nernst equation is written in terms of the reaction quotient Q:

E_cell = E°_cell − (RT/nF) ln Q

Substituting R = 8.314 J K⁻¹ mol⁻¹, F = 96500 C mol⁻¹, T = 298 K, and converting ln to log₁₀ (factor 2.303), this simplifies to the commonly used form:

E_cell = E°_cell − (0.0591/n) log Q (at 298 K)

At equilibrium, the cell can do no further work, so E_cell = 0 and Q becomes the equilibrium constant K. Substituting gives an important relation between the standard cell potential and the equilibrium constant of the reaction:

log K = nE°_cell/0.0591

Electrochemistry is also linked directly to thermodynamics: the maximum electrical work obtainable from a cell equals the decrease in Gibbs energy of the reaction, giving:

ΔG = −nFE_cell and, under standard conditions, ΔG° = −nFE°_cell

Worked example 1 (Nernst equation): Find E_cell at 298 K for Zn(s) | Zn²⁺(0.1 M) || Cu²⁺(1.0 M) | Cu(s), given E°_cell = 1.10 V.

The cell reaction is Zn(s) + Cu²⁺(aq) → Zn²⁺(aq) + Cu(s), with n = 2 and Q = [Zn²⁺]/[Cu²⁺] = 0.1/1.0 = 0.1, so log Q = −1.

E_cell = 1.10 − (0.0591/2) × (−1) = 1.10 + 0.02955 = 1.13 V

Worked example 2 (K and ΔG° from E°cell): For the same Daniell cell (n = 2, E°_cell = 1.10 V):

log K = (2 × 1.10)/0.0591 = 2.20/0.0591 ≈ 37.2, so K ≈ 1.7 × 10³⁷, showing the reaction goes essentially to completion.

ΔG° = −nFE°_cell = −(2)(96500 C mol⁻¹)(1.10 V) = −212300 J mol⁻¹ = −212.3 kJ mol⁻¹, confirming the reaction is highly spontaneous.

Electrolytic solutions conduct electricity through the movement of ions. The conductivity (κ) of a solution is the reciprocal of its resistivity and is measured using a conductivity cell with two platinum electrodes of area A separated by distance l. The ratio l/A is called the cell constant (G*). Since resistance R is measured experimentally using a Wheatstone-bridge-based conductivity meter:

κ = G*/R = (l/A) × (1/R)

Conductivity depends on the number of ions per unit volume, so a more useful quantity for comparing electrolytes is molar conductivity (Λ_m), defined as the conductivity contributed by one mole of the electrolyte:

Λ_m = κ × 1000 / C (C in mol L⁻¹, Λ_m in S cm² mol⁻¹)

On dilution, κ decreases (fewer ions per unit volume), but Λ_m always increases because the increase in volume containing one mole of electrolyte more than compensates. For strong electrolytes (fully dissociated), Λ_m increases only slightly with dilution and can be extrapolated linearly to zero concentration to obtain the limiting molar conductivity Λ°_m (molar conductivity at infinite dilution). For weak electrolytes (partially dissociated, e.g. acetic acid), Λ_m rises sharply near infinite dilution because dissociation increases, and Λ°_m cannot be obtained by extrapolation — it is instead calculated using Kohlrausch's law of independent migration of ions, which states that at infinite dilution each ion contributes to the total molar conductivity independently of the other ion present:

Λ°_m = ν₊λ°₊ + ν₋λ°₋

where λ°₊ and λ°₋ are the limiting molar ionic conductivities of the cation and anion, and ν₊, ν₋ are the number of cations and anions per formula unit. This lets us calculate Λ°_m for a weak electrolyte from the Λ°_m values of strong electrolytes containing the same ions (e.g. Λ°_m(CH₃COOH) = Λ°_m(HCl) + Λ°_m(CH₃COONa) − Λ°_m(NaCl)). Kohlrausch's law also allows calculation of the degree of dissociation (α) of a weak electrolyte at any concentration, α = Λ_m/Λ°_m, and hence its dissociation constant via the Ostwald dilution law.

Worked example: The conductivity of 1.028 × 10⁻³ mol L⁻¹ acetic acid is 4.95 × 10⁻⁵ S cm⁻¹. Given Λ°_m(CH₃COOH) = 390.5 S cm² mol⁻¹, find α and K_a.

Λ_m = κ × 1000/C = (4.95 × 10⁻⁵ × 1000)/(1.028 × 10⁻³) = 48.15 S cm² mol⁻¹

α = Λ_m/Λ°_m = 48.15/390.5 = 0.1233 (12.33%)

Using the Ostwald dilution law, K_a = Cα²/(1−α) = (1.028 × 10⁻³ × 0.1233²)/(1−0.1233) = (1.028 × 10⁻³ × 0.01520)/0.8767 = 1.78 × 10⁻⁵ mol L⁻¹, close to the accepted value of acetic acid's dissociation constant.

Unlike a galvanic cell, an electrolytic cell uses an external source of electrical energy (like a battery) to force a non-spontaneous redox reaction to occur — this process is called electrolysis. In electrolysis, the electrode connected to the positive terminal of the external battery is the anode (oxidation still occurs here), and the electrode connected to the negative terminal is the cathode (reduction still occurs here) — note that in an electrolytic cell the anode is positive and the cathode is negative, the reverse polarity compared to a galvanic cell, even though oxidation is always at the anode and reduction is always at the cathode in both cases. During electrolysis of molten salts or aqueous solutions, cations migrate to the cathode and are reduced, while anions migrate to the anode and are oxidised; in aqueous solutions, competing reduction/oxidation of water itself may occur depending on relative electrode potentials and overpotential effects.

Faraday's laws of electrolysis quantify the relationship between the charge passed and the amount of chemical change:

First law: The mass (m) of a substance deposited or liberated at an electrode is directly proportional to the quantity of charge (Q) passed through the electrolyte: m ∝ Q, i.e. m = ZQ = ZIt, where Z is the electrochemical equivalent of the substance and I is the current in amperes passed for time t seconds, so that Q = It (in coulombs).

Second law: When the same quantity of charge is passed through different electrolytes connected in series, the masses of different substances deposited/liberated at their respective electrodes are proportional to their chemical equivalent weights (M/n, where M is molar mass and n is the number of electrons involved per ion/atom in the electrode reaction).

Combining both laws, the mass deposited is given by:

m = (M × I × t)/(n × F)

where F is the Faraday constant (≈ 96500 C mol⁻¹), the charge carried by one mole of electrons.

Worked example: Calculate the mass of copper deposited at the cathode when a current of 2 A is passed through a CuSO₄ solution for 1 hour (Cu = 63.5 g mol⁻¹, n = 2 since Cu²⁺ + 2e⁻ → Cu).

Charge passed, Q = It = 2 A × 3600 s = 7200 C

m = (M × Q)/(n × F) = (63.5 × 7200)/(2 × 96500) = 457200/193000 = 2.37 g of copper

A battery is a practical, self-contained source of electrical energy consisting of one or more galvanic cells connected in series. Batteries are broadly of two types.

Primary batteries cannot be recharged — once the reactants are consumed, the cell becomes dead and is discarded. The common dry cell (Leclanché cell) has a zinc container as anode and a carbon rod surrounded by manganese dioxide and powdered carbon as cathode, with a moist paste of NH₄Cl and ZnCl₂ as electrolyte; it gives about 1.5 V and is used in torches, transistor radios, and clocks. The mercury cell uses a zinc-mercury amalgam anode and a paste of HgO and carbon as cathode, in a KOH-ZnO electrolyte paste; it gives a very steady voltage of about 1.35 V throughout its life (since the overall cell reaction does not involve ions whose concentration changes), making it suitable for watches and hearing aids.

Secondary batteries can be recharged by passing a current in the reverse direction, regenerating the original reactants (essentially running the discharge reaction backward as an electrolytic process). The lead storage battery, widely used in vehicles, has a lead anode and a grid of lead packed with lead dioxide (PbO₂) as cathode, both dipped in dilute sulphuric acid. On discharge:

Anode: Pb(s) + SO₄²⁻(aq) → PbSO₄(s) + 2e⁻

Cathode: PbO₂(s) + SO₄²⁻(aq) + 4H⁺(aq) + 2e⁻ → PbSO₄(s) + 2H₂O(l)

On recharging by an external source, these reactions are reversed, regenerating Pb, PbO₂, and H₂SO₄. The nickel-cadmium (Ni-Cd) cell is another rechargeable battery, more expensive but longer-lasting than the lead storage battery, useful where a lightweight rechargeable source is needed.

A fuel cell is a galvanic cell that generates electricity continuously as long as fuel and oxidant are supplied from outside, unlike batteries where reactants are stored inside. The best-developed example is the hydrogen-oxygen fuel cell, used in spacecraft, where H₂ and O₂ gases are bubbled through porous carbon electrodes containing catalysts (Pt or Pd) into concentrated aqueous KOH electrolyte:

Cathode (reduction): O₂(g) + 2H₂O(l) + 4e⁻ → 4OH⁻(aq)

Anode (oxidation): 2H₂(g) + 4OH⁻(aq) → 4H₂O(l) + 4e⁻

Overall: 2H₂(g) + O₂(g) → 2H₂O(l)

Fuel cells are highly efficient and pollution-free (the only product is water), and are actively being developed as clean alternative power sources for vehicles and stationary power generation.

Corrosion is the slow, spontaneous degradation of metals by the action of atmospheric gases, moisture, and other substances in their environment, converting the metal into an oxide, sulphide, carbonate, or similar compound. It is fundamentally an electrochemical phenomenon: it involves oxidation of the metal at one region (behaving as anode) and reduction of atmospheric oxygen at another region (behaving as cathode) of the same metal surface, with the moisture film on the metal acting as the electrolyte connecting these micro-electrochemical cells.

The most familiar example is the rusting of iron. At the anodic region of the iron surface, iron is oxidised:

Fe(s) → Fe²⁺(aq) + 2e⁻

The electrons released flow through the metal to a nearby cathodic region, where dissolved oxygen (in the presence of H⁺ ions, from atmospheric CO₂ dissolving in the moisture film) is reduced:

O₂(g) + 4H⁺(aq) + 4e⁻ → 2H₂O(l)

The Fe²⁺ formed is further oxidised by dissolved oxygen to Fe³⁺, which combines with water to form hydrated iron(III) oxide, Fe₂O₃·xH₂O, commonly known as rust. Corrosion causes enormous economic loss by damaging buildings, bridges, ships, and all objects made of iron, and can also weaken structures leading to safety hazards.

Corrosion can be minimised by several practical methods:

• Barrier protection: covering the metal surface with paint, oil, grease, or a coating so that moisture and oxygen cannot reach it.
• Galvanisation: coating iron with a layer of a more reactive metal like zinc; even if the coating is scratched, zinc (being more easily oxidised) corrodes preferentially, protecting the iron underneath.
• Cathodic (sacrificial) protection: connecting the iron structure to a more active metal (like magnesium or zinc) which acts as a sacrificial anode and is oxidised in preference to iron, commonly used to protect ships' hulls and underground pipelines.
• Alloying: mixing iron with other metals (e.g. chromium and nickel) to form stainless steel, which resists corrosion much better than pure iron.

Corrosion prevention is essential in engineering and construction, and understanding its electrochemical basis (formation of tiny anodic and cathodic regions on the same metal surface) is key to designing effective protective strategies.