Chapter 3 — Electrochemistry

Overview: Electrochemistry studies the relationship between electrical energy and chemical changes. It deals with redox (oxidation–reduction) reactions that involve transfer of electrons and the devices that convert chemical energy to electrical energy (galvanic cells) or use electrical energy to drive chemical change (electrolytic cells).

Key terms and definitions

• Oxidation: Loss of electrons (increase in oxidation state). Example: Fe -> Fe2+ + 2e−.
• Reduction: Gain of electrons (decrease in oxidation state). Example: Cu2+ + 2e− -> Cu.
• Oxidizing agent: Species that causes oxidation of another (itself is reduced).
• Reducing agent: Species that causes reduction of another (itself is oxidized).
• Half-cell: An electrode in contact with an ionic solution where a half-reaction (oxidation or reduction) occurs.
• Electrode: A conductor (metal or inert like Pt) where electrons enter or leave the electrolyte.
• Anode: Electrode where oxidation occurs (electron source). In a galvanic cell the anode is negative; in an electrolytic cell it is positive (sign depends on device).
• Cathode: Electrode where reduction occurs (electron sink). In a galvanic cell the cathode is positive; in an electrolytic cell it is negative.
• Salt bridge: Porous medium or tube containing electrolyte that completes the circuit and maintains charge balance by ion flow without mixing the half-cell solutions.
• Cell notation (cell diagram): Short-hand: Anode | Anode solution (conc.) || Cathode solution (conc.) | Cathode. Example: Zn(s) | Zn2+(aq) || Cu2+(aq) | Cu(s).
• Electromotive force (EMF) / Cell potential (Ecell): The potential difference between two electrodes of a cell under specified conditions (no current). It drives electron flow through the external circuit.
• Standard electrode potential (E°): Potential of a half-cell measured against the standard hydrogen electrode (SHE, defined as 0.00 V) at 1 bar (or 1 atm) and 25 °C, with 1 M concentrations for solutes.
• Redox couple: A pair consisting of oxidized and reduced forms (e.g., Cu2+/Cu).
• Faraday (F): Charge carried by 1 mole of electrons ≈ 96485 C mol−1.
• Electrolyte: Substance that produces ions in solution and conducts electricity (strong vs weak electrolytes).
• Conductivity (κ): Measure of a solution's ability to conduct electricity (S m−1 or S cm−1). Resistivity ρ = 1/κ.
• Molar conductivity (Λm): Conductivity of an electrolyte solution normalized to concentration (Λm = κ × 1000/c when c in mol L−1).

Direction of electron and conventional current flow: Electrons flow from anode to cathode through the external circuit. Conventional current is defined as the direction positive charges would move (from cathode to anode externally).

EMF and spontaneity: A galvanic cell (spontaneous redox) has positive Ecell and negative ΔG. Basic relations link E to thermodynamics and equilibrium (see formulas).

Practical devices: Common galvanic cells: Daniell cell (Zn/Cu), dry cell (Leclanché), lead–acid battery; electrolytic processes: electroplating, electrolysis of water, extraction of metals (Al via Hall–Héroult).

Basic definitions
Resistance (R) is the opposition offered by a material to the flow of electric current. Conductance (G) is the reciprocal of resistance and measures how easily current flows. For an electrolytic solution, ions carry current, so conductance depends on ion concentration, charge and mobility.

Simple relations
For a uniform conductor of length l and cross‑sectional area A (including an electrolytic cell):

• R = ρ l / A, where ρ is resistivity.
• G = 1 / R = κ A / l, where κ (kappa) is conductivity (κ = 1/ρ).
• Cell constant (L) = l / A. Hence κ = G × (cell constant).

Conductivity of electrolytic solutions
Conductivity (κ) of an ionic solution depends on the concentration of ions, their charge and mobility, and on temperature. Molar conductivity (Λm) is the conductivity of a solution containing one mole of electrolyte placed between electrodes 1 cm apart and large enough area so that the solution between them contains one mole of electrolyte.

Relation between molar conductivity, concentration and conductivity
Λm = (κ × 1000) / c, where κ is in S cm⁻¹ and c is mol L⁻¹. Units of Λm: S cm² mol⁻¹.

Limiting molar conductivity and Kohlrausch law
At infinite dilution (ionic interactions negligible) Λm → Λm° (limiting molar conductivity). For strong electrolytes (dilute region) Kohlrausch's law gives an empirical dependence on concentration:

Λm = Λm° − K √c (where K is an empirical constant and c is mol L⁻¹).

Factors affecting conductance

• Concentration: κ increases with concentration, but Λm decreases with concentration for strong electrolytes (because ion‑ion interactions reduce mobility); for weak electrolytes Λm increases sharply on dilution because degree of ionisation increases.
• Ion charge and mobility: higher charge and higher ionic mobility → higher conductivity.
• Temperature: conductivity increases with temperature (viscosity decreases, mobility increases).
• Cell geometry: embodied in the cell constant L = l/A used to convert measured conductance to κ.

Practical measurements
A conductivity cell measures conductance G between two electrodes; using the cell constant, κ = G × L is obtained, and then Λm from concentration. Conductivity meters are widely used to assess water purity, salinity and process control.

Connection to Ohm's law
For an electrolytic cell obeying Ohm's law, V = IR. With conductance G, I = GV.

Introduction
Conductivity of an electrolyte solution depends on how many ions are present (concentration), how freely they move (mobility) and how strongly they interact. Two useful quantities are specific conductance (conductivity) k and molar conductivity Λm.

Definitions
k (kappa) = specific conductance (S m^-1) of the solution.
Λm (molar conductivity) = k / c, where c is molar concentration (mol m^-3 or mol L^-1 with consistent units). More commonly for class 12: Λm = k × 1000 / C (if C in mol L^-1) or simply Λm = k/c when units are chosen consistently.

Variation with concentration

1. Strong electrolytes
Strong electrolytes (e.g., NaCl, KCl, HCl) are almost fully ionized. As solution is diluted, molar conductivity Λm increases slowly and approaches a limiting value Λm0 (at infinite dilution). The increase is due to reduced interionic attraction and greater ionic mobility. For many strong electrolytes Kohlrausch empirical law applies at low concentrations:

Λm = Λm0 - K sqrt(c)
Here K is an empirical constant and c is concentration. Thus Λm vs sqrt(c) is approximately a straight line extrapolating to Λm0 at c = 0.

Because specific conductance k = Λm · c, the graph of k vs c for a strong electrolyte typically rises at low concentrations (because more ions are added) but, after a certain point, further concentration increases reduce mobility significantly and k may reach a maximum and then decrease (or level off) at high concentrations.

2. Weak electrolytes
Weak electrolytes (e.g., acetic acid CH3COOH) are only partially ionized and their degree of ionization α depends strongly on concentration. For a weak electrolyte with dissociation constant Ka, approximately α ≈ sqrt(Ka/c) at low concentration (from Ka = α^2 c / (1-α) ≈ α^2 c). Since Λm = α Λm0, we get Λm ≈ Λm0 sqrt(Ka/c) which means Λm increases sharply on dilution (as c decreases). This is why Λm vs c for a weak electrolyte rises steeply as concentration → 0. Specific conductance k = Λm · c ≈ Λm0 sqrt(Ka c) so k increases with sqrt(c) for weak electrolytes (no maximum like strong electrolytes).

Physical reasons
- Dilution reduces interionic attractions and electrophoretic effects, increasing ionic mobility.
- For weak electrolytes dilution increases the degree of ionization, producing many more charge carriers per mole.
- At high concentrations, crowding and ion-pairing reduce mobility, lowering conductivity relative to ideal.

Variation with temperature
Conductivity generally increases with temperature. Reasons:

• Viscosity of the solvent (water) decreases with rising temperature, increasing ion mobility (u approximately inversely proportional to viscosity).
• Thermal energy increases so ions move faster.
• For weak electrolytes, increased temperature usually increases degree of ionization (if dissociation is endothermic), further increasing conductivity.

As a rule of thumb for aqueous solutions, conductivity increases by a few percent per degree Celsius (exact change depends on ion type and concentration). Temperature dependence can be approximated by an Arrhenius-type relation or linear coefficient in limited ranges.

Practical implications
- Conductometric titrations rely on predictable changes of k and Λm with concentration.
- Water quality and salinity measurements use conductivity as a proxy for ionic content; temperature compensation is necessary.
- Battery and electroplating performance depends on electrolyte conductivity and its temperature behaviour.

Summary points
- Λm increases on dilution for both strong and weak electrolytes; increase is small for strong electrolytes and large for weak ones.
- For strong electrolytes Λm follows Kohlrausch law: Λm = Λm0 - K sqrt(c).
- Specific conductance k = Λm · c; for strong electrolytes k may show a maximum with concentration, for weak electrolytes k increases roughly as sqrt(c).
- Conductivity increases with temperature due to higher ionic mobility and lower viscosity; temperature corrections are often applied.

Statement: At infinite dilution (limiting molar conductivity), the molar conductivity of an electrolyte is the sum of the independent contributions of its constituent ions. Each ion makes a definite contribution to the total molar conductivity that is independent of the nature of the counter‑ion.

Mathematical form: For an electrolyte that produces ν+ cations and ν− anions per formula unit, the limiting molar conductivity (Λm°) is

Λm° = ν+ λ+° + ν− λ−°

Here λi° (ionic limiting molar conductivity) is the contribution of ion i at infinite dilution. The concentration dependence for molar conductivity (for many strong electrolytes) near infinite dilution is often written as

Λm = Λm° − A √c

where c is concentration (in mol L−1) and A is a constant that depends on temperature, solvent and ion types. The linear relation of Λm vs √c allows extrapolation to √c = 0 to obtain Λm°.

Physical basis (brief): At infinite dilution electrostatic interactions and ion‑ion friction are negligible, so each ion migrates through the solvent almost independently under an electric field. Therefore its contribution to molar conductivity becomes a constant characteristic of that ion (and the temperature/solvent).

Related formulas and connections:

• Molar conductivity from specific conductance: Λm = κ × 1000 / c (when κ is in S cm−1 and c in mol L−1, Λm in S cm2 mol−1).
• Ionic mobility relation: λi° = F |zi| μi where F is Faraday constant (≈ 96500 C mol−1), zi is ionic charge and μi is ionic mobility (in appropriate units).
• Transference (transport) numbers at infinite dilution: t+ = ν+ λ+° / Λm° , t− = ν− λ−° / Λm°.

Why useful? Kohlrausch's law allows determination of limiting molar conductivities for weak electrolytes (by extrapolation) and helps to split the total Λm° into ionic contributions. With ionic λ° values one can calculate transference numbers, ionic mobilities and use conductivity data to determine degree of dissociation or dissociation constants of weak electrolytes.

Overview
Ionic mobility and transport (transference) number are concepts that describe how ions move in an electrolyte under an electric field and how much of the electric current is carried by each ionic species.

Ionic mobility (μ)
Ionic mobility is the drift velocity of an ion per unit electric field. If an ion moves with velocity v under an electric field E, its mobility μ is defined as:

μ = v / E

Units: commonly m² V⁻¹ s⁻¹ (or cm² V⁻¹ s⁻¹). Mobility depends on the ion's charge, size (hydrated radius), solvent viscosity and temperature. Smaller ions and lower viscosity give higher mobility. H+ and OH− show very high mobilities in water because of the Grotthuss proton-hopping mechanism.

Microscopic picture (Stokes approximation)
For a spherical ion of charge q = z·e and hydrodynamic radius r moving through a viscous medium of viscosity η, a simple picture (Stokes law) gives:

μ = q / (6π η r) = z·e / (6π η r)

This shows μ ∝ 1/η and μ ∝ 1/r (approximate, classical view).

Relation to ionic (molar) conductance
The contribution of a single ionic species to molar conductance (often written λi or Λi) is proportional to its mobility:

λi = |zi| · F · μi

where F is the Faraday constant (C mol⁻¹). The total molar conductance Λm of an electrolyte (at infinite dilution) is the sum of the ionic contributions: Λm = λ+ + λ−.

Transport number (transference number) ti
The transport number ti of ion i is the fraction of the total current carried by that ion:

ti = Ii / I_total

For a multicomponent electrolyte, expressing currents in terms of mobility gives (for ion i of valence zi and concentration ci):

Ii = zi·F·μi·ci·E·A,

so

ti = (zi·μi·ci) / Σj (zj·μj·cj)

For a simple binary 1:1 electrolyte with equal concentrations and unit charges (z = 1):

t+ = μ+ / (μ+ + μ−), t− = μ− / (μ+ + μ−), and t+ + t− = 1.

Important points

• Transport numbers are dimensionless and depend on ion mobilities and concentrations; they change with concentration and temperature.
• Transport numbers determine concentration polarization during current flow (important in batteries, electroplating, and fuel cells). If one ion carries most of the current (large t), concentration changes near electrodes are less for the other ion.
• Experimentally measured transport numbers are often given at infinite dilution (limiting values) because interactions at higher concentration complicate behavior.

Experimental determination (brief)
Two classical methods:

• Hittorf (concentration-change) method: pass a known charge and measure concentration changes in compartments near electrodes—changes are used to calculate the fraction of charge carried by each ion.
• Moving-boundary method: track the movement of a sharp boundary between two solutions under a current. For a uni-univalent electrolyte, the cation transport number is proportional to the distance the boundary moves.

Both methods measure how much each ionic species migrates under the applied current and thus determine ti.

Applications / Relevance
Transport numbers are crucial in: electroplating (deposition efficiency), batteries and fuel cells (ionic conduction and polarization), electrophoresis (separation based on mobility), desalination and ion-exchange membranes (selectivity), and conductivity measurements.

Definition
Transport number (transference number) of an ion is the fraction of the total electric current carried by that ion. For a binary electrolyte with cation (+) and anion (−):
t+ = I+ / I (current carried by cation divided by total current), and t+ + t− = 1.

Physical basis
In an electric field different ions move with different velocities (mobilities). Transport numbers depend on ionic mobilities and concentration. For general valencies:

t+ = (z+ u+) / (z+ u+ + z− u−),

where u+ and u− are ionic mobilities and z+ , z− are charges (absolute values).

Main experimental methods

1. Hittorf (electrochemical) method
Principle: Passage of current causes ions to migrate; local concentrations near electrodes change. By measuring concentration changes in compartments adjacent to electrodes after passing a known charge Q, the amount of charge carried by each ion is deduced.

• Setup: A cell divided into three or more compartments (anode side, middle, cathode side) filled with same electrolyte concentration. Metal electrodes at ends. A known current is passed for a known time (charge Q = I·t).
• Procedure: After current passage, withdraw solution from compartments and determine concentration changes (e.g., by titration).
• Calculation (binary electrolyte): Let Δn+(cat) be change in moles of cation in cathode compartment (final − initial), and Δn−(an) be change in moles of anion in anode compartment (initial − final). Then

t+ = Δn+ (cathode) / (Q / F) and t− = Δn− (anode) / (Q / F),

where F = Faraday constant (96485 C mol−1). (Either expression may be used depending on which compartment concentration change is measured.)

Notes/limitations: Accurate concentration measurements are needed; convection and diffusion must be minimized; works best for moderately concentrated solutions and non-reactive ions.

2. Moving-boundary method
Principle: A sharp boundary between an electrolyte (whose transport number is to be measured) and another inert electrolyte (sharing a common ion) moves when current is passed. The boundary displacement is due to different velocities of the ions.

• Setup: A long, uniform tube (capillary) is filled with solution A (e.g., test electrolyte). Solution B (marker solution) containing a common ion makes a visible sharp boundary. Electrodes at tube ends, current applied along tube axis.
• Procedure: Apply constant current I and measure displacement l of boundary in time t. Determine electrolyte concentration c and cross-sectional area A of the tube.
• Formula (for a 1:1 electrolyte):

t+ = (c · A · l · F) / (I · t)

where c is concentration in mol m−3 (use mol L−1 converted to mol m−3), A is cross-sectional area (m2), l is boundary displacement (m) in time t (s), and F is Faraday constant. For ions with other charges, include the ionic charge (z) in the numerator appropriately.

Notes/limitations: Requires a sharp, non-diffusing boundary and no side reactions; suitable for dilute solutions and ions that give a visible boundary. Convection must be avoided.

Relation to ionic mobility
For a binary electrolyte at given conditions (dilute, no ion association):

t+ = (z+ u+) / (z+ u+ + z− u−) , t− = 1 − t+

This provides a link between transport numbers and measured ionic mobilities (obtained from conductivity measurements).

Practical importance / Where it matters
Transport numbers affect concentration polarization, electrode polarization and efficiency in electroplating, batteries (Li+ transport number influences rate capability and dendrite formation), fuel cells, chlor-alkali electrolysis, electrodialysis and ion-exchange membranes.

Typical experimental precautions

• Minimize convection and diffusion (use temperature control and careful cell design).
• Avoid side reactions at electrodes (use inert electrodes or appropriate electrode reactions).
• Use accurate concentration or boundary position measurements and account for solution volume changes.

Overview
Arrhenius theory of electrolytic dissociation (1887) explains electrical conduction in aqueous solutions by asserting that certain substances (electrolytes) dissociate into ions when dissolved. Ions are charge carriers; their presence makes the solution conductive. Electrolytes are classified as strong (nearly complete dissociation) or weak (partial dissociation).

Key concepts of Arrhenius theory

• Electrolyte: a substance that on dissolution produces ions. Example: NaCl → Na+ + Cl−.
• Degree (extent) of dissociation (α): fraction of original molecules that dissociate into ions.
• Strong electrolytes: α ≈ 1 (e.g., HCl, NaCl). Weak electrolytes: α << 1 and increases on dilution (e.g., CH3COOH, NH3).
• Molar conductance (Λm): conductance of 1 mol of electrolyte between electrodes placed 1 cm apart. It depends on concentration and approaches a limiting value Λm° at infinite dilution.

Conductance relations used with Arrhenius idea

• Measured conductivity (κ) relates to molar conductance: Λm = κ × 1000 / c (where κ in S cm−1, c in mol L−1, so Λm in S cm2 mol−1).
• For weak electrolytes the fraction ionized equals the ratio of observed to limiting molar conductance: α = Λm / Λm°.

Ostwald's dilution law (applies to weak electrolytes)
For a weak electrolyte HA dissociating as HA ⇌ H+ + A−, with initial concentration c and dissociation α, equilibrium concentrations are [H+] = cα, [A−] = cα, [HA] = c(1 − α). The dissociation constant Ka is:

Ka = [H+][A−] / [HA] = (cα)(cα) / (c(1 − α)) = (α^2 c) / (1 − α)

Thus, Ostwald's dilution law gives a relation between α, concentration c and Ka. For very weak electrolytes (α << 1), rise to the approximation:

α ≈ sqrt(Ka / c)

This shows that for weak electrolytes the degree of dissociation increases on dilution (c decreases → α increases).

Experimental link via conductance
Because α = Λm / Λm°, and Λm can be measured at different dilutions, Ostwald's law can be tested experimentally by plotting the appropriate functions (see graphs below). For strong electrolytes molar conductance varies weakly with dilution and follows Kohlrausch's law: Λm = Λm° − A√c (A is an empirical constant), whereas weak electrolytes show a strong increase of Λm with dilution approaching Λm°.

Limitations

• Arrhenius theory is qualitative; it does not account for ionic interactions (ionic atmosphere) and fails for concentrated solutions and fused salts. Debye–Hückel and Onsager theories provide improvements.
• Ostwald's law is valid only for sufficiently dilute solutions of weak electrolytes (where activity ≈ concentration and ideal behaviour holds).

Practical/physical significance
These ideas are foundational for understanding electrolytic behavior in batteries, biological fluids, electroplating, conductivity measurements for water quality, acid–base chemistry and titrations.

Electrode potential (E) is the electrical potential developed at the interface between a metal (or conducting electrode) and an ionic solution, when an oxidation–reduction (redox) equilibrium exists at that interface. Each half-reaction written as a reduction (Ox + ne– → Red) has a characteristic reduction potential that measures the tendency of the species to gain electrons.

Half-cell and reference: A half-cell consists of an electrode in contact with a solution containing its ions. A single electrode potential cannot be measured in isolation — it must be measured relative to a reference electrode. The standard hydrogen electrode (SHE: H2(g, 1 atm) | H+ (1 M) ) is chosen as the reference and assigned E° = 0.00 V.

Standard electrode potential (E°) is the potential of a half-cell measured under standard conditions: 298 K (25 °C), 1 atm gas pressure, and 1 M concentrations (or activities = 1). E° is tabulated for reduction half-reactions. A more positive E° means a greater tendency to be reduced; a more negative E° means a greater tendency to be oxidized (when compared under standard conditions).

Cell emf from standard potentials: For a galvanic cell made from two half-cells (written as reductions), the standard cell emf is
E°cell = E°(cathode) – E°(anode)
(i.e., E° of the reduction at the cathode minus E° of the reduction at the anode). If E°cell > 0 under standard conditions, the cell reaction is spontaneous.

Nernst equation (non-standard conditions): Electrode potentials depend on concentration (activity), pressure and temperature. For a half-reaction Ox + ne– ⇌ Red,
E = E° – (RT/nF) ln Q
At 298 K this is commonly written as
E = E° – (0.05916/n) log10 Q
where Q is the reaction quotient of the half-reaction (ratio of activities of products to reactants), n is electrons transferred, R is gas constant, T temperature in K and F is Faraday constant.

Thermodynamic relations:
ΔG° = –nFE°cell (Gibbs free energy change) — negative ΔG° means spontaneous.
Also, K (equilibrium constant for the overall redox) and E° are related at 298 K by
log10 K = (nE°cell)/0.05916 (so a positive E°cell gives K > 1).

Interpretation and use: E° values form a reduction-potential table (more positive = stronger oxidant as reduction). By comparing E° values, you can predict direction of redox reactions, cell voltages, corrosion tendencies, and feasibility of electrochemical processes (electroplating, batteries).

Important practical points:

• Standard conditions: 1 M for solutes, 1 atm for gases, pure liquids/solids, 25 °C.
• Activity (not raw concentration) is the correct thermodynamic quantity; for dilute solutions activities ≈ concentrations.
• Single electrode potentials are measured against a reference (SHE or standard reference electrodes such as Ag/AgCl, calomel electrode).

Worked example (Daniell cell):
Half-reactions (reductions):
Cu2+ + 2e– → Cu E° = +0.34 V
Zn2+ + 2e– → Zn E° = –0.76 V
E°cell = E°(cathode) – E°(anode) = (+0.34) – (−0.76) = +1.10 V
So the Daniell cell has a standard emf of 1.10 V and is spontaneous under standard conditions.

What is an electrochemical cell?
An electrochemical (galvanic/voltaic) cell converts chemical energy into electrical energy by spontaneous redox reactions. It consists of two half‑cells: one where oxidation occurs (anode) and one where reduction occurs (cathode). The two half‑cells are connected electrically (external wire) and ionically (salt bridge or porous separator).

EMF (electromotive force) of a cell
The emf (Ecell) is the potential difference between the two electrodes when no current flows (open circuit). It represents the maximum reversible work per unit charge the cell can deliver. For a spontaneous galvanic cell Ecell > 0.

Electrode (reduction) potentials
Each half‑reaction has a standard electrode potential E° (reduction potential) measured under standard conditions (1 M, 1 bar, 298 K) relative to the standard hydrogen electrode (SHE, E° = 0.00 V). For a cell, the standard cell potential is:

• E°cell = E°cathode − E°anode (use reduction potentials for both electrodes)

Cell notation (cell diagram)
Cell notation is a compact way to represent the cell components and the direction of electron flow. Rules and conventions:

• Left side = anode (oxidation), right side = cathode (reduction).
• Single vertical line | = phase boundary (e.g., metal | aqueous ion).
• Double vertical line || = salt bridge or junction between half‑cells.
• Different species in the same phase are separated by commas.
• Include concentrations in parentheses when nonstandard or to show composition.
• If a half‑cell has no solid conductor (e.g., gas electrodes), an inert electrode (Pt) is shown.

Example: Zn(s) | Zn^{2+}(aq, 1.0 M) || Cu^{2+}(aq, 1.0 M) | Cu(s) is the Daniell cell (Zn is anode, Cu is cathode).

Nernst equation (effect of concentrations & temperature)
For nonstandard conditions, the cell potential is given by the Nernst equation:

Ecell = E°cell − (RT / nF) ln Q

At 298 K (25 °C) this is often written as:

Ecell = E°cell − (0.05916 / n) log10 Q

where R = 8.314 J mol−1 K−1, T = temperature (K), F = 96485 C mol−1, n = number of electrons transferred, and Q = reaction quotient.

Thermodynamic relations

• ΔG = −nFEcell (Gibbs free energy change related to cell potential)
• At standard conditions: ΔG° = −nFE°cell and E°cell = (RT / nF) ln K

Measurement and emf vs operating voltage
Emf is measured under open‑circuit (no current). When the cell supplies current, internal resistance causes the terminal voltage V = Ecell − i rint (i = current, rint = internal resistance). A potentiometer measures true emf without drawing current; a voltmeter reads terminal potential under load.

Concentration cells and special cases
A concentration cell has identical electrodes but different ion concentrations. E°cell = 0, but Ecell ≠ 0 if concentrations differ; Ecell is given by the Nernst equation with Q depending on concentration ratio. Example: Ag(s) | Ag+ (c1) || Ag+ (c2) | Ag(s), E = (0.05916 / n) log (c2 / c1) at 298 K.

Factors affecting emf

• Concentrations (via Q and the Nernst equation)
• Temperature (RT/nF term)
• Pressure for gas‑involving electrodes
• Internal resistance (affects terminal voltage under load, not open‑circuit emf)

Summary / Practical points
- Write half‑reactions as reductions to use the E° table correctly; the more positive E° is the cathode (reduction) in a spontaneous cell.
- E°cell is the difference of reduction potentials: E°(right) − E°(left).
- Positive Ecell means spontaneous reaction; negative ΔG.

What it is: The Nernst equation gives the electrode (or cell) potential under non‑standard conditions (i.e., when reactant/product concentrations or pressures are not 1 M or 1 atm). It links thermodynamics (Gibbs free energy) with electrochemical potential and shows how concentration changes alter the EMF.

Derivation (concise):

1. Gibbs free energy change for a redox cell: ΔG = -nFE, where n = number of electrons transferred and F = Faraday constant.
2. Relation to reacting mixture: ΔG = ΔG° + RT ln Q, where Q is the reaction quotient and ΔG° = -nFE°.
3. Combine: -nFE = -nFE° + RT ln Q → E = E° - (RT/nF) ln Q. This is the Nernst equation in natural logarithm form.

Common usable form at 25 °C (298 K): E = E° - (0.05916/n) log₁₀ Q. (0.05916 V = (2.303 RT)/F at 298 K)

Key points / interpretation:

• If Q < 1 (more reactants), log Q < 0 so E > E°. If Q > 1 (more products), E < E°.
• At equilibrium Q = K and E = 0, giving ΔG° = -RT ln K and E° = (RT/nF) ln K.
• For concentration cells (same electrodes, different ion concentrations), E depends only on the concentration ratio: E = (0.05916/n) log([higher]/[lower]) at 25 °C.
• Temperature matters: use E = E° - (RT/nF) ln Q when T ≠ 298 K.

Single electrode (half‑cell) potentials: The potential of a single electrode reaction depends on the activity (approx. concentration) of ionic species via the Nernst equation. Example (hydrogen electrode): for 2H⁺ + 2e^- ⇌ H₂(g), with p(H₂) = 1 atm, E = E° - (0.05916) pH (so E = -0.05916·pH at 25 °C).

Biological form: For ion X^z+, the Nernst (membrane) potential is often written as E = (RT/zF) ln([X]out/[X]in) — used to compute equilibrium potential across cell membranes.

Applications / significance: pH meters (glass electrodes), concentration cells, calculation of real battery voltages under load or with depleted reactants, electroplating control, and physiological membrane potentials.

Overview
In electrochemistry the thermodynamic driving force (Gibbs free energy change ΔG), the cell potential (E) and the equilibrium constant (K) are directly related. These relations let you tell whether a redox reaction is spontaneous, how far it proceeds, and how cell voltage depends on concentrations and temperature.

Key quantities and constants
R = 8.314 J mol⁻¹ K⁻¹ (gas constant), F = 96485 C mol⁻¹ (Faraday constant), T = temperature in K, n = number of electrons transferred.

1. Relation between ΔG and cell potential E
For a redox reaction occurring in an electrochemical cell, electrical work is related to free energy change by:
ΔG = −n F E
This gives the actual (nonstandard) Gibbs free energy change ΔG corresponding to the observed cell potential E.

2. Standard quantities
Under standard conditions (standard states), the relation becomes:
ΔG° = −n F E°

3. Relation with reaction quotient Q (Nernst equation)
Thermodynamics gives:
ΔG = ΔG° + R T ln Q
Combine with ΔG = −n F E and ΔG° = −n F E° to eliminate ΔG terms and get the Nernst equation:
E = E° − (R T / n F) ln Q
In base-10 logarithm form (commonly used at 298 K):
E = E° − (0.05916 / n) log₁₀ Q (at T = 298 K)

4. At equilibrium (Q = K)
At equilibrium ΔG = 0 and Q = K, hence from ΔG = ΔG° + R T ln K:
0 = ΔG° + R T ln K → ΔG° = −R T ln K
Using ΔG° = −n F E° gives:
−n F E° = −R T ln K → E° = (R T / n F) ln K
Or in base-10 at 298 K:
E° = (0.05916 / n) log₁₀ K

5. Useful rearrangements
K = e^(n F E° / R T) or log₁₀ K = (n E°) / 0.05916 (at 298 K)
Sign implications:
• E° > 0 → ΔG° < 0 → K > 1 → reaction is product-favored (spontaneous in the forward direction under standard conditions).
• E° < 0 → ΔG° > 0 → K < 1 → reactant-favored.

Physical meaning
E measures the electrical potential difference that the redox reaction can produce. ΔG measures the maximum non-expansion work obtainable. K measures the extent of reaction at equilibrium. All three describe the same thermodynamic balance in different units.

Practical notes
• The Nernst equation shows cell voltage falls as Q approaches K; at equilibrium E = 0.
• Large positive E° corresponds to extremely large K (reaction essentially complete) and very negative ΔG° (strongly spontaneous).
• Temperature affects these relations through the RT term; E° can change with temperature if ΔG° is temperature dependent.

Overview
Measurement of emf and potentiometry are methods to determine the electrical potential (emf) of electrochemical cells and the potentials of electrodes/solutions without drawing current. The potentiometer is a null-method device used to measure emf accurately by comparison with a known reference. Potentiometry is the technique of measuring electrode potentials (e.g., pH electrode, ion-selective electrodes) to determine concentrations or titration end-points.

1. Potentiometer — Principle
A potentiometer works on the null-deflection principle: when no current flows through the cell under test, the potential difference between the test cell and a portion of a known uniform wire becomes zero at a certain length. The balancing length is directly proportional to the emf of the test cell, so emfs are obtained by comparison with a standard cell.

2. Basic construction

• Driver (primary) cell or stabilized DC source that produces a current through a long uniform resistance wire AB.
• Uniform wire AB (standard length, good mechanical support) providing a potential gradient along its length.
• Galvanometer and jockey (sliding contact) to detect the null point (zero current).
• Standard reference cell (known emf) and the test cell connected in turn to the galvanometer circuit.
• Rheostat to adjust the current through the wire so the potential gradient is appropriate.

3. Procedure (measuring unknown emf)

1. Calibrate the potential gradient: connect a standard cell (E_std) and find balance length l_std such that E_std = k · l_std, where k is potential per unit length.
2. Replace with the unknown cell and find balance length l_x such that E_x = k · l_x.
3. Therefore E_x = E_std · (l_x/l_std).

4. Determination of internal resistance of a cell using a potentiometer
Find the open-circuit emf E (balance length l_o) and then connect a known external resistor R and measure the terminal potential V (balance length l). The current I = V/R. Internal resistance r is obtained from r = (E − V)/I. This method is accurate because measurement of E and V are done under null conditions (no current through detector).

5. Advantages of potentiometer

• High accuracy because measurement is done by null deflection (no current drawn from test cell).
• Independent of internal resistance of measuring instrument.

6. Potentiometry (electrode potential measurements)
Potentiometry measures the potential difference between an indicator (working) electrode and a reference electrode without passing current. It is widely used for pH measurement (glass electrode), ion-selective electrodes (F⁻, Na⁺), and potentiometric titrations (redox and precipitation titrations).

7. Potentiometric titration
In a potentiometric titration an electrode potential is measured as titrant is added. The equivalence point is located by the large potential change (inflection) in the E vs volume curve. Example: Fe²⁺ titrated against Ce⁴⁺ — the potential of the Fe³⁺/Fe²⁺ system changes sharply at equivalence.

8. Theoretical basis — Nernst equation
The potential of an electrode under non-standard conditions is given by the Nernst equation. At temperature T (K):
E = E° − (RT/nF) ln Q
At 298 K in base-10 logarithm: E = E° − (0.05916/n) log Q, where Q is the reaction quotient, n is number of electrons transferred, R is gas constant and F is Faraday constant.

9. Comparison with voltmeter
A voltmeter draws a small current and gives a direct reading. Potentiometer (null method) is more accurate for small emfs and for finding internal resistance because no current is drawn from the test cell during measurement.

10. Practical tips & precautions

• Use a stable standard cell for calibration (e.g., Weston cell or any known standard).
• Keep the driver current steady and the wire clean and at constant temperature to maintain uniform potential gradient.
• Always find a clear null point (zero deflection) by careful jockey placement and small adjustments.

Electrolysis — basic idea: Electrolysis is a chemical change produced by passing electric current through an ionic conductor (molten salt or aqueous solution). An external power source forces non-spontaneous redox reactions: cations move to the cathode where they are reduced, anions move to the anode where they are oxidized.

Electrolytic cell components: electrodes (cathode = negative, anode = positive), electrolyte (ionic conductor), and an external DC source. Example cells: molten NaCl (produces Na and Cl₂), aqueous CuSO₄ with Cu electrodes (electrorefining), water electrolysis (H₂ and O₂).

Electrode reactions — examples:

• Molten NaCl: Cathode: Na⁺ + e⁻ → Na (reduction). Anode: 2Cl⁻ → Cl₂ + 2e⁻ (oxidation).
• Aqueous CuSO₄ with inert anode: Cathode: Cu²⁺ + 2e⁻ → Cu. Anode (if inert): 2H₂O → O₂ + 4H⁺ + 4e⁻ (or Cl⁻ oxidation if present).
• Water electrolysis (acidic): Cathode: 2H⁺ + 2e⁻ → H₂. Anode: 2H₂O → O₂ + 4H⁺ + 4e⁻.

Selective discharge and overpotential: In aqueous solutions, whether water or ions are discharged depends on standard potentials and concentrations — the species with less positive (or more negative) standard oxidation potential is oxidized. Overpotential (extra voltage required) and kinetics can change which species is actually evolved (e.g., O₂ vs Cl₂).

Faraday's laws of electrolysis:

• First law: The mass (m) of a substance deposited or liberated at an electrode is directly proportional to the total electric charge (Q) passed through the electrolyte. Mathematically: m ∝ Q.
• Second law: For the same quantity of electric charge, the masses of different substances deposited are proportional to their chemical equivalent masses (equivalent weight = M/n, where M is molar mass and n is number of electrons exchanged per formula unit).

Key mathematical relations:

• Charge passed: Q = I × t (I in amperes, t in seconds, Q in coulombs).
• Faraday constant: F ≈ 96485 C·mol⁻¹ (charge of 1 mole of electrons).
• Mass deposited: m = Z × Q, where Z is electrochemical equivalent (mass per unit charge).
• Electrochemical equivalent: Z = M / (n F), where M = molar mass, n = electrons transferred per ion.
• Combined formula: m = (M I t) / (n F). This is the most used working formula.

Derivation (brief): Passing charge Q corresponds to Q/F moles of electrons. If n electrons reduce one mole of species, moles of substance deposited = (Q/F) / n = Q/(nF). Multiplying by molar mass M gives mass m = (M Q)/(n F). Using Q = I t gives m = (M I t)/(n F).

Practical considerations: Real electrolysis may deviate due to side reactions, electrode material dissolution, concentration polarization, cell resistance, and overpotential. Current efficiency (percentage of current used for desired reaction) must be considered: m_observed = (current efficiency) × m_theoretical.

Applications: electroplating, electrorefining (Cu), extraction of metals (Al by Hall–Héroult), chlor-alkali industry (Cl₂, H₂, NaOH), manufacture of chemicals and hydrogen production.

Typical numeric constants: Faraday constant F = 96485 C·mol⁻¹; elementary charge e = 1.602×10⁻¹⁹ C; Avogadro number N_A = 6.022×10²³ mol⁻¹ (F = e × N_A).

What is electrolysis?
Electrolysis is the chemical decomposition of an electrolyte (molten salt or aqueous solution) by passing an electric current through it. The external source forces non-spontaneous redox reactions: oxidation occurs at the anode and reduction at the cathode.

Basic components of an electrolytic cell

• Electrolyte (molten salt or aqueous solution) that conducts by ions.
• Two electrodes: cathode (negative, reduction) and anode (positive, oxidation).
• External DC source providing electrons and driving the reaction.

Electrode processes

• At the cathode: cations gain electrons → reduction. Example: M^{n+} + n e− → M (metal deposition).
• At the anode: anions or solvent lose electrons → oxidation. Example: 2Cl− → Cl2(g) + 2 e− or 2H2O → O2(g) + 4H+ + 4 e−.

Types of electrolysis

• Molten-electrolysis (no solvent): only constituent ions are present (e.g., molten NaCl gives Na(s) and Cl2(g)).
• Aqueous-electrolysis: solvent (water) also participates; competition between reduction/oxidation of ions and water leads to selective discharge.

Selective (preferential) discharge in aqueous solutions
Which species is discharged depends on standard electrode potentials, concentration, and overpotentials. Typical order at the cathode: more positive reduction potential gets reduced first (e.g., if metal ion reduction potential is more positive than H+/H2, metal plates out). At the anode, halide oxidation (Cl−, Br−) often occurs preferentially over water oxidation to O2 because of lower overpotential.

Faraday's laws (quantitative electrolysis)

• 1st law: Mass of substance deposited/oxidized at an electrode ∝ total charge passed (Q).
• 2nd law: Masses of different substances deposited by same charge are proportional to their chemical equivalent weights.

Key practical considerations

• Decomposition potential: minimum external voltage required to drive the non-spontaneous electrolysis — includes thermodynamic cell potential plus overpotentials and IR drops.
• Overpotential (η): extra potential required due to kinetic barriers (e.g., hydrogen evolution on many electrodes).
• Current efficiency (coulombic efficiency): fraction of passed charge that produces the desired reaction (losses due to side reactions reduce it).

Common industrial and laboratory applications

• Electrorefining and electrolytic purification of metals (e.g., copper): impure metal acts as anode, pure metal plates at cathode; impurities settle as anode mud.
• Electroplating (jewellery, corrosion protection): deposition of a thin metal layer on an object (cathode) from a suitable metal-ion bath.
• Extraction of reactive metals: Hall–Héroult process for aluminium (electrolysis of Al2O3 dissolved in molten cryolite); electrolysis of molten NaCl for Na and Cl2.
• Chlor–alkali process: electrolysis of brine to produce Cl2, H2 and NaOH (industrial manufacture of caustic soda and chlorine).
• Water electrolysis for hydrogen production (H2 fuel) and oxygen.
• Anodization (surface oxide layers for corrosion resistance and dyeing aluminum).
• Electrosynthesis (organic reactions like Kolbe electrolysis), electrocoagulation for water treatment.

Practical examples (brief reaction notes)

• Molten NaCl: 2Cl− → Cl2(g) (anode); Na+ + e− → Na(s) (cathode).
• Chlor–alkali (membrane cell, brine): 2Cl− → Cl2(g) (anode); 2H2O + 2e− → H2(g) + 2OH− (cathode) → net: 2NaCl + 2H2O → Cl2 + H2 + 2NaOH.
• Hall–Héroult (Al): Al2O3 dissolved in cryolite: at cathode Al3+ + 3e− → Al(l); at carbon anode C + O2− → CO/CO2 + e− (consumes carbon anodes).
• Electrorefining of Cu: impure Cu (anode) → Cu2+ + 2e−; Cu2+ + 2e− → Cu (cathode). Impurities (Ag, Au) collect as anode mud.

Overview
In electrochemical cells, the electrode potential under current flow deviates from the equilibrium (open-circuit) potential. This deviation and the extra driving potential required to sustain a current arise from kinetic and transport limitations. Closely related concepts are side reactions, overpotential and polarization.

Side reactions
Side (or parasitic) reactions are unwanted electrochemical processes that compete with the intended electrode reaction because their standard or actual potentials are close to that of the desired reaction. They consume charge, lower current efficiency, change product distribution and may damage electrodes.

• Examples: hydrogen evolution during metal plating, oxygen evolution during anodic oxidation of chloride solutions, electrolyte decomposition in batteries.
• Why they occur: similar equilibrium potentials, local concentration changes, surface catalytic properties.

Polarization
Polarization is the shift of an electrode potential from its equilibrium value when current flows. It is often defined as the change in potential ΔE = E_equilibrium − E_actual (magnitude indicates how far the electrode is polarized). Polarization has three main types:

• Activation (kinetic) polarization — caused by slow electron-transfer kinetics (reaction activation energy).
• Concentration (diffusion) polarization — caused by concentration gradients near the electrode (mass-transport limitation).
• Ohmic polarization (IR drop) — potential drop due to resistance of electrolyte, electrodes and contacts (voltage lost = iR).

Overpotential (η)
Overpotential is the extra potential (beyond the equilibrium potential) that must be applied to drive an electrode reaction at a given rate (current). It quantifies how much the electrode potential is displaced under current: η = E_applied − E_equilibrium. Sign convention: a positive η usually denotes anodic overpotential; a negative η denotes cathodic overpotential. Overpotential comprises contributions from activation, concentration and ohmic effects:

η_total = η_activation + η_concentration + η_ohmic

Electrode kinetics (basic relations)

• Nernst equation (equilibrium potential): E = E° − (RT/nF) ln Q, where R is gas constant, T temperature, n electrons, F Faraday constant, Q reaction quotient.
• Butler–Volmer equation (current–overpotential relationship): i = i₀[exp((α n F η)/(R T)) − exp(−((1−α) n F η)/(R T))], where i is current density, i₀ exchange current density, α transfer coefficient.
• For large |η| the Tafel approximation applies (single exponential dominates): η = (R T / α n F) ln(i / i₀) for anodic branch (or η = −(R T /(1−α) n F) ln(i / i₀) for cathodic).
• Concentration overpotential (approximate): η_conc = (R T / n F) ln(c_bulk / c_surface).
• Ohmic drop: η_ohmic = i · R (R = resistance of cell path).

Consequences and control
Side reactions reduce current efficiency and may change product composition (e.g., H₂ evolution during copper plating makes deposits porous). Large overpotentials increase energy consumption (electrolyzers, batteries) and can lead to electrode degradation. Control methods include choosing suitable electrode materials (catalysts), adjusting concentration and temperature, adding inhibitors, using higher exchange current density catalysts, minimizing cell resistance, and controlling current density.

What is corrosion? Corrosion is the spontaneous deterioration of a metal due to chemical or electrochemical reactions with its environment, usually converting the metal to an oxide, hydroxide, sulfide or other compound. For most engineering metals (e.g. iron) the common form is electrochemical corrosion (rusting).

Types of corrosion

• Dry (chemical) corrosion: Direct reaction with gases (e.g. hot metallic sulfide formation in SO2 or H2S atmospheres).
• Wet (electrochemical) corrosion: Occurs in presence of an electrolyte; local anodic and cathodic sites form on the metal surface and electrons are transferred through the metal while ions move through the electrolyte.

Mechanism of electrochemical corrosion (example: iron rusting)

• Anodic reaction (metal oxidation): Fe → Fe²⁺ + 2e⁻
• Cathodic reaction (oxygen reduction in neutral/basic medium): O₂ + 2H₂O + 4e⁻ → 4OH⁻
• Overall (simplified) in neutral/aqueous air: 4Fe + 3O₂ + 6H₂O → 4Fe(OH)₃ → Fe₂O₃·xH₂O (hydrated iron(III) oxide, “rust”)
• Local differences in composition, stress, or oxygen concentration create anodic and cathodic sites; the corrosion rate is controlled by the anodic reaction, cathodic reaction, and ionic/electronic transport.

Factors affecting corrosion

• Nature of metal and its electrode potential (noble vs active)
• Presence of electrolytes (salt accelerates corrosion)
• pH and dissolved oxygen concentration
• Temperature and mechanical stress
• Contact with dissimilar metals (galvanic corrosion)

Prevention methods and how they work

• Barrier methods (coatings): Paints, varnishes, polymer coatings and greases physically separate metal from environment.
• Metallic coatings (galvanizing, tinning, chrome): A more active metal (e.g. Zn on iron) can act sacrificially (galvanizing) — it corrodes preferentially protecting the base metal. Electroplating provides barrier and aesthetic protection.
• Alloying and passivation: Alloying elements like chromium (in stainless steel) form a thin, adherent oxide (Cr₂O₃) that passivates the surface and prevents further attack.
• Cathodic protection: (a) Sacrificial anode: attach a more active metal (Zn, Mg, Al) which oxidizes instead of the protected metal. (b) Impressed current: an external DC source forces the structure to cathodic potentials to stop oxidation.
• Corrosion inhibitors: Chemical species added in small amounts to the environment (anodic, cathodic or mixed inhibitors) that reduce corrosion rates (e.g. chromates, phosphates; many are toxic so alternatives are used).
• Design and environment control: Avoiding crevices, drainage, controlling humidity, reducing chloride exposure and using suitable materials for the environment.
• Maintenance: Regular inspection, touch-up painting, replacing sacrificial anodes and cleaning to remove corrosive deposits.

Practical notes

• Galvanized iron: zinc coating provides both barrier and sacrificial protection; when scratched, zinc oxidizes preferentially.
• Aluminium and copper form protective oxide/patina layers that slow further corrosion (passive behavior).
• Bronze/copper statues develop green patina (basic copper carbonate) which often protects underlying metal.

Understanding electrochemical principles (electrode potentials, kinetics and transport) helps choose the right preventive strategy for each application.

Overview: A galvanic (voltaic) cell converts chemical energy into electrical energy by spontaneous redox reactions. A battery is one or more electrochemical cells connected to provide a required voltage/current. A fuel cell is an electrochemical device that continuously converts the chemical energy of an externally supplied fuel and oxidant into electricity.

Basic components of a cell:

• Electrodes: Anode (site of oxidation) and cathode (site of reduction).
• Electrolyte: Provides ionic conduction between electrodes.
• Salt bridge or porous membrane: Completes circuit by allowing ionic flow and maintaining electrical neutrality.
• External circuit: Allows electron flow from anode to cathode producing current.

Example: Daniell cell (classical galvanic cell)

• Cell notation: Zn | Zn₂₊(aq) || Cu²⁺(aq) | Cu
• Half-reactions:
  • Anode (oxidation): Zn(s) → Zn²⁺(aq) + 2e^-
  • Cathode (reduction): Cu²⁺(aq) + 2e^- → Cu(s)
• Standard emf: E°cell = E°(Cu²⁺/Cu) − E°(Zn²⁺/Zn) = 0.34 − (−0.76) = 1.10 V

Cell emf and thermodynamics:

• Under standard conditions the cell emf is E°cell. For non-standard conditions, use the Nernst equation:

E = E° − (RT/nF) ln Q (general form)

At 25 °C: E = E° − (0.05916/n) log Q

• Here, n = number of electrons exchanged, Q = reaction quotient, R = 8.314 J mol⁻¹ K⁻¹, T in K, F = 96485 C mol⁻¹.
• Relation to Gibbs free energy: ΔG = −nFE. Thus a positive E implies ΔG < 0 (spontaneous).
• Equilibrium constant: E° = (RT/nF) ln K ⇒ K = e^nFE°/RT (or in base 10: log K = nE°/0.05916 at 25 °C).

Internal resistance and terminal voltage:

Real cells have internal resistance r. The terminal voltage under load V = Ecell − I r. This causes voltage drop and heating during discharge.

Types of cells/batteries:

• Primary cells (non-rechargeable): e.g., alkaline cell, Leclanché dry cell. Used until reaction is exhausted.
• Secondary cells (rechargeable): e.g., lead-acid, Ni–Cd, Ni–MH, Li-ion. Chemical reactions are (mostly) reversible on charging.
• Fuel cells: Continuous supply of fuel and oxidant. Example: H₂–O₂ fuel cell (PEM fuel cell).

Important battery examples and reactions:

• Lead–acid battery (automobile): overall discharge reaction: Pb(s) + PbO₂(s) + 2H₂SO₄(aq) → 2PbSO₄(s) + 2H₂O(l). Per cell E ≈ 2.05 V.
• Nickel–cadmium (Ni–Cd): reversible redox between Cd and NiO(OH)/Ni(OH)₂. Used for rechargeable portable applications (memory effect historically).
• Lithium-ion (Li-ion): intercalation/deintercalation reactions (e.g., LiCoO₂/graphite). High energy density, widely used in electronics and EVs.

Fuel cells (H₂–O₂ example):

• Anode: H₂(g) → 2H⁺ + 2e^-
• Cathode: 1/2 O₂(g) + 2H⁺ + 2e^- → H₂O(l)
• Overall: H₂(g) + 1/2 O₂(g) → H₂O(l), E° = 1.23 V (standard)
• Types: PEM (proton exchange membrane), alkaline, phosphoric acid, solid oxide. Advantages: high efficiency, low emissions (if H₂ is clean).

Practical aspects:

• Battery capacity is often quoted in mAh or Ah; energy = capacity × average voltage.
• Discharge profile: many batteries maintain near-constant voltage for much of discharge (plateau) and then fall rapidly near end of capacity.
• Factors affecting performance: temperature, rate of discharge (C-rate), internal resistance, state of charge, electrode surface area, electrolyte concentration.

Safety and environmental notes: Lead–acid and Ni–Cd contain toxic metals; proper recycling is essential. Li-ion cells require protection circuitry to avoid overcharge/overdischarge and thermal runaway.

Summary: Cells and batteries exploit redox chemistry to produce electrical energy; the Nernst equation quantifies how emf depends on concentration and temperature. Fuel cells differ by continuously supplying reactants and can offer high efficiencies for power generation.

Definition. The electrochemical series (also called the activity series of metals in electrochemical form) is a list of standard electrode (reduction) potentials, E° (in volts), of half-cells written as reduction reactions under standard conditions (1 M, 1 bar, 25 °C). It orders species according to their tendency to gain electrons (be reduced).

How it is constructed. Each entry is a half–cell reduction potential, for example: Cu2+ + 2e− → Cu (E° = +0.34 V), Zn2+ + 2e− → Zn (E° = −0.76 V). The list is arranged from the most positive E° (strongest oxidizing agents / easiest to reduce) at the top to the most negative E° (strongest reducing agents / easiest to oxidize) at the bottom.

Key principles and uses.

• For a galvanic (spontaneous) cell made from two half cells, E°_cell = E°_cathode − E°_anode. If E°_cell > 0, the reaction is spontaneous under standard conditions.
• Species with more positive E° values are better oxidizing agents (they get reduced); species with more negative E° values are better reducing agents (they get oxidized).
• From the series one can predict whether a metal will displace another from solution: a metal higher (more negative as a reducer / lower E° as reduction) will displace ions of a metal lower in the series (more positive E° as reduction).
• Thermodynamic relations: ΔG° = −nFE° (gives standard free energy change), and log K = (nE°)/0.05916 at 298 K (base-10). These connect potentials to equilibrium and spontaneity.

Nernst equation (non-standard conditions). E = E° − (RT/nF) ln Q. At 298 K this is often written as E = E° − (0.05916/n) log₁₀ Q. This shows how cell potential depends on concentrations (reaction quotient Q).

Examples of application (short list). Predicting spontaneity of redox reactions, selecting anode/cathode materials for batteries and electroplating, choosing sacrificial anodes for corrosion protection, deciding whether a metal can be extracted by reduction or needs electrolysis.

Important notes. (1) Values are standard (1 M, 1 bar, 298 K). Under other conditions use the Nernst equation. (2) E° values are given for reduction half-reactions; take care to reverse sign when writing the oxidation as an anode if needed. (3) The series applies to aqueous redox chemistry—very negative potentials may correspond to reactions that are limited by kinetics.