Redox chemistry

The term "redox" is a portmanteau of reduction and oxidation. These chemical processes involve the transfer of electrons from one reactant to another. The participating substances are either reduced when they accept electrons or oxidized when they donate electrons. Since many chemical reactions involve electron transfer, redox chemistry is of fundamental importance. To simplify the description of redox processes, chemists devised the concept of oxidation numbers, which is explained in detail here.

In addition to classic chemical redox processes, this article also presents the most important biological redox systems. In the human body, these systems are responsible for transferring electrons and are essential for all metabolic functions.

Because redox processes are based on the movement of electrons, there is a direct connection to electricity. The area of overlap is called electrochemistry. By spatially separating the reduction and oxidation processes, a flow of current can be generated in so-called galvanic cells. The function of batteries is based on this principle. In a medical context, electrochemistry is particularly important for understanding nerve impulse conduction in the body (see also "Resting potentials and action potentials").

The formalism of oxidation numbers provides a clear framework to accurately determine which elements undergo oxidation and reduction, as well as the number of electrons transferred in a redox reaction.

• Definition: a theoretical charge assigned to an atom within a molecule or compound, calculated based on a set of systematic rules, which reflects the hypothetical electron distribution if the compound were composed of purely ionic bonds.
  • Positive oxidation number: loss of electrons
  • Negative oxidation number: gain of electrons
• Nomenclature: typically represented as signed Arabic numerals (e.g., +1, -2)
• Rules for determining the oxidation number (also known as oxidation state):
  • Monatomic particles
    • Pure elements: the oxidation number is always zero (e.g., Na, O₂, P₄)
    • Pure ions: the oxidation number equals the ion's charge (e.g., Fe³⁺ = +3; Cl^- = -1)
  • Polyatomic particles: units of two or more atoms that are covalently bonded together and that carry a positive or a negative charge (e.g., NH4⁺, OH^-)
    • The oxidation numbers of the individual atoms within the particle must sum up to its overall charge.
      • The sum must add up to zero for pure elements.
        • E.g., NaCl: Na = +1 and Cl = x → sum of oxidation numbers must equal 0: (+1) + x = 0 → x = -1 –> In NaCl, the oxidation number of chlorine (Cl) is -1.
      • The sum must equal the ion's charge for ions.
        • E.g., SO₄^2–: S = x and O = 4 × (–2) → sum of oxidation numbers must equal -2: x + (-8) = -2 –> x = +6 →The oxidation number of sulfur is +6.

The primary application of oxidation numbers is to identify which species are being oxidized (oxidation number increases) and which are being reduced (oxidation number decreases) in a reaction.

Certain elements consistently show the same oxidation numbers in their compounds. The most important oxidation numbers are listed below with examples:

The oxidation number of any uncombined element is zero (e.g., Zn, H₂), and the oxidation number of an element in a monoatomic ion is always the same as the charge (e.g., Fe³⁺ = +3 or Cl^- = -1)

Group 1 metals (Li, Na, K, etc.) are always +1. Group 2 metals (Be, Mg, Ca, etc.) are always +2. The oxidation state of hydrogen is usually +1 when bonded to nonmetals (e.g., H₂O, HCl) and -1 when bonded to metals (e.g., NaH).

The oxidation state of oxygen is usually -2. The main exceptions are peroxides (like H₂O₂), where it is -1, and when bonded to fluorine (as in OF₂), where it is +2.

Other halogens (Cl, Br, I) usually have an oxidation state of -1, except when bonded to oxygen or a more electronegative halogen.

The sum of the oxidation states in a neutral compound is 0, while in a polyatomic ion, it must equal the ion's charge.

Examples

1. H₂S
   • 2 H atoms = 2 x (+1) = +2
   • The overall charge of the compound = 0
   • The oxidation number of 1 S atom = –2
2. CaCO₃
   • 3 O atoms = 3 x (–2) = –6
   • 1 Ca atom = +2
   • The overall charge of the compound = 0
   • The oxidation number of 1 C atom = +4
3. MnO₄⁻
   • 4 O atoms = 4 × (–2) = –8
   • The overall charge of the ion = –1
   • The oxidation number of 1 Mn atom = +7

The key definitions for redox reactions are summarized below:

Reduction

• Definition: the gain of electrons
• Example: Cu²⁺ + 2e⁻ ⟶ Cu
• Oxidation number: decreases (becomes less positive or more negative) when a substance is reduced
• Reducing agent: a substance that donates electrons, thereby reducing another substance and being oxidized itself

Oxidation

• Definition: the loss of electrons
• Example: Fe ⟶ Fe³⁺ + 3e⁻
• Oxidation number: increases (becomes more positive or less negative) when a substance is oxidized
• Oxidizing agent: a substance that accepts electrons, thereby oxidizing another substance and being reduced itself

Overall reaction

• Definition: composed of two half-reactions: one reduction and one oxidation
• Oxidation numbers: In a balanced redox reaction, the total increase in oxidation numbers must equal the total decrease in oxidation numbers; in other words, the number of electrons lost must equal the number of electrons gained.
• Redox couple: the oxidized and reduced forms of a substance, e.g., Cu²⁺/Cu
• Balancing: Both charge and mass must be balanced.
• Example
  1. Reduction: Cu²⁺ + 2e⁻ ⟶ Cu
  2. Oxidation: Fe ⟶ Fe³⁺ + 3e⁻
  3. Balanced redox reaction: 3Cu²⁺ + 2Fe ⟶ 3Cu + 2Fe³⁺

A helpful mnemonic is "LEO the lion says GER," which stands for Loss of Electrons is Oxidation, and Gain of Electrons is Reduction.

Special cases

• Disproportionation reaction
  • Definition: a redox reaction in which a single element is simultaneously oxidized and reduced, starting from an intermediate oxidation state to form two new species
  • Example
    • Hydrogen peroxide decomposition: H₂O₂ → 2 H₂O + O₂ (Oxygen moves from the -1 state to both -2 and 0.)
      • Reactant: Oxygen in H₂O₂ is -1.
      • Product 1: Oxygen in H₂O is -2 (reduced).
      • Product 2: Oxygen in O₂ is 0 (oxidized).
• Comproportionation reaction (reverse idea)
  • Definition: a redox reaction in which two species of the same element in different oxidation states react to form a single product with an intermediate oxidation state
  • Example: SO₂(S = +4) + H₂S (S = −2) ⟶ 3S (S = 0) + 2H₂O

The enzyme superoxide dismutase catalyzes the disproportionation of superoxide radicals (O₂^-), protecting cells from oxidative stress. 2 O₂^- (O = -1/2) + 2 H⁺ → O₂ (O = 0) + H₂O₂ (O = -1).

In biology, several important redox couples are involved in electron transfer processes or, like the cystine/cysteine pair, have a structural role. Some key biochemical redox couples are presented here:

Quinone/hydroquinone redox couple

• Reduced form: hydroquinone
• Oxidized form: quinone
• Reaction: quinone + 2e⁻ + 2H⁺ ⇄ hydroquinone
  • Semiquinone: if only one electron is transferred, a semiquinone radical is formed, which has an unpaired electron
• Occurrence
  • Ubiquinone (Coenzyme Q₁₀)
    • High concentrations in the heart, lungs, liver, and kidneys
    • Because ubiquinone is lipophilic (fat-soluble), it moves freely within the phospholipid bilayer of the inner mitochondrial membrane
    • Acts as a mobile electron carrier between complex I/II and complex III of the mitochondrial respiratory chain
    • Reduced (active) form: ubiquinol is a potent antioxidant, neutralizing reactive oxygen species (ROS) or lipid peroxyl radicals, preventing damage to the mitochondrial membrane
  • Forms of vitamin K
    • Phylloquinone (K₁): found in green leafy vegetables; primarily involved in blood clotting
    • Menaquinone (K₂): produced by gut bacteria; closely linked to calcium metabolism and bone health

A one-electron transfer creates semiquinone, a radical intermediate, which is a potential source of reactive oxygen species (ROS).

FAD/FADH₂ redox couple

• Reduced form: FADH₂
• Oxidized form: FAD
• Reaction: FAD + 2e⁻ + 2H⁺ ⇄ FADH₂
• Occurrence
  • FADH₂ acts as a reducing agent in cellular metabolism, for example, in the citric acid cycle (succinate dehydrogenase).
  • Prosthetic group (permanently bound to enzymes)

FMN/FMNH₂ redox couple

• Reduced form: FMNH₂
• Oxidized form: FMN
• Reaction: FMN + 2e⁻ + 2H⁺ ⇄ FMNH₂
• Occurrence
  • Acts as a cofactor for various oxidoreductase enzymes
  • FMN is a component of complex I of the mitochondrial respiratory chain.
  • Prosthetic group (permanently bound to enzymes)

NAD⁺/NADH redox couple

• Reduced form: NADH
• Oxidized form: NAD⁺
• Reaction: NAD⁺ + H⁺ + 2e⁻ ⇄ NADH
• Occurrence
  • NADH is a major electron carrier and acts as a reducing agent in many metabolic pathways, such as glycolysis, TCA cycle, β-oxidation, and the mitochondrial respiratory chain.
  • It is a freely diffusing coenzyme.

NADP⁺/NADPH redox couple

• Reduced form: NADPH
• Oxidized form: NADP⁺
• Reaction: NADP⁺ + H⁺ + 2e⁻ ⇄ NADPH
• Occurrence
  • NADPH is a key reducing agent in anabolic pathways, such as fatty acid and cholesterol synthesis, and maintains the antioxidant pool (glutathione)
  • It is a freely diffusing coenzyme.

Cystine/cysteine redox couple

• Reduced form: cysteine (monomer with sulfhydryl group)
• Oxidized form: cystine (disulfide-linked dimer)
• Reaction: cystine + 2H⁺ + 2e⁻ ⇄ 2 cysteine
• Occurrence: the formation of disulfide bonds between cysteine residues (forming cystine) is crucial for stabilizing the three-dimensional structure of many proteins (tertiary structure)

The cystine/cysteine balance is determined by the redox potential of the cellular compartment (e.g., the cytosol is reducing, while the endoplasmic reticulum and extracellular space are oxidizing).

Electrochemical reactions

A redox reaction where the oxidizing or reducing agent is an electrode is called an electrochemical reaction. The simplest setup involves direct contact between two substances with different redox potentials, a phenomenon encountered in applications like corrosion protection.

• Local element: an electrochemical arrangement created by direct contact between two different conductive materials in the presence of an electrolyte (like water), resulting in a redox reaction
  • Example: an iron nail wrapped with copper wire and placed in water
• Corrosion protection: to prevent the corrosion of iron (rusting), it is often coated with another metal
  • Zinc layer: Zinc is more easily oxidized than iron. If the zinc layer is scratched, it is preferentially oxidized (corrodes), protecting the iron underneath. This method is called cathodic protection, and the zinc acts as a sacrificial anode.
  • Tin layer: Tin is less easily oxidized than iron but still provides a protective barrier . However, if this layer is scratched, it can accelerate the corrosion of the underlying iron because a local element is formed where iron is the more active metal.

Local electrochemical cells can form in the moist, electrolyte-rich environment of the mouth. When different metals (such as gold and amalgam) are placed close together, a small galvanic current may occur, sometimes causing a metallic taste.

The electrochemical cell

An electrochemical cell is a device that generates an electric current from spontaneous redox reactions (galvanic cell) or uses an electric current to drive non-spontaneous reactions (electrolytic cell). In an electrochemical cell, the reduction and oxidation half-reactions are spatially separated.

General structure

• Oxidation half-cell: the half-cell where oxidation occurs, containing the anode
• Reduction half-cell: the half-cell where reduction occurs, containing the cathode
• Experimental setup: typically consists of two beakers (half-cells), each with a different metal electrode submerged in an electrolyte solution
  • Electrode
    • The surface where the electrochemical reaction takes place
    • The electrodes are connected by an external wire to complete the electrical circuit.
      • Charging (electrolytic cell): the positive pole is the anode; the negative pole is the cathode
      • Discharging (galvanic cell): the positive pole is the cathode; the negative pole is the anode
  • Electrolyte: a salt solution containing anions and cations
    • Anions
      • Maintain charge neutrality during the reaction
      • Usually the same in both half-cells
      • Move between the half-cells via a salt bridge or a semipermeable membrane
      • Are not directly involved in the electrochemical reaction
    • Cations
      • Reactants or products of the electrochemical reaction
      • Usually different in the two half-cells
      • Remain and only move within their respective half-cells

For an electrochemical cell, regardless of the cell type, "An Ox" and a "Red Cat" (Anode = Oxidation; Reduction = Cathode) and "Fat Cat" (Electrons flow From Anode To Cathode) always apply.

Galvanic cells

• Galvanic cell: an electrochemical cell in which a reaction proceeds spontaneously, driven by the difference in the standard potentials of the reactants
  • Example reaction: Zn + Cu²⁺ ⟶ Zn²⁺ + Cu
    • The more reactive (less noble) zinc is oxidized
    • The less reactive (more noble) copper is reduced
  • Importance: used as a direct current source, e.g., in batteries
  • Cell notation: a shorthand for representing a galvanic cell, e.g., the zinc-copper Daniell cell
    • The two redox couples are written with a vertical line (|) to symbolize a phase boundary: e.g., Zn|Zn²⁺
    • The redox couple of the anode is written before the redox couple of the cathode
    • A double vertical line (||) symbolizes the salt bridge or membrane separating the two half-cells: anode || cathode
    • By convention, the ionic form of each redox couple is written closer to the salt bridge symbol: Zn|Zn²⁺ || Cu²⁺|Cu

In galvanic cells, a spontaneous reaction occurs, where electrons flow from the negative anode (oxidation) to the positive cathode (reduction). The driving force is the difference in standard electrode potentials of the reactants (E°).

Concentration cells

• Definition: a specific type of galvanic cell where both half-cells consist of the same electrode and the same electrolyte, but the electrolyte concentrations are different; a reaction proceeds spontaneously, driven by the concentration difference
  • Tendency: The cell operates to equalize the concentrations in the two half-cells.
  • Anode: the half-cell with the lower electrolyte concentration, where oxidation occurs to increase the cation concentration
  • Cathode: the half-cell with the higher electrolyte concentration, where reduction occurs to decrease the cation concentration
  • Electrons flow from the more dilute half-cell to the more concentrated half-cell.
  • Calculation: determined by the Nernst equation, where E° is 0 V (since the electrodes are the same)
  • Equilibrium: The cell potential becomes zero when the concentrations in both half-cells are equal.

In concentration cells, electrons flow from the lower-concentration anode (oxidation) to the higher-concentration cathode (reduction). The driving force is the concentration gradient.

Electrolytic cells

• Definition: an electrochemical cell that uses an external electrical energy source to drive a non-spontaneous redox reaction
  • Spontaneity: The reaction is non-spontaneous, meaning it has a positive Gibbs free energy change (ΔG > 0) and a negative electromotive force (E_cell < 0).
  • Energy input: requires a voltage source (e.g., a battery) with a voltage greater than the negative E_cell of the reaction to force the electrons to flow in the non-spontaneous direction
  • Anode: considered positive; it is attached to the positive terminal of the external power source
  • Cathode: considered negative; it is attached to the negative terminal of the external power source
  • Despite the change in polarity signs, oxidation still occurs at the anode and reduction still occurs at the cathode.
  • Anions: migrate towards the anode
  • Cations: migrate towards the cathode
  • First law: The mass of a substance produced at an electrode is directly proportional to the amount of charge (in coulombs) passed through the cell.
  • Second law: To produce one mole of a substance, a specific number of moles of electrons (Faradays) is required, which is determined by the ion's charge.
    • For example, producing one mole of Cu from Cu²⁺ requires two moles of electrons (2 Faradays of charge).

In electrolytic cells, a non-spontaneous reaction occurs, where electrons flow from the positive anode (oxidation) to the negative cathode (reduction). The driving force is an external voltage applied.

Batteries

• Definition: a self-contained electrochemical device with one or more galvanic cells that store chemical energy and convert it into electrical energy
  • Primary batteries: non-rechargeable; the electrochemical reaction is irreversible
  • Secondary batteries: rechargeable; the electrochemical reaction can be reversed by applying an external electric current
  • Lead-acid battery
    • Anode: lead (Pb)
    • Cathode: lead dioxide (PbO₂)
    • Electrolyte: sulfuric acid (H₂SO₄)
    • Characteristics: low energy density; commonly used in cars
  • Nickel-cadmium (Ni-Cd) battery
    • Anode: cadmium (Cd)
    • Cathode: nickel(III) oxide-hydroxide (NiO(OH))
    • Electrolyte: potassium hydroxide (KOH)
    • Characteristics: higher energy density than lead-acid batteries; exhibit a memory effect if not fully discharged before recharging
  • Lithium-ion battery
    • Anode: graphite with intercalated lithium ions
    • Cathode: typically a metal oxide, e.g., lithium cobalt oxide (LiCoO₂)
    • Characteristics: high energy density and no memory effect; widely used in portable electronics

The electrochemical series

An electrochemical cell contains two different electrodes, and the voltage between them depends on their respective redox couples. The electrochemical series was developed to predict the voltage of any electrochemical cell. It lists the standard electrode potentials of individual half-reactions relative to a standard electrode.

• Standard electrode potential (E°): the voltage generated by a half-reaction when all solutes are 1 M and all gases are at 1 atm, measured relative to the standard hydrogen electrode
  • Interpretation
    • The more positive E°, the greater the tendency to be reduced (“more noble”)
    • The more negative E°, the easier to oxidize (“less noble”)
• Electrochemical series: a list of redox couples sorted by their standard electrode potential
  • Reference value: Standard electrode potentials are measured against the standard hydrogen electrode (SHE), whose potential is defined as exactly 0 V.
  • Hydrogen electrode
    • Electrode reaction: 2H⁺ + 2e⁻ ⟶ H₂ or in aqueous solution: 2H₃O⁺ + 2e⁻ ⇄ H₂ + 2H₂O
    • Standard conditions for the SHE: T = 298 K (25 °C), p = 1 atm, c(H⁺) = 1 mol/L

The more positive the standard electrode potential, the greater the tendency for the substance to be reduced (i.e., the "more noble" it is). When a less noble metal is added to a solution containing ions of a more noble metal, the more noble metal will be deposited as the less noble one dissolves.

The Nernst equation

The voltage that arises between the two half-cells of an electrochemical cell is called the electromotive force (EMF), or cell potential (E_cell). It indicates whether a reaction will proceed spontaneously. The Nernst equation is used to calculate this potential under non-standard conditions (i.e., when concentrations are not 1 M).

• Nernst equation: describes the dependence of a half-cell potential on the concentrations of the oxidized and reduced species
  • Formula: E = E° - (RT/nF) log Q; under standard temperature (298 K): E = E° - (0.0592 V/n) log Q
  • Unit: volts (V)
  • E = electrode potential, E° = standard electrode potential, R = ideal gas constant (8.314 J/K⋅mol), T = absolute temperature in kelvins, F = Faraday constant (96485 C/mol), n = the number of moles of electrons transferred, Q = reaction quotient [concentration of products]/[concentration of reactants]
    • If Q = 1, the system is at standard conditions, and E_cell = E°_cell.
    • If Q < 1, the reaction has an excess of reactants. The reaction will be more spontaneous than at standard conditions, so E_cell > E°_cell.
    • If Q > 1, the reaction has an excess of products. The reaction will be less spontaneous, so E_cell < E°_cell.
• Electromotive force (cell potential): E_cell = E_cathode - E_anode
  • Unit: volts (V)
  • Interpreting the cell potential
    • E_cell > 0: the reaction proceeds spontaneously in the forward direction
    • E_cell < 0: the reaction is non-spontaneous and requires an external energy source to proceed

Example calculation

Calculate the cell potential (electromotive force) for the reaction 2Na + Cu²⁺ ⟶ 2Na⁺ + Cu for a concentration of c(Na⁺) = 0.1 mol/L and c(Cu²⁺) = 0.5 mol/L at temperature (T) = 298 K.

• Find: electromotive force E_cell
• Given: reaction equation, concentrations c(Na⁺) = 0.1 M,c(Cu²⁺) = 0.5 M, standard reduction potentials E^o_Na= −2.71 V, E^o_Cu= +0.34 V
  • Identify half-reactions
    • Oxidation (anode): 2Na ⟶ 2Na⁺ + 2e⁻
    • Reduction (cathode): Cu²⁺ + 2e⁻ ⟶ Cu
    • The number of electrons lost (2) equals the number of electrons gained (2). Therefore, n = 2 for this reaction.
  • Determine the standard cell potential: E^o_cell = E^o_cathode - E^o_anode = 0.34 V - (-2.71 V) = 3.05 V
  • Determine the reaction quotient (Q):
    • Q = [products]/[reactants] = [Na⁺]²/[Cu²⁺]
    • Q = (0.1)²/(0.5) = 0.01/0.5 = 0.02
  • Apply the Nernst equation: E_cell = E°_cell− 0.0592/n × logQ
    • E°_cell = 3.05 V; n = 2 (this is the number of moles of electrons transferred in the balanced reaction); Q = 0.02
    • E_cell= 3.05 V - (0.0592 / 2) × log(0.02) = 3.05 V - (0.03) × (-1.7) = 3.05 V + 0.051 = 3.10 V
    • E_cell > E°_cell: the reaction will be more spontaneous than at standard conditions

The Nernst equation can be simplified to E_cell = E°_cell - (0.06/n) × log(Q) at standard temperature (298 K).

The cell potential (electromotive force) for an electrochemical cell is given by: E_cell = E_cathode − E_anode.

Electrolysis

• Electrolysis: an electrochemical process that uses an external electric current to drive a non-spontaneous reaction
  • Electromotive force: E_cell < 0 for the spontaneous reaction in the reverse direction
  • Example reaction: Fe²⁺ + Cu ⟶ Fe + Cu²⁺
  • Importance: the electrolysis of water produces hydrogen and oxygen, which can be used as energy carriers and converted back into electrical energy in a fuel cell
    • Example: 2H₂O ⟶ 2H₂ + O₂
      • Cathode reaction: 2H₂O + 2e⁻ ⟶ H₂ + 2OH⁻
      • Anode reaction: 2H₂O ⟶ O₂ + 4H⁺ + 4e⁻

Electrochemistry in medicine

For healthcare professionals, electrochemical principles are crucial for understanding impulse transmission in nerve and muscle cells. Details on these processes can be found in the articles on "Resting potentials and action potentials", "Cardiac physiology", and "Muscle tissue". Additionally, electrochemical gradients are essential for substance transport at the cellular level, as described in the article on "The cell".