Chapter 8 Notes: Reduction and Oxidation (Inorganic Chemistry I)

Introduction

Oxidation and reduction definitions
- Oxidation: gaining oxygen, losing hydrogen, or losing one or more electrons.
- Reduction: losing oxygen, gaining hydrogen, or gaining one or more electrons.
- Redox stands for reduction-oxidation.
Redox in electrochemistry
- In an electrolytic cell, an external electrical current drives a redox reaction.
- In a galvanic (voltaic) cell, a spontaneous redox reaction generates an electrical current.
Oxidation state changes
- Oxidation process is accompanied by an increase in oxidation state of the element.
- Reduction process is accompanied by a decrease in oxidation state of the element.
Example context: formation of metal oxides from elements (illustrative redox changes)
- Example balance checks (conceptual):
- For Fe-containing oxides, oxygen is often −2 per O atom; Fe oxidation state can be deduced from overall charge balance.
- Example reasoning sketches (shown in lecture):
  - Fe₂O₃: O in oxide is −2, total from O is −6, to balance to 0 total charge, Fe must sum to +6, so each Fe is +3.
  - Mn in MnO₂: O is −2, total from O is −4, Mn must contribute +4 overall; Mn in MnO₂ has oxidation state +4.
Balancing redox reactions – quick guidelines
- Oxidation state conventions (common rules used in lecture):
- ON(O) = −2 for oxygen in most oxides.
- ON(H) = +1 for hydrogen in most acids and water.
- Balancing strategy (example sketches from lecture):
- Identify oxidation states of all elements in participating species.
- Balance electrons transferred between oxidation and reduction half-reactions.
Redox in acidic solution: common copper example
- Cu metal dissolving in nitric acid can form copper(II) species, water, and nitrogen oxides (NO₂ or related species) depending on conditions.
- Redox representation (illustrative):
- Oxidation: Cu → Cu²⁺ + 2 e⁻
- Reduction: NO₃⁻ + 4 H⁺ + 3 e⁻ → NO₂ + 2 H₂O (illustrative half-reaction; actual balanced form depends on species in solution)
More redox pairing examples (conceptual summaries)
- MnO₂ + Cl⁻ + H⁺ in acid can yield Mn²⁺, Cl₂, and H₂O (MnO₂ is reduced from +4 to +2; Cl⁻ is oxidized to Cl₂).
- Stepwise balancing involves converting MnO₂ to Mn²⁺ via reduction, while Cl⁻ is oxidized to Cl₂ via oxidation.
- Additional example themes shown in lecture include balancing MnO₂ with oxidants such as Cl⁻ and H⁺, then including spectator ions (e.g., sulfate) to reach full ionic/electrolyte balance.
General approach for complex reaction sets
- When multiple species participate, ignore spectator ions that do not undergo redox changes.
- Balance only the redox-active species and then add spectator ions to achieve full chemical equation in the chosen medium.

Standard Reduction Potentials

Definition
- Standard reduction potential E° is defined for a half-reaction under standard conditions.
Standard cell potential
- E^\u0305{ ext{cell}} = E^\u0305{ ext{cathode}} - E^\u0305_{ ext{anode}}
Interpretation of potentials
- Higher E°red values indicate species are stronger oxidizers at standard state.
- Lower (more negative) E°red values indicate species are weaker oxidizers (or stronger reducers when considered as oxidants).
- Example interpretations from lecture:
- E°red(Li⁺/Li) = −3.04 V; E°ox(Li/Li⁺) = +3.04 V. Lithium metal is a very strong reductant.
- E°red(F₂/F⁻) = +2.89 V; fluorine is a very strong oxidant.
- Rough qualitative ranges (from lecture visuals):
- E° around +3.0 V to +1.5 V indicates strong spontaneity in the forward (reduction) direction.
- E° around 0 V to +0.5 V indicates modest spontaneity.
- E° from −1.5 V to −3.0 V indicates strong spontaneity in the reverse (oxidation) direction for the corresponding redox couple.
Combining half-reactions and potentials (example)
- When Cl₂ gas is bubbled into a NaI solution, Cl₂ is reduced and I⁻ is oxidized:
- Reduction: ext{Cl}2(g) + 2 e^- ightarrow 2 ext{Cl}^-(aq) with E^\u0305{ ext{Cathode}} = 1.36 ext{ V}
- Oxidation: 2 ext{I}^-(aq)
  ightarrow ext{I}2(aq) + 2 e^- with E^\u0305{ ext{Anode}} = 0.53 ext{ V}
- Cell potential: E^\u0305{ ext{cell}} = E^\u0305{ ext{Cathode}} - E^5_{ ext{Anode}} = 1.36 - 0.53 = 0.82 ext{ V}
- Spontaneity is indicated by a positive E°cell.
Faraday relations (stoichiometry of electrochemistry)
- Faraday's laws connect electric charge and chemical change.
- Mass of product formed is proportional to:
- The electric current i (in Amps),
- The time t (in seconds) that the current flows,
- The molar mass of the product,
- The number of electrons transferred per ion in the redox step.
- Quantitative constants:
- Charge per mole of electrons: F = 96485 ext{ C mol}^{-1}
  - Equivalent to: a mole of electrons carries 96,485 C of charge.
- Example: silver deposition/reduction
- To reduce Ag⁺ to Ag(s): one mole of electrons yields one mole of Ag(s).
- Cost (in electrons) scales with the required oxidation state change; e.g., reducing Al³⁺ to Al requires three electrons per Al atom.
- Practical relation (q = i t) and Faraday constant underpin electroplating and metal production processes.

The Effect of Complex Formation or Precipitation on M²⁺/M Reduction Potentials

Complexation effect
- The formation of complex ions with ligands (or precipitation of sparingly soluble salts) can shift the observed reduction potentials of metal couples (M²⁺/M).
- Complexation can stabilize certain oxidation states, altering the ease of reduction/oxidation relative to the free ion couple.
Practical implication
- Shifts in E° can influence which species act as oxidants or reductants under given solution conditions.

Disproportionation Reactions

Definition
- A disproportionation reaction is thermodynamically favorable when a single species is simultaneously oxidized and reduced to form two different species.
- Example framework: 2 M⁺(aq) ⇌ M²⁺(aq) + M(s) (illustrative for metal ions and metal)
Thermodynamics via reduction potentials
- Equilibrium constants for disproportionation can be calculated from reduction potentials (Latimer/Frost-Ebsworth framework).
Stabilization by precipitation
- Species unstable with respect to disproportionation can be stabilized by precipitation of a sparingly soluble salt (e.g., CuCl) that removes product from solution.
Illustrative example from lecture
- Cu⁺(aq) disproportionates to Cu²⁺(aq) and Cu(s) under certain conditions, with precipitation or complexation affecting the equilibrium.

Potential Diagrams

Purpose
- Provide useful oxidation-reduction information by graphing relationships between oxidation states and redox properties.
Three main diagram types mentioned
- Latimer Diagrams
- Frost-Ebsworth Diagrams
- Pourbaix Diagrams

Latimer Diagrams (Potential Diagrams)

Concept
- Latimer diagrams connect standard reduction potentials between various oxidation states of an element.
- The more positive the standard reduction potential, the more readily the left-hand species is reduced to the right-hand species.
Interpretation
- A highly positive potential indicates the left species is a strong oxidizing agent.
- A negative or less positive potential indicates the right-hand species is a good reducing agent.
Example (Mn species in acidic and alkaline solutions)
- The diagram shows standard reduction potentials linking Mn species across oxidation states in different media.
Utility
- Half-reactions can be read and written directly from Latimer diagrams.

Frost-Ebsworth Diagrams (Oxidation State Diagrams)

Concept
- Frost or oxidation-state diagrams plot relative free energy versus oxidation state for a given element.
- They can be constructed from Latimer diagrams.
Plotting values
- Y-axis values are obtained by multiplying the number of electrons transferred during a given oxidation-state change by the standard reduction potential for that change.
What the diagram reveals
- Thermodynamic stability: the lower on the diagram, the more stable (thermodynamically) the species from an redox perspective.
- Example: Mn(II) is among the most thermodynamically stable Mn species on the diagram.
- Disproportionation tendencies:
- A convex portion indicates a tendency to disproportionate (e.g., MnO₄²⁻ and Mn(III) tend to disproportionate).
- A concave region typically does not disproportionate (e.g., MnO₂ does not disproportionate).
- Relative oxidizing/reducing power:
- Species located on the upper-left are strong oxidizing agents (e.g., MnO₄⁻).
- Species on the upper-right are reducing agents (e.g., Mn metal).
- Example data (illustrative): Mn₂⁺/Mn(s) couple: E° ≈ −1.19 V (gradient calculation from the line slope, representing the two-electron transfer context).

Pourbaix Diagrams (Potential-DpH Diagrams)

Concept
- Pourbaix diagrams depict the thermodynamically stable form of an element as a function of potential and pH.
- They are a type of predominance diagram, showing the dominant species under given environmental conditions.
- Useful in geochemical, environmental, and corrosion contexts; kinetics are not included.
Reading a Pourbaix Diagram
- Vertical lines separate species related by acid-base equilibria (not redox).
- Non-vertical lines separate species related by redox equilibria (not involving H⁺/OH⁻).
- Horizontal lines separate species in redox equilibria not involving H⁺/OH⁻.
- Diagonal boundaries separate redox equilibria that involve H⁺ or OH⁻.
- Dashed boundaries enclose the practical water stability region against oxidation/reduction.
Information you can extract
- Any point on the diagram gives the thermodynamically most stable form of the element at that potential and pH.
- Top regions indicate strong oxidizing conditions (e.g., permanganate is a strong oxidizer over all pH ranges; boundaries are high at the top).
- Bottom regions indicate reducing conditions (e.g., Mn metal is a strong reducing agent, especially in basic conditions).
- Disproportionation tendencies become apparent when the predominance region for an oxidation state disappears with pH changes (e.g., MnO₄²⁻ tends to disproportionate under certain pH conditions).
- A species spanning from top to bottom at a given pH has no oxidizing or reducing power at that pH.

The Relationship Between Standard Reduction Potentials and Other Quantities

General idea
- One can represent a dissolution process in steps using half-reactions and standard potentials to analyze thermodynamics.
Example general dissolution framework
- For a salt MX(s) dissolving to M⁺(aq) and X⁻(aq):
- ext{MX(s)}
  ightleftharpoons ext{M}^+(aq) + ext{X}^-(aq)
- The standard Gibbs energy of dissolution relates to standard formation energies via:
- ext{Δ}G^{ ext{sol}} = ext{Δ}G^f( ext{M}^+(aq)) + ext{Δ}G^f( ext{X}^-(aq)) - ext{Δ}G^f( ext{MX(s)})
Applications to ore extraction
- Redox chemistry governs ore extraction processes.
- Example framing in lecture: SnO₂ + C → Sn + CO₂ as a redox reaction used to extract tin; the choice of reducing agent depends on thermodynamics.
Ellingham diagrams (brief context)
- Ellingham diagrams help determine appropriate reducing agents and conditions for ore reduction.
- Three key takeaways from the lecture figure:
  1) As temperature T increases (in Kelvin), each metal oxide becomes less thermodynamically stable.
  2) Carbon monoxide (CO) becomes more thermodynamically stable at higher temperatures.
  3) Relative oxide stabilities at a given temperature can be read directly from the diagram.
Related problems
- Selected problems listed: 8.1, 8.2, 8.3, 8.7, 8.11, 8.15, 8.20 (practice for applying these concepts).

Summary of Key Equations and Concepts (compact reference)

Standard cell potential:
- E^\u0305{ ext{cell}} = E^\u0305{ ext{cathode}} - E^5_{ ext{anode}}
Relationship between oxidation/reduction potentials and spontaneity
- More positive E°red means a stronger oxidizing agent.
- More negative E°red means the reverse direction (or the oxidized form) is less favorable.
Faraday relationships
- q = i t
- 1 mole of electrons corresponds to F = 96485\ ext{C mol}^{-1}
- For a reduction requiring n electrons per formula unit, the charge and time determine the amount of product formed.
Example potentials and interpretations
- E^\u0305_{ ext{red}}( ext{Li}^+/ ext{Li}) = -3.04\ ext{V}
- E^5_{ ext{ox}}( ext{Li}/ ext{Li}^+) = +3.04\ ext{V}
- The Li/Li⁺ couple shows Li metal is a very strong reducing agent.
- E^5{ ext{red}}( ext{Cl}2/ ext{Cl}^-) = +1.36\ ext{V}
- E^5{ ext{ox}}( ext{I}^-/ ext{I}2) = -0.53\ ext{V}
- Resulting cell potential example: E^5_{ ext{cell}} = 1.36 - 0.53 = 0.83\ ext{V} (illustrative from the lecture).

Notes on terminology and scope

Complex formation/precipitation effects
- These effects can shift M²⁺/M reduction potentials by altering the activity of metal ions in solution.
Disproportionation and stabilization
- Disproportionation reactions are driven by relative reductions of species; stabilization by precipitation can prevent undesired disproportionation.
Thermodynamics vs kinetics
- Frost-Pourbaix diagrams are thermodynamic tools and do not account for kinetic barriers.
Practical context
- These concepts underpin ore extraction strategies, corrosion science, and environmental geochemistry.

Selected Problems (reference)

8.1, 8.2, 8.3, 8.7, 8.11, 8.15, 8.20 (practice applying redox balancing, potentials, and diagram interpretations).