Oxidation-Reduction and Electrochemistry

Oxidation States

The oxidation state (oxidation number) is the hypothetical charge an atom would have if all bonds were purely ionic. It is a bookkeeping tool — the actual charge distribution in a covalent bond is not full electron transfer, but oxidation numbers let you track where electrons are moving. The rules, in order of priority: (1) The oxidation state of an atom in its elemental form is zero (Na, O2, P4, C). (2) For a monatomic ion, the oxidation state equals the ion's charge (Na+ = +1, Cl− = −1, Fe3+ = +3). (3) Fluorine is always −1 in compounds. (4) Hydrogen is +1 when bonded to nonmetals, −1 when bonded to metals (metal hydrides like NaH). (5) Oxygen is −2 in most compounds, except in peroxides (O2^2−, where O = −1) and when bonded to fluorine (OF2, where O = +2). (6) Group 1 metals (Li, Na, K, etc.) are +1; Group 2 metals (Mg, Ca, etc.) are +2. (7) The sum of oxidation states in a neutral compound is zero; in a polyatomic ion, the sum equals the ion's charge. For example, in MnO4−: each O is −2 × 4 = −8; total must be −1, so Mn = +7. In Cr2O7^2−: each O is −2 × 7 = −14; total = −2, so 2 Cr = +12, Cr = +6. Oxidation is an INCREASE in oxidation state; reduction is a DECREASE in oxidation state. Remember OIL RIG: Oxidation Is Loss (of electrons), Reduction Is Gain (of electrons). The MCAT often tests oxidation states in the context of transition metals and redox titrations; for example, potassium permanganate (MnO4−, Mn = +7) is a deep purple color, and when reduced to Mn2+ (colorless), the color change signals the titration endpoint.

Redox Reactions

A redox reaction is any reaction in which oxidation states change. The species that is oxidized (loses electrons) is the reducing agent — it causes reduction in the other species. The species that is reduced (gains electrons) is the oxidizing agent — it causes oxidation in the other species. The total number of electrons lost in oxidation must equal the total number gained in reduction. Balancing redox reactions in aqueous solution requires the half-reaction method. For acidic solution: (1) Split into oxidation and reduction half-reactions. (2) Balance all atoms except H and O. (3) Balance O by adding H2O. (4) Balance H by adding H+. (5) Balance charge by adding electrons (e−). (6) Multiply each half-reaction by the factor needed to equalize electrons. (7) Add the half-reactions and cancel H2O, H+, and e− that appear on both sides. For basic solution, after step 7, add OH− to both sides to neutralize any H+ (forming H2O), then cancel excess water. Example: balancing MnO4− + Fe2+ → Mn2+ + Fe3+ in acidic solution. Reduction: MnO4− + 8H+ + 5e− → Mn2+ + 4H2O. Oxidation: Fe2+ → Fe3+ + e− (× 5). Combined: MnO4− + 5Fe2+ + 8H+ → Mn2+ + 5Fe3+ + 4H2O. Recognizing redox reactions: if any atom's oxidation state changes, it is a redox reaction. Single-displacement reactions, combustion, corrosion, respiration, and photosynthesis are all redox. Double-displacement (precipitation) and acid-base neutralization — where no oxidation states change — are NOT redox. The MCAT loves to distinguish these: NaCl + AgNO3 → AgCl + NaNO3 has unchanged oxidation states and is NOT a redox reaction.

Galvanic (Voltaic) Cells

A galvanic cell converts chemical energy from a spontaneous redox reaction (ΔG < 0) into electrical energy (E°_cell > 0). The cell physically separates the two half-reactions into two half-cells connected by a conducting wire (for electron flow) and a salt bridge (for ion migration to maintain charge neutrality). The half-cell where oxidation occurs is the ANODE; the half-cell where reduction occurs is the CATHODE. Electrons flow from anode to cathode through the external wire — so current (conventional, positive charge flow) runs cathode to anode. At the anode, the metal electrode dissolves (M → M^n+ + n e−); at the cathode, metal ions plate out (M^n+ + n e− → M). Over time, the anode loses mass and the cathode gains mass. The salt bridge contains an inert electrolyte (e.g., KNO3) whose ions migrate to balance charge: anions move toward the anode to offset the buildup of positive metal ions, and cations move toward the cathode to replace the metal ions being consumed. Without the salt bridge, charge separation would quickly build up, halting electron flow — the salt bridge completes the circuit. Cell notation (line notation) compactly represents the cell: anode | anode solution || cathode solution | cathode. For a Zn-Cu cell: Zn(s) | Zn2+(aq, 1 M) || Cu2+(aq, 1 M) | Cu(s). Phase boundaries are shown by a single vertical line |; the salt bridge by a double vertical line ||. The MCAT may ask you to interpret cell notation, identify anode/cathode, or predict mass changes at each electrode.

Electrolytic Cells

An electrolytic cell uses an external voltage source (a battery or power supply) to drive a non-spontaneous redox reaction (ΔG > 0, E°_cell < 0). The sign conventions are the same — oxidation at the anode, reduction at the cathode — but the polarity is reversed relative to galvanic cells because the external power source imposes the direction. In an electrolytic cell, the ANODE is POSITIVE (connected to the positive terminal of the battery) and the CATHODE is NEGATIVE (connected to the negative terminal). Electrons are pulled from the anode and pushed to the cathode by the external source; they still flow anode → cathode through the external circuit. Applications: (1) Electrolysis of molten NaCl produces Na(l) at the cathode and Cl2(g) at the anode — the classic Downs cell. (2) Electrolysis of aqueous NaCl is more complex because water can be oxidized or reduced instead: at the cathode, water is reduced (2H2O + 2e− → H2 + 2OH−) rather than Na+; at the anode, Cl− is oxidized (2Cl− → Cl2 + 2e−) rather than water because of overpotential effects. (3) Electroplating uses an electrolytic cell to deposit a thin layer of metal onto a conductive surface — the object to be plated is the cathode. (4) Rechargeable batteries (lithium-ion, lead-acid) operate as galvanic cells during discharge and as electrolytic cells during charging. The MCAT often tests your ability to distinguish galvanic from electrolytic cells by comparing spontaneity, sign of E_cell, and anode/cathode polarity.

Cell Potential

The cell potential (E_cell or emf) is the driving force for electron flow — the voltage difference between the cathode and anode. For standard conditions (1 M, 1 atm, 25°C): E°_cell = E°_cathode − E°_anode, where E° values are standard REDUCTION potentials from a table. A positive E°_cell means the reaction is spontaneous as written (ΔG° < 0). The relationship between cell potential and Gibbs free energy is: ΔG° = −n F E°_cell, where n is the number of moles of electrons transferred and F is Faraday's constant (96,485 C/mol e−, approximately 10^5 C/mol for MCAT estimation). Watch the sign: a positive E°_cell gives a negative ΔG° (spontaneous); a negative E°_cell gives a positive ΔG° (non-spontaneous). You can also calculate the equilibrium constant: E°_cell = (RT/nF) ln K. At 298 K, E°_cell = (0.0592/n) log10 K. This means: for every factor of 10 in K, E°_cell changes by 0.0592/n volts. A reaction with K = 10^10 and n = 2 has E°_cell ≈ (0.0592/2)(10) = 0.30 V. This conversion is frequently tested on the MCAT — given E°_cell, find K; or given K, find E°_cell. Cell potential is an intensive property: it does NOT depend on the amount of material. If you multiply a half-reaction by a coefficient to balance electrons, the E° value does NOT change — unlike ΔG°, which scales with the number of moles. This is the single most common trap in electrochemistry: students multiply E° by the same coefficient used to balance electrons, but E° is a potential per electron and is invariant to scaling.

Standard Reduction Potentials

The standard reduction potential (E°) measures a half-reaction's tendency to gain electrons (be reduced) under standard conditions (1 M, 1 atm, 25°C). All half-reactions are written as reductions: M^n+ + n e− → M. The more positive the E°_red, the stronger the oxidizing agent — it wants to be reduced. The more negative the E°_red, the stronger the reducing agent — it wants to be oxidized (the reverse reaction has a positive potential). The standard hydrogen electrode (SHE: 2H+ + 2e− → H2) is defined as E° = 0.00 V, and all other potentials are measured relative to it. Key E° values to internalize: F2/F− (+2.87 V, strongest oxidizing agent), Li+/Li (−3.04 V, strongest reducing agent). Metals above H2 (negative E°) in the activity series can be oxidized by H+ (dissolve in acid); metals below H2 (positive E°) cannot. For example, Zn (E° = −0.76 V) dissolves in HCl (Zn + 2H+ → Zn2+ + H2), but Cu (E° = +0.34 V) does not. The MCAT will provide a table of standard reduction potentials — you do NOT need to memorize them, but you must know how to: (1) identify the stronger oxidizing/reducing agent by comparing E° values, (2) calculate E°_cell by subtracting (cathode − anode), and (3) recognize that reversing a half-reaction flips the sign of E°. A common pitfall: when you reverse a reduction half-reaction to make it an oxidation, E°_ox = −E°_red. But when you add half-reactions, potentials do NOT add — you use E°_cell = E°_cathode − E°_anode, not E°_cell = E°_red + E°_ox.

The Nernst Equation

The Nernst equation adjusts the cell potential for non-standard concentrations: E = E° − (RT/nF) ln Q, where Q is the reaction quotient in the same form as the equilibrium expression. At 298 K, using base-10 log: E = E° − (0.0592/n) log Q. As a reaction proceeds toward equilibrium in a galvanic cell, Q increases (products build up), so E decreases. When Q = K (equilibrium), E = 0 — the battery is dead. The Nernst equation lets you calculate: (1) the cell potential at any given set of concentrations, (2) the concentration of one species given E and all other concentrations, and (3) the pH from a cell whose potential depends on [H+] (concentration cell). A concentration cell is a galvanic cell where both half-cells contain the same species but at different concentrations — the voltage arises purely from the concentration difference, with E°_cell = 0. For a cell with Cu(s) | Cu2+(dilute) || Cu2+(concentrated) | Cu(s), the Nernst equation gives E = −(0.0592/2) log([Cu2+]_dilute/[Cu2+]_conc). The cell runs until concentrations equalize. The MCAT loves concentration cells as a Nernst equation application: the voltage depends on the concentration ratio, and at equal concentrations, E = 0. The Nernst equation also explains why a neuron's resting membrane potential (~−70 mV) arises from unequal K+ and Na+ concentrations across the membrane — the biological Nernst potential for an ion X is E = (RT/zF) ln([X]_out/[X]_in). This is a direct B/B crossover.

How it works

Redox and electrochemistry unify three core principles: (1) electron bookkeeping via oxidation states — assign numbers, identify what is oxidized (increase) and reduced (decrease); (2) energy conversion via cell potential — E°_cell tells you whether electron transfer is spontaneous (E° > 0) or requires external drive (E° < 0), with ΔG° = −nFE° linking electrochemistry to thermodynamics; and (3) concentration dependence via the Nernst equation — E shifts from E° as Q deviates from 1, and at equilibrium (Q = K), E = 0, giving E° = (RT/nF) ln K. The practical workflow for an MCAT electrochemistry passage: identify the two half-reactions from the substances present; determine which is reduced (higher E°_red) and which is oxidized (lower E°_red); compute E°_cell = E°_cathode − E°_anode; assess spontaneity (E°_cell > 0 → spontaneous as galvanic; E°_cell < 0 → requires electrolysis); then apply the Nernst equation if concentrations are non-standard. For balancing: split into half-reactions, balance atoms with H+/H2O (acid) or OH−/H2O (base), balance charge with electrons, combine. The anode always hosts oxidation; the cathode always hosts reduction. Electrons flow anode → cathode. In a galvanic cell, the anode is negative and cathode is positive; in an electrolytic cell, the polarity is reversed by the external power supply. Faraday's law quantifies electroplating: moles of electrons = It/F (current × time / Faraday's constant), and the mass deposited = (moles e− / n) × molar mass.

How it works

Redox and electrochemistry unify three core principles: (1) electron bookkeeping via oxidation states — assign numbers, identify what is oxidized (increase) and reduced (decrease); (2) energy conversion via cell potential — E°_cell tells you whether electron transfer is spontaneous (E° > 0) or requires external drive (E° < 0), with ΔG° = −nFE° linking electrochemistry to thermodynamics; and (3) concentration dependence via the Nernst equation — E shifts from E° as Q deviates from 1, and at equilibrium (Q = K), E = 0, giving E° = (RT/nF) ln K. The practical workflow for an MCAT electrochemistry passage: identify the two half-reactions from the substances present; determine which is reduced (higher E°_red) and which is oxidized (lower E°_red); compute E°_cell = E°_cathode − E°_anode; assess spontaneity (E°_cell > 0 → spontaneous as galvanic; E°_cell < 0 → requires electrolysis); then apply the Nernst equation if concentrations are non-standard. For balancing: split into half-reactions, balance atoms with H+/H2O (acid) or OH−/H2O (base), balance charge with electrons, combine. The anode always hosts oxidation; the cathode always hosts reduction. Electrons flow anode → cathode. In a galvanic cell, the anode is negative and cathode is positive; in an electrolytic cell, the polarity is reversed by the external power supply. Faraday's law quantifies electroplating: moles of electrons = It/F (current × time / Faraday's constant), and the mass deposited = (moles e− / n) × molar mass.

Comparisons

• C/P (Thermodynamics): ΔG° = −nFE°_cell and E°_cell = (RT/nF) ln K. At 298 K, E°_cell = (0.0592/n) log K. These equations link cell potential, free energy, and equilibrium — all three appear together in integrated C/P passages.
• C/P (Acids and Bases): Redox balancing in acidic vs. basic solution; pH-dependent half-reactions (e.g., MnO4− + 8H+ + 5e− → Mn2+ + 4H2O — the potential depends on [H+] as described by the Nernst equation).
• C/P (Solutions): Concentration cells exploit concentration gradients; the Nernst equation predicts voltage from concentration ratios. Ksp applications: redox can dissolve insoluble salts by oxidizing or reducing one ion.
• C/P (Stoichiometry): Faraday's law and electroplating involve mole-to-mass calculations. Current (A) × time (s) = charge (C); charge / F = moles of e−; moles e− / n = moles of metal deposited.
• B/B (Membrane potential): The Nernst equation governs the equilibrium potential for each ion across a cell membrane: E_ion = (RT/zF) ln([ion]_out/[ion]_in). The Goldman equation extends this for multiple permeant ions.
• B/B (Electron transport chain): The mitochondrial ETC is a biological galvanic cell: Complex I → IV transfers electrons from NADH to O2, pumping protons and creating a proton gradient. The reduction of O2 to H2O (E° = +0.82 V at pH 7) is the terminal electron acceptor. The free energy released drives ATP synthesis.
• B/B (Redox in metabolism): NAD+/NADH and FAD/FADH2 are biological electron carriers. Their reduced forms carry high-energy electrons to the ETC. The MCAT may ask you to identify which species is oxidized/reduced in metabolic reactions.

Common confusions

• Multiplying E° when balancing half-reactions: E° is an intensive property — it does NOT scale with the stoichiometric coefficient. If you multiply a half-reaction by 2 to balance electrons, E° stays the same. ΔG° and K DO scale. Students routinely multiply E° by the coefficient and get a wrong cell potential.
• Confusing anode and cathode: AN OX and RED CAT: ANode = OXidation, REDuction = CAThode. Electrons flow anode → cathode. In a galvanic cell, the anode is negative (−) and the cathode is positive (+). In an electrolytic cell, the anode is positive (+) and the cathode is negative (−). Sign reversal is the most common electrolytic cell trap.
• Adding half-cell potentials instead of subtracting: E°_cell = E°_cathode − E°_anode (both as reduction potentials). Do NOT add E°_red + E°_ox — that double-counts. If you reverse a half-reaction, flip the sign, then use the cathode-minus-anode formula with the original reduction potentials.
• Forgetting the salt bridge: The salt bridge completes the circuit by allowing ion migration. Anions → anode, cations → cathode. Without it, charge buildup would halt electron flow within milliseconds. The MCAT may ask which direction ions move in the salt bridge.
• Misapplying the Nernst equation: The log term is log(Q) = log([products]/[reactants]), matching the balanced equation. At equilibrium, Q = K and E = 0, giving E° = (0.0592/n) log K. For a concentration cell, E°_cell = 0 but E ≠ 0 — the voltage comes purely from the concentration ratio. Students often mistakenly think E°_cell is needed for concentration-cell calculations.
• Confusing E° sign conventions: E°_cell > 0 means spontaneous (galvanic). E°_cell < 0 means non-spontaneous (requires electrolysis). A positive E° for a half-reaction means it is easily reduced (strong oxidizing agent). A negative E° means it is easily oxidized (strong reducing agent).
• Overpotential effects in aqueous electrolysis: When multiple species can be oxidized or reduced, the one with the more favorable (less negative for oxidation, more positive for reduction) potential reacts — but overpotential can shift this. In aqueous NaCl electrolysis, water reduction (2H2O + 2e− → H2 + 2OH−, E° = −0.83 V) is favored over Na+ reduction (E° = −2.71 V), and Cl− oxidation is favored over water oxidation due to overpotential. The MCAT may test this reasoning — you must compare standard potentials and recognize when overpotential alters the expected outcome.
• Omitting pure solids and liquids from the Nernst Q expression: Just like equilibrium constants, solids and pure liquids have activity = 1 and are omitted from Q in the Nernst equation. For Zn(s) | Zn2+ || Cu2+ | Cu(s): Q = [Zn2+]/[Cu2+], with no terms for the solid electrodes.
• Faraday's law unit conversions: Current in amperes (C/s) × time in seconds = charge in coulombs. MCAT passages may give time in minutes or hours — you must convert to seconds. Charge / 96,485 = moles of electrons. Moles of metal = moles e− / n (where n is the number of electrons per ion reduced). Mass = moles × molar mass.

Quick review

• OIL RIG: Oxidation Is Loss (of e−, oxidation state increases), Reduction Is Gain (of e−, oxidation state decreases).
• Reducing agent is oxidized; oxidizing agent is reduced. The species that loses electrons causes reduction in the other.
• Oxidation state rules: elements = 0; monatomic ions = charge; F = −1; H = +1 (with nonmetals) or −1 (metal hydrides); O = −2 (except peroxides = −1, OF2 = +2); Group 1 = +1; Group 2 = +2; sum = overall charge.
• Galvanic cell: spontaneous (ΔG < 0, E°_cell > 0), anode (−) oxidation, cathode (+) reduction. Electrons flow anode → cathode through wire.
• Electrolytic cell: non-spontaneous (ΔG > 0, E°_cell < 0), anode (+) oxidation, cathode (−) reduction. External voltage drives the reaction.
• Salt bridge: anions → anode, cations → cathode. Maintains charge neutrality. Without it, electron flow stops.
• E°_cell = E°_cathode − E°_anode (both as reduction potentials). Do NOT multiply E° by stoichiometric coefficients — E° is intensive.
• ΔG° = −nFE°_cell. F = 96,485 C/mol e−. Positive E°_cell → negative ΔG° → spontaneous.
• At 298 K: E°_cell = (0.0592/n) log K. E = E° − (0.0592/n) log Q (Nernst equation).
• When Q = K, E = 0 (dead battery, equilibrium). E° = (0.0592/n) log K.
• Concentration cell: same species, different concentrations. E°_cell = 0. E depends on concentration ratio via Nernst equation.
• Faraday's law: charge (C) = current (A) × time (s). Moles e− = charge / 96,485. Mass deposited = (moles e− / n) × molar mass.
• Half-reaction balancing: acidic → add H2O for O, H+ for H, e− for charge. Basic → do acidic steps, then add OH− to neutralize H+.
• Electrolysis of aqueous NaCl: cathode → H2 + OH− (water reduced, not Na+); anode → Cl2 (Cl− oxidized). Overpotential effects matter.
• Recharging a battery: galvanic (discharge) → electrolytic (charge). E°_cell sign reverses; anode and cathode polarity reverse.