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Química Geral · Electrochemistry

Redox e eletroquímica

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O que você vai aprender

  • Assign oxidation states to atoms in molecules and ions, including the oxidation level of a single carbon atom in an organic molecule.
  • Balance redox half-reactions and overall equations in acidic and in basic solution.
  • Calculate E°cell, ΔG° and K from standard reduction potentials and use them to predict whether a reaction is spontaneous.
  • Describe galvanic and electrolytic cells and use Faraday's law to relate charge passed to the amount of substance changed.
  • Use the Nernst equation to predict how concentrations and pH change a cell or electrode potential.

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Oxidation states are electron bookkeeping

An oxidation state is the charge an atom would carry if every bond were fully ionic, with the shared electrons given to the more electronegative atom. Free elements are 0; a monatomic ion has its charge; fluorine is always −1; oxygen is usually −2 but −1 in peroxides such as H₂O₂ (drawn) and positive only when bonded to fluorine; hydrogen is +1 with nonmetals but −1 in metal hydrides such as NaH. The oxidation states in a species add up to its overall charge, so in Cr₂O₇²⁻ the two chromium atoms share 14 − 2 = 12, and each is +6. When the atoms of one element are not equivalent, the formula gives only an average, which can be a fraction: sulfur in S₄O₆²⁻ averages +2.5. Oxidation is an increase in oxidation state (loss of electrons) and reduction a decrease (gain of electrons). The species that is reduced is the oxidizing agent; the species that is oxidized is the reducing agent. When one element in a single oxidation state is both oxidized and reduced, as chlorine is in Cl₂ + 2OH⁻ → Cl⁻ + OCl⁻ + H₂O, the reaction is a disproportionation.

The oxidation level of a carbon atom

In organic molecules, assign one carbon at a time. Count +1 for each bond to a more electronegative atom (O, N, a halogen; a double bond counts twice), −1 for each bond to hydrogen and 0 for each bond to another carbon, then add any formal charge on that carbon. The one-carbon ladder drawn here climbs in steps of two: methane −4, methanol −2, formaldehyde 0, formic acid +2, carbon dioxide +4. Each step up is a two-electron oxidation, which is why ethanol (carbinol carbon −1) is oxidized to ethanal (+1) and then to ethanoic acid (+3). Hydride reagents such as NaBH₄ reduce a carbonyl carbon by delivering a hydride (H⁻, two electrons) to it. An aldehyde can even be its own hydride source: in concentrated hydroxide, formaldehyde disproportionates (the Cannizzaro reaction) into formate (+2) and methanol (−2). Adding H–OH across a C=C bond is not a redox reaction: one carbon gains a bond to oxygen (+1) while the other gains a bond to hydrogen (−1), so the total is unchanged.

Balancing half-reactions

Split the reaction into an oxidation and a reduction half-reaction. In each, balance every atom except O and H, then balance O by adding H₂O, then H by adding H⁺, then charge by adding electrons. Multiply the half-reactions so that the electrons lost equal the electrons gained, add them and cancel anything that appears on both sides. Permanganate in acid gains five electrons: MnO₄⁻ + 8H⁺ + 5e⁻ → Mn²⁺ + 4H₂O. In basic solution, balance as if in acid, then add one OH⁻ to both sides for every H⁺, combine H⁺ + OH⁻ into H₂O and cancel water; permanganate then stops at MnO₂: MnO₄⁻ + 2H₂O + 3e⁻ → MnO₂ + 4OH⁻. Always finish by checking that atoms and total charge both balance.

Cell potential, free energy and K

Standard reduction potentials rank half-reactions: the higher E°, the stronger the oxidizing agent on the left (Cl₂ +1.36 V, Ag⁺ +0.80 V, Cu²⁺ +0.34 V, H⁺ 0.00 V, Zn²⁺ −0.76 V), and the lower E°, the stronger the reducing agent on the right. The Cl₂/Cl⁻ couple drawn here sits near the top of the table, so chlorine is a strong oxidizing agent and chloride a very weak reducing agent. For a redox reaction, E°cell = E°(reduction half, cathode) − E°(oxidation half, anode); for Zn + Cu²⁺ → Zn²⁺ + Cu it is 0.34 − (−0.76) = +1.10 V. E° is an intensive quantity, energy per unit charge, so it is never multiplied when a half-reaction is multiplied by a coefficient. Free energy is extensive and scales with the n electrons transferred: ΔG° = −nFE°, with F = 96485 C/mol. A positive E°cell means ΔG° < 0 and K > 1. At 25 °C, log K = nE°/0.0592 V. To combine two half-reactions into a third half-reaction, add their ΔG° values (−nFE°) rather than their potentials, because the electrons do not cancel.

Galvanic and electrolytic cells

In every electrochemical cell, oxidation happens at the anode and reduction at the cathode. A galvanic cell runs a spontaneous reaction (E > 0) and its anode is the negative terminal: electrons leave the anode through the external wire, and the salt bridge lets ions migrate so that both compartments stay electrically neutral, anions toward the anode and cations toward the cathode. Cell notation lists the anode on the left and the cathode on the right, with | for a phase boundary and || for the salt bridge: Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s). An electrolytic cell uses an external power supply to drive a nonspontaneous reaction, so its anode is the positive terminal. Faraday's law links the charge passed to the amount changed: moles of electrons = It/F, and each mole of metal deposited from Mⁿ⁺ needs n moles of electrons. In aqueous electrolysis, water competes with the dissolved ions: in brine, water (−0.83 V) is reduced to H₂ in preference to Na⁺ (−2.71 V), and chloride is oxidized to Cl₂ because O₂ evolution has a large overpotential.

The Nernst equation

Away from standard conditions, E = E° − (RT/nF) ln Q, which at 25 °C is E = E° − (0.0592 V/n) log Q. Q is written like an equilibrium expression, products over reactants, with pure solids omitted; for the zinc–copper cell Q = [Zn²⁺]/[Cu²⁺]. Raising a reactant concentration lowers Q and raises E; raising a product concentration lowers E. A concentration cell has E° = 0 and runs only because the two concentrations differ. Half-reactions that consume H⁺ depend on pH: for O₂ + 4H⁺ + 4e⁻ → 2H₂O, E falls by about 0.059 V per pH unit, from +1.23 V at pH 0 to about +0.82 V at pH 7. As a galvanic cell discharges, Q rises toward K; at equilibrium Q = K, ΔG = 0 and E = 0.

What to carry forward

Assign oxidation states to find what is oxidized and what is reduced, balance the half-reactions so atoms, charge and electrons all agree, then use E°cell = E°cathode − E°anode with ΔG° = −nFE° to predict spontaneity, Faraday's law to count electrons in electrolysis, and the Nernst equation to correct for concentration.

Problemas de prática (40)

Praticar é grátis com uma conta.

Desenhe o mecanismo 2

Oxidation states

  • Cannizzaro disproportionation of formaldehydeDraw hydroxide addition to formaldehyde, hydride transfer to a second formaldehyde and the final proton transfer, and identify which carbon is oxidized and which is reduced.
  • Borohydride reduction of ethanal to ethanolDraw hydride transfer from borohydride to the carbonyl carbon of ethanal and protonation of the alkoxide by methanol, and track the two-electron reduction of the carbonyl carbon from +1 to −1.

Preveja o produto 7

Balancing redox equations

  • Balanced dichromate half-reactionIdentify the correctly balanced reduction half-reaction of dichromate in acid by checking atoms and charge.
  • Permanganate half-reaction in baseChoose the correctly balanced half-reaction for permanganate reduced to MnO₂ in basic solution.

Galvanic and electrolytic cells

  • Products of brine electrolysisPredict the electrode products of aqueous electrolysis by comparing ion and water half-reactions, including overpotential.

Oxidation states

  • Two-electron oxidation of ethanolPredict the product of a two-electron oxidation of a primary alcohol from carbon oxidation states.

Cell potentials and free energy

  • Which reaction is spontaneous?Predict which of several redox reactions is spontaneous under standard conditions by calculating E°cell for each.
  • Which metal dissolves in 1 M acid?Predict which metal reduces H⁺ to H₂ by comparing its reduction potential with that of the standard hydrogen electrode.

The Nernst equation

  • Add more Cu²⁺ to a Daniell cellPredict qualitatively how changing a reactant concentration shifts a cell potential through Q.

Classificar 6

Oxidation states

  • Which compound has a carbon at +3?Assign oxidation states to individual carbon atoms by counting bonds to oxygen, hydrogen and carbon.
  • Chlorine in cold hydroxideClassify a reaction in which one element is both oxidized and reduced as a disproportionation.
  • Which reaction is not a redox reaction at carbon?Decide whether an organic transformation is an oxidation, a reduction or neither by summing carbon oxidation states.
  • Find the oxygen at −1Recognize the peroxide and oxygen fluoride exceptions to the rule that oxygen is −2.
  • Which species is the reducing agent?Identify the reducing agent in a metal displacement reaction from the changes in oxidation state.

Galvanic and electrolytic cells

  • Galvanic versus electrolytic cellsDistinguish galvanic and electrolytic cells by spontaneity and electrode polarity while keeping the anode as the site of oxidation.

Comparar 2

Oxidation states

  • Rank one-carbon compounds by carbon oxidation stateOrder one-carbon compounds by the oxidation state of carbon from methane to carbon dioxide.

Cell potentials and free energy

  • Rank oxidizing agents from a table of potentialsRank oxidizing agents by strength using standard reduction potentials.

Calcular 13

Oxidation states

  • Oxidation state of chromium in dichromateFind the oxidation state of a metal in a polyatomic ion from the oxygen rule and the ion's charge.
  • Average oxidation state of sulfur in tetrathionateCalculate a fractional average oxidation state from a formula and explain what it means.

Balancing redox equations

  • Electrons transferred when copper dissolves in dilute nitric acidFind the total number of electrons transferred in a balanced equation whose half-reactions involve different electron counts.
  • Electrons gained by permanganate in acidCount the electrons in a reduction half-reaction from the change in oxidation state of the metal.
  • Protons in the permanganate–iron(II) titrationCombine two half-reactions with equal electrons and read a coefficient from the balanced overall equation.

Cell potentials and free energy

  • Standard potential of the Daniell cellCalculate a standard cell potential from two standard reduction potentials as E°cathode − E°anode.
  • Combine two iron half-reactionsCombine two half-reactions into a third half-reaction by adding their free energies rather than their potentials.
  • Equilibrium constant from E°Calculate log K for a redox reaction from standard reduction potentials without scaling E° by the coefficients.
  • Standard free energy of the Daniell cell reactionConvert a standard cell potential into a standard free-energy change with ΔG° = −nFE°.

Galvanic and electrolytic cells

  • Time to deposit aluminiumRearrange Faraday's law to find the electrolysis time needed to deposit a given mass of a trivalent metal.
  • Mass of copper platedUse Faraday's law to calculate the mass of metal deposited by a given current and time.

The Nernst equation

  • Copper concentration cellCalculate the potential of a concentration cell, whose E° is zero, from the Nernst equation.
  • Daniell cell with dilute zinc ionCalculate a nonstandard cell potential with the Nernst equation.

Encontre o erro 2

Balancing redox equations

  • What is wrong with this equation?Diagnose a redox equation that balances atoms but not charge or electrons.

The Nernst equation

  • Find the error in a Nernst calculationDiagnose an inverted reaction quotient in a Nernst equation calculation.

Interprete as evidências 2

Cell potentials and free energy

  • What does a negative E°cell mean?Interpret the sign of a standard cell potential in terms of ΔG°, K and the direction of spontaneous change.

Galvanic and electrolytic cells

  • Read the anode from cell notationInterpret cell notation with an inert electrode to write the anode half-reaction.

Trabalhe de trás para frente 1

  • Identify the metal from the cell potentialWork backwards from a measured standard cell potential to the unknown half-cell's reduction potential.

Planeje uma síntese 1

  • Order the half-reaction methodSequence the steps of the half-reaction method for balancing a redox equation in acidic solution.

Explique por quê 4

Cell potentials and free energy

  • Why E° is not multipliedExplain why a standard reduction potential is not scaled when a half-reaction is multiplied, while ΔG° is.

The Nernst equation

  • Why a discharged cell reads zeroExplain why a galvanic cell's potential reaches zero when its reaction reaches equilibrium.
  • How pH changes the oxygen electrodeExplain why a half-reaction that consumes H⁺ has a pH-dependent potential and estimate the size of the effect.

Galvanic and electrolytic cells

  • What does the salt bridge do?Explain how a salt bridge completes the circuit by ion migration that keeps each compartment electrically neutral.

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