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Química Geral · Exam review

Revisão para a prova: energia livre e eletroquímica

Uma lição resolvida gratuita e 40 problemas de prática em que você mesmo desenha cada seta curva.

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O que você vai aprender

  • Predict and calculate entropy changes and use ΔG = ΔH − TΔS, with consistent units, to decide spontaneity and find crossover temperatures.
  • Interconvert ΔG°, K and ΔG under non-standard conditions, including temperature effects and coupled reactions.
  • Analyse galvanic cells: electrode roles, electron and ion flow, E°cell from tables, and combination of half-reaction potentials.
  • Link E°cell, ΔG° and K with ΔG° = −nFE° and log K = nE°/(0.0592 V), and apply the Nernst equation forwards and backwards.
  • Predict electrolysis products and solve Faraday's-law problems for mass, gas volume, time, current, charge number, energy and efficiency.

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Entropy and the sign of ΔG

Sign convention: every Δ is final minus initial for the system, and heat absorbed by the system is positive. A process is spontaneous when the entropy of the universe rises, ΔSuniv = ΔSsys + ΔSsurr > 0, with ΔSsurr = −ΔH/T. At constant temperature and pressure this is the same as ΔG = ΔH − TΔS < 0. Predict the sign of ΔS° mainly from the change in moles of gas; at equal moles of gas, compare S° values from a table (ΔS°rxn = ΣnS°products − ΣnS°reactants, and elements do not have S° = 0). For substances in the same phase, larger and more complex molecules have more ways to rotate and vibrate, so S° rises with molecular size (CO(g) 197.7 versus CO₂(g) 213.8 J mol⁻¹ K⁻¹). The four cases: ΔH < 0 and ΔS > 0 is spontaneous at every temperature; ΔH > 0 and ΔS < 0 at none; when the signs match, the crossover temperature T = ΔH/ΔS separates the two regimes (above it when both are positive, below it when both are negative). Example: CaCO₃(s) → CaO(s) + CO₂(g), ΔH° = +178.3 kJ, ΔS° = +160.5 J/K, so ΔG° < 0 above T = 178 300 J ÷ 160.5 J/K = 1111 K. The two classic traps: ΔH is in kJ but ΔS in J/K, so convert one of them; and T must be in kelvin. A negative ΔG says nothing about rate: a spontaneous reaction can be immeasurably slow.

Free energy and equilibrium

ΔG° = −RT ln K links the standard free energy change to the equilibrium constant (R = 8.314 J mol⁻¹ K⁻¹, so ΔG° must be in J/mol). ΔG° < 0 means K > 1; ΔG° > 0 means K < 1, but some product still forms. Example: ΔG° = +10.0 kJ/mol at 298 K gives ln K = −10 000 ÷ (8.314 × 298) = −4.036 and K = 0.0177. In a mixture that is not at standard conditions, ΔG = ΔG° + RT ln Q = RT ln(Q/K): the reaction runs forward while Q < K (ΔG < 0) and stops when Q = K (ΔG = 0, while ΔG° keeps its value). Multiplying an equation by 2 doubles ΔG° and squares K; adding equations adds ΔG° values, which is how an unfavourable step is driven by coupling it to a favourable one. With ΔH° and ΔS° taken as constant, ln K = −ΔH°/RT + ΔS°/R, so the two-point form ln(K₂/K₁) = −(ΔH°/R)(1/T₂ − 1/T₁) gives ΔH° from K measured at two temperatures. K for a vapour equilibrium such as H₂O(l) ⇌ H₂O(g) is the vapour pressure in bar.

Galvanic cells and standard potentials

In a galvanic cell oxidation happens at the anode, which is the negative terminal, and reduction at the cathode, which is positive. Electrons travel through the external wire from anode to cathode; ions carry the current inside, and in the salt bridge anions move toward the anode compartment and cations toward the cathode compartment. Line notation lists the anode on the left: Zn(s) | Zn²⁺(aq) || Cu²⁺(aq) | Cu(s). E°cell = E°cathode − E°anode, using reduction potentials for both; a positive E°cell means the reaction as written is spontaneous under standard conditions. Potentials are intensive: never multiply E° by a stoichiometric coefficient. To combine two half-reactions into a third half-reaction, add their free energies instead: n₃E°₃ = n₁E°₁ + n₂E°₂, because the electrons do not cancel. Example: Fe³⁺ + e⁻ → Fe²⁺ (+0.77 V) plus Fe²⁺ + 2e⁻ → Fe (−0.44 V) gives Fe³⁺ + 3e⁻ → Fe with E° = (0.77 − 0.88) ÷ 3 = −0.04 V.

Linking E°, ΔG° and K

ΔG° = −nFE°, where n is the number of electrons transferred in the balanced reaction and F = 96 485 C/mol; 1 C × 1 V = 1 J, so the result is in joules per mole of reaction. Combining with ΔG° = −RT ln K gives, at 25 °C, log K = nE°/(0.0592 V). Daniell cell: Zn + Cu²⁺ → Zn²⁺ + Cu has E° = 0.34 − (−0.76) = 1.10 V and n = 2, so ΔG° = −2 × 96 485 × 1.10 = −212 300 J/mol = −212.3 kJ/mol and log K = 2 × 1.10 ÷ 0.0592 = 37.2. The three signs always agree: E° > 0, ΔG° < 0 and K > 1 together. ΔG° scales with n, so a reaction with a smaller E° but more electrons can release more free energy per mole of reaction. Keep ΔG° in joules when it goes into an exponential; mixing kJ with R in J is the commonest error.

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 from the balanced overall reaction, with coefficients as exponents, products over reactants, gases as pressures in bar, and pure solids and liquids left out. Example: Zn(s) | Zn²⁺(0.10 M) || Cu²⁺(0.0010 M) | Cu(s) has Q = 0.10 ÷ 0.0010 = 100, so E = 1.10 − (0.0592/2)(2.00) = 1.04 V. Each tenfold rise in Q lowers E by 0.0592/n V. As a cell discharges, Q rises toward K and E falls toward zero. Working backwards, a measured E gives an unknown concentration or pH: for a half-reaction that consumes H⁺, raising the pH lowers the reduction potential.

Electrolysis and Faraday's law

An electrolytic cell uses an external supply to drive a non-spontaneous reaction. Oxidation is still at the anode and reduction at the cathode, but now the anode is the positive terminal. In water, compare each ion with water itself: water is reduced to H₂ (with OH⁻) more easily than Na⁺, K⁺ or Al³⁺, and water is oxidized to O₂ (with H⁺) more easily than F⁻, SO₄²⁻ or NO₃⁻; Cu²⁺ and Ag⁺ are reduced to the metal, and Br⁻ and I⁻ are oxidized to the halogen. The minimum applied voltage equals −E°cell of the reaction being forced. Faraday's law: charge Q = I × t (amperes × seconds), moles of electrons = Q/F, moles of product = moles of electrons ÷ electrons per formula unit. Example: 2.00 A for 1.00 h through CuSO₄(aq) passes 7200 C = 0.07462 mol e⁻, which deposits 0.03731 mol = 2.371 g of copper (Cu²⁺ + 2e⁻ → Cu). Electrical energy = charge × voltage (1 kWh = 3.6 × 10⁶ J), and current efficiency = actual product ÷ the amount the charge could have made.

What to carry forward

Keep units honest (ΔH in kJ, ΔS in J/K, T in K, ΔG in J inside an exponential) and let the signs talk: ΔG < 0, E > 0 and Q < K all mean the reaction runs forward. Move between ΔG°, K and E° with ΔG° = −RT ln K = −nFE°, use Q and the Nernst equation for real mixtures, and turn current into chemistry with moles of e⁻ = It/F.

Problemas de prática (40)

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Preveja o produto 5

Galvanic cells and the Nernst equation

  • Electrons and ions in a cobalt–silver cellPredict electrode roles, electron flow and salt-bridge ion migration in a galvanic cell.
  • Which mixture reacts?Predict which redox reaction is spontaneous under standard conditions from a table of reduction potentials.

Electrolysis and Faraday's law

  • Electrolysis of aqueous copper(II) bromidePredict cathode and anode products of an aqueous electrolysis by comparing each ion with water.
  • Electrolysis of aqueous sodium fluoridePredict products and local pH changes when neither ion of a dissolved salt is discharged in aqueous electrolysis.

Entropy and free energy

  • Which reaction gains the most entropy?Predict which reaction has the most positive ΔS° from the change in moles of gas.

Classificar 2

Entropy and free energy

  • Classify the decomposition of N₂OUse the signs of ΔH° and ΔS° to place a reaction in one of the four spontaneity cases.

Free energy and equilibrium

  • What a positive ΔG° meansClassify the size of K and the behaviour of a mixture for a reaction with a positive ΔG°.

Comparar 4

Entropy and free energy

  • Rank alkane gases by standard molar entropyRank gases of increasing molecular complexity by standard molar entropy without a data table.

Galvanic cells and the Nernst equation

  • Rank Daniell cells by voltageRank the potentials of one cell at several concentrations by comparing reaction quotients.
  • Rank reactions by ΔG°Rank redox reactions by ΔG° per mole of reaction when both E° and the number of electrons differ.

Free energy and equilibrium

  • Doubling a redox equationCompare how ΔG°, K and E° respond when every coefficient of a cell reaction is doubled.

Calcular 19

Electrolysis and Faraday's law

  • Electrical energy to make a kilogram of aluminiumCombine Faraday's law with electrical energy = charge × voltage to find the energy cost of an electrolytic process.
  • Volume of chlorine from brine electrolysisCombine Faraday's law with the ideal gas law to find the volume of gas released at an electrode.
  • Mass of silver platedConvert current and time into moles of electrons and then into a mass of silver deposited.
  • Time to pass one mole of electronsRelate the Faraday constant, current and time to find how long a mole of electrons takes to flow.
  • Total gas from electrolysing waterUse the different electron counts at the two electrodes to find the combined gas volume from electrolysing water.

Entropy and free energy

  • When does ammonium chloride decompose?Combine ΔH°f and S° tables to find the temperature above which a decomposition becomes spontaneous under standard conditions.
  • Reducing iron ore with carbon monoxideCalculate ΔG° for a blast-furnace reaction from standard free energies of formation, including stoichiometric coefficients and elements.
  • Steam reforming of methane at 1100 KBuild ΔH° and ΔS° from formation enthalpies and absolute entropies, then evaluate ΔG° at a high temperature.

Free energy and equilibrium

  • Driving a phosphorylation with ATPAdd the free energies of coupled reactions and convert the overall ΔG° into log K at body temperature.
  • ΔG° at body temperatureCalculate ΔG° from K at a temperature other than 298 K.
  • Solubility of CaF₂ from ΔG°Convert a standard free energy of dissolution into Ksp and then into the molar solubility of a 1:2 salt.
  • Is PCl₅ decomposing in this mixture?Combine ΔG° from formation data with RT ln Q to find ΔG for a gas mixture far from standard conditions.
  • Reverse water–gas shift at 1200 KEstimate an equilibrium constant at high temperature from ΔH° and ΔS° via ΔG° = ΔH° − TΔS° and ΔG° = −RT ln K.
  • Vapour pressure of water from ΔG°fRecognise that K for a liquid–vapour equilibrium is the vapour pressure and calculate it from free energies of formation.

Galvanic cells and the Nernst equation

  • ΔG° for the dichromate titration of iron(II)Find n from the oxidation-state change of a polyatomic oxidant and use it in ΔG° = −nFE°.
  • Does Fe²⁺ disproportionate?Combine two half-reactions of the same element into a disproportionation and convert E° into log K.
  • Standard potential of a magnesium–tin cellCalculate E°cell from the cell notation and two standard reduction potentials.
  • Permanganate to Mn²⁺ from two stepsCombine two half-reaction potentials into a third half-reaction by adding free energies, weighting each E° by its electron count.
  • Nernst equation with a squared concentrationWrite Q with stoichiometric exponents for an unequal-electron cell and apply the Nernst equation.

Encontre o erro 2

Entropy and free energy

  • Find the error in a ΔG° calculationSpot the use of a Celsius temperature in ΔG = ΔH − TΔS and correct the result.

Galvanic cells and the Nernst equation

  • A suspiciously small KFind the unit error that turns a large equilibrium constant calculated from E° into a value near 1.

Interprete as evidências 2

Electrolysis and Faraday's law

  • Current efficiency of a copper plating runCompare the measured mass of a plated metal with the Faraday's-law maximum to obtain the current efficiency.

Entropy and free energy

  • Crossover temperature from two ΔG° valuesExtract ΔH° and ΔS° from ΔG° measured at two temperatures and locate the temperature where ΔG° = 0.

Trabalhe de trás para frente 3

Electrolysis and Faraday's law

  • Which chromium ion was plated?Work back from current, time and mass deposited to the number of electrons each metal ion gains.

Free energy and equilibrium

  • ΔH° from K at two temperaturesWork back from equilibrium constants measured at two temperatures to the standard enthalpy change.

Galvanic cells and the Nernst equation

  • pH from a hydrogen–copper cellRearrange the Nernst equation for a cell with a hydrogen anode to find the pH of the anode solution.

Planeje uma síntese 1

  • Choosing the plating currentPlan the current needed to deposit a target mass of metal within a set time.

Explique por quê 2

Entropy and free energy

  • Why hydrogen peroxide keeps on the shelfSeparate thermodynamic favourability from rate for a reaction that is spontaneous at every temperature.
  • What every spontaneous process has in commonIdentify the one thermodynamic criterion that holds for every spontaneous process at constant temperature and pressure.

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