Transcript Chapter 9
Atkins & de Paula: Elements of Physical Chemistry: 5e Chapter 9: Chemical Equilibrium: Electrochemistry End of chapter 9 assignments Discussion questions: • 1, 4 Exercises: • 1, 3, 9, 12, 13 (include last 3?) Use Excel if data needs to be graphed Homework assignments • Did you: – Read the chapter? – Work through the example problems? – Connect to the publisher’s website & access the “Living Graphs”? – Examine the “Checklist of Key Ideas”? – Work assigned end-of-chapter exercises? • Review terms and concepts that you should recall from previous courses Terms, Units, & Symbols Build Yourself a Table… TERM UNITS SYMBOL Potential volts V Resistance ohms Current amp I Siemens -1 (ohm-1) S Resistivity ohm meter Conductivity ohm-1 meter-1 Molar conductivity S m2 mol-1 m Ionic conductivity mol/dm3 mS m2 mol-1 + – is an uppercase Foundational concepts • What is the most important difference between solutions of electrolytes and solutions of non-electrolytes? • Long-range (Coulombic) interactions among ions in solutions of electrolytes The Debye-Hückel theory • Activity, a, is roughly “effective molar concentration” • 9.1a aJ = JbJ/b b = 1 mol/kg • 9.1b aJ = JbJ = activity coefficient – treating b as the numerical value of molality • If a is known, you can calculate chemical potential: μJ = μJ + RT ln aJ (9.2) The mean activity coefficient Mean activity coefficient = (+ – )½ For MX, = (+ –)½ • For MpXq, = (+p –q)1/s s= p+q • So for Ca3(PO4)2, = (+3 – 2)1/5 Debye-Hückel theory • Fig 9.1 (203) • A depiction of the “ionic atmosphere” surrounding an ion • The energy of the central ion is lowered by this ionic atmosphere Debye-Hückel theory • Debye-Hückel limiting law: log = –A|z+z–| I ½ – is the mean activity coefficient – I = ionic strength of the solution I = ½(z+2 b+ + z–2 b– ) [b = molality] – A is a constant; A = 0.509 for water – z is the charge numbers of the ions p.203 The extended Debye-Hückel law ½ A |z z | I + – • log = – 1 + B. I ½ + C.I – is the mean activity coefficient – I = ionic strength of the solution I = ½(z+2 b+ + z–2 b– ) – A is a constant; A = 0.509 for water – B & C = empirically determined constants – z = the charge numbers of the ions p.203 Debye-Hückel theory • Fig 9.2 (203) • (a) the limiting law for a 1,1-electrolyte (B & C = 1) • (b) the extended law for B = 0.5 • (c) the extended law extended further by the addition of the C I term [in the graph, C=0.2] The migration of ions • Ions move • Their rate of motion indicates: – Size, effect of solvation, the type of motion • Ion migration can be studied by measuring the electrical resistance in a conductivity cell • V = IR The migration of ions • V = IR • Resistivity () and conductivity () • And = 1/ and = 1/ • Drift velocity, s = uE • Where u (mobility) depends on a, the radius of the ion and , the viscosity of the solution Conductivity cell • Fig 9.3 (204) • The resistance is typically compared to that of a solution of known conductivity • AC is used to avoid decomposition products at the electrodes Conductivity bridge T9.1 Ionic conductivities, /(mS m2/mol)* Do you see any trends? Cations H (H3O) Anions 34.96 OH 19.91 Li 3.87 F 5.54 Na 5.01 Cl 7.64 K 7.35 Br 7.81 Rb 7.78 I 7.68 Cs 7.72 CO 2– 3 13.86 10.60 NO 3– 7.15 11.90 SO 2– 4 16.00 11.89 CH3CO 2– 4.09 HCO 2– 5.46 2 Mg 2 Ca Sr 2 NH 4 7.35 [N(CH3)4] 4.49 [N(CH2CH3)4] 3.26 * The same numerical values apply when the units are S m 1 (mol dm3)1. T9.2 Ionic mobilities in water at 298 K, u/(10-8 m2 s-1 V-1) Do you see any trends? Cations H (H3O) Anions 36.23 OH 20.64 Li 4.01 F 5.74 Na 5.19 Cl 7.92 K 7.62 Br 8.09 Rb 8.06 I 7.96 Cs 8.00 CO 2– 3 7.18 5.50 NO 3– 7.41 6.17 SO 2– 4 8.29 2 Mg 2 Ca Sr 2 6.16 NH 4 7.62 [N(CH3)4] 4.65 [N(CH2CH3)4] 3.38 The hydrodynamic radius • The equation for drift velocity (s) and the equation for mobility (u) together indicate that the smaller the ion, the faster it should move… s = uE • But the Group 1A cations increase in radius and increase in mobility! The hydrodynamic radius can explain this phenomenon. • Small ions are more extensively hydrated. Proton conduction through water • Fig 9.4 (207) The Grotthus mechanism • The proton leaving on the right side is not the same as the proton entering on the left side Determining the Isoelectric Point • Fig 9.5 (207) • Speed of a macromolecule vs pH • Commonly measured on peptides and proteins (why?) • Cf “isoelectric focusing” Types of electrochemical rxns • Galvanic cell—a spontaneous chemical rxn produces an electric current • Electrolytic cell—a nonspontaneous chemical rxn is “driven” by an electric current (DC) Anatomy of electrochemical cells Fig 9.6 (209) Fig 9.7 (209) The salt bridge overcomes difficulties that the liquid junction introduces into interpreting measurements Half-reactions • For the purpose of understanding and study, we separate redox rxns into two half rxns: the oxidation rxn (anode) and the reduction rxn (cathode) • Oxidation, lose e–, increase in oxid # • Reduction, gain e–, decrease in oxid # • Half rxns are conceptual; the e– is never really free Fig 9.8 (213) Direction of e– flow in electrochemical cells Reactions at electrodes • Fig 9.9 (213) • An electrolytic cell • Terms: – Electrode – Anode – Cathode A gas electrode • Fig 9.10 (213) Standard Hydrogen Electrode • Is this a good illustration of the SHE? • Want to see a better one? Standard Hydrogen Electrode Reduction Reaction 2e- + 2H+ (1 M) 2H2 (1 atm) E0 = 0 V Standard hydrogen electrode (SHE) 19.3 Standard Hydrogen Electrode Oxidation Reaction H2 (1 atm) 2H+ (1 M) + 2e- E0 = 0 V Standard hydrogen electrode (SHE) 19.3 Standard Hydrogen Electrode H2 gas, 1 atm Pt electrode SHE acts as cathode SHE acts as anode Metal-insoluble-salt electrode • Fig 9.11 (214) • Silver-silver chloride electrode • Metallic Ag coated with AgCl in a solution of Cl– • Q depends on aCl ion Variety of cells • Electrolyte concentration cell • Electrode concentration cell • Liquid junction potential Redox electrode • Fig 9.12 (215) • The same element in two non-zero oxidation states The Daniell cell • Fig 9.13 (215) • Zn is the anode • Cu is the cathode The cell reaction • Anode on the left; cathode on the right Cell Diagram Zn (s) + Cu2+ (aq) Cu (s) + Zn2+ (aq) [Cu2+] = 1 M & [Zn2+] = 1 M Zn (s) | Zn2+ (1 M) || Cu2+ (1 M) | Cu (s) anode cathode Measuring cell emf Fig 9.13 (217) Cell emf is measured by balancing the cell against an opposing external potential. When there is no current flow, the opposing external potential equals the cell emf. The electromotive force • The maximum non-expansion work (w’max) equals G [T,p=K] (9.12) • Measure the potential difference (V) and convert it to work to calculate G • rG = –FE (F = 96.485 kC/mol) • E = – rG F The electromotive force • rG = –FE • rG = rG + RT ln Q RT • E = E – ln Q F rG • E = F • At 25°C, RT = 25.693 mV F • E is independent of how the rxn is balanced Cells at equilibrium • At equilibrium, Q = K and a rxn at equilibrium can do no work, so E = 0 • So when Q = K and E = 0, the Nernst equation RT E = E – ln Q , becomes…. F FE ln K = RT Cells at equilibrium FE ln K = RT Is simply an electrochemical expression of rG = – RT ln K Cells at equilibrium • If E > 0, then K > 1 and at equilibrium the cell rxn favors products • If E < 0, then K < 1 and at equilibrium the cell rxn favors reactants 218 Standard potentials • SHE is arbitrarily assigned E = 0 at all temperatures, and the standard emf of a cell formed from any pair of electrodes is their difference: • E = Ecathode – Eanode OR • E = Eright – Eleft • Ex 9.6: Measure E, then calculate K The variation of potential with pH If a redox couple involves H3O+, then the potential varies with pH Table 9.3 Standard reduction potentials at 25°C (1) Eo/V Reduction half-reaction Oxidizing agent Reducing agent Strongly oxidizing F2 2 e 2 F 2.87 S2O 82– 2 e 2 SO 2– 4 2.05 Au e Au 1.69 4 2 e Pb Ce 4 e Ce MnO 4– 8 H 5 e Mn Cl2 2 e 2 Cl Cr2O 72– 14 H 6 e 2 Cr O2 4 H 4 e 2 H2O Pb 2 1.67 3 1.61 2 4 H2O 3 1.51 1.36 7 H2O 1.33 1.23, 0.81 at pH 7 Br2 2e 2 Br Ag e Ag 0.80 Hg 2 2 2 e 2 Hg 0.79 Fe e Fe 0.77 I2 e 2 I 0.54 O2 2 H2O 4 e 4 OH 0.40, 0.81 at pH 7 3 2 1.09 Table 9.3 Standard reduction potentials at 25°C (2) Eo/V Reduction half-reaction Oxidizing agent 2 Cu Reducing agent 2 e 0.34 Cu Ag Cl 0.22 H2 0, by definition Fe 2e HO 2 2 e Pb 0.13 2 2 e Sn 0.14 2 2 e Fe 0.44 Zn 2 2 e Zn 0.76 2 H2O 2 e H2 2 OH 0.83, 0.42 at pH 7 3 3 e Al 1.66 Mg 2 e Mg 2.36 Na e Na 2.71 AgCl 2H 3 Fe O2 H2O Pb Sn Fe Al 2 2 Ca K Li e 2e 3e 2e 0.04 – 2 OH 0.08 Ca 2.87 K 2.93 Li 3.05 e e Strongly reducing For a more extensive table, see the Data section. The determination of pH • The potential of the SHE is proportional to the pH of the solution • In practice, the SHE is replaced by a glass electrode (Why?) • The potential of the glass electrode depends on the pH (linearly) A glass electrode • Fig 9.15 (222) • The potential of a glass electrode varies with [H+] • This gives us a way to measue pKa electrically, since pH = pKa when [acid] = [conjugate base] The electrochemical series • A couple with a low standard potential has a thermodynamic tendency to reduce a couple with a higher standard potential • A couple with a high standard potential has a thermodynamic tendency to oxidize a couple with a lower standard potential • E0 is for the reaction as written • The more positive E0 the greater the tendency for the substance to be reduced • The more negative E0 the greater the tendency for the substance to be oxidized • Under standard-state conditions, any species on the left of a given half-reaction will react spontaneously with a species that appears on the right of any half-reaction located below it in the table (the diagonal rule) • The half-cell reactions are reversible • The sign of E0 changes when the reaction is reversed • Changing the stoichiometric coefficients of a half-cell reaction does not change the value of E0 • The SHE acts as a cathode with metals below it, and as an anode with metals above it The determination of thermodynamic functions • By measuring std emf of a cell, we can calculate Gibbs energy • We can use thermodynamic data to calculate other properties (e.g., rS) F(E – E’) • rS = T – T ’ Determining thermodynamic functions • Fig 9.16 (223) • Variation of emf with temperature depends on the standard entropy of the cell rxn Key Ideas Key Ideas Key Ideas The End …of this chapter…” Box 9.1 pp207ff Ion channels and pumps