Redox Reaction - the basics Ch.14-16 Electrochemistry ox1 + red2 <=> red1 + ox2 Oxidizing Agent Reducing Agent Redox reactions: involve transfer of electrons from one species to another. Oxidizing agent (oxidant): takes electrons Reducing agent (reductant): gives electrons Redox Reaction - the basics Reduced Oxidized ox1 + red2 <=> red1 + ox2 Oxidizing Agent Balance Redox Reactions (Half Reactions) Reducing Agent Redox reactions: involve transfer of electrons from one species to another. Oxidizing agent (oxidant): takes electrons Reducing agent (reductant): gives electrons 1. Write down the (two half) reactions. 2. Balance the (half) reactions (Mass and Charge): a. Start with elements other than H and O. b. Balance O by adding water. c. balance H by adding H+. d. Balancing charge by adding electrons. (3. Multiply each half reaction to make the number of electrons equal. 4. Add the reactions and simplify.) Fe3+ + V 2+ → Fe 2+ + V 3+ Example: Balance the two half reactions and redox reaction equation of the titration of an acidic solution of Na2C2O4 (sodium oxalate, colorless) with KMnO4 (deep purple). MnO4-(aq) + C2O42-(aq) → Mn2+ (aq) + CO2(g) 16H+(aq) + 2MnO4 + → 2Mn2+(aq) + 8H2O(l) + 10CO2(g) -(aq) 5C2O42-(aq) Example: Balance Sn2+ + Fe3+ <=> Sn4+ + Fe2+ Fe2+ + MnO4- <=> Fe3+ + Mn2+ Important Redox Titrants and the Reactions Oxidizing Reagents (Oxidants) (1) Potassium Permanganate − MnO 4 + 8 H + + 5e − → Mn 2 + + 4 H 2 O − MnO4 + 4 H + + 3e − → MnO2 ( s ) + 2 H 2O MnO + e → MnO − 4 2− − 4 1 Important Redox Titrants and the Reactions Important Redox Titrants and the Reactions Oxidizing Reagents (Oxidants) Oxidizing Reagents (Oxidants) (2) Potassium Dichromate (3) Potassium Iodate Cr2O7 2− Cr2 O 7 2− + 14 H + + 6e − → 2Cr 3+ + 7 H 2O + 3U 4+ + 2H + → 2Cr 3+ + 3UO 2 − IO3 + 6 H + + 5e − → 2+ + H 2O Important Redox Titrants and the Reactions Reducing Reagent ( Reductants ) 1 I 2 + 3 H 2O 2 Important Redox Titrants and the Reactions Reducing Reagent ( Reductants ) (1) Potassium Iodide (2) Sodium Thiosulfate 2S2O32- 1 I → I 2 + e− 2 − Galvanic Cells - Components S4O62- +2e¯ Galvanic Cells - Line Notation A galvanic (voltaic) cell uses a spontaneous chemical reaction to generate electricity. – Electrodes (cathode and anode). – Salt bridge: cations move from anode to cathode, anions move from cathode to anode. Line notation Cd(s) | Cd(NO3)2 (aq) || AgNO3 (aq) | Ag(s) Phase boundary Salt bridge Phase boundary 2 Standard Electrode Potentials Standard Reduction (Half-Cell) Potentials Standard hydrogen electrode (S.H.E.) Standard reduction potential (Eo) is the voltage associated with a reduction reaction at an electrode when all solutes are 1 M and all gases are at 1 atm. Cathode Reduction Reaction 2H+ (1 M ) + 2eEo = H2 (1 atm) 0V • The S.H.E. is the cathode. It consists of a Pt electrode in a tube placed in 1 M H+ solution. H2 is bubbled through the tube. • For the S.H.E., we assign 2H+ (aq, 1M) + 2e- → H2 (g, 1 atm) • E°red of zero. • The potential of a cell can be calculated from standard reduction potentials: E °cell = E °red (cathode ) − E °red (anode ) Standard Potentials Standard Reduction (Half-Cell) Potentials We use hydrogen (S.H.E.) • Consider Zn(s) → Zn2+(aq) + 2e-. We measure Ecell relative to the S.H.E. (cathode): E°cell = E°red(cathode) - E°red(anode) 0.76 V = 0 V - E°red(anode). • Therefore, E°red(anode) = -0.76 V. • Standard reduction potentials must be written as reduction reactions: Zn2+(aq) + 2e- → Zn(s), E°red = -0.76 V. H +(aq) + e − ↔ 1/2H 2 ( g ) E ° ≡ 0.000 We can measure Eº for other half-reactions, relative to the hydrogen reaction, e.g. for silver: Ag +(aq) + e − ↔ Ag(s) E ° = 0.799 Standard reduction potentials are listed in Ap. H in your book. Eº for the H2 reaction is for the reaction at 25º C Nernst Equation for a Half-Reaction • The Nernst Equation relates the potential of the half reaction to reagent concentrations • For the half-reactions: aA + ne ↔ bB - E E = E° − ° aA + bB + ne - ↔ cC + dD E = E° − E° RT ln Q nF E = E° − RT [B] ln nF [A]a b RT [C] [D] ln nF [A ]a [B]b c d # of moles of electrons 3 Nernst Equation for a Half-Reaction Nernst Equation for a Complete Reaction At 298K (25oC) ox1 + red2 <=> red1 + ox2 E = E° − 0.05916V log Q n E = E+ − E− Example (Net Reaction) Example (Nernst) • Write the Nernst equation for the reduction of phosphoric acid to solid white phosphorous: H 3PO 4 + 5H + + 5e - ↔ 1/4P4 ( s) + 4H 2O 0.05916 1 E = −0.402 − log 5 [H 3PO 4 ] H + E ° = -.402 Cd + + 2e − ↔ Cd( s) [ ] 5 • Note that multiplying the reaction by any factor does not affect Eº or the calculated E: 2H3 PO 4 + 10H + + 10e- ↔ 1/2P4 ( s) + 8H 2 O 0.05916 1 E = −0.402 − log 10 [H 3PO 4 ]2 H + E ° = -.402 [ ] 10 Determination of the Equivalence Point Aox + Bred <=> Ared + Box At equivalence point, Ecell=0: ° EA − 0.0592 [A ] 0.0592 [B ] ° log red = EB − log red nA [ Aox ] nB [ Box ] Ared = Box and Bred = Aox at the equivalence point E= o n A E A + nB E B n A + nB o • Find the voltage for the Ag-Cd cell and state if the reaction is spontaneous if the right cell contained 0.50 M AgNO3(aq) and if the left contained 0.010 M Cd(NO3)2(aq) • 1) 2Ag + + 2e − ↔ 2Ag( s) E+° = 0.799 V Valid for simple Redox expressions E−° = −0.402 V • 2) E+ = 0.799 − 0.05916 log 1 = 0.781 V 2 [0.50]2 • 3) E = −0.402 − 0.05916 log 1 = −0.461V − [0.010] 2 • 4) E = E+ − E− = 0.781 − ( −0.461) = +1.242 V • 5) + − 2Ag + 2e ↔ 2Ag( s) Cd( s) + 2Ag + ↔ Cd 2+ + 2Ag( s) Cd + + 2e − ↔ Cd ( s ) Redox Titration Curve EXAMPLE: Derive the titration curve for 50.00 mL of 0.0500 M Fe2+ with 0.00, 15.00, 25.00, 26.00 mL 0.1000 M Ce4+ in a medium that is 1.0 M in HClO4. Potential of saturated calomel electrode is 0.241 V. 4 EXAMPLE: Derive the titration curve for 50.00 mL of 0.0500 M Fe2+ with 0.00, 15.00, 25.00, 26.00 mL 0.1000 M Ce4+ in a medium that is 1.0 M in HClO4. Potential of saturated calomel electrode is 0.241 V. Titration reaction: Fe2+ + Ce4+ <=> Ce3+ + Fe3+ Fe3+ + e- <=> Fe2+ Ce4++ e- <=> Ce3+ Eo = 0.767 V Eo = 1.70 V At 0.00 mL of Ce4+ added, initial point no Ce4+ present; minimal, unknown [Fe3+]; thus, insufficient information to calculate E E = E° − 0.0592 [ Fe 2+ ] log − 0.241 n [ Fe 3+ ] EXAMPLE: Derive the titration curve for 50.00 mL of 0.0500 M Fe2+ with 0.00, 15.00, 25.00, 26.00 mL 0.1000 M Ce4+ in a medium that is 1.0 M in HClO4. Potential of saturated calomel electrode is 0.241 V. Fe2+ + Ce4+ <=> Ce3+ + Fe3+ At 15.00 mL of Ce4+ added, VFeMFe > VCeMCe “Buffer region” [ Fe 3+ ] = 2.308 ×10−2 M V M −V M [ Fe ] = Fe Fe Ce Ce VFe + VCe EXAMPLE: Derive the titration curve for 50.00 mL of 0.0500 M Fe2+ with 0.00, 15.00, 25.00, 26.00 mL 0.1000 M Ce4+ in a medium that is 1.0 M in HClO4.Potential of saturated calomel electrode is 0.241 V. Fe2+ + Ce4+ <=> Ce3+ + Fe3+ At 15.00 mL of Ce4+ added, VFeMFe > VCeMCe “Buffer region” [ Fe 3+ ] = = VCe M Ce VFe + VCe (15.00mL)(0.1000M ) = 2.308 ×10 −2 M (50.00 + 15.00)mL EXAMPLE: Derive the titration curve for 50.00 mL of 0.0500 M Fe2+ with 0.00, 15.00, 25.00, 26.00 mL 0.1000 M Ce4+ in a medium that is 1.0 M in HClO4. Potential of saturated calomel electrode is 0.241 V. Fe2+ + Ce4+ <=> Ce3+ + Fe3+ At 15.00 mL of Ce4+ added, VFeMFe > VCeMCe “Buffer region” Half-reactions: Fe3+ + e- <=> Fe2+ Eo = 0.767 V [ Fe3+ ] = 2.308 × 10 −2 M 2+ = (50.00mL)(0.0500M ) − (15.00mL)(0.1000M ) = 1.54 ×10 −2 M (50.00 + 15.00)mL EXAMPLE: Derive the titration curve for 50.00 mL of 0.0500 M Fe2+ with 0.00, 15.00, 25.00, 26.00 mL 0.1000 M Ce4+ in a medium that is 1.0 M in HClO4. Potential of saturated calomel electrode is 0.241 V. Fe2+ + Ce4+ <=> Ce3+ + Fe3+ At 25.00 mL of Ce4+ added, VFeMFe = VCeMCe, Equivalence point Half-reactions: Fe3+ + e- <=> Fe2+ Eo = 0.767 V 4+ 3+ Ce + e <=> Ce Eo = 1.70 V E= = nFe EFe + nCe ECe − 0.241 nFe + nCe 0.767 + 1.70 − 0.241 = 1.23 − 0.241 = 0.99 V 1+1 E = E° − [ Fe 2+ ] = 1.538 ×10 −2 M 0.0592 [ Fe 2 + ] log − 0.241 n [ Fe3+ ] = 0.767 − 0.0592 1.54 ×10 −2 log − 0.241 = 0.533V 1 2.038 ×10 −2 EXAMPLE: Derive the titration curve for 50.00 mL of 0.0500 M Fe2+ with 0.00, 15.00, 25.00, 26.00 mL 0.1000 M Ce4+ in a medium that is 1.0 M in HClO4. Potential of saturated calomel electrode is 0.241 V. Fe2+ + Ce4+ <=> Ce3+ + Fe3+ At 26.00 mL of Ce4+ added, VFeMFe < VCeMCe, After equivalence point [Ce3+ ] = = VFe M Fe VFe + VCe (50.00mL)(0.0500 M ) = 3.29 ×10 − 2 M (50.00 + 26.00) mL 5 EXAMPLE: Derive the titration curve for 50.00 mL of 0.0500 M Fe2+ with 0.00, 15.00, 25.00, 26.00 mL 0.1000 M Ce4+ in a medium that is 1.0 M in HClO4. Potential of saturated calomel electrode is 0.241 V. EXAMPLE: Derive the titration curve for 50.00 mL of 0.0500 M Fe2+ with 0.00, 15.00, 25.00, 26.00 mL 0.1000 M Ce4+ in a medium that is 1.0 M in HClO4. Potential of saturated calomel electrode is 0.241 V. Fe2+ + Ce4+ <=> Ce3+ + Fe3+ Fe2+ + Ce4+ <=> Ce3+ + Fe3+ At 26.00 mL of Ce4+ added, VFeMFe < VCeMCe, After equivalence point At 26.00 mL of Ce4+ added, VFeMFe > VCeMCe After equivalence point Fe3+ + e- <=> Fe2+ Half-reactions: Ce4++ e- <=> Ce3+ [Ce3+ ] = 3.29 × 10 −2 M V M −V M [Ce 4+ ] = Ce Ce Fe Fe VFe + VCe = (26.00mL)(0.1000 M ) − (50.00mL)(0.0500M ) = 1.32 × 10 −3 M (50.00 + 26.00)mL [Ce3+ ] = 3.29 × 10 −2 M E = E° − = 1.70 − Eo = 0.767 V Eo = 1.70 V [Ce 4+ ] = 1.32 × 10 −3 M 0.0592 [Ce 3+ ] log − 0.241 n [Ce 4+ ] 0.0592 3.29 ×10 −2 log − 0.241 = 0.63 V 1 1.32 ×10−3 Galvanic Cells A galvanic (voltaic) cell uses a spontaneous chemical reaction to generate electricity. Theoretical curve for titration of 100.0 mL of 0.50 0 M Fe2+ with 0.100 M Ce4+ in 1 M HClO4. (p.330-331) – Electrodes (cathode and anode). – Salt bridge: cations move from anode to cathode, anions move from cathode to anode. – produces electricity when the cell reaction is not at equilibrium. 0.0592 [ Fe 2+ ] log − 0.241 [ Fe 3+ ] n 0.0592 = 0.767 − log 1 − 0.241 = 0.526 V 1 E = E° − Free Energy and Electrochemical Reaction E and Equilibrium Constants • The free energy change, ∆G, for a chemical reaction at constant T, P equals the maximum possible electrical work that can be done by the reaction on its surroundings. • A galvanic cell produces electricity because the cell reaction is not at equilibrium • At equilibrium, E for the net reaction can thus be related to K aA + ne - ↔ cC E+° Work = − ∆G = E × q ∆G = − nFE • A spontaneous reaction (∆G<0) E>0 • Think: how the equilibrium constant can be related to free energy? dD + ne - ↔ dD E = E+ − E− = E+° − E = E° − E-° .05916 .05916 [C] [B] log a − E−° − log d n n [A] [D] c b 0.05916 0.05916 [C] [D] log a b = E ° − log Q n n [A] [B] E = 0 → E° = c 0.05916 log K n d at 25°C K = 10 at 25°C nE ° 0.05916 at 25° C When the cell is at equilibrium, E=0 and Q=K 6 Cells as Chemical Probes Example: Find the equilibrium constant 3+ 2+ Cu ( s ) + 2Fe ↔ Cu + 2Fe Two Equilibria: 2+ (1) Equilibrium between two half-cells (2) Equilibrium within each half-cell AgCl ( s) + e − ↔ Ag (s ) + Cl - (aq,0.10M ) E+° = 0.222 V This can be divided into two half reactions: 2Fe 3+ + 2e − ↔ 2Fe 2+ ( s) 2 H + ( aq, ? M ) + 2e - ↔ H 2 ( g ,1.00bar ) E+° = 0.771 V Cu 2+ + 2e- ↔ Cu (s ) •The half-reaction that you write must involve species that appear in two oxidation states in the cell. E o- = 0.339 V E ° = E+° − E−° = 0.771− 0.339 = 0.432 V K = 10 nE ° 0.05916 •The reaction is in equilibrium in the right cell is not the net cell reaction: (2)(0.432) = 10 ( 0.05916) = 4 ×1014 AgCl( s ) ↔ Ag + (aq) + Cl − ( aq) Important Biochemical Reactions Survival Tips Electrochemistry, chemical equilibrium, solubility, complex formation, and acid-base chemistry (1) Write half-reactions and their standard potentials (2)Write Nernst equation for the net reaction and put in all the known quantities. (3) Solve for the unknown concentration and use that concentration in the chemical equilibrium equation to solve the problems. E o- = 0 V • Formal potential, Eº’, meant to define potentials under conditions of biochemistry Ex. p.286-287 Potentiometry • Potentiometry: the use of electrodes to measure voltages from chemical reactions. • Electroactive species: can donate or accept electrons at an electrode; can be measured as the part of a galvanic cell (analyte) • Reference electrode: we then connect the analyte halfreaction to a second cell with a fixed composition (known potential), the 2nd half-cell is called reference electrode. • Indicator electrode: responds to analyte - Metal electrodes: inert metals, e.g., Pt, Au - Ion-selective electrodes: respond to specific analytes S.H.E. (again) The standard reduction potential, Eo, for each halfcell is measured when different half-cells are connected to S.H.E. S.H.E. || Ag+ (aq. =1) | Ag(s) Standard means that the activities of all species are unity. Not practical for regular use due to the hydrogen gas 7 Reference Electrodes Reference Electrodes Detect Fe2+ /Fe3+ in solution: a Pt wire (indicator electrode) in the half-cell and connect this half cell to a 2nd half-cell at a constant potential. Reference Electrode Fe3+ + e - ↔ Fe 2+ AgCl ( s ) + e ↔ Ag ( s) + Cl − [Fe ] [Fe ] = 0.222 - .059log[Cl ] The entire left half-cell containing appropriate solutions and a salt bridge. ° - E = 0.222 V 2+ E+ = 0.771 − .059 log E- Indicator Electrode E+° = 0.771 V - 3+ - Fe 3+ + e - ↔ Fe 2 + E = E+ − E- E+° = 0.771 V AgCl( s) + e ↔ Ag( s ) + Cl − - Silver-Silver Chloride Electrode E-° = 0.222 V Saturated Calomel Electrode (S.C.E.) Ag | AgCl Electrode : AgCl( s) + e - ↔ Ag ( s) + Cl− E-° = +0.222 V w/ saturated KCl E = +0.197 V Hg | Hg2Cl2 Electrode: • The difference in E is due to activity coefficients. • A double junction electrode: avoid to mix Cl- with the analyte Voltage Conversions between Different Reference Scales 1/2Hg 2 Cl 2 ( s) + e - ↔ Hg(l ) + Cl − E ° = +0.268 V w/ saturated KCl E = +0.241 V Indicator Electrodes - Metal Electrodes • Metal electrodes: develop potential in response to a redox reaction on their surface • Pt is mostly inert, not participating in reactions An indicator electrode has a potential of -0.351 V with respect to an S.C.E., what’s its potential with respect to an S.H.E.? – It simply allows electron transfer to/from solution • Platinum is the most common metal indicator electrode Gold is also an inert metal indicator electrode • Carbon electrodes are often used because many redox reactions are very fast on a carbon surface - 0.351V + 0.241V = -0.110V 8 Indicator Electrodes-Metal electrodes • Metal electrodes: develop potential in response to a redox reaction on their surface • Inert metal indicator electrode: allows electron transfer to/from the solution but not participating in reactions, e.g., Pt (the most common one), Au. • Silver Indicator Electrode Ag + ( s ) + e- ↔ Ag( s ) E+° = 0.799 V 1/2Hg 2Cl 2 ( s ) + e - ↔ Hg (l ) + Cl − E−° = 0.241 V 1 E = E+ − E− = 0.799 − 0.059 log Ag + [ ] − 0.241 [ ] E = 0.558 + 0.059 log Ag + Junction Potential Example: 100.0 mL solution containing 0.100 M NaCl was titrated with 0.100 M AgNO3 and monitored with a S.C.E. What voltage reading would be observed after 65.0 mL? + − Ag + Cl → AgCl( s ) Ve = 100.0 mL [ ] E = 0.558 + 0.05916log Ag + [Cl ] = (0.350)(0.100 M) 100.0 165.0 − K 1.8 ×10 [Ag ] = [Cl ] = 0.021 + sp − −10 = 0.021 M = 8.5 ×10 −9 E = 0.558 + 0.05916 log (8.5 ×10-9 ) = 0.081 V Ion Mobilities and Liquid Junction Potentials • Junction potential: A voltage difference develops whenever dissimilar electrolyte solutions are in contact. • Happens at the salt bridge/solution interface since different ions have different mobilities in water. • A major (fundamental) source of error in a potential measurement. Ion-Selective Electrodes (ISE) Glass Electrode (pH Combination Electrode) • The most common ISE • A glass membrane selectively binds H+ • Two Ag|AgCl reference electrodes measure the potential difference across the glass membrane • An ion-exchange equilibrium is on the surface of the glass membrane • Responds selectively to one ion using an ionselective membrane • Do not involve redox reactions • The electric potential across the membrane depends on [analyte] • E is measured by two reference electrodes E = constant + 0.05916 log [C n + ] Out at 25°C n = charge of analyte Ag(s) | AgCl(s) | Cl - (aq) || H + (aqout ) | H + (aqin ), Cl − (aq) | AgCl( s ) | Ag( s) 9 Errors in pH Measurement The Glass Membrane of a pH Electrode •Cross section of the glass membrane of a pH electrode. 1. 2. 3. 4. 5. •H+ can diffuse into the membrane to replace the metal ions through binding to oxygen in glass (ionexchange equilibrium). 6. 7. Response of the electrode : E = constant + β (0.0592) log[H ] E = constant − β (0.0592) pH at 25 C + Out O Out 8. 9. β: ~1.00, electromotive efficiency measured during calibration. Specifications for Electrochemical Techniques Selectivity Coefficient k A,X response to X = response to A k K + , Na + = 1× 10 k K + , Cs + = 0.44 K + , Rb + = 2.8 Advantages • The selectivity coefficient: the relative response of the electrode to different species −5 Linear response to analyte over wide dynamic range Nondestructive Short response times Unaffected by color/turbidity (limited matrix effects) Cheap • The smaller k is, the less interference there is due to ion X Response of ion - selective electrode : k E = constant ± β ( [ 0.0592 ) log a + n A x ] (k a ) A,X x Calibration standards (±0.01 pH) Junction potential (~0.01 pH) Junction potential drift (recalibrate every 2 hrs) Sodium error (when [H+] is low and [Na+] is high) Acid error (strong acid, the glass surface is saturated with H+) Equilibration time (~30s with adequate stirring) Hydration of glass (A dry electrode requires several hours of soaking) Temperature (calibrate at same T as measurement) Cleaning (remove hydrophobic liquid) Disadvantages Sensitivity (High detection limits) Not universal at 25 C O Voltammetry A collection of techniques in which the relation between current and voltage is observed during electrochemical process. • Can be used to (1) Study electroactivity of ions and molecules at the electrode/solution interface (2) Probe coupled chemical reactions and measure electron transfer rates (3) Examine electrode surfaces • An electrochemical cell consists of a working (analyzing) electrode, an auxiliary (counter) electrode, and a reference electrode. The control device is a potentiostat. ip • [A] Calibration Curve 10 Stripping Analysis Anodic stripping voltammetry (ASV): analytes are reduced and deposited into (onto) an electrode. They are reoxidized during the stripping step. e.g. Cd2+(aq) + 2e = Cd(Hg) Deposition Step Cd(Hg) – 2e = Cd2+ (aq) Stripping Cathodic stripping voltammetry (CSV): typically anions are oxidized and deposited onto an electrode with subsequent stripping via a negative potential scan. e.g. 2I- + 2Hg -2e = Hg2I2 at a Hg electrode Deposition step Hg2I2 + 2e = 2 Hg + 2I- cathodic stripping, reduction Trace analysis (enhanced sensitivity) can be realized since sample analytes are preconcentrated from a large-volume dilute solution into (onto) a small-volume electrode under forced convection. 11
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