Yonsei University Fundamentals of Electrochemistry References Electrochemical Methods : Fundamentals and Applications, 2nd edition. by A. J. Bard and L.R. Faulkner • Makes use of electrochemistry for the purpose of analysis • A voltage (potentiometry) or current (voltammetry) signal originating from an electrochemical cell is related to the activity or concentration of a particular species in the cell. • Excellent detection limit (10-8 ~ 10-3 M): 1959, Nobel Prize (Polarography) • Inexpensive technique. • Easily miniaturized : implantable and/or portable (biosensor, biochip) Electrochemical cells Galvanic cell Digital High input impedance voltmeter A B e- Anode reaction Zn Zn2+ + 2e- : oxidation e- Cathode reaction Cu2+ + 2e- Cu (-)KCl (+) : reduction Zn Cu Salt bridge Zn + Cu2+ Zn2+ + Cu K+ - - 2e Cl 2e- Cell potential : a measure of difference in electron Zn2+ energy between the two electrodes 2- SO4 Zn Cu Open-circuit potential (zero-current potential) Zn2+ Cu2+ 2+ 2+ Zn 2- 2- Cu : can be calculated from thermodynamic data, ie. SO4 SO 4 standard cell potentials of the half-cell reactions. Anode Cathode Fig. 27.1 Electrochemical cell consisting of a zinc electrode in 0.1 M ZnSO4, a copper electrode in 0.1 M CuSO4, and a salt bridge. Galvanic cell. (From Heineman book) Standard Electrode Potential Table 22.1 Standard Electrode Potentials Reaction E0 at 25 ℃, V - - Cl2(g) + 2e 2Cl +1.359 + - O2(g) + 4H +4e 2H2O +1.229 - - Br2(aq) + 2e 2Br +1.087 - - Br2(l) + 2e 2Br +1.065 Ag+ + e- Ag(s) +-.799 Reduction 자발적 Fe3+ + e- Fe2+ +0.771 - - - I3 + 2e 3I +0.536 Cu2+ + 2e- Cu(s) +0.337 - - Hg2Cl2(s) + 2e 2Hg(l) + 2Cl +0.268 AgCl(s) + e- Ag(s) + Cl- +0.222 3- - 2- A quantitative description of the relative driving force Ag(S2O3)2 + e Ag(s) + 2S2O3 +0.010 for a half-cell reaction. + - SHE 2H + 2e H2(g) 0.000 A relative quantity vs standard hydrogen electron AgI(s) + e- Ag(s) + I- -0.151 assigned to zero volt. E0(SHE)=0 - 2- PbSO4(s) + 2e Pb(S) + SO4 -0.350 Oxidation Cd2+ + 2e- Cd(s) -0.403 Fig. 22.5 Definition of the standard electrode 자발적 Zn2+ + 2e- Zn(s) -0.763 potential for M2+(aq) + 2e- M(s). Nernst Equation (activities of all species = 1) Le Chatelier’s principle: increasing reactant concentrations drives the reaction to the right The net driving force of the reaction is expressed by the Nernst equation The Nernst equation tells us the potential of a cell whose reagents are not all unit activity Nernst Equation for a Half-Reaction R: gas constant = 8.314 J/Kmol - aA + ne bB T: temperature (K) RT Ab o B ------- (14.13) E E ln a nF AA ∆G = ∆Go + RT lnQ (Q; reaction quotient) -nFE = -nFEo + RT lnQ (양변을 nF 로 나누어 준다) E = Eo –(RT/nF) lnQ Eo and Equilibrium Constant • A galvanic cell produces electricity because the cell reaction is not at equilibrium • The potentiometer allows negligible current to flow The concentration in each half-cell remains unchanged 0.412 V At the outset [Cu2+] 증가 [Ag+] 감소 0 V At equilibrium Liquid Junction Potential (Elj) Elj (diffusion potential) Develops at the interface between two liquids as a result of differences in the rates with which ions move from one liquid to the other. Type 1 Type 2 Type 3 0.01 M 0.1 M 0.1 M 0.1 M 0.1 M 0.05 M HCl HCl HCl KCl HCl KNO3 H+ H+ H+ Cl- - + Cl K K+ - NO3 + - - + - + Fig. 27.4 Types of liquid junction. Arrows show the direction of net transfer for each ion, and their lengths indicate relative mobilities. The polarity of the junction potential is indicated in each case by the circled signs. Table 27.4 Liquid Junction Potentials of 0.1 M Concentrations of Electrolytes Elj Elj Elj Elj Junction observed Junction observed Junction observed Junction observed (mV) (mV) (mV) (mV) HCl : KCl 26.78 HCl : NH4Cl 28.40 KCl : NH4Cl 2.16 NaCl : NH4Cl -4.21 HCl : NaCl 33.09 KCl : LiCl 8.79 NaCl : LiCl 2.62 LiCl : NH4Cl -6.93 KCl : LiCl 34.86 KCl : NaCl 6.42 Cell Potential Ecell = Eright –Eleft + Elj -EiR Eright = Ecathod Eleft = Eanode Elj = liquid junction potential EiR = Ohmic loss (iR drop) : The potential of an EC cell when electrolysis occurring is diminished by resistance of the cell to current. Electrochemical cells Electrolytic cell (-) Power (+) - e Supply e- (-)KCl (+) Anode reaction 2+ - Zn Cu : oxidation Cu Cu + 2e Salt bridge Cathode reaction Zn2+ + 2e- Zn : reduction K+ Cl- - 2e 2e- Cu + Zn2+ Cu2+ + Zn 2- 2+ SO4 Cu Zn Cu Zn2+ Cu2+ 2+ 2+ Zn 2- 2- Cu SO4 SO4 Cathode Anode Fig. 27.1 Electrochemical cell consisting of a zinc electrode in 0.1 M ZnSO4, a copper electrode in 0.1 M CuSO4, and a salt bridge. Electrolytic cell. Reduction and oxidation process We observe or control the potential of the working electrode with respect to the reference. → Controlling the energy of the electrons within the working electrode. Reduction A + e- → A- Oxidation A - e- → A+ Electrode Solution Electrode Solution e Vacant MO Vacant - (LUMO) - MO Energy level Potential Potential of electrons e Energy level of electrons + Occupied MO + Occupied (HOMO) MO The critical potentials at which these processes occur are related to the Standard Potentials, E0, for the specific chemical substances in the system. Determination of HOMO-LUMO Band Gap Energy - Use of cyclic voltammetry (CV) or differential pulse voltammetry (DPV) - UV absorption spectrum - Photoluminescence spectrum Determination of HOMO-LUMO Band Gap Energy 3.18 eV 3.59 eV Definition of words (What is current?) Faraday’s law relate the amount of electrical charge passed through an electrochemical cell to the quantity of material that has undergone electrolysis Q = n F N (1.3.1) F : faraday constant (96,485 C/mol) N : the number of moles electrolyzed n : the number of electrons involved in the electrode or redox reaction dQ dN i = = nF (1.3.3) rearrangement dt dt of 1.3.3 dN i Rate (mol/s) = = dt nF Potentiometry Measurement of cell voltages Chemical information (activity) Potentiometry Measurement of the difference in potential between the two electrodes of a galvanic cell under the condition of zero current are described by the term potentiometry Equilibrium Method Accurate measurements of (a) activities or concentration (b) free-energy change and equilibrium constants of many solution reactions pH/mV meter Reference Indicator Electrode Electrode Ecell = Eind –Eref + Elj The indicator electrode is chosen Sample or so that its half-cell potential responds to standard the activity of a particular species in solution whose activity or concentration Magnetic is to be measured Stirring bar Fig. 28.1 Schematic diagram of apparatus for potentiometry. Magnetic Stirrer Electrode and Potentiometry Reference Electrodes : provides a constant potential Votmeter Reference Electrode : Ag + Cl- → AgCl(s) + e- Salt bridge Anode : E-° = 0.222 V KCl Indicator Electrode (Pt) : Fe3+ + e- → Fe2+ Ag Cathode : E+° = 0.771 V 2+ 3+ E+ = 0.771 - 0.0592 log[Fe ]/[Fe ] AgCl Saturated Pt - KCl solution E- = 0.222 – 0.0592 log[Cl ] variable 2+ 3+ Fe3+, Fe2+ E = E+ -E- = (0.771-0.0592 log[Fe ]/[Fe ]) Solid KCl Measured - Anode Cathode – (0.222 – 0.0592 log[Cl ]) - - 3+ - 2+ voltage Ag + Cl ↔ AgCl +e Fe +e ↔ Fe Constant ; depend on KCl solubility 3+ - 2+ Ag(s)/AgCl(s)/Cl-(aq)//Fe +e ↔ Fe (aq)/Pt(s) saturated solution Fig. 15.1 A galvanic cell that can be used to measure the quotient [Fe2+]/[Fe3+] in the right half-cell. The Pt wire is the indicator electrode, and the entire left half-cell plus salt bridge (enclosed by the dash line) can be considered to be a reference electrode. Reference Electrode: Ag/AgCl Reference Electrode : Ag | AgCl | Cl− + Salt Bridge → Constant potential V Anode Cathode Pt : indicator electrode Ag/AgCl/Cl- plus Salt bridge reference electrode Fe2+, Fe3+ Fig. Another view of Figure 15.1. The contents of the colored box in Figure 15.1 are now considered to be a reference electrode dipped into the analyte solution. Ion Selective Electrode (ISE) Ca2+-binding ligand (ionophore) soluble in membrane + - 0.01 M Ca2+ 0.1 M Ca2+ + - (0.01+)M Ca2+ (0.1-)M Ca2+ 0.02 M Cl- 0.2 M Cl- + - 0.02 M Cl- 0.2 M Cl- + - Ca2+ Ca2+ + - + - Aqueous Aqueous solution Membrane solution Low conc. + Membrane - High conc. (a) (b) Fig. Mechanism of ion-selective electrode. (a) Initial conditions prior to Ca2+ migration across the membrane. (b) After moles of Ca2+ per liter have crossed the membrane, giving the left side a charge of +2 mol/L and the right side a charge of -2 mol/L. Ion Selective Electrode (ISE) Concentration difference → free energy difference : membrane potential A1 ∆G = -RT ln A2 ∆G = -nFE A1 -RT ln = -nFE A2 A1 0.05916 A1 E = RT/nF ln = log (volts at 25℃) memb A2 n A2 Ememb: membrane potential 1: Sample solution, 2: Internal solution Ca2+ → n = 2 10-fold change in [Ca2+] → 59.16/2 = 29.58 mV change Ion Selective Electrode (ISE) Ecell = Eref·ext -Eref·int + Ememb + Elj RT E = E -E + RT ln 1 + E + ln (a ) sample cell ref·ext ref·int lj ZF i ZF (ai)int Constant mV meter RT E = K + ln (a ) sample cell ZF i 0.05916 E = K + log (a ) sample cell n i Internal reference External (n = Z) at 25 ℃ electrode reference electrode Internal Solution Liquid junction (ai) internal potential Potential(V) ai sample = constant log [ai] Selectivity Coefficients in ISE Since membrains respond to a certain degree to ions other than the analyte (i.e.