BIOMEMS Class III. Electrochemistry Background (II) Winter 2009 Dr. Marc Madou Contents Oxidants and reductants Battery Reference Electrodes Standard Reduction Potentials Thermodynamic Significance of Potentials How do Cell Potentials Change if We are Not at Standard State? Nernst-Equation Cyclic voltammetry Potentiometric sensors Amperometric sensors Oxidants and Reductants oxidant = oxidizing agent – reactant which oxidizes another reactant and which is itself reduced reductant = reducing agent – reactant which reduces another reactant and which is itself oxidized Oxidants and Reductants Identify the oxidant and reductant in each of the following reactions: a) Karl Fischer reaction – for quantitation of moisture: I2 + SO2 + H2O = 2HI + SO3 b) Hall Heroult process – production of Al: 2Al2O3 + 3C = 4Al + 3CO2 c) the Thermite reaction – used to produce liquid iron for welding 2Al + Fe2O3 = 2Fel + Al2O3 Oxidants and Reductants Reactions occur pair wise: One cannot have oxidation without reduction Charge must be conserved: Number of electrons lost in oxidation must equal number of electrons gained in reduction Suppose we add a strip of Zinc metal to a solution of CuSO4 Zn - 2e- = Zn2+ 2+ + 2e- = Cu Zn strip Cu CuSO4 Oxidants and Reductants It is the relative tendencies of oxidants and reductants to gain/lose electrons that determines the extent of a redox reaction Strong oxidant + strong reductant completion What if we could separate the oxidant from the reductant? We would have set up a constant flow of electrons = current = electricity! 1.1 V salt bridge Zn strip Zn Cu CuSO4 ZnSO4 CuSO4 1836 The Daniell Cell Battery Electrode – anode = electrode at which oxidation occurs – cathode = electrode at which reduction occurs Salt bridge = completes the electrical circuit – allows ion movement but doesn’t allow solutions to mix – salt in glass tube with vycor frits at both ends Since electrons flow from one electrode to the other in one direction, there is a potential difference between the electrodes This difference is called – The electromotive force (EMF) – Cell voltage Battery Since all redox reactions occur pair wise, i.e., reduction and oxidation always occur at the same time we cannot measure the cell potential for just one half cell reaction and this means we must establish a RELATIVE scale for cell potentials Problem: True or False In the Daniell cell, zinc metal is reduced to zinc(II) at the cathode and copper is oxidized to copper(II) at the anode In the Daniell cell, zinc is the oxidant and copper is the reductant Reference Electrodes Electrodes with a potential independent of solution H2(gas) composition Standard hydrogen electrode (SHE) – 1 M H+(aq)+ 2e- = H2(g) (1 atm) – We define E0 0 V for this electrode » where 0 stands for standard HCl state: 1 M all solutes Pt black 1 atm all gases 250C (298 K) Reference Electrodes Reference Electrodes 2H+(1M) + 2e- H2(g,1atm Eoredn = 0.0V Reference Electrodes a Ag aCl E E o 0.0592log a AgCl E E o 0.0592log aCl Reference Electrodes 0.244 V v. SHE Reference Electrodes Reference Electrodes Standard Reduction Potentials Li+ + e- = Li -3.0 V 2H2O + 2e- = H2 + 2OH- -0.83 V Zn2+ + 2e- = Zn -0.76 V 2H+ + 2e- = H2 0 V (SHE) Cu2+ + 2e- = Cu 0.34 V MnO4- +8H+ +5e- = Mn2+ 1.51 V Standard Reduction Potentials Always write the redox ractions as shown : Standard Reduction Potentials Halfcell reactions are reversible, i.e., depending on the experimental conditions any half reaction can be either an anode or a cathode reaction Changing the stoichiometry does NOT change the reduction potential (intensive property) Oxidation potentials can be obtained from reduction potentials by changing the sign Ecell = Eanode + Ecathode Standard Reduction Potentials Li+ + e- = Li -3.0 V Problem: 2H2O + 2e- = H2 + 2OH- -0.83 V Zn2+ + 2e- = Zn -0.76 V Calculate the cell 2H+ + 2e- = H2 0V potential for the (SHE) Daniell cell. Cu2+ + 2e- = Cu 0.34 V MnO4- +8H+ +5e- = Mn2+ 1.51 V Standard Reduction Potentials Standard Reduction Potentials Zn --> Zn2+ + 2e- Cu2+ + 2e- -->Cu oxidation reduction Standard Reduction Potentials Anode reaction appears leftmost while cathode reaction appears rightmost All redox forms of reagents present should be listed. Phase and concentration specified in brackets, e.g., ZnSO4(aq, 1 M) A single vertical line (|) is used to indicate a change of phase (s to l to g) A double vertical line (||) indicates a salt bridge A comma should be used to separate 2 components in the same phase Thermodynamic Significance of Potentials We usually operate electrochemical cells at constant P and T Recall, – G = H - T S (change in Gibbs free energy) – H = E + (PV) So, GT,P=welec = -qE = -(nF)E – since q = n F – Recall, F is Faraday’s constant 96,485 C/mole Thermodynamic Significance of Potentials The maximum electrical work done by an electrochemical cell equals the product of the charge flowing and the potential difference across which it flows. The work done on the cell is: – W = -E x Q, where E is the Electromotive Force of the Cell (EMF), and Q is the charge flowing: Q = n x NA x e – where n is the number of moles of electrons transferred per mole of reaction, NA is Avogadro's Number (6.02 x 1023), and e is the charge on an electron (-1.6 x 10-19 C). Note: NA x e = F (one Faraday). Thus: W = - nFE Thermodynamic Significance of Potentials Recall sign of G provides information on spontaneity: G negative spontaneous reaction G positive non-spontaneous reaction So, since G = - nFE E positive spontaneous reaction E negative non-spontaneous reaction a b A + ne = B reac tan t product Ox + ne = Red Thermodynamic Significance of Potentials Since half-cell potentials are measured relative to SHE, they reflect spontaneity of redox reactions relative to SHE More positive potentials more potent oxidants (oxidants want to be reduced) More negative potentials more potent reductants (reductants don’t want to be reduced; they spontaneously oxidize) Thermodynamic Significance of Potentials Galvanic – Chemical energy electrical energy – Spontaneous (so Ecell is positive) EXAMPLES: » Primary (non-rechargeable) Le Clanche (dry cell) » Secondary (rechargeable) Lead storage battery »Hydrogen-Oxygen Fuel Cell Thermodynamic Significance of Potentials Electrolytic – Electrical energy chemical energy – Non-spontaneous (Ecell is negative) EXAMPLE: – Lead storage battery when recharging – Electrolysis of water Thermodynamic Significance of Potentials Thermodynamic Significance of Potentials Thermodynamic Significance of Potentials Thermodynamic Significance of Potentials Thermodynamic Significance of Potentials Thermodynamic Significance of Potentials-Problems Arrange the following in order of increasing oxidizing strength: – MnO4- in acidic media – Sn2+ – Co3+ Co3+ + e- = Co2+ 1.82 V MnO4- + 4H+ + 3e- = MnO2 + 2H2O 1.70 V MnO4- + 8H+ + 5e- = Mn2+ + 4H2O 1.51 V Sn2+ + 2e- = Sn -0.14 V So, Co3+ > MnO4- > Sn2+ Thermodynamic Significance of Potentials-Problems A galvanic cell consists of a Mg electrode in a 1.0 M Mg(NO3)2 solution and a Ag electrode in a 1.0 M AgNO3 solution. Calculate the standard state cell potential and diagram the cell. Consider the following cell: Ag(s)/AgNO3(aq, 1 M)//CuSO4(aq, 1 M)/Cu(s) a) what is the anode reaction? b) what is the cathode reaction? c) what is the net number of electrons involved? d) what is the net reaction? e) what is the cell potential at standard state? f) is the cell galvanic or electrolytic? Thermodynamic Significance of Potentials -Problems Is the following redox reaction spontaneous? Mg2+ + 2Ag = Mg + 2Ag+ given: Ag+ + e- = Ag +0.80 V Mg2+ + 2e- = Mg -2.37 V Thermodynamic Significance of Potentials Using a table of standard reduction potentials, any species on the left of a given half reaction will react spontaneously with any species appearing on the right of any half reaction that appears below it when reduction potentials are listed from highest and most positive to lowest and most negative. Thermodynamic Significance of Potentials -Problems What would the cell potential be for the following cell? Ag(s)/AgNO3(aq, 1 M)//CuSO4(aq, 0.5 M)/Cu(s) This represents a set of non-standard state conditions so we need derive an equation relating the standard state to the non-standard state or the Nernst Equation Standard state: – Temperature 250C (K = 273.15 + 0C) – Pressure 1 atm – Concentrations of all solutes 1 M – 0 (not) is used to indicate at standard state – Example: E0 = cell potential at standard state Change if We are Not at Standard State? Forthe reaction: aA + bB = cC + dD G = G0 + 2.303 RT log Q where Q is the reaction quotient: Q a b c d Where c is the activity for product C Change if We are Not at Standard State? Since G = - nFE then E = E0 - 2.303 (RT/nF) log Q At standard state, E = E0 - (0.0591 V/n) log Q This is called the Nernst equation Apply the Nernst Equation to a pH sensor: pH=- log[H+] What is the cell potential for the following electrochemical cell? What type of cell is it? Ni(s) | Ni2+ (aq, 0.1 M) || Co2+ (aq, 2.5 M) | Co(s) Nernst Equation G G o RT ln Q Nernst Equation The Nernst equation underlies the operating principle of potentiometric sensing electrodes and reference electrodes Electrolysis vs. battery is determined by Eo sign Two-electrode and three-eletrode cells, potentiostat, galvanostat Electrolytic cell (example): – Au cathode (inert surface for e.g. Ni deposition) – Graphite anode (not attacked by Cl2) Two electrode cells (anode, cathode, working and reference or counter electrode) e.g. for potentiometric measurements (voltage measurements) (A) Three electrode cells (working, reference and counter electrode) e.g. for amperometric measurements (current measurements)(B) Cyclic voltammetry: activation control At equilibrium the exchange current density is given by: (1 )F e F e kT kT ie i k c zF e RT i k a zF e RT h h The reaction polarization is then given by: e i i i The measurable current density is then given by: (1 )F F i ie (e RT e RT ) (Butler-Volmer) For large enough overpotential: a blog(i) (Tafel law) Cyclic voltammetry: diffusion control Since C x=0 i l - i From activation control to C 0 i l we get : diffusion control: C dC C 0 x x 0 nFc dX i il (1 e RT ) Concentration difference leads to another overpotential i.e. concentration polarization: RT C x=0 c ln nF C 0 Using Faraday’s law we may write also: 0 C Cx0 i nFAD0 At a certain potential C x=0=0 and then:nFAD C 0 I l 0 Cyclic voltammetry and potentiometric and amperometric sensors Scan the voltage at a given speed (e.g. from + 1 V vs SCE to -0.1 V vs SCE and back at 100 mV/s) and register the current Potentiometric: the voltage between the sensing electrode and a reference electrode is registered Amperometric: the current at a fixed voltage in the diffusion plateau is registered Ferricyanide Cyclic voltammetry (also polarography) and potentiometric and amperometric sensors Homework 1. Calculate the potential of a battery with a Zn bar in a 0.5 M Zn 2+ solution and Cu bar in a 2 M Cu 2+ solution. 2. Show in a cyclic voltammogram the transition from kinetic control to diffusion control and why does it really happen ? 3. Derive how the capacitive charging of a metal electrode depends on potential sweep rate. 4. What do you expect will be the influence of miniaturization on a potentiometric sensor and on an amperometric sensor?
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