Dr. Marc Madou BIOMEMS Class III. Electrochemistry Background (II) Winter 2009

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: I 2 + SO 2 + H 2 O = 2HI + SO 3 b) Hall Heroult process – production of Al: 2Al 2 O 3 + 3C = 4Al + 3CO 2 c) the Thermite reaction – used to produce liquid iron for welding 2Al + Fe 2 O 3 = 2Fe l + Al 2 O 3

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 CuSO 4  Zn - 2e - = Zn 2+  Cu e - = Cu Zn strip CuSO 4

 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! Oxidants and Reductants Zn strip CuSO 4 ZnSO 4 CuSO 4 Zn Cu salt bridge 1.1 V 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 –Cell potential

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 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

Reference Electrodes  Electrodes with a potential independent of solution composition  Standard hydrogen electrode (SHE) –1 M H + (aq) + 2e - = H 2(g) (1 atm) –We define E 0  0 V for this electrode »where 0 stands for standard state:  1 M all solutes  1 atm all gases  25 0 C (298 K) HCl Pt black H 2 (gas)

Reference Electrodes

2H + (1M) + 2e-  H 2 (g,1atm) E o redn = 0.0V

Reference Electrodes

0.244 V v. SHE

Reference Electrodes

Standard Reduction Potentials  Li + + e - = Li-3.0 V  2H 2 O + 2e - = H 2 + 2OH V  Zn e - = Zn-0.76 V  2H + + 2e - = H 2 0 V (SHE)  Cu e - = Cu0.34 V  MnO H + +5e - = Mn V

 Always write the redox ractions as shown : Standard Reduction Potentials

 Half cell 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 E cell = E anode + E cathode Standard Reduction Potentials

Problem:  Calculate the cell potential for the Daniell cell. n Li + + e - = Li-3.0 V n 2H 2 O + 2e - = H 2 + 2OH V n Zn e - = Zn-0.76 V n 2H + + 2e - = H 2 0 V (SHE) n Cu e - = Cu0.34 V n MnO H + +5e - = Mn V Standard Reduction Potentials

Zn --> Zn e- oxidation Cu e- -->Cu reduction

 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., ZnSO 4 (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 Standard Reduction Potentials

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,  G T,P =w elec = -qE = -(nF)E –since q = n F –Recall, F is Faraday’s constant 96,485 C/mole

 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 C).  Note: NA x e = F (one Faraday). Thus: W = -nFE and: W =  G = -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

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)

 Galvanic –Chemical energy  electrical energy –Spontaneous (so E cell 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 (E cell is negative) EXAMPLE: –Lead storage battery when recharging –Electrolysis of water Thermodynamic Significance of Potentials

Thermodynamic Significance of Potentials-Problems  Arrange the following in order of increasing oxidizing strength: –MnO 4 - in acidic media –Sn 2+ –Co 3+  Co 3+ + e - = Co V  MnO H + + 3e - = MnO 2 + 2H 2 O1.70 V  MnO H + + 5e - = Mn H 2 O1.51 V  Sn e - = Sn-0.14 V  So, Co 3+ > MnO 4 - > Sn 2+

 A galvanic cell consists of a Mg electrode in a 1.0 M Mg(NO 3 ) 2 solution and a Ag electrode in a 1.0 M AgNO 3 solution. Calculate the standard state cell potential and diagram the cell. Thermodynamic Significance of Potentials-Problems  Consider the following cell: Ag(s)/AgNO 3 (aq, 1 M)//CuSO 4 (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?

 Is the following redox reaction spontaneous? Mg Ag = Mg + 2Ag + given: Ag + + e - = Ag+0.80 V Mg e - = Mg-2.37 V Thermodynamic Significance of Potentials -Problems

 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

 What would the cell potential be for the following cell? Ag(s)/AgNO 3 (aq, 1 M)//CuSO 4 (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 Thermodynamic Significance of Potentials -Problems  Standard state: –Temperature 25 0 C (K = C) –Pressure 1 atm –Concentrations of all solutes 1 M – 0 (not) is used to indicate at standard state –Example: E 0 = cell potential at standard state

How do Cell Potentials Change if We are Not at Standard State?  For the reaction: aA + bB = cC + dD   G =  G RT log Q where Q is the reaction quotient:  Where  c is the activity for product C

How do Cell Potentials Change if We are Not at Standard State?  Since  G = - nFE then E = E (RT/nF) log Q  At standard state, E = E 0 - ( 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) | Ni 2+ (aq, 0.1 M) || Co 2+ (aq, 2.5 M) | Co(s)

Nernst Equation

 The Nernst equation underlies the operating principle of potentiometric sensing electrodes and reference electrodes  Electrolysis vs. battery is determined by E o sign Nernst Equation

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 Cl 2 )  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 (Butler-Volmer) (Tafel law)  At equilibrium the exchange current density is given by:  The reaction polarization is then given by:  The measurable current density is then given by:  For large enough overpotential:

Cyclic voltammetry: diffusion control  From activation control to diffusion control:  Concentration difference leads to another overpotential i.e. concentration polarization:  Using Faraday’s law we may write also:  At a certain potential C x=0 =0 and then:  Since we get :

 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 Cyclic voltammetry and potentiometric and amperometric sensors 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?