dr. marc madou biomems class iii. electrochemistry background (ii) winter 2009

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: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 welding2Al + Fe2O3 = 2Fel + Al2O3


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+

Cu2+ + 2e- = CuZn stripZn strip

CuSO4CuSO4

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!


Zn stripZn strip

CuSO4CuSO4 ZnSOZnSO44 CuSOCuSO44

ZnZn CuCusalt bridgesalt bridge

1.1 V1.1 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 reactionand 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- = H2(g) (1 atm)– We define E0 0 V for this electrode »where 0 stands for standard state:

1 M all solutes 1 atm all gases 250C (298 K)

HClHCl

Pt blackPt black

HH22(gas)(gas)


2H+(1M) + 2e- H2(g,1atm)

Eoredn = 0.0V


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E = Eo − 0.0592 logaAgaCl −

aAgCl

E = Eo − 0.0592 logaCl −


0.244 V v. SHE

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

Always write the redox ractions as shown :


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 signEcell = Eanode + Ecathode


Problem: Calculate the cell potential for the Daniell cell.

LiLi++ + e + e-- = Li = Li -3.0 V-3.0 V 2H2H22O + 2eO + 2e-- = H = H22 + 2OH + 2OH-- -0.83 V-0.83 V

ZnZn2+2+ + 2e + 2e-- = Zn = Zn -0.76 V-0.76 V 2H2H++ + 2e + 2e-- = H = H22 0 V (SHE)0 V (SHE)

CuCu2+2+ + 2e + 2e-- = Cu = Cu 0.34 V0.34 V MnOMnO44

-- +8H +8H++ +5e +5e-- = Mn = Mn2+2+ 1.51 V1.51 V



Zn --> Zn2+ + 2e-oxidation

Cu2+ + 2e- -->Cureduction

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

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 = -nFEand: W = G = -nFE


Thermodynamic Significance of Potentials Recall sign of G provides information on spontaneity:G negative spontaneous reactionG positive non-spontaneous reaction

So, since G = - nFE E positive spontaneous reactionE negative non-spontaneous reaction

Aa + ne = Bb

reac tant 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)

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


Electrolytic– Electrical energy chemical energy– Non-spontaneous(Ecell is negative)

EXAMPLE:– Lead storage battery when recharging– Electrolysis of water


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+

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.

Thermodynamic Significance of Potentials-Problems

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?

Is the following redox reaction spontaneous?Mg2+ + 2Ag = Mg + 2Ag+ given:Ag+ + e- = Ag +0.80 VMg2+ + 2e- = 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.


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

Thermodynamic Significance of Potentials -Problems

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

How do Cell Potentials Change if We are Not at Standard State? For the reaction:aA + bB = cC + dD

G = G0 + 2.303 RT log Qwhere Q is the reaction quotient:

Where c is the activity for product C

ba

dc

Q =

How do Cell Potentials Change if We are Not at Standard State? Since G = - nFE thenE = E0 - 2.303 (RT/nF) log Q

At standard state,E = E0 - (0.0591 V/n) log QThis 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

QRTGG o ln+=

The Nernst equation underlies the operating principle of potentiometric sensing electrodes and reference electrodes

Electrolysis vs. battery is determined by Eo 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 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

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ie = i←

= k←

c zFkT

he

(1− β )FΔφeRT = i

→= k

→

a zFkT

he

−βFΔφeRT

η=φ−φe

i = i→− i←

i=ie(e(1−β )Fη

RT − e−βFηRT )

η=a + blog(i)

(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:

-ηIncreasing stirring rateilAnodicCathodic+i-i+η

Cyclic voltammetry: diffusion control

dCdX

=Cx=∞

0 −Cx=0

δ

ηc =RTnF

lnCx=0

C∞0

i =nFAD0

C∞0 −Cx=0

δ

I l =nFAD0C∞

0

δ

i =il (1 −enFηcRT )

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 Cx=0

C∞0 =

i l - ii lwe 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

Homework1. 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?

dr. marc madou biomems class iii. electrochemistry background (ii) winter 2009

Documents

daniell cell slide

oxidized slide

gas slide

cell potentials

reductants oxidant

reductants zn strip

half cell reaction

reductants reactions