Fuel Cells and Hydrogen - West Virginia Universitywu/mae493/2-fuel cell-1.pdf · Fuel Cells and...

Fuel Cells and Hydrogen

MAE 493R/593V- Renewable Energy Devices

Fuel Cells and Hydrogen

Outline

• Basics of electrochemistry

• Polymer electrolyte membrane (PEM) fuel cells

• Solid oxide fuel cells (SOFCs)

• Hydrogen production and storage

• Coal-fired plants and integrated gasifier fuel cell (IGFC) systems

Basics of Electrochemistry

All course notes only for class students.

The slides are modified from the original slide provided by Dr. C. S. Wang at University of Maryland

•• Batteries, fuel cells, and Batteries, fuel cells, and solar cellssolar cells

•• CorrosionCorrosion

Why Study Electrochemistry?Why Study Electrochemistry?

•• Industrial production of Industrial production of chemicals such as Clchemicals such as Cl22, , NaOH, FNaOH, F22 and Aland Al

•• Biological redox reactionsBiological redox reactions

The heme groupThe heme group

Why Study Electrochemistry?Why Study Electrochemistry?Conventional fossil energy devices:

Fossil fuels combustion (hydrocarbons+ oxygen)→ energy stored in the working fluid (internal energy or enthalpy) converted to mechanical energy by passing the working fluid to devices (such as turbines)

Renewable energy devices:For example, fuel cells are to directly convert chemical energy to electric work

Why Study Electrochemistry?Why Study Electrochemistry?

6

http://www.fueleconomy.gov/feg/tech/fuelcell.gif

Anode side: 2H2 →4H+ + 4e-

Cathode side:O2 + 4H+ + 4e- →2H2O

Net reaction:2H2 + O2 →2H2O

Image from: http://en.wikipedia.org/wiki/File:Fc_diagram_pem.gif

Operating temp: around 80 oC

Basic knowledge of electrochemistry

redox reaction-oxidation reaction and reduction reaction- reducing agent and oxidation agent

electrochemical cells- electrolyte, anode, cathode- voltaic cells, electrolytic cells

cell potential and Nernst equation

Table of Contents:

cell potential and Nernst equation

Gibbs free energy

Kinetic of electrochemical reaction- polarization (ohmic, activation and concentration polarization)

voltammetry (CV)- linear-sweep voltammetry- cyclic voltammetry

electrochemical impedance spectroscopy (EIS)

Terminology for Redox ReactionsTerminology for Redox Reactions

Oxidation Reaction Reduction ReactionExample: 2 Cu + O2 → 2 CuO Example: CuO + H2 → Cu + H2O

• loss of electrons• increase in oxidation state

• gain of electrons• decrease in oxidation stateincrease in oxidation state

• addition of oxygen• loss of hydrogen

decrease in oxidation state• loss of oxygen• addition of hydrogen

copper is losing electrons Cu 2+ in CuO is gaining electrons

You can’t have one… without the other!

• Reduction (gaining electrons) can’t happen without an oxidation to provide the electrons.

• You can’t have 2 oxidations or 2 reductions in the same equation. Reduction has to occur at the cost of oxidation

LEOLEO the lion saysthe lion says GERGER!!LEOLEO the lion says the lion says GERGER!!oossee

lleeccttrroonnss

xxiiddaattiioonn

aaiinn

lleeccttrroonnss

eedduuccttiioonn

GER!GER!

•• OXIDATIONOXIDATION——loss of electron(s) by a species; increase loss of electron(s) by a species; increase in oxidation number; increase in oxygen.in oxidation number; increase in oxygen.

•• REDUCTIONREDUCTION——gain of electron(s); decrease in oxidation gain of electron(s); decrease in oxidation number; decrease in oxygen; increase in hydrogen.number; decrease in oxygen; increase in hydrogen.

•• OXIDATIONOXIDATION——loss of electron(s) by a species; increase loss of electron(s) by a species; increase in oxidation number; increase in oxygen.in oxidation number; increase in oxygen.

•• REDUCTIONREDUCTION——gain of electron(s); decrease in oxidation gain of electron(s); decrease in oxidation number; decrease in oxygen; increase in hydrogen.number; decrease in oxygen; increase in hydrogen.

Terminology for Redox ReactionsTerminology for Redox Reactions

•• OXIDIZING AGENTOXIDIZING AGENT——electron acceptor; species is electron acceptor; species is reduced.reduced.

•• REDUCING AGENTREDUCING AGENT——electron donor; species is oxidized.electron donor; species is oxidized.

•• OXIDIZING AGENTOXIDIZING AGENT——electron acceptor; species is electron acceptor; species is reduced.reduced.

•• REDUCING AGENTREDUCING AGENT——electron donor; species is oxidized.electron donor; species is oxidized.

Review of Oxidation Numbers

The charge the atom would have in a molecule (or anionic compound) if electrons were completely transferred.

1. Free elements (uncombined state) have an oxidation number of zero.

Na Be K Pb H O P = 0Na, Be, K, Pb, H2, O2, P4 = 0

2. In monatomic ions, the oxidation number is equal to the charge on the ion.

Li+ (+1); Fe3+ (+3); O2- (-2)3. The oxidation number of oxygen is usually –2. In H2O2

and O22- it is –1.

4.4

Oxidation‐Reduction Reactions:A Quick Review

Cu → Cu2+Cu → Cu2+ + 2e–Ag+ → AgAg+ + e– → Ag

CuCu(s)(s) in AgNOin AgNO3(aq)3(aq) QuickTime Movie

Ag e → Ag2Ag+ + 2e– → 2AgCu → Cu2+ + 2e–Overall cell reaction:Cu +2Ag+→2Ag + Cu2+Cu loses e‐: oxidizedAg+ gains e‐: reduced

Redox Reactions• Zinc is added to a blue

solution of copper(II) sulfate

• The blue colour disappears…the zinc metal “dissolves”, and

Zn (s) + CuSO4 (aq) ZnSO4 (aq) + Cu (s)

metal dissolves , and solid copper metal precipitates on the zinc strip

• The zinc is oxidized (loses electrons)

• The copper ions are reduced (gain electrons)

Zn (s) + Cu2+ (aq) Zn2+ (aq) + Cu (s)

Harnessing the Electricity• Electrons flow from the zinc atoms to the copper ions During the

spontaneous redox reaction.

• Electricity can be thought of as the “flow of electric charge”.

• How to utilize the electricity: the flow of electrons from the zinc atoms to the copper ions?

Answer: Separate the Cu ions from the Zn atoms. This will force the electrons from the zinc atoms to travel through an external path to reach the copper ions.

Electrochemical Cells• Electrochemical Cell– a device that uses a

spontaneous redox reaction to produce electricity

• Anode– the electrode where

oxidation occurs• Cathode

– the electrode where reduction occurs

• Salt Bridge– connects two “half-cells” to

complete the electric circuit.– for example, a U-tube filled

with salt solution

A salt bridge has three functions:

1) It allows electrical contact between the two

half-cells

2) I i i f h l d l i

Electrochemical Cells

2) It prevents mixing of the electrode solutions

3) It maintains electrical neutrality in each half-

cell as ions flow into and out of the salt bridge

Terms Used for Electrochemical CellsTerms Used for Electrochemical Cells CHEMICAL CHANGE CHEMICAL CHANGE ------>>ELECTRIC CURRENTELECTRIC CURRENT

CHEMICAL CHANGE CHEMICAL CHANGE ------>>ELECTRIC CURRENTELECTRIC CURRENT

Zn metalZn metalWith time, Cu plates out onto Zn metal strip, and Zn strip “disappears.”

With time, Cu plates out onto Zn metal strip, and Zn strip “disappears.”

Cu2+ ionsCu2+ ions

p ppp pp

••Zn is oxidized Zn is oxidized and is the reducing agent and is the reducing agent Zn(s) Zn(s) ------> Zn> Zn2+2+(aq) + 2e(aq) + 2e--••CuCu2+2+ is reduced is reduced and is the oxidizing agentand is the oxidizing agentCuCu2+2+(aq) + 2e(aq) + 2e-- ------> Cu(s)> Cu(s)

Electrochemical Cell:An Atomic‐Level View QuickTime

Movie

Cell potential• Water only spontaneously flows one way in a waterfall.

• Likewise, electrons only spontaneously y p yflow one way in a redox reaction—from higher to lower potential energy.

Electrochemical Cells

V lt i llV lt i ll El t l ti llEl t l ti ll

QuickTime Movie

• Voltaic: spontaneous chemical reaction produceselectrical energy

• Electrolytic: electrical energy forces a nonspontaneousreaction to occur

Voltaic cellVoltaic cell Electrolytic cellElectrolytic cell•• An apparatus that allows a redox reaction to occur by An apparatus that allows a redox reaction to occur by transferring electrons through an external connector.transferring electrons through an external connector.

AnodeAnode CathodeCathode

ElectrolyteElectrolyte

ee––

ElectrolyteElectrolyte

ee––

Some Electrochemical Terms

LoadVoltaic cellVoltaic cell

PowerElectrolytic cellElectrolytic cell

• Electrode: surface where redox reaction occurs

Anode: oxidation Cathode: reduction

Active: part of redox Inert: does not react

• Electrolyte: conducting solution (has ions)

• Electric current due to electron and ion flow

CHEMICAL CHANGE CHEMICAL CHANGE ELECTRIC CURRENTELECTRIC CURRENTCHEMICAL CHANGE CHEMICAL CHANGE ELECTRIC CURRENTELECTRIC CURRENT

Galvanic Cells

anodeOxidation

negative electrode

cathodeReduction

Positive electrode

spontaneous

••To obtain a useful current, we separate the oxidizing and reducing agents To obtain a useful current, we separate the oxidizing and reducing agents so that electron transfer occurs thru an external wire. so that electron transfer occurs thru an external wire.

This is accomplished in a This is accomplished in a GALVANICGALVANIC or or VOLTAICVOLTAIC cell.cell.A group of such cells is called a A group of such cells is called a batterybattery..

predox reaction

A Voltaic Cell: A Voltaic Cell: The The DaniellDaniell (Zn(Zn--Cu) CellCu) Cell

Electrolytic CellQuickTime

Movie

Anode (+): 4OHAnode (+): 4OH––(aq)(aq) →→ OO2(g)2(g) + 2H+ 2H22OO(l)(l) + 4e+ 4e––

Cathode (Cathode (––): 4H): 4H22OO(l)(l) + 4e+ 4e-- →→ 2H2H2(g)2(g) + 4OH+ 4OH––

Overall: 2HOverall: 2H22OO(l)(l) →→ OO2(g)2(g) + 2H+ 2H2(g)2(g)

BatteryBattery WaterWater

ElectrochemistryTwo broad areas

Galvanic Rechargeable ElectrolysisCells batteries Cells

Electrolytic vs Voltaic Cells

• nonspontaneous reaction forced to occur

• Oxidation: anodeReduction: cathode

l d l i

• spontaneous reaction generates electricity

• Oxidation: anodeReduction: cathode

l d l i• Electrode Polarity:Anode: positiveCathode: negative

• e–flow: anode to cathode

• Ion flow: anions to anode; cations to cathode

• Electrode Polarity:Anode: negativeCathode: positive

• e–flow: anode to cathode

• Ion flow: anions to anode; cations to cathode

Voltaic Cell Diagram

The Daniell cell:Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s)

may be represented by a cell diagram:

Zn | Zn2+(1.0 M) || Cu2+(1.0 M) | Cu}}

OxidationOxidation R d tiR d ti

}

OxidationOxidationhalfhalf--cellcell

ReductionReductionhalfhalf--cellcell

The ANODE is described before the CATHODE.Concentrations of ions are indicated in brackets.A vertical line represents a phase boundary.A double vertical line represents the salt bridge.

The Cu‐Ag Cell A Comparison of Cell Potentials

• Zn‐Cu cell potential: 1.10 VZn(s) + Cu 2+

(aq) → Zn2+(aq) + Cu(s)

• Cu‐Ag cell potential: 0.46 VCu(s) + 2Ag+(aq) → Cu 2+

(aq) + 2Ag(s)

• Oxidizing power: Ag+ > Cu 2+ > Zn 2+

• Cell potential (voltage) depends on:

nature of electrodes and ions

concentrations of ions

temperature of cell

The Cell Potential

• The magnitude of the cell potential, Ecell, is a measure of the spontaneity of a redox reaction

• The more positive the cell potential, the greater the driving force for the redox reaction to proceed as writteng p

• The standard cell potential, Eocell, is for a cell operating under standard conditions

Standard Electrode Potentials:

• The standard electrode potential, Eohalf‐cell, isthe potential of a given half‐cell when allcomponents are in their standard states

• By convention, the standard electrodey ,potential refers to a half‐reaction written as areduction

• The more positive the potential, the greaterthe tendency for the reaction to proceedforward

• The E°cell calculated is for the cell operating

under standard state conditions

• For electrochemical cell standard conditions are:

l t t 1 M n ntr ti n

Standard Electrode Potentials:

-solutes at 1 M concentrations

- gases at 1 atm partial pressure

- solids and liquids in pure form

• All at some specified temperature, usually 298 K

Standard Electrode Potentials

• The potential of a half‐cell is referenced with respect to the standard hydrogen electrode (SHE)

• By convention:By convention:SHE Half‐Reaction Eohalf‐cellH2 → 2H+ + 2e– 0.00 V2H+ + 2e– → H2 0.00 V

Standard Hydrogen Electrode (SHE)

SHE - the reference electrode

Reference Electrode

Standard ReductionPotentials

Acidic Solution SRP, Eo(volts)

Li+(aq) + e– → Li(s) –3.045Al3+(aq) + 3e–→ Al(s) –1.66 Cr2+( ) + 2e–→ Cr( ) –0.91

(The Electromotive Series)

Cr (aq) + 2e → Cr(s) 0.91 Zn2+(aq) + 2e–→ Zn(s) –0.763 Cr3+(aq) + 3e–→ Cr(s) –0.74 Cr3+(aq) + e– → Cr2+(aq) –0.41 2H+

(aq) + 2e–→ H2(g) 0.00 Cu2+(aq) + e–→ Cu+(aq) 0.153Cu2+(aq) + 2e–→ Cu(s) 0.337 F2(aq) + 2e–→ 2F–(aq) 2.87

Things to Remember about Eo

• The more positive the Eo, the greater the tendency for the reaction to occur in the forward direction

• The more negative the Eo for a reaction, the greater the tendency for the reaction to occur in the reverse direction

• If a reaction is reversed, the sign of its Eo is reversed

• If a reaction is multiplied by a factor, its potential stays the same; Eo is not multiplied by the factor

• If half-reactions are summed up to give an overall reaction, potentials can be summed up to give an overall cell potential

Relative Oxidizing & Reducing Strengths

To determine which is a stronger oxidizing agent between Cl2 and Pb2+:

• Compare their reduction potentialsCl2 + 2e– → 2Cl– Eo = 1.360 V Pb2++ 2e– → Pb Eo = –0.126 V

• The stronger oxidizing agent is more easily reduced; i.e., has more positive Eo

⇒ Cl2 is the stronger oxidizing agent

Eo (V)

Cu2+ + 2e- Cu +0.34

oxidizingability of ion

Table Of Standard Reduction Potentials

22 H+ + 2e- H 0.00

Zn2+ + 2e- Zn -0.76

reducing abilityof element

To determine an oxidation To determine an oxidation from a reduction table, just from a reduction table, just take the opposite sign of the take the opposite sign of the reduction!reduction!

Table of Standard Reduction Potentials Oxidizing and Reducing Agents

• The strongest oxidizers have the most positive reduction potentials.

• The strongest reducers have the most negative reduction potentials.

Predicting Reaction Spontaneity

• Diagonal Rule for the Electromotive Series: Any specieson the left half‐cell reaction will react spontaneouslywith a species on the right half‐cell reaction locatedabove it

Zn2+ + 2e–→ Zn Eo = 0 76 VZn2+ + 2e → Zn Eo = – 0.76 VCu2+ + 2e–→ Cu Eo = 0.34 V

• Spontaneous if Eocell is positiveZn → Zn2+ + 2e– Eo = 0 .76 V

Cu2+ + 2e–→ Cu Eo = 0. 34 VZn + Cu2+ → Zn2+ + Cu Eo = 1.10 V

Cell Potentials

Determination of Cell Potentials

• Choose appropriate half‐reactions from theTable of Standard Potentials

• Write half‐reaction with more positive Eohalf‐cellas a reduction

• Write less positive half‐reaction as an oxidation;re erse sign of Eoreverse sign of Eohalf‐cell

• Balance number of electrons; do not multiplyEohalf‐cell by factors used to multiply electrons

• Sum up reactions and potentials to give Eocell• If Eocell > 0: reaction is spontaneous

(1) A half-reaction can be multiplied through by any number without affecting the reduction (or oxidation) potential

• Fe3+(aq) + e → Fe2+(aq); Ered= +0.771 V

• 3Fe3+(aq) + 3e → 3Fe2+(aq); Ered= +0.771 V

(2) Subtraction of reduction (or oxidation) potentials of half-reactions having the same number of electronics.

Determination of Cell Potentials

g• Cl2(g) +2e → 2Cl-(aq); Ered= +1.36 V

• Zn2+(aq) +2e → Zn(s); Ered= -0.763 V

• Therefore for• Cl2(g) +Zn(s) → 2Cl-(aq) +Zn2+(aq); Ecell= +2.123

What is the standard potential of an electrochemical cell made of a Cd electrode in a 1.0 M Cd(NO3)2 solution and a Cr electrode in a 1.0 MCr(NO3)3 solution?

Cd2+ (aq) + 2e- Cd (s) E0 = -0.40 V

Cr3+ (aq) + 3e- Cr (s) E0 = -0.74 V

Cd is the stronger oxidizer

Cd will oxidize Cr

Cr (s) Cr3+ (1 M) + 3e-Anode (oxidation): x 2

The Cell Potential

2e- + Cd2+ (1 M) Cd (s)

( ) ( )( )

Cathode (reduction):

2Cr (s) + 3Cd2+ (1 M) 3Cd (s) + 2Cr3+ (1 M)

x 3

E0 = Ecathode + Eanodecell0 0

E0 = -0.40 + (+0.74) cell

E0 = 0.34 V cell

•• Electron transfer reactions are Electron transfer reactions are oxidationoxidation‐‐reductionreduction

or or redoxredox reactions.reactions.

•• Results in the generation of an electric current Results in the generation of an electric current

( l i i ) b d b i i l i( l i i ) b d b i i l i

Electron Transfer ReactionsElectron Transfer Reactions

(electricity) or be caused by imposing an electric (electricity) or be caused by imposing an electric

current. current.

•• Therefore, this field of chemistry is often called Therefore, this field of chemistry is often called

ELECTROCHEMISTRY.ELECTROCHEMISTRY.

Electrochemistry

• Deals with the inter‐conversion betweenelectrical energy and chemical energy

• Involves oxidation‐reduction (redox)reactions in electrochemical cells

ThermodynamicsThe Gibbs free energy is defined as:G = H − TSWhereH = U + PV

U is the internal energy (SI unit: J)P is pressure (SI unit: Pa)V is volume (SI unit: m3)T is the temperature (SI unit: K)S is the entropy (SI unit: J/K)

G is a thermodynamic properties.G is a state functionG is NOT a path function.

Gibbs energy is the capacity of a system to do non-mechanical work and ΔG measures the non-mechanical work done on it. The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system; this maximum can be attained only in a completely reversible process.

http://en.wikipedia.org/wiki/Gibbs_free_energy

S is the entropy (SI unit: J/K)H is the enthalpy (SI unit: J)

ThermodynamicsThe change in the Gibbs free energy of the system that occurs during a reaction is:

If the reaction is run at constant temperature, this equation can be :

If the data are collected under standard-state conditions, the result is the standard-state free energy of reaction,

51

Standard-state conditions:

• The partial pressures of any gases involved in the reaction is 0.1 MPa.• The concentrations of all aqueous solutions are 1 M. • Measurements are also generally taken at a temperature of 25 oC (298 K)

This equation is to determine the relative importance of the enthalpy and entropy terms as driving forces behind a particular reaction. The change in the free energy of the system that occurs during a reaction measures the balance between the two driving forces that determine whether a reaction is spontaneous.

Thermodynamics of Chemical Reactions

Favorable, or spontaneous reactions: Go < 0

Any reaction for which is negative should be favorable, or spontaneous

Unfavorable or non‐spontaneous reactions: Go > 0

Any reaction for which is positive is therefore unfavorable.

52

Reactions can be classified according to the change in enthalpy (heat):

A larger amount of the energy released in the reaction is subtracted from a smaller amount of the energy used for the reaction.

<0

Thermodynamics of Chemical ReactionsFor a chemical reaction, Standard-State Free Energy of Formation

The standard-state free energy of reaction can be calculated from the standard-state free energies of formation as well. It is the sum of the free energies of formation of the products minus the sum of the free energies of formation of the reactants

The Gibbs free energy is the maximum amount of non-expansion work that can be extracted from a closed system; this maximum can be attained only in a completely reversible process.

Thermodynamics of Chemical Reactionsa A + b B → c C + d D For a reaction:

ba

dc

BADCQ

][][][][

=

Chemical quotient (reaction quotient) is defined as:

If Q d t ilib i t ti th th b i i

In a chemical process, chemical equilibrium is the state in which the chemical activities or concentrations of the reactants and products have no net change over time.

If Q correspond to equilibrium concentrations, then the above expression is called the equilibrium constant and its value is denoted by K (or Kc or Kp.)

K is thus the special value that Q has when the reaction is at equilibrium

If K > Q, a reaction will proceed forward.If K < Q, the reaction will proceed in the reverse direction,

converting products into reactants.If Q = K then the system is already at equilibrium

Thermodynamics of Chemical ReactionsExample: 0.035 moles of SO2, 0.5 moles of SO2Cl2, and 0.08 moles of Cl2are combined in an evacuated 5 L flask and heated to 100 oC. What is Q before the reaction begins? Which direction will the reaction proceed in order to establish equilibrium?

Solution:

55

0.078 (K) > 0.011 (Q)

Since K >Q, the reaction will proceed in the forward direction in order to increase the concentrations of both SO2 and Cl2 and decrease that of SO2Cl2 until Q = K.

http://www.chem.purdue.edu/gchelp/howtosolveit/equilibrium/Reaction_Quotient.htm

Thermodynamics of Chemical ReactionsFor any chemical process, the free-energy change under any conditions, ΔG, is given by:

R is the ideal-gas constant, 8.314 J/mol · K; T is the absolute temperature; and Q is the reaction quotient

When a system (a reaction) is at equilibrium: ΔG = 0, and K=Q Thus, at equilibrium, the equation above can be rewritten as

56

The relationship between ΔGo and K can be summarized as follows <0: K>1 = 0: K>1>0: K<1

Electrolysis and Mass Changes

charge (Coulombs) = current (Amperes) x time (sec)

Thermodynamics of Chemical Reactions

1 mole e- = 96,500 C = 1 Faraday

Mols of metal dissolved are obtained by dividing the mols of electron by n:

nFItM = (mol)

I –current (A); t –time (s); n- number of electrons transferred;F –Faraday constant (96500 C)

Faraday’s Law:

Free Energy

Thermodynamics of Electrochemical Cells

ΔG for a redox reaction can be found by using the equation

ΔG = −nFE

where n is the number of moles of electrons transferred, and Fis a constant, the Faraday.1 F = 96,485 C/mol = 96,485 J/V-mol

The Cell Potential :The Cell Potential :Work done in a redox reaction = - n FEcell

Units: Joules = moles x (coul/mole) x volts = coul x volt = J– 1 coulomb x 1 volt = 1 joule or Joule / Coulomb = volt– Since a spontaneous redox rxn does work on the surroundings,


59

Since a spontaneous redox rxn does work on the surroundings, the sign is “-”: W = - nFEcell = ΔG

Free Energy, ΔG = maximum useful work doneΔG = - nFEcellAt 1M concentrations, 1 atm pressure & 25 oC: ΔG = ΔGo

ΔGo = - nFEocell

Nernst Equation

• Remember thatΔG = ΔG° + RT ln Q


• This means−nFE = −nFE° + RT ln Q

The Nernst Equation:• At nonstandard conditions, the cell potential may becalculated using the Nernst equation:

E = Eo – 2.303 RTnF

log QSS


nF

mol electronsmol electronstransferredtransferred

ReactionReactionquotientquotient

AbsoluteAbsolutetemperaturetemperature

Gas constant,Gas constant,8.314 J/mol K8.314 J/mol K

Faraday,Faraday,96,500 J/Vmol e96,500 J/Vmol e--

StandardStandardcell cell

potentialpotential

ΔG = -nFEcell

ΔG0 = -nFEcell0

n = number of moles of electrons in reaction

F = 96,500J

V • mol = 96,500 C/mol

ΔG0 = -RT ln K = -nFEcell0

RT l K(8.314 J/K•mol)(298 K)


Ecell0 =

RTnF

ln K( )( )

n (96,500 J/V•mol)ln K=

= 0.0257 Vn ln KEcell

0

= 0.0592 Vn log KEcell

0

The Nernst Equation

• Substitution of the values for the gas constant Rand the Faraday into the Nernst equation at 25oCgives:


gives:

EE == EE oo –– 0.05920.0592nn loglog QQ

The Cell Potential andthe Progress of a Reaction

• For the reaction: Zn + Cu2+ → Zn2+ + Cu

• the cell potential is given by:


E = Eo – 2.303 RTnF

log [ Zn 2+][ Cu 2+]

AtAt standardstandard conditionsconditions:: EEcellcell == EEoocellcell

AsAs cellcell operatesoperates:: ZnZn22++ increases,increases, CuCu22++ decreases,decreases,loglog QQ increases,increases, EEcellcell decreasesdecreasesWhen EWhen Ecellcell = 0 (equilibrium); cell “runs down”= 0 (equilibrium); cell “runs down”

The Cell Potential and the Reaction Quotient Q

E = E o – 2.303 RTnF

log Q


• When:Q < 1: [reactant] > [product], Ecell > E

ocell

Q = 1: [reactant] = [product], Ecell = Eocell

Q > 1: [reactant] < [product], Ecell < Eocell

E = E o – 0.0592n log Q

The Relationships BetweenEocell, ΔGo and Keq

• Eocell, is related to ΔGo by:

ΔGo = –nFEocell• Since ΔGo = –2.303 RTlog K:


–nFEocell = –2.303 RTlog K

• Solving for Eocell or for K:

EE oo== 2.3032.303 RTRTnFnF

loglog KK

EE oo== 0.05920.0592nn loglog KK

loglog KK == nFEnFE oo2.3032.303 RTRT

loglog KK == nEnE oo0.05920.0592

Eocell, ΔGo and K: A Summary

Forward Reaction ΔGo Eocell KS t + >1


Spontaneous – + >1

Equilibrium 0 0 =1

Nonspontaneous + – <1


Calculating Equilibrium Constants• When an electrochemical cell operates, the concentrations of the ions change until Q = K .

• When the cell reaches equilibrium, Ecell = 0.

• Combining these facts with the Nernst equation gives:

( )KlRTE0E o

• Rearranging, we can derive an equation to calculate the equilibrium constant for a redox reaction:

( )KlnF n

E0Ecell −== o

( )KlnF n

RTE =o

Calculating K for a Redox Reaction

• Calculate K for the reaction that occurs at 25 oC when Mg is added to a solution of AgNO3.

• The net reaction is:

Mg + 2 Ag+ Mg2+ + 2 Ag

247 = ln (K) so K = e247 = HUGE

( )KlnFn

RTE =o

( )KlnC/mol)mol)(96500(2K)8(8.314)(2917.3 =V

Alkaline BatteryAlkaline Battery QuickTime Movie

Anode (Anode (--): ): Zn + 2 OHZn + 2 OH-- ------> ZnO + H> ZnO + H22O + 2eO + 2e--Cathode (+): Cathode (+): 2 MnO2 MnO22 + H+ H22O + 2eO + 2e-- ------> Mn> Mn22OO33 + 2 OH+ 2 OH--

Corrosion QuickTime Movie

Corrosion PreventionBecause since is a stronger reducing agent ( i.e. more easily oxidized) than Fe, it will act as a “sacrificial” anodein place of Fe, therefore preventing the iron metal from corroding.

Sacrificial Anode

Kinetics of Electrochemical Reaction

Polarization

nFItM = (mol)

I – current (A);t – time (s); n - number of electrons transferred;F – Farady constant (96500 C)

Faraday’s Law:

nFIM

tMr ==

The mass dissolution rate:

Exchange Current DensityAt equilibrium in a reaction such as

Electron flow must be the same in both directions (forward and reverse), i,e.,

so at equilibrium: nFI

rr rf0==

where io = exchange current density, related to the current flow in an equilibrium situation q

• At the equilibrium potential of a reaction, a reduction and an oxidation reaction occur, both at the same rate.

• For example, H ions are converted gas and released from the gas at the same rate

• The net reaction rate and net current density are zero

Polarizationexchange current density, related to the current flow in an equilibrium situation

Polarization• Electrode reactions deviates from the equilibrium

state due to the flow of an electrical current through an electrochemical cell causing a change in the electrode potential. This electrochemical phenomenon is referred to as polarization.

• The deviation from equilibrium causes an electrical potential difference between the polarized and the equilibrium (unpolarized) electrode potential known as overpotential

Polarization

Equilibrium potential for cathodic reaction = Eoc Cathodic Overpotential:

ηc = E – Eoc < 0

Real potential = E

Equilibrium potential for anodic reaction = Eoa

anodic Overpotential:

ηa = E – Eoa > 0

PolarizationEcorr = corrosion potential or mixed potential

corrosion rate: icorr = ia = rate of anodic dissolution in a system equilibrium

Zn in acidic water

Polarization

• Depending on the type of resistance that limits the reaction rate, we are talking about three different kinds of polarization

• activation polarization• concentration polarization and • resistance (ohmic) polarization or IR Drop

Activation Polarizationactivation polarization:• An electrochemical reaction may consist of several steps

• The slowest step determines the rate of the reaction which requires• The slowest step determines the rate of the reaction which requires activation energy to proceed

• Subsequent shift in potential or polarization is termed activation polarization

Activation Polarizationactivation polarization:• The overpotential due to the activation polarization is determined

by Tafel equation

whenever η = zero (i.e. no polarization), i = io, exchange current

nFRTβ

α3.2

=

Hydrogen Overpotential:

• Hydrogen evaluation at a platinum electrode:– H+ + e‐ → Hads

– 2Hads→ H2

Activation Polarization

2Hads→ H2

• Step 2 is rate limiting step and its rate determines the value of hydrogen overpotential on platinum

Source: K. B. Kabir

• Sometimes the mass transport within the solution may be rate determining – in such cases we have concentration polarization

• Concentration polarization

Concentration Polarization

Concentration polarization implies either there is a shortage of reactants at the electrode or that an accumulation of reaction product occurs

O2H4e4HO 22 →++ −−

Source: K. B. Kabir

• Fick’s Law:

• where dM/dt is the mass transport in x direction in mol/cm2s, D is the diffusion coefficient in cm2/s, and cis the concentration in mol/m3

d ’ l

(1) 10 3−×−=dxdcD

dtdM


iIM• Faraday’s law:

• Under steady state, mass transfer rate = reaction rate

(3) 0

δCCDnFi B −

=

Where δ is the width of the depletion zone

(2) nFi

AnFI

tAM

==Δ

• Maximum transport and reaction rate are attained when C0approaches zero and the current density approaches the limiting current density:

(4) δCDnFiL =


• The most typical concentration polarization occurs when there is a lack of reactants, and (in corroding systems) therefore mosta lack of reactants, and (in corroding systems) therefore most often for reduction reactions

• This is the case because reduction usually implies that ions or molecules are transported from the bulk of the liquid to the electrode surface, while for the anodic (dissolution) reaction, mass is transported from the metal, where there is a large reservoir of the actual reactant

Source: K. B. Kabir

• Equations (1) to (4) are valid for uncharged particles, as for instance oxygen molecules

• If charged particles are considered, migration will occur in addition to the diffusion and the previous


occur in addition to the diffusion and the previous equation must be replaced by

where N is the transference number of all ions in solution except the ion getting reduced

(5) N

CDnFi L δ=

Overpotential due to concentration polarization• If copper is made cathode in a solution of dilute CuSO4 in which

the activity of cupric ion is represented by (Cu2+ ), then the potential in absence of external current, is given by the Nernst equation:

)log(Cu320.337)(Cu

1log320.337 221

++ +=−=

nFRT.

nFRT.E

• When current flows, copper is deposited on the electrode, thereby decreasing surface concentration of copper ions to a level at (Cu2+)s. The potential of the electrode becomes:

S2

S22 )log(Cu320.337

)(Cu1log320.337 +

+ +=−=nF

RT.nF

RT.E

Source: K. B. Kabir

• Since (Cu2+ )s is less than (Cu2+ ), the potential of the polarized cathode is less noble, or more active, than in the absence of external current. The difference of potential, E2 − E1 , is the concentration polarization ,

Overpotential due to concentration polarization

equal to:

)(Cu)(Culog32

2S

2

12 +

+

=−nF

RT.EE

Source: K. B. Kabir

−=

+

++

L

S

NiC

DnFNiCuCu

)(

)()(

2

22

δ

δ

Overpotential due to concentration polarization

(5) N

CDnFi L δ=

⎟⎟⎠

⎞⎜⎜⎝

⎛−=−=

=+

L

L

ii

nFRTEE

DnFNiCu

1log3.2

)(

12Conc

2

η

δ

Source: K. B. Kabir

Concentration Polarization IR Drop• When polarization is measured with a potentiometer and a

reference electrode-Luggin probe combination, the measured potential includes the potential drop due to the electrolyte resistance and possible film formation on the electrode surface

• The drop in potential between the electrode and the tip of Luggin probe equals iR.

• If l is the length of the electrode path of cross sectional area s, kis the specific conductivity, and i is the current density then resistance

• iR drop in volts =

klR =

kil

Combined Polarization• Total polarization of an electrode is the sum of the individual

contributions: rcaT ηηηη ++=

Typical polarization curve http://www.electrochem.org/dl/interface/fal/fal04/IF8-04-Pages17-19,45.pdf

A voltage or current source

W E

V

ohmη

R E

V

R E

potentiostat

Third electrode

C E

WEactη

ohmη

WEconcη

REactη

REconcη

n act conc uE E IR− = η = η + η +

cab

ConstantConstant--Potential Potential CoulometryCoulometry

Cur

rent

/ATime after application of potential at which species is electrolyzed

Cha

rge/

C

∫∫ I dtI dt

VoltammetryVoltammetry

Measurement of (Faradaic) current as a function of applied potentialMeasurement of (Faradaic) current as a function of applied potential

Analyte concentration is related to peak or limiting currentAnalyte concentration is related to peak or limiting current

LinearLinear--Sweep VoltammetrySweep VoltammetryStirred SolutionsStirred Solutions

IILL ≡≡ Limiting Current = KCLimiting Current = KCAA

EE1/21/2 ≡≡ HalfHalf--wave Potential = Ewave Potential = E°°

LinearLinear--Sweep VoltammetrySweep VoltammetryUnstirred SolutionsUnstirred Solutions

EEAppliedApplied >> EE1/21/2 EEAppliedApplied << EE1/21/2

Electrode surface is depleted of reactants after prolonged reaction timesElectrode surface is depleted of reactants after prolonged reaction times

(Non(Non--Hydrodynamic) LinearHydrodynamic) Linear--Sweep Cyclic VoltammetrySweep Cyclic Voltammetry

For a reversible (Nernstian) couple:For a reversible (Nernstian) couple:IIpcpc = = ––IIpapa

EEpapa -- EEpcpc = 0.0592/n= 0.0592/nEE°° = (E= (Epapa + E+ Epcpc)/2)/2IIpp = KC= KCAA

IIFF = I= IDLDL = Diffusion= Diffusion--limited currentlimited currentIIFF I IDLDL Diffusion Diffusion limited currentlimited current

For an irreversible couple:For an irreversible couple:IIpcpc ≠ ≠ ––IIpapa

EEpapa -- EEpcpc > 0.0592/n> 0.0592/nEE°° = (E= (Epapa + E+ Epcpc)/2)/2Voltammogram is nonVoltammogram is non--symmetricsymmetricUsed mainly for qualitative analysisUsed mainly for qualitative analysis

StartStart

Electrochemical Impedance Spectroscopy

Electrochemical Impedance Spectroscopy• Ohms Law:

• Where V is the applied voltage and I is the current• R is a resistor. It follows Ohm’s Law at all current and voltage

levels• The resistance value is independent of frequency• AC current and voltage signals through a resistor are in phase

IVR =

• AC current and voltage signals through a resistor are in phase with each other

R: resistance, unit: Ωρ: resistivity, Ω cmC: capacitance, F

ε: permittivity, F cm‐1

LAC

ALR

ε=

ρ=

Electrochemical Impedance Spectroscopy• Impedance is a general expression for resistance under the

alternating current (AC) excitation signal

• For a sinusoidal current, the voltage is expressed by

E = E0 sin ωt

t: time

The current is

I = I0 sin (ωt + θ)

f: frequencyω: angular frequency = 2πfωt: phase angle

θ: phase shift

Electrochemical Impedance SpectroscopyImpedance can be given with an expression analogous to Ohm's Law as:

With Eulers relationship,

Then the potential is described as

and the current response as

The impedance is then represented as a complex number,

The impedance is composed of a real and an imaginary part

The expression for Z(w) is composed of a real and an imaginary part. If the real part is plotted on the Z axis and the imaginary part on the Y axis of a chart, we get a "Nyquist plot". N ti th t i thi l t th


Notice that in this plot the y-axis is negative and that each point on the Nyquist plot is the impedance at one frequency.

low frequency data are on the right side of the plot and higher frequencies are on the left. This is true for EIS data where impedance usually falls as frequency rises (this is not true of all circuits).

Nyquist Plot (or Cole-Cole plot)of Impedance

EIS data is commonly analyzed by fitting it to an equivalent electrical circuit model. Most of the circuit elements in the model are common electrical elements such as resistors, capacitors, and inductors. To be useful, the elements in the model should have a basis in the physical electrochemistry of the system.

Electrical Circuit Elements


Component Current Vs. Voltage

Impedance

resistor E= IR Z = R

inductor E = L dI/dt Z = jωL

capacitor I = C dE/dt Z = 1/j ωC


• An alternating current can be phase shifted with respect to the voltage

• The phase shift depends on what kind of sample the current passes

Electrical Circuit Elements

p

• To describe the response from a sample on the alternating current, we introduce 3 passive circuit elements (R, C and L)

• The current and voltage through a resistor, R, is not phase shifted the impedance is not dependant on frequency

• A resistor only contributes to the real part of the impedance

Electrochemical Impedance Spectroscopy• The inductor is an ideal conductor, and an ideal isolator• The inductor only contributes to the imaginary part of the impedance• The impedance of an inductor increases as frequency increases. An inductor's current is phase shifted 90 degrees with respect to the voltage

0

6

0 2 4 6 8

-6

-4

-2

L = 10-6 H

-X /

Ω

R / Ω

Increasingfrequency

a pure inductor Nyquist plotSouce: H. Fjeld

Electrochemical Impedance Spectroscopy• The capacitor (C ) can

store electrical charge:

ε: permittivity

ε0: permittivity of free space

εr: relative dielectric

LA

LAC rεε=ε= 0

εr: e at e d e ect cconstant

A capacitor only contributes to the imaginary part of the impedance. A capacitor's impedance decreases as the frequency is raised.

a pure capacitor Nyquist plot

Souce: H. Fjeld

Electrochemical Impedance Spectroscopy• Capacitors often do not behave ideally. Instead, they act like a

constant phase element (CPE) as defined below

Th CPE i il

( )[ ] 1−ω= n

Q jYZ

• The CPE is very versatile:

If n = 1, CPE represents an ideal capacitor

If n = 0, CPE represents a resistor

If n = -1, CPE represents an inductor

If n = 0.5, CPE represents a Warburg element

CPE

ctR

Impedance of Constant Phase Element (CPE)


2ctR

ctRZ’

Cdl

CPE

-Z”

Another common plot format of impedance spectra is the Bode plot. In general it depicts two curves. The x-axis shows the logarithm of the frequency. The left axis gives th l ith f th

Bode plot

the logarithm of the impedance, while the right axis gives the phase angle.

Bode plots of Impedance


The Simplified Randles cell is one of most common cell models. It includes a solution resistance, a double layer capacitor and a charge transfer (or polarization resistance).

Simplified Randles Cell

Source: Gamry.com

equivalent circuit for a Simplified Randles Cell


The polarization resistance was calculated to be 250. A capacitance of 40 μF/cm2 and a solution resistance of 20 Q were also assumed

Simplified Randles Cell

Nyquist plot of The Simplified Randles cell

Electrochemical Impedance SpectroscopySimplified Randles Cell

Source: Gamry.com

Nyquist plot of The Simplified Randles cell

Diffusion can create an impedance known as the Warburg impedance. At high frequencies the Warburg impedance is small since diffusing reactants don't have to move very far. At low frequencies the reactants have to diffuse farther, thereby increasing the Warburg impedance.

Warburg impedance of Diffusion


The equation for the "infinite" Warburg impedance is:

Where is the Warburg Constant.On a Nyquist plot the infinite Warburg impedance appears as a diagonal line with a slope of 0.5. On a Bode plot, the Warburg impedance exhibits a phase shift of 45°.

Warburg impedance is only valid if the diffusion layer has an infinite thickness. Quite often this is not the case. If the diffusion layer is bounded, the impedance at lower frequencies no longer obeys the equation above. Instead, we get the form:


Warburg impedance of Diffusion

we get the form:

with,δ = Nernst diffusion layer thicknessD = an average value of the diffusion coefficients of the diffusing species

Impedance of electrochemical reaction at the electrode with infinite diffusion

In case a charge transfer is also influenced by diffusion to and from the electrode, the Warburg impedance will be seen in the impedance plot. The Warburg element is easily recognized by a line with an angle of 45 °in the lower frequency region. The equivalent of this electrochemical cell is called Randles' circuit.

Or CPE


circuit showing the solution resistance, double layer capacitance (or CPE), charge transfer resistance and Warburg impedance


Or CPE


Complex plane plots for the circuit of Fig 5 with an ideal double layer capacitance (which means n=1) (a) and a CPE (b) with n = 0.88.



Peak frequency: ω0 = (RC)-1


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