Chem 4003

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Introduction

Definitions:

Electrochemistry

Electrochemical Engineering

Challenges

Course Content

Major Applications

History

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Electrochemistry

Electrochemistry is the branch of chemistryconcerned with the interrelation of electrical andchemical effects

Deals withThe study of chemical changes caused by the

passage of a current

The production of electrical energy by chemicalreactions

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The use of chemical engineering fundamentalprinciples for the study and analysis of

electrochemical systemsThermodynamics

Transport phenomena

kinetics

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What is an electrochemicalsystem?

System characterized by:

Strong interactions among solute and with the

solvent (ionic species)Passage of a current

Potential

Electrical energy transformed into chemicalenergy or vice versa

e.g., batteries, fuel cells, etc

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Challenges

No much cover on other courses

Chemistry

ThermodynamicsPhysical chemistry

Electrochemical systems are different

Break any myths about electrochemical systems

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Course Content

Basic concepts

Thermodynamics

Electrode kinetics Transport mechanisms

Modeling

Applications

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Applications

Production of Al and Cl

Corrosion

Batteries and Fuel Cells Electroplating

Cathodic protection

Super capacitors

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Major Products based onelectrochemical technology

Process or Product (data from

National Research Council)

Annual Market

($ billion)

Aluminium

Sodium Hydroxide

ChlorineCopper

Other metals and chemicals

Electroplating

Batteries

Semiconductor Processing

4

3

22

2

10

4

1

Total 28

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History

Discoveries started around 1800

Allesandro Volta (first battery)

Michael Faraday (Faradays law) David Grove (1839) discovered the fuel cell

Georges Leclanche (1868) constructed the carbon

zinc battery

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History

Hall-Heroult aluminum process (1886) reduced theprice from $100/lb to $2/lb

Walter Nernst Julius Tafel

Great advances in electroplating (1920-1940s)

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History

The formal synthesis of electrochemistry andengineering began in 1950s

Norbert Ibl in SwitzerlandCharles Tobias in US

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Summary

Electrochemistry


What is an electrochemical system? Major applications of electrochemistry

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OutlineChapter 1: Basic Concepts

Redox reactions Electrochemical Cells-definition Standard electrode Standard cell potential Electrochemical cells

Representation Galvanic cells Electrolytic cells

Nernst equation Faradays law Current and voltage efficiency Ion conduction Transfer numbers

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Redox reactions: Oxidation

Oxidation

Process by which an element losses electrons

(increases its oxidation number)The electrode at which oxidation takes place is

called the anode

e.g.,

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Redox reactions: Reduction

ReductionProcess by which an element gains

electrons (decreases its oxidationnumber)

The electrode at which reduction takes

place is called the cathodee.g.,

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Exercise # 1

Classify the following redox reactions, include theelectrodes name

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Electrochemical Cells

Consists of:At least two electrodes where reactions occur

Electrolyte, for conduction of ionsExternal conductor, to guarantee continuity of

the circuit

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Electrochemical Cells

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Key information

Electrochemical reactions ALWAYS take place onelectrodes NOT in the bulk

A potential is always measured respect toANOTHER electrode

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Standard Electrode Potentials

The universal reference electrode is hydrogen (SHE)

Standard conditions:

Temperature 25oC

Unit activity coefficient of H+ ions

Reaction

E: Electrode potential

0: Standard conditions

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SHE

Consists of a Pt wire immersed in a solution of 1 MH+

Hydrogen gas is bubble at 1 atm The Pt wire provides a surface area for the reaction

to take place

The gas stream keeps the solution saturated at theelectrode site

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SHE

It is a theoretical electrode

It cant be manufactured because it is impossible to

have hydrogen ion activity of 1.00 M However, hydrogen electrodes can be

manufactured

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Building a H2 Electrode

Begin with aPyrex testtube

Step 1: Usingglassblowingtechniques, add ashort glass tube tothe side of thetube

Step 2: Spotweld (or silversolder) a 1 cm x1 cm square of

platinum foil as aPlatinum wire

Step 3: Again,usingglassblowing,seal the

platinum wireinto the base ofthe test tube

Making a simple, standard Hydrogen electrode

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Meaning of Potential

The potential represents the maximum electricalenergy available from a cell

Its related to the Gibbs free energy of the cell by:

n: number of electronsF: Faraday's constant (96485 C/eq)

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Questions?

What should be the sign of the potential E0 for areaction to be spontaneous?

Answer: POSITIVEPositive potentials mean that the reaction is

spontaneous

Negative potentials mean that the reaction is notspontaneous

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Standard Potentials inElectrochemical Cells

Appendix B of the book summarizes the standardelectrode potentials

Standard electrode potentials can be used tocalculate the Standard potential of anelectrochemical cell

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Standard cell potential: Calculations

1. Choose the electrode reactions from the standard

electrode potentials table2. Reverse the sense of the reactions according to

your system

1. Reverse the sign of your standard potential3. Balance the number of electrons multiplying by a

positive number

4. Add the electrode reactions to obtain overallreaction

5. Add the potentials to obtain the overall potentialof the cell

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Standard Cell potential: Calculations

You can balance the stoichiometry of the equationby multiplying by any positive constant

This operation does not alter the potential of thecell (potential is an intensive quantity, unaffected

by the number of electrons)

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Schematic Representation ofElectrochemical Cells

Include all the phases involved

Separate the phases using bars

Include information about solvent andconcentrations if available

e.g.:

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Exercise #2

Calculate the standard potential of the cell

What is the anode?

What is the cathode?

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Galvanic Cells

It is an energy producing cell

Also known as:

Driving cellSpontaneous cell

They are used as batteries (several cells in series)

The standard potential is the maximum potentialthat can be provided by the cell

The anode is assigned a negative sign (negativeelectrode)

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Galvanic Cells: continued

The cathode is assigned a positive sign (positiveelectrode)

Sign of current:Positive if it leaves the electrode to the

electrolyte

Negative if it enters the electrode from theelectrolyte

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Exercise #3

Write the reactions, identify positive and negativeelectrodes, identify cathode and anodes, identify

direction of the current, and draw the cell includingexternal circuit and flow of electrons, for thefollowing reaction

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Electrolytic Cells

It is an energy consumer cell

Also known as:

Driven cellNon Spontaneous cell

Opposite process of a battery (required energy to

operate) The standard potential is the minimum necessarypotential required for the cell to operate

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Electrolytic Cells: continued

The cathode is assigned a negative sign (negativeelectrode)

The anode is assigned a positive sign (positiveelectrode)

Sign of current:

Positive if it leaves the electrode to theelectrolyte

Negative if it enters the electrode from theelectrolyte

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Exercise #4

Write the reactions, overall reaction, calculate thetotal standard potential of the cell, identify positive

and negative electrodes, identify cathode and anodes,identify direction of the current, and draw the cellincluding external circuit and flow of electrons, forthe following reaction:

Cu + Zn 2+ Cu 2+ + Zn

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Hint It is recommended that for every problem that you

solve you start by:

Writing reactionsCalculating open circuit potential (identifying type

of cell)Drawing schematic of cell and identifying:

Positive and negative electrodes Anode and cathode Direction of the current

Direction of electrons

This is important to understand your problem and thedata that you are given

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Electrolysis of Brine

Membrane: bi-layer membrane made of perfluorocarboxylicand perfluorosulfonic acid-based films

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Summary

Where do electrochemical reactions take place?

What is oxidation? What is reduction?

What is the meaning of potential? Define galvanic and electrolytic cell

Calculate the standard potential of a cell

Define +,-, cathode, anode, current sign, flow ofelectrons

Draw schematic of electrochemical cell

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Nernst Equation

Express relationship between the potential of thecell and the concentration (no standardconcentration)

si

: stoichiometric coefficient of species i

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Nernst Equation

The electrode reaction is written in simplified form as

si: positive for products and negative for reactants

Mi: symbol for the chemical species

zi: charge number of the chemical species

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Steps to use Nernst Eq.

Write down electrode reactions

Determine # of electrons transferred (balance

equations) Use Eq. 1 accordingly

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Exercise #6

In a Zn/Cu cell, If the reaction is done in a cell in5.00 M Zn+2 and 0.30 M Cu+2 at 25oC, what is the

cell voltage?

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Faradays Law

Relationship between charge passed (Q) andamount of substance oxidized or reduced (m) at anelectrode

The amount of product formed is directlyproportional to the charge passed

For a specified quantity of charge passed, themasses of products formed are proportional tothe electrochemical equivalent weights of the

products

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Faradays Law Eq.

M: atomic or molecular weightI: current, At: time elapsed, sF: Faradays constant, 96,485 C/equiv or 26.8 Ah/equiv (last

one is very useful in battery applications)

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Faradays Law Eq.

The product of: (It) is known as total charge passed(Q)

If current changes with time, it should be integratedover time to obtain Q

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Deviations from Faradays Law

Some causes of deviation from Faradays law are:Consumption of some of the charge by parasitic

processesAll of the reactants are not consumedThe postulated process is not the actual processSome of the material from the sample falls of

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Units and Formula Reminder

Power is the product of current by voltage:

P = I V

(units are Win international system)W = AV

W = J/s

A = C/s

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Exercise #7

Solve Ex. 2 of the book (Ch2, p26), parts a, b, andc.

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Current efficiency

For electrolytic process

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Current efficiency

For galvanic process, known as faradays efficiency

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Voltage efficiency

For electrolytic process:

For galvanic process:

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Energy efficiency

Product of the current and voltage efficiencies:

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Exercise #8

Solve problem 4 of the book (Ch2, p. 27)

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Ion Conduction

ConductivityThe measure of the materials capability to

transfer electrical energy

Electrical conductivity (electronic conductivity)is used in metalsIonic conductivity is used in electrolytes (ions

transfer the current)

Conductivity of metals much higher than ionicconductivityUnits: S/cm (Siemens)

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Order of Magnitude ofConductivities

In an aqueous system at room temperature:

10-2 S/cm

Much lower than metals, order of magnitude formetals is:

105 S/cm

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Ionic Conductivity

This Equations assumes complete dissociation ofspecies

ui: ionic mobility, cm2

-mol/J-szi: charge of species, dimensionless

Ci: concentration of species, mol/cm3

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Charged particlein electrified model

Assumes:

Ions are spheres

Continuous viscous mediumLow Reynolds numbers

Uses Stokes law to calculate the drag force

Uniform electric field

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Charged particle model continued

r : radius of particle, cm

Ef: forced field, V/cm. For calculations

assume 1 V/cme : charge of an electron, 1.6x10-19 C/chg

: viscosity, g/cm-s

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Units Reminder

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Procedure to use chargeparticle model

Calculate velocity using Eq. 11. AssumeEf =

1V/cm

Check value ofRe number

d: ion diameter, cm: density, g/cm3

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Procedure continued

Calculate current density

Since the field is proportional to the negative of thepotential gradient, the conductivity can becalculated

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Equivalent conductance model

Equivalent conductance (, cm2/ohm-equiv) doesnot change abruptly with concentration

Correlated with square root of concentration (Fig.2.4)

Extrapolating to zero gives the equivalentconductance at dilute conditions ()

Kohlrausch noticed that the difference between having a common ion was approximately constant

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Equivalent conductance model

Kohlrausch concluded that the equivalentconductance can be considered the sum of twoionic components acting independently:

Equivalent conductances are given in Appendix C

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Mobility and diffusivity

Equivalent ion conductance is related to mobility:

At dilute conditions Nernst-Einstein equationrelates mobility to diffusivity:

Di: diffusion coefficient of species i, cm2/s

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Calculation of ionic conductivityusing ion conductance

Get equivalent conductance (Appendix C, CRC,etc)

Calculate mobility using Eq. 14 Calculate conductivity using Eq.10

This procedure is not valid at high concentrations(see Fig. 2.6)

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Exercise #9

Calculate the ionic conductivity of a 0.1 N KClsolution using two different methods. Compareyour values. The crystal radius of K is 1.33

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Effect of Temperature onionic conductivity

As a general rule ionic conductivity increases withincreasing temperature

Rule of thumbs:

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Problem

What would be the conductivity of KCl at 60 oC?

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Transference number

Represents the fraction of current carried by aspecified ion in the absence of concentrationgradients

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Useful Expression

Combining Eqs 18 and 14:

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Transference number

The fractional current carried by each species mustadd up to the total current, then

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Transference number

For a binary electrolyte

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Exercise #10

Solve problem 6 of the book, Ch2 (p. 27). Thetransference number of Cu+2 in a copper sulfatesolution in water is 0.44

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Summary

Use and understand Nernst equation

Calculate theoretical amount of reactants and

products using Faradays law Determine current, voltage and energy efficiency

Calculate ionic conductivity

Calculate transference numbers

Chapter 2:Th d i f l h i l

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Outline

Cell thermodynamics

Temperature and Pressure effects

Nernst Equation Pourbaix Diagram

Equilibrium constant

Reversible heat transfer

Thermodynamics of Electrochemical Systems

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Cell Thermodynamics

Meaning of potential

n :number of electrons

F: Faraday's constant (96485 C/eq)

Previously we used

the definition of potential

0 0G n F E=

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Cell Thermodynamics

Need to relate thermodynamic (reversible) potentialto state variables

Electrochemical cells are treated at constant T andP

Consider closed system (transport of materialbetween system and surrounding is not permitted)at constant T and P to start relationships

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Cell thermodynamics

Using first law of thermodynamics (closedsystem):

The work can be associated with

Mechanical changes

Other sources: magnetic, surface, or electricwork

U q w=

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Cell thermodynamics

For a reversible change at constant temperature, theheat transferred is given by

S: change in entropy

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Cell thermodynamics

The canonical state variable for a system operatingat constant T and P is the Gibbs free energy:

The enthalpy change is given by:

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Cell thermodynamics

Combining Eqs. 1 to 4:

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Cell thermodynamics

Substituting Eqs. 6 and 7 into 5 yields:

Reversible work, therefore it is the maximum workthat can be obtained from the system

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Cell thermodynamics

The maximum electrical energy available in anexternal circuit is equal to the number of chargesmultiplied by the maximum potential difference

(reversible work):

By using: F in C/ eq and E in V, your work will give

you J

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Cell thermodynamics

Equating Eqs. 8 and 9:

Equation 10 demonstrates that we can obtainthermodynamics information from electrochemicalmeasurements, and vice measurements, and vice-

versa

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Cell thermodynamics

Because Gibbs free energy is a state function (itdoes not depend on trajectory) we can manipulateequations mathematically to obtain reversible

potentials, e.g.:

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Cell thermodynamics

Substituting Eq. 10 into 11:

Dividing by F and simplifying:

Eq. 13 is ALWAYS TRUE

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Thought

We said before:

You can balance the stoichiometry of the

equation by multiplying by any positive constantThis operation does not alter the potential of thecell (potential is an intensive quantity,unaffected by the number of electrons)

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Answer to thought

Yes it is true because we were multiplying theindividual reactions to eliminate the electrons fromthe total reaction

However, Eq. 13 is still true

See demonstration on the board

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Thought

What happen when the final reaction involveelectrons?

1. Choose the electrode reactions from thestandard electrode potentials table

2. Reverse the sense of the reactions according toyour system

3. Reverse the sign of your standard potentials4. Add the potentials using Eq. 13 to obtain the

potential of the total reaction

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Cell thermodynamics:conclusions

Eq. 13 is always valid

If your overall reaction does not involve electrons

you dont need to correct the potentials (useprocedure explain before)

If your final reaction has electrons involved youneed to strictly use Eq. 13.

Standard Potentialand Gibbs free energy

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and Gibbs free energy

According to Eq. 10 the standard potential of the

cell can be calculated from the Gibbs free energy Gibbs Free energy for a reaction:

Where:

s: stoichiometric coefficient (positive for products and

negative for reactantsG: free energy of formation. Information tabulated

see Thermo chemical data handout

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Exercise 1

Solve Problem 2 of the book

(Ch 3,p. 46)

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Temperature Effect

We can calculate the reversible electrode potentialat other temperature by calculating the Gibbs freeenergy at a specified T and Using Eq. 10

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Temperature Effect

Consider a reversible process were only mechanicalwork is permitted, then the first law is

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Temperature Effect

The enthalpy is defined by

A differential change in enthalpy is given by

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Temperature Effect

The Gibbs free energy is defined by

A differential change in Gibbs free energy is givenby

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Temperature Effect

Combining Eqs. 14, 16, and 18

Consider a process from state 1 to state 2, we canwrite Eq. 19 for each state as:

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Temperature Effect

At constant pressure Eq. 19 becomes:

Substituting Eq. 10 into Eq. 21 yields:

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Temperature Effect

Using Eq. 22 we can calculate the effect oftemperature on the reversible potential.

Over a small temperature range a constant entropychange of reaction is usually justifiable, thenintegrating Eq. 22:

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From thermodynamics

The enthalpy, entropy, or Gibbs free energy of areaction is given by:

Where:

M: property (H, S or G)

s: stoichiometry coefficient (positive for

products and negative for reactants)

ff

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Temperature Effect:Important considerations

It is very important to include the phases in thecalculation, that is, make sure that you read the

properties of the compounds at the T physical stage

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Exercise 2

In a fuel cell the overall reaction is given by:

Write the electrode reactions Estimate the standard cell potential Calculate the change in reversible potential with

temperature (mV/K) near room temperature What is the reversible potential of the cell at 35 oC.

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Pressure Effect

The change in the reversible potential with pressurecan also be calculated from Eq. 19 by taking itsderivate at constant temperature:

Change of volume in the reaction

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Pressure Effect

Substituting Eq. 10 into Eq. 24 yields:

At low pressure the ideal gas assumption is valid,then:

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Pressure Effect

Substituting Eq. 26 into Eq. 25 and integrating:

Eq. 27 can be used at low pressures where the idealgas assumption is valid

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Exercise 3

Calculate the reversible potential of the celldescribed in Exercise 2 at 3 atm

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Thermodynamics Properties

Thermodynamics properties can be obtained bymeasuring electrochemical potential, e.g., enthalpycan be calculated by

Entropy change of a reaction can be calculated byusing Eq. 22

Nernst Equation

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Nernst Equation

Walther Nernstdeveloped an equation thatcorrelates the voltage of the cell with its properties

To calculate the reversible potential at conditions

different to standard we can use the Eq:

Where a is the activity coefficient of species i

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Nernst Equation

As an approximation, we can ignore activitycoefficient corrections and use concentrations in

place of activities:

Ass mptions

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Assumptionswhen using Nernst Equation

Neglects:

Activity coefficients

Potential that arise from bringing two differentliquid phases into contact

Nernst Equation:

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Nernst Equation:Important considerations

It cant be used to make T and concentrationcorrections simultaneously.

In such a case:

Use Eq. 22 or Eq. 25 to make T and Pcorrections, respectively

Applied Nernst Eq. at the new T or P.

Nernst Equation:

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Nernst Equation:Conventions to activity coefficients

Assume activity coefficient of 1 for the followingcases:

Substances in excess (e.g., solvents)

solids

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Pourbaix Diagram

Consists of plotting the potential vspH

This type of diagram is useful because it allowsidentifying phases in equilibrium providing criticalinformation on the behavior of the system

It was proposed by Marcel Pourbaix

Procedure to buildPourbaix Diagram

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Pourbaix Diagram

Write down all the equations involved in the system Use Nernst equation Express all reactions as a function of potential, pH, or

both

Plot Potential vs. pHEqs. independent of pH are plotted as a horizontal

lineEqs. independent of potential are plotted as a

vertical lineEqs. dependent on both (pH & potential) are plotted

as an oblique line

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Pourbaix diagram other assumptions

Typical assumptions

Concentrations of ions 10-6 M

Gases at 1 atm

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Exercise 4

Build the Pourbaix diagram for the lead-watersystem (also known as le Plant battery). Take intoconsideration the following reactions

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Equilibrium Constant

When the reversible potential equals zero, meansthat the driving force for the electrochemicalreaction is zero, which represents the stable

equilibrium state for the cell

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Equilibrium Constant

Since the potential is zero at equilibrium, we candetermine the equilibrium constant from thestandard open circuit potential:

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Exercise 5

Calculate the equilibrium constant for theDaniellCell

Zn/Zn+2 /Cu+2 /Cu

Heat Transfer

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2.122

Because the system works at constant T and

Pressure, we expect to see some transfer of heat tothe medium

Heat transfer includes: reversible and irreversible

heat (always negative, loss to ambient) The reversible heat is given by

IfS>0 the process is endothermic

IfS

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For a reversible process in an open system, the energy

balance is given by:

:partial molar quatity (includes mixing energy)

Most of the time mixing energy is low compared toenergy of reaction, then the change can be calculated

based on pure components

S

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Summary

Meaning of potential (related to Gibbs free energy)

For temperature effects use the entropy change (becareful with the physical change stage of thereactants and products)

For pressure change use the volume change(include only gases in the change calculation)

Use assumptions in Nernst Equation

S

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2.125

Summary

You cant correct for T, P and concentration effectssimultaneously Correct for T and P Correct for concentration effect

Know how to build and interpret Pourbaix diagram Calculate equilibrium constants Calculate heat transfer in open systems

Whats the meaning of a positive and negativeentropy change?

Chapter 3: Electrode Kinetics

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Outline

Interface Role

Electric Double Layer

Helmholtz model Electrode Kinetics Models

Butler-Volmer Equation

Tafel Equation

Reference Electrodes

f l

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Interface Role

Electrode kinetics are governed by the potentialdifference across a thin (order 10 A) layer adjacentto the electrode surface

This layer is called the double-layer

Potential difference across the thin layer is about0.1 V

Large magnitude of electric field (106 V/cm)

f l

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Interface Role

Large driving force for the electrode reaction

Because of the large electric field we will havecharge separation in the double layer

Electroneutrality condition does not apply in thedouble layer region

I f R l

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Interface Role

At equilibrium (thermodynamics relationships areused) theres no current applied

When current is applied the potential will deviatefrom equilibrium

The difference between the potential and theequilibrium potential is called the overpotential (or

surface overpotential)

I f R l

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Interface Role

The surface overpotential is given by:

I ith El t d Ki ti

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Issues with Electrode Kinetics

Electrode reactions are heterogeneous. This impliesthat a conductive surface must be in contact withthe electrolyte

This arrangement produces a number of issues (weneed a clean surface to evaluate pure kinetics):Film formationChanges in electrode microstructure

Electrolyte contaminationAll of them cause variations in current-potentialmeasurements

E i t l S l ti

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Experimental Solutions

Careful electrode surface preparation (e.g., polishthe surface, in corrosion we need a rough surfaceinstead)

Electrolyte purification (e.g., deoxygenation of theelectrolyte)

Control of mass transport to the electrode surface

(mixing)

Typical KineticsE i t l S t

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Experimental Set-ups

1-reference electrode

2-gas in

3-gas out4-Luggin capillary

5-platinum counter electrode

6-rotating electrode

7-temperature probe

8-pH electrode

9-working electrode.

Typical Kinetics

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ypExperimental Set-ups

The electrode rotates to have control of the masstransfer limitations

The flow profile is known in this type of systems

Classical arrangements:

Rotating disk electrode (use for laminar flows)

Rotating cylinder electrode (use for turbulent

flows)

More Issues with

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Electrode Kinetics

Accurate measurement of the potential is difficult Because we cant measure an absolute value for the

potential, we are forced to use a reference electrode

Reference electrodes are chosen based on:reversibility, stability, and convenience (cost) Suitable placement of the reference electrode is

another issue (need to correct for ohmicdifferences)

El t i D bl L

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When we apply a potential to an electrode thecharges that accumulate at the surface of theelectrode attract opposite charges from the

electrolyte We expect to have a distribution of charges in order

to balance the charges at the surface with the

charges from the electrolyte


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There are different models to determine the effect(or to simulate the effect) of the double layer:

Helmholtz model

Gouy and Chapman model

Stern model

Helmholtz Model

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Helmholtz Model

It was developed in 1879 Its the simplest model for

double layer

Two parallel layers ofcharges are separated bysolvent molecules

The distance (d) representsthe outer Helmholtz plane

Fixed distribution of layer(charges)

Helmholtz Model

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Helmholtz Model

Double layer model as a simple parallel platecapacitor

C: capacitance per unit area (F/m2 or mF/cm2)

D: dielectric constant (or relative permittivity)

d: Separation between charges, cm

0: Permittivity of free space, 8.8542x10-14 F/cm

Helmholtz Model

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Helmholtz Model

The potential distribution is a linear functionbetween the two layers of charge

Because the distribution of the charges does notchange the potential is constant, also C is constant

Helmholtz Model

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Helmholtz Model

For water D10, d10 A, then:

Helmholtz Model

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Experimentalmeasurements use a NaFsolution in a mercuryelectrode

Mercury offers a uniform

surface and NaF is notadsorbed Capacitance in the right

order of magnitude but itis not constant

Only for highconcentrations thecapacitance tends to beconstant

Fig. Capacitance vs. potential

relative to the point of zero chargefor a NaF solution on a mercuryelectrode at 25oC (experimentaldata)

Gouy-Chapman Model

It d l d i 1910

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It was developed in 1910 Its analogous to the Debye-

Hckel theory The thickness of the double layer

represents a compromise betweenelectrical forces (tending to

maintain the ordering) andthermal forces (tending to makethe arrangement random)

No fixed charges

Significant deviation fromelectroneutrality occurs on theDebye length

Gouy Chapman Model

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Gouy-Chapman Model

The capacitance is given by

Gouy-Chapman Model

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Its good at potentials near the zero charge region Atpotentials ore than 0.5 V in either direction the observedflattering of the capacitance is not predicted

Fig. Capacitance vs. potential relative to

the point of zero charge for a NaF solution,calculated using Gouy-Chapmanmodel (Eq. 3)

Fig. 5.2 Capacitance vs. potential relativeto the point of zero charge for a NaFsolution on a mercury electrode at 25oC(experimental data)

Stern Model

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Combines the Helmholtz model

and the Gouy-Chapman model Some of the charge is fixed (d

region) and some of the charge isdiffuse or spread out

The total length of the boundarylayer is given by the fixed region

plus the diffuse region

Stern Model

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Stern Model

Because the capacitances are in series thecapacitance of the double layer is given by:

Stern Model

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Stern Model

The smallest capacitance is the one that governs thebehavior of the system:

If CH CG-C then CSCG-C

If CH

CG-C

then CS

CH

Eq. 5

Stern Model

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Stern Model

Assuming that CH is

constant

The Stern model predictsthe experimental datavery well

Fig. Capacitance of 0.001 M NaF vs. potential relative to

the point of zero charge at 25oC. The experimental data(circles) agrees very well with the model (Stern Model, Eq.4)

Consequences

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of the Double-Layer

Species outside the Helmholtz region are toodistant to react

The driving force for the reaction is the potential

drop across the Helmholtz region rather than thepotential drop across the whole double layer

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Electrode Kinetics

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Electrode Kinetics

In ordinary kinetics weexpress the progress of areaction by plotting the

reaction coordinate vs. theenergy of the species(assuming transition statetheory)

Electrode Kinetics

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Electrode Kinetics

Let us consider one elementary stepelectrochemical reaction:

WhereO+: oxidized species

R: reduced specieskc: cathodic reaction rate constant

ka: anodic reaction rate constant

Electrode Kinetics

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A more negative potential (morepositive energy) tends to promotereduction

At progressively more negativepotential, the energy of the oxidized

species is increased

3: reduction is favored

1

: oxidation is favored

2: equilibrium potential, no netreaction takes place

Electrode Kinetics

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Electrode Kinetics

Consider the case where we start an experiment atthe potential 1 and we reduce it to 2

The activation energy for the first process (Eac1) is

higher than for the second process (Eac2)

Electrode Kinetics

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We can express the activation energy for the secondprocess as a function of the first process by:

Where

is the symmetry factor (transfer coefficient)

represents the fraction of energy that has been usedto reduce the activation energy of the reaction

Electrode Kinetics

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Similarly the activation energy for the anodicprocess (which increases) can be expressed by:

n: is the number of electrons transferred in thereaction. For elementary steps n is most of the time1, it is unusual to have more than1 electron

involved in an elementary step

Electrode Kinetics

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The form of our kinetic expression is the same asthat for chemical reactions (using an Arrheniusdependence of temperature):

Where

k: is the a constant, cm/s G: is the free energy of activation

Electrode Kinetics

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The rate of electrochemical reaction is directlyproportional to the current density:

Wherer: reaction rate, mol/s cm2

i: current density, A/cm2 (the area is the electrode surface area)c: is the reactant concentration (mol/cm3)

Electrode Kinetics

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For the general anodic reaction given in Eq.6 (firstorder reaction), we substitute Eq. 8 into Eq. 10

We have assumed a reference potential, therefore thesubscripts 1 and 2 have been dropped

Electrode Kinetics

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We can redefine the reaction constant including theactivation energy at our reference potential:

Electrode Kinetics

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Similarly for the cathodic reaction:

The net current density (i=ia-ic) is the difference

between the anodic and cathodic current densities(Eq. 12-Eq. 13)

Electrode Kinetics

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At equilibrium the net current density is zero, butthe rates of the anodic and cathodic reaction are notzero. The magnitude of both (ia and ic) are the same

and this is called exchange current density (i0)

Electrode Kinetics

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If we designate the equilibrium potential as 0

Taking the logarithm of Eq. 15 and rearranging:

Electrode Kinetics

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Substituting Eq. 16 into Eq. 14 and using thedefinition of overpotential:

Electrode Kinetics

Rearranging Eq. 17:

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Eq. 18 is a general kinetics expression for the first orderelementary step given in Eq. 6

The concentration of the reactants are at the surface of theelectrode The cathodic and anodic kinetic constants can be

evaluated at equilibrium from the exchange current

density:

Where the superscript 0 represents equilibrium conditions

Eq.18

Electrode Kinetics

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Substituting the kinetic constants into Eq. 18 weobtain:


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Redefining the transfer coefficients for the anodic and

cathodic components as:

And assuming the concentration at the surface is equal tothe concentration at the bulk which will be the case ofequilibrium condition, then Eq. 19 becomes:

Eq. 20 is known as theButler-VolmerEquation


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Three variables a, c, and i0 need to be determined to useButler-Volmer Equation

Butler-Volmer equations gives a good representation of

experimental data for many systems The exchange current density is a strong function of

temperature When the exchange current density is very large, the

reactions is said to be reversible


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When two reactions take place simultaneously, onthe same electrode surface, we can use the Butler-Volmer equation for each of them

We will have to determine the individualparameters for both reactions

Linear form ofButler-Volmer Equations

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Butler-Volmer Equations

One of the disadvantages of the Butler Volmerequation is that the overpotential cant be expressedimplicitly

To confront this several approximations have beenmadeSmall surface overpotentialLarge surface overpotential


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Butler-Volmer Equations

When the overpotential is very small, theexponential term in Eq.20 can be expanded usingMaclaurin series, neglecting some of the terms in

the series:


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Eq. 21 is the linear form of the Butler-VolmerEquation

The current density is a function of only oneparameter (i0 and the transfer coefficients can bedefined as one constant)

It is used to model systems operating at low currentdensities

Its often used when the overpotential is 10mV orless

If the current density does not vary widely (30%),the linear expression can be used even in the highcurrent density

Tafel Equation

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If the overpotential is large and positive, the secondterm in Eq. 20 can be neglected:

If the overpotential is large and negative, the firstterm in Eq. 20 can be neglected:

Tafel Equation

Eqs. 22 and 23 are known as Tafelti

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equations

Taking the logarithm of Eq.22 andrearranging:

The constantB is called the Tafel Slope Use of the Tafel approximation depends on the error thatcan be tolerated

It is general used when the overpotential is at least 50 to100 mV

Th T f l l i b t 30 t 300 V/d d

andWhere

Tafel Equation

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Values of the exchange current density and thetransfer coefficient are obtained experimentally

Plot overpotential vs. log(i). The slope of the linewill give the transfer coefficient, and the interceptwill give the exchange current density

Example 1

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Solve problem 3 of chapter 5 in your text book

Example 2

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Solve problem 2 of chapter 5 in your text book


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3.179

So far we have learned how to estimate kineticexpressions as a function of the overpotential

We have also learned that the overpotential is givenby:


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3.180

When using the overpotential equation, we need tomake sure that the potential that we measure is onlydue to the electrochemical reaction

One of the ways to accomplish that is by usingreference electrodes Before discussing more details about reference

electrodes, we will present a discussion in the

factors that affect the potential

Contributions tothe Potential in Galvanic Cells

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The maximum potential that we can measure in agalvanic cell is the equilibrium potential.

The equilibrium potential is only obtained when

no current (or very small current) flows throughthe circuit

When a current flows through the circuit the

potential measure will always be smaller than theequilibrium potential


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The decrease in the potential of the cell is due toseveral limitations, and this is often calledPotential loss, Eloss

Therefore, the potential of a cell is defined as:

Where

E: equilibrium potential : potential of the cell


Th t ti l li it ti i l d

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The potential limitations include:

Surface overpotential limitations, due to kineticslimitations

Concentration overpotential, due to diffusion andconvection limitations in the electrolyte (also knownas liquid-junction potential)

Ohmic drop, due to the mobility limitations (ioninteractions)

Solid diffusion limitations, due to diffusionlimitations in porous electrodes, e.g., electrodes thatthe ones used in lithium ion batteries


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Accounting for all the limitations the potential lossis given by:

Where:


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In an electrolytic cell the minimum potential thatwe need to apply for the reaction to take place isthe equilibrium potential

Therefore the potential in an electrolytic cell isgiven by:

The potential loss is calculated using Eq. 25.

Reasons for UsingReference Electrodes

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Measurement of the potential at equilibriumconditions is relatively easy. All we need to makesure is that the current that flows through the circuit

is very small Such determination depends on the use of a

counter-electrode having a known reversiblepotential


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Under load the measurement of the potentialrespect to a reference electrode becomes morecomplicated (due to theEloss). In addition we will

have significant reactions at both electrodes Then a simple two electrode approach is not longersatisfactory for making accurate measurements

A technique to overcome this problem is to use a

third electrode into the electrolyte


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The reference electrode should beplace very close to the workingelectrode

In theory it should be placed justoutside the electrical double layer

However, the electrical field of theelectrode can affect themeasurement of the overpotential

A rule of thumbs suggest to place

the reference electrode at least4diameters (of the referenceelectrode) away from the workingelectrode


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An approach to avoid theeffect of the referenceelectrode field on the

working electrode is to usea luggin capillary Ohmic drop in the capillary

tube is small because the

current that flows through itis very small


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Sometimes a second reference electrode is added tomeasure the ohmic drop between two points in thesolution. This approach is known as the four

electrode arrangement Another use of reference electrodes is to measure

current distributions in a cell having a non uniformcurrent distribution


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Summarizing the reasons for using referenceelectrodes are:

Accurate measurement of surface overpotentials

Measurement of ohmic drops in solutionMeasurement of current distribution

Types of ReferenceElectrodes

When choosing a reference electrode we have the followingi i

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criteriaReproducibilityStabilitySmall temperature sensitivity

Sometimes a reference electrode of the same type as theworking electrode is chosen, this is known as a pseudoreference electrode:Avoids:

Contamination problems Liquid junction potential problems

The problem with doing this is that sometimes the resultsare not reproducible and they are more difficult togeneralize


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Generally the reference electrode should be chosenthat is reversible to one of the ions in solution.However, this is difficult to accomplish all the time

The practical approach is to choose a referenceelectrode that is standard built for some electrolyteconditions


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Typical reference electrodes

Hydrogen electrode

Calomel electrode (SCE)

Mercury-Mercuric oxide electrode

Mercury-mercurous sulfate electrode

Silver-Silver Chloride electrode

Calomel Electrode

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It is constructed by covering a pool of mercury withmercurous chloride (calomel)

Potassium chloride is the electrolyte for the

following reaction:

Calomel Electrode

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The equilibrium potential is given by:

Commercial electrodes are commonly preparedwith three concentrations of KCl: 0.1 N, 1 N andsaturated

The calomel electrode is best used in acid solutions Reproducibility is about 2 mV

Ag/AgCl Electrode

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It is used when mercury contamination is notallowed

KCl is used as the electrolyte. The most common

concentration is 4M It is also used in acidic solutions

The reaction involved is:

The equilibrium potential is given by:

Mercury/Mercurous electrode

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It is used in acid solution

When chloride contamination is not allowed

The reactions if given by:

Mercury/Mercuric oxideelectrode

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It is used in basic solutions

It uses KOH as the electrolyte

The reaction is given by:

Calculation of overpotentials

For the calculation of overpotential we need to use Eq.

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3.200

For the calculation of overpotential we need to use Eq.

Because the applied potential is measured respect to a

reference electrode, the Equilibrium potential for thereaction needs to be expressed respect to the referenceelectrode:

Ew: equilibrium potential of the working electrodeEref: equilibrium potential of the reference electrode

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Summary

At the end of this chapter you must be able to:

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3.202

p y

Use and understand the different expression to expresselectrode kinetic rates

Calculate over potentials

Correct surface overpotentials from other loss effectsKnow the uses and applications of reference electrodesUnderstand the effect of the double layer on the

electrode kinetics (e.g., what do you do experimentally

do reduce this effect?)

Outline

Chapter 4: Mass Transport

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Fundamental relationships

Mass transport boundary layer

Concentration Overpotential

Limiting Current Density

Fundamental Relationships

A general description of an electrochemical system

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A general description of an electrochemical systemtakes into account:Species fluxes

Material conservation (material balance)

Current flowElectroneutrality

Electro-kinetics

Global reactionsHydrodynamics

Species Flux

Using dilute concentration theory (considers only

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Using dilute concentration theory (considers only

interactions between solute-solvent), the flux ofspecies is given by:

Comparing to general chemical engineering systems

the difference in the flux is given by the migrationterm (potential generated due to the ion interactions)

Species Flux

Where:

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Where:

Ni: flux of species, mol/cm2 s

zi: charge number of species i, eq/mol

ui: mobility of species i, cm2-mol/Jsci: concentration of species i, mol/cm3

: electrostatic potential, V

Di: diffusion coefficient of species i, cm2/s

v: fluid velocity, cm/s

The flux is perpendicular to the surface area (as usual)

Current Flow

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Current will arise from the motion of the chargesand is given by:

Material Balance

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The material balance is given by:

Where Ri represents a chemical reaction ccurring insolution (mol/cm3).

Eq. 3 assumes constant volume

Electroneutrality Equation

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Because the electrical forces between chargedspecies are so large, significant charge separationcannot occur. Therefore, in the bulk the

electroneutrality assumption is valid:

Simulations

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4.210

To carry out a simulation of the performance on anelectrochemical system, Eqs. 1-4 need to be solvedsimultaneously

We need a description of the flow pattern toaccount for v in Eq. 1

Eqs. 1 to 4 apply at the bulk, the electrode kineticsis used as boundary conditions for the solution ofthe differential equations

Common simplifications

If bulk concentrations can be ignored we can demonstrate

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bu co ce t at o s ca be g o ed we ca de o st ate

that the gradient of the current is given by:

When concentration variations can be neglected weobtained ohms law instead of Eq. 2:

Where k (conductivity) is given by:

This Eq. is known as conservation of charge

Common simplifications

Another important definition is the transport

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Another important definition is the transport

number:

When concentration variations are important,ohms law becomes modified ohms law:

Common Simplifications

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When migration is negligible (in excess of a supportingelectrolyte), the coefficient of the potential gradient inEq. 1 is large, then the potential gradient must be small

The material balance can be obtained from substitutingsimplified Eq. 1 into Eq. 3

Common simplifications(supporting electrolyte)

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This equation is known as the convective diffusionequation:

The potential distribution can still be obtained by

solving the modified ohms law equation

Mass transport boundary layer

For systems where the concentration gradient issignificant, one common simplification is to treat

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g , p

the boundary layer region as a region with a linearconcentration gradient

This is known as Nernst diffusion layer

Mass transport boundarylayer

Nernst approximation for the concentration gradient is

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expressed as:

Where:

c: concentration at the bulk

c0: concentration at the surface: thickness of the boundary layer.The thickness of this layer is between 0.05-0.001 cm

Example 1

Use the transport equations to derive an expression

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4.217

p q p

for the current for a copper deposition reaction as afunction of the surface and bulk concentration. Theelectrolyte is composed of copper, water and H2SO4

(added to increase conductivity)

Write down expressions for your transportproperties

Consequences of addingsupporting electrolytes

Reduces ohmic losses

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Reduces limiting current density

Increases the viscosity of the solution and thereforedecreases the maximum velocity

Reduces the magnitude of the electric field


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4.219

Concentration overpotential is associated with themass transport limitations

It results from:

The concentration difference between bulk and

electrode surfaceFrom the potential gradient (see modified Ohms

law, second term)


Assuming that the variations in the ionic

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4.220

conductivity are small (small current densities or asupporting electrolyte is used). The concentrationoverpotential can be obtained by:


When the conductivity is large the equation can be

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4.221

approximated with:

This is the concentration overpotential for a cathodicreaction. The concentration overpotential for acathodic reaction is negative (as well as its surfaceoverpotential)


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For an anodic reaction, the concentrationoverpotential is positive and can be estimated (forlarge conductivities) by:

Limiting current

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When the current at the surface is equal to zero, thecurrent measured is known as the limiting current

For the boundary layer assumption, the current is

defined as (we demonstrated this in Example 1):

Limiting current

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Then the limiting current for the Nernst diffusionlayer is given as:

The limiting current density is a function of the

flow pattern. It is up to 100 order of magnitudelarger in stirred solutions

Limiting current

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The overpotential can be expressed as a function ofthe limiting current, for example for highconductivities the cathodic concentration

overpotential is given by Eq. 6, which can beexpressed as:

Limiting current

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At currents higher than the limiting currentadditional reactions takes place

After the limiting current the two reactions take

place in parallel with the secondary reaction takingover the primary reaction

Limiting current

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Supporting electrolytes reduce ohmic losses buttend to reduce the limiting current

Supporting electrolytes increase the viscosity of the

solution and decreases the mobility of the ions

Diffusion coefficient

The transport equations require the use of thediffusion coefficient.

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diffusion coefficient.

The diffusion coefficient for ionic species can becalculate by using the Nernst-Einstein equation:

For a binary electrolyte the diffusion coefficient

becomes:

Diffusion coefficient

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Because the ionic diffusion coefficient is related tothe mobility, it can be calculated using theequivalent conductances:

Values of diffusion coefficients of selected ions at infinitedilution in water at 25oC p284

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4.230

Estimation of limiting current

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4.231

The limiting current can be estimated from themass transfer correlations

Usually mass transfer limitations are expressed as:

Where km is the mass transfer coefficient (cm/s)


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4.232

At the limiting current the surface concentration iszero, therefore, the limiting current is related to themass transfer coefficient:

The mass transfer coefficient is related to theSherwood number (Sh) which is a function of theReynolds (Re) and the Schmidt (Sc) numbers


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4.233

The following correlations are used

WhereL is the characteristic length, v is the velocity of thefluid, and v is the kinematic viscosity (cm2/s) (v = /)


Some correlations require the use of the Grashof

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4.234

number (Gr). This number is used when the mass transport is

affected by density differences

Where:g: acceleration due to gravity

: bulk density0: surface density, equal to the solvent density


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4.235

Correlations for the Sherwood number has beendetermine for specific geometries where the flow

pattern is well known

The correlations are summarized in appendix E ofthe book

Example 2

For the cathodic deposition of copper from 0.5 M CuSO4and 0.5 M H2SO4 electrolyte, the kinetic parameters are

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4.236

c=0.5 and i0=1 mA/cm2. If the applied potential is 100mV respect to a SCE. Calculate:

A. The current density for copper deposition expected ifonly kinetics limitations are involved

B. The limiting current density if two plane parallelcopper electrodes, 2 cm long are used in a beaker ofunstirred electrolyte

C. Estimate the thickness of the Nernst diffusion layer

Summary

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4.237

At the end of this chapter you should be able to:

Calculate diffusion coefficients for ionic species

Determine limiting current for different geometries

Calculate currents when kinetics and mass transportlimitations are involved

Write down the fundamental equations to model an

electrochemical system assuming dilute solutiontheory

Outline

Chapter 5:Industrial applications of Electrochemical Engineering

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Batteries and Fuel cells:Working Principle, types, applications and

design aspects

Production and refining of metals : Applications in chemical industries Corrosion Prevention

Fuel cells-An introduction

Output of conventional batteries are limited.

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They are polluting. Continuous operation results in fall in efficiency. Output not stable under long durations of operations.

Fuel cellAn Electrochemical energy conversion deviceProduces electricity from external fuel and oxidant.Can operate virtually continuously as long as the

necessary flows are maintained.

Basic Fuel Cell Concept

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Fuel cells-Working principle

A fuel cell is an electrochemical device that converts the

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chemical energy in fuels (e.g. hydrogen, methane, butane oreven gasoline and diesel) into electrical energy. It exploits the natural tendency of oxygen and hydrogen to

react to form water.

The direct reaction is prevented by the electrolyte, whichseparates the two reactants.

Therefore two half-reactions occur at the electrodes:

Anode: Fuel (e.g. H2, CO, CH4) is oxidized

Cathode: Oxygen is reduced

The ions are transported to the other electrodethrough the electrolyte.

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The fuel cell contains no moving parts and onlyfour active elements:cathode,anode,

electrolyte and interconnect;

It is a simple and robust system.

A fuel cell uses a chemical reaction to provide anexternal voltage, as does a battery, but differs froma battery in that the fuel is continually supplied in

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the form of hydrogen and oxygen gas.

It can produce electrical energy at a higherefficiency than just burning the hydrogen to

produce heat to drive a generator

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Types of Fuels cells

The general design of most fuel cells is similar

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except for the electrolyte. The six main types of fuel cells, as defined by theirelectrolyte, areAlkaline Fuel Cells,

Proton Exchange Membrane Fuel Cells,Phosphoric Acid Fuel Cells,Molten Carbonate Fuel Cells,Direct Methanol Fuel Cells,

Solid Oxide Fuel Cells.

Alkaline Fuel Cell

Electrolyte is a porous matrix

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saturated with aqueousalkaline solution (normallyKOH)

Provides heat, electricity andpotable water as outputs.

Used in Apollo Mission tomoon. 1: Hydrogen 2:Electron flow

3:Charge4:Oxygen 5:Cathode

6:Electrolyte

7:Anode 8:Water 9:Hydroxyl

Ions

Chemical reaction

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The chemical reaction that occurs at the anode is:2H2 + 4OH 4H2O + 4 e-

The reaction at the cathode occurs when theelectrons pass around an external circuit and reactto form hydroxide ions, OH :

O2 + 4e + 2H2O4OH

Types of alkaline Fuel cell

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Mobile Electrolyte-eg. Pure H2 Fuel-Electrolyte pumped

through a circuit

Static Electrolyte- eg. Pure H2 Fuel-But electrolyte is held

in a matrix material

Dissolved Fuel Electrolyte-eg. Hydrazine Fuel

Fuels used in Alkaline Fuel Cells

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Metal HydrideAbility to be recharged with electrical energyLow operating temperatures (down to -20C);

Fast kinetics;Extended shelf life;Absorbs and stores hydrogen within the cell.

Fuels used in Alkaline Fuel Cells

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Direct borohydride cell

A solution of sodium borohydride is used as thefuel.

Prevents the conversion of KOH to K2CO3Cheaper than traditional fuel cells as it does not

need platinum electrodes.

Advantages

Features of Alkaline fuel cell

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Cathode reaction faster in alkaline electrolyte,higher performance

Byproduct is pure water, can be used for other

purposes.Gives out heat which can be used for heating

purposes.

Disadvantages

Expensive removal of CO2 from the cell

required.

lk li f l ll d bl

Features of Alkaline fuel cell

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Alkaline fuel cells encountered many problemsincluding cost, reliability, ease of use, durability,and safety which were not easily solved.

Attempts at solving these problems proved to beuneconomical given the other sources of energy atthe time.

Th t h b ( k

PEMFC-Proton Exchange Membrane Fuel Cell

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The proton exchange membrane (a.k.a.Polymer Electrolyte membrane) fuel cell uses a

polymeric electrolyte.

This proton-conducting polymer forms the heart ofeach cell and electrodes (usually made of porouscarbon with catalytic platinum incorporated intothem) are bonded to either side of it to form a one-

piece membrane-electrode assembly (MEA).

Advantages

A i k i f k d h

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A quick overview of some key advantages thatmake PEMs such a promising technology for theautomotive markets:Low temperature operation, and henceQuick start upNo corrosive liquids involvedWill work in any orientation (or zero g for that

matter)Thin Membrane-electrode assemblies allow

compact cells

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Reactions in PEMFC

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Molten Carbonate Fuel Cells

O hi h

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Operates at hightemperature

Molten carbonate is

used as electrolyte. Produces water and

CO2 as byproducts.

Delivers high power,of the order 100 MW

Features of MCFC

Ad t

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AdvantagesHigh efficiencyFuel flexibility

Can use a variety of catalystsSuitable for CHP Disadvantages

High temperature speeds corrosion andbreakdown of cell components

Complex electrolyte managementSlow start-up

PAFCPhosphoric Acid Fuel Cell

El t l t d i Ph h i A id

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Electrolyte used is Phosphoric Acid Not affected by CO in the hydrogen stream

Works above a temperature of 400C.

If working at 150 to 200 C, expelled water can beconverted to steam and used for heating. Combinedheat and power efficiency of 80 %.

Large weight and size

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SOFCSolid oxide fuel cells

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Solid oxide fuel cells (SOFCs) use a hard, non-

porous ceramic compound as the electrolyte.

Because the electrolyte is a solid, the cells do not

have to be constructed in the plate-like

configuration typical of other fuel cell types.

SOFCs are expected to be around 50%60%

efficient at converting fuel to electricity

SOFCSolid oxide fuel cells

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Solid oxide fuel cells operate at very high temperatures

d 1 000C (1 830F)

Solid oxide fuel cells (SOFCs)

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around 1,000C (1,830F). High-temperature operation removes the need for

precious-metal catalyst, thereby reducing cost. It also allows SOFCs to reform fuels internally, which

enables the use of a variety of fuels and reduces the costassociated with adding a reformer to the system. SOFCsare also the most sulfur-resistant fuel cell type; they can

tolerate several orders of magnitude more of sulfur thanother cell types.

In addition the are not poisoned b carbonid (CO) hi h b d f l

Solid oxide fuel cells (SOFCs)

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In addition, they are not poisoned by carbonmonoxide (CO), which can even be used as fuel.This property allows SOFCs to use gases madefrom coal.

have the distinct advantage of being able to run onbiogas (which delivers the most energy per hectareof crops), natural gas, propane, ethanol, diesel or

biodiesel and don't require hydrogen,
http://www.fz-juelich.de/ief/ief-3/datapool/page/179/bild4_b-e.gif

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Fuel Cel l Type OperatingTemperature Sys tem Output ApplicationsPEM Fuel Cell 50 - 100C

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Small distributedgenerationTransportation

Solid Oxide FC 650 - 1000C 5kW 3MW Auxiliary powerElectric utility

Large distributedgeneration

Alkaline Fuel Cell 90 - 100C 10kW 100kW MilitarySpace

Phosphoric Acid FC 150 - 200C 50kW 1MW Distributed

generationMolten Carbonate FC 600 - 700C

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dDcCbBaA ++

bpapdpcpRTGG

ba

dco

.

.ln+=

1.The maximum energy output from a fuel cell isequal to its Gibbs energy (at Standard

conditions)

Emax

=GO=H

f- TS= H

f- E

loss

Correction due to variation in Standard conditions:

Where pi

is the partial pressure of the reactants

and products.

From Nernst Equation,

2.The Electric potential can be calculated from the

equationG = n F E

cell

bpap

dpcpRTEE

ba

dcocell

.

.ln+=

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3.The theoretical efficiency of the Fuel cell,max.

fff

lossf

H

nFE

H

G

H

EH

=

=

=

max

f

Ivf ..max=

4.The practical fuel cell efficiency,

is the practical fuel cell efficiency

v is the voltage efficiencyIis the current efficiency

CRfO ..=

5.The Overall system efficiency,

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CRfO

R

C

is the Reformer efficiency

is the DC/AC converter efficiency

Batteries-Electrochemical cells

What is a battery?

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What is a battery? A battery is an electrochemical cell that converts

chemical energy into electrical energy. It comprises of two electrodes: an anode (the

positive electrode) and a cathode (the negativeelectrode), with an electrolyte between them. At each electrode a half-cell electrochemical

reaction takes place.

Basic principles-The Electrochemical series

Different metals (and their compounds) have

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Different metals (and their compounds) havedifferent affinities for electrons.

When two dissimilar metals (or their compounds)are put in contact through an electrolyte, there is a

tendency for electrons to pass from one material toanother.

The metal with the smaller affinity for electronsloses electrons to the material with the greateraffinity, becoming positively charged.

The metal with the greater affinity becomesnegatively charged.

The ElectrochemicalSeries

Most wants to reduce (gainelectrons)

Gold

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Gold Mercury

Silver

Copper

Lead

Nickel

Cadmium

Iron

Zinc

Aluminum Magnesium

Sodium

Potassium

LithiumMost wants to

oxidize (loseelectrons)

Types of Batteries

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Primary (Nonrechargeable) Batteries

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Secondary (Rechargeable) Batteries

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Battery Reactions and Chemistry

Discharge

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g Electrode 1 is an anode: the electrode is oxidised, producing

electrons. Electrode 2 is a cathode: the electrode is reduced, consuming

electrons.

In the fully charged state, there is a surplus of electrons on theanode (thus making it negative) and a deficit on the cathode (thusmaking it positive).

During discharge, electrons therefore flow from the anode to thecathode in the external circuit and a current is produced.

Therefore in simple terms batteries work as electron pumps in theexternal circuit, preferably with only ionic current flowing throughthe electrolyte.

If the anode were zinc and the cathode were copper the half

reactions would proceed as follows:

At the anode: Zn Zn2+(aq) + 2e Eo = 0.76V

At the cathode: Cu2+(aq) + 2e Cu Eo = 0.34V

Thus the total potential for this cell is 1.10 V.

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us e o a po e a o s ce s 0

During use as a battery, discharge leads todissolution of Zn at the anode and the

deposition of Cu at the cathode. Such a cell is embodied in the Daniell Cellintroduced in 1836. As a practical cell thisrequired two electrolytes (typically zinc

sulphate and copper sulphate aqueoussolutions) to avoid polarisation.The electrolytes are separated from each otherb a salt brid e or a orous membrane which

ChargeWhen the cell potential is depleted the battery can be recharged.

When a current is applied to the cell in the opposite direction the

anode becomes the cathode, and vice versa.Thus electrode 2 that was oxidised upon discharge is now reduced

and the electrode 1 that was reduced is now oxidised so the

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electrodes are returned to their former state, ready to be discharged

again.

This time the anode would be copper and the cathode would be

zinc, and the half reactions would proceed as follows:At the anode: Zn2+(aq) + 2e Zn Eo = -0.76VAt the cathode: Cu Cu2+(aq) + 2e Eo = -0.34VThe minimum potential required for charging will be 1.10 V, as this

is the potential of the cell. In reality much higher potentials will be

required to overcome the polarisation.

Lead Acid Battery-An automobile industryapplication

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In the charged state, each cell contains electrodes of elemental lead (Pb)and Lead (IV) Oxide (PbO

2) in an electrolyte of approximately 33.5% v/v (4.2

Molar) sulfuric acid (H2SO

4).

In the discharged state both electrodes turn into lead(II) sulfate (PbSO4) and

the electrolyte loses its dissolved sulfuric acid and becomes primarily water.Due to the freezing point depression of water as the battery discharges

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Due to the freezing-point depression of water, as the battery dischargesand the concentration of sulfuric acid decreases, the electrolyte is more likely

to freeze during winter weather.

The chemical reactions are (discharged to charged):

Anode (oxidation):

Cathode (reduction):

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Electrorefining

Electro refining of a metal by electrolysis is a wayf ifi ti f t l i l t t d b

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Electro refining of a metal by electrolysis is a wayof purification of a metal previously extracted byclassical metallurgical or electrochemical processes

In electro refining, the anodes consist of unrefinedimpure metal, and as the current passes through theacidic electrolyte the anodes are corroded into thesolution so that the electroplating process depositsrefined pure metal onto the cathodes.

Electrorefining

In the case of electrorefining of copper, the anode is

made of impure copper, while cathode is made of a

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made of impure copper, while cathode is made of athin sheet of pure copper. The electrolyte is an

aqueous solution of copper sulphate acidified with

sulphuric acid. The reactions taking place during

electrolysis are,

Anode - oxidation: Cu metal (impure)---> Cu+2 + 2 electronsCathode - reduction: Cu+2 + 2 electrons ---> Cu metal (pure)

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Steps in Electro refining

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Steps in Electro refining

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Industrial Applications-Copperrefining

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Electrorefining of copper

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Extraction of Aluminium from bauxite-Three stageprocess

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Refining of aluminium(Hoopes process)

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Refining of aluminium(Hoopes process)

The cell consists of an iron tank lined with carbon at thebottom.

A molten alloy of copper, crude aluminium and silicon is

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y pp ,used as the anode. It forms the lower most layer in the cell.

The middle layer consists of molten mixture of fluorides, ofsodium aluminium and barium (cryolite + BaF2).

The upper most layer consists of molten aluminium. A set of graphite rods dipping in molten aluminium serve as

cathode. On passing current aluminium ions from the fused electrolyte

are discharged at cathode and pure aluminium collects as thetop layer. Meanwhile, an equivalent quantity of aluminium from crude

alloy at the bottom goes into electrolyte in the middle layer.

Performance evaluation inElectrorefining

The amount of metal deposited was determined bythe weight change (W) observed in the cathode

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p ythe weight change (W) observed in the cathodebefore and after electrolysis. The theoreticalamount of metal that can be deposited for the

quantity of electricity passed during the experimentwas determined

Using the Faraday's law: whereWm is the theoretical amount of metal deposited,

the termI t(current time) is the quantity ofelectricity supplied,

n is the number of electrons transferred in theelementary act of the electrode reaction,

Am is the atomic weight of the metal and

Fisthe Faraday constant (96485 Coulombs).

Current efficiency (eff), which is defined as the

ratio of the actual amount of metal deposited to thatexpected theoretically , was calculate

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