Farrell Electrochemistry Lecture

8/13/2019 Farrell Electrochemistry Lecture

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Electrochemical Cells

In electrochemistry we are interested in the processes thataffect the transport of charge at interfaces usually between aconductor (electrode) and an ionic conductor (electrolyte).

Electrode charge is carried by electrons e.g. electrodesinclude solid metals (Pt, Au), liquid metals (Hg), carbon(graphite) and semiconductors. Electrolyte charge is carriedby ions e.g. H+, Cl- in water or ions in non-aqueous

solutions.

An electrochemical cell consists of at least of two electrodesin contact with an electrolyte.

The electrolyte and the electrodes are the electrodecompartment. If the electrolytes are different the twocompartments can be joined by a salt bridge which is a

concentrated electrolyte solution (KNO3) that completes thecircuit.


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Interfacial region (0.5-100 nm)

Non-FaradicIonic concentrations

different from the bulksolution because ofpolarization effectsand production of a

double layerThis affects currentsand cell potentials

Bulk Solution

mass transfer from bulksolution to electrode.

Kinetics governed bydiffusion and convection

Many events occur at and near electrodes

Faradicelectron

transfer atelectrodesurface

Electrode


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Redox reactions and half-cells

A reaction in which there is a transferof electron(s) from one species toanother is called a redox reaction

Any redox reaction can berepresented as the difference of twohalf-reactions

Write the overall chemical reactiontaking place in a cell in terms of twohalf-reactions, which describe thechemical changes that occur at thetwo electrodes

Each half reaction responds to theinterfacial potential difference at thecorresponding electrode

Oxidation occurs at the anode andreduction occurs at the cathodeZn Zn2+ + 2e Cu2+ + 2e Cu

anode cathode

Ve e


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By convention one writes each halfreaction as a reduction.

Anode

H+(aq) + e 1/2H2 (g)

CathodeAgCl(s) + e Ag(s) + Cl

-(aq)

Potential of cell isEcell = Ecathode - Eanode

Sometimes written as

Ecell = ERight - ELeft

At standard stateEo = Eocathode- E

oanode

Example

H2(g)+ AgCl(s) H+

(aq) + Ag(s) + Cl-(aq)

anode cathode


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Standard state for all other species in solution, solidor in a gas is when they have an activity, a =1.

Standard state of a component considered asa solvent is taken to be the pure liquid orpure solid at one atmosphere pressure and atthe temperature in question.

Standard state of a component considered tobe a solute. It is a hypothetical state in

which the solute would exist at unit molality(mol/kg) or (molarity) (mol/liter) and oneatmosphere, but would still have theenvironment typical of a dilute ideal solution


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Ecell= Eocathode-Eoanode

Eoanode = ESHE= 0.0 V

Therefore

Eocell = Eocathode = +0.2223 V

We find that the standard cellpotential (Eo) is positive.

Standard cell potential, Eo of Ag/AgCl is + 0.2223 V

H+(aq) + e H2 (g) AgCl(s) + e Ag(s) + Cl-

anode cathode


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What does a positive, standard cell potential, EO imply?

Use mathematics and language ofreversible thermodynamics toillustrate what a positive Eo implies

By thermodynamically reversible. Weimply that the reaction can respond toan infinitesimal small driving force andreverse its direction

From second Law, S theentropy is

For the reversible processE.1 becomes

E.1zFEpdVdqdwdqdU =+=E.3zFEpdVTdSdU =

iofmoles:in

potentialchemical:energysGibb':G

enthalpy:Hentropy:S

Potential:constantFaraday:

charges#orvalence:zvolume:

pressure:work:

heat:energyinternal:

EF

V

pw

qU

Lets consider a reversible redox reactionthat is closed to its surroundings. Thechange in energy, dU can be expressedin terms of work and heat

E.2T

dqdS=

mechanical electrical


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EO > 0 dG0 < 0 spontaneous reaction

In an open system Gibbs energy atconstant P and T

, E.5

E.4intoE.3Substitute

E.4

TPzFEdG

SdTVdPnFEdGSdTTdSVdPpdVzFEpdVTdSdG

SdTTdSVdPpdVdUdGTSpVUTSHG

=

+=++=

++=+

In terms of Gibbs energy, G (also calledfree enthalpy or Gibbs free energy) E.3becomes

When n is constant

E.7)(,,

zFEdGinTP

=

E.8)(,,ozFEodGinTP

=

When n is constant with activity of oneand measurements are at standard statethen

E.6dnzFEdG ii

i+=

Eo > 0 dGO < 0 spontaneous reaction

Eo < 0 dGO > 0 energy is required to drivethe reaction

Eo is often called the electronmotiveforce or EMF of the cell.

E.3zFEpdVTdSdU =


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Positive Eo implies the reaction is favorable thermodynamicallyNegative Eo implies the reaction requires energy to proceed

Eo negativee.g.,

Zn2+(aq) + H2(g) Zn(s) + H+(aq)

is not favorable

Zn2+ cannot be readily reduced by H2 to form Zn.

Zn2+ is a better electron donor or reducing agent.

Eo positivee.g.,

AAgCl(s) + 1/2H2(g) Ag(s) + Cl-(aq) + H

+

reaction will proceed spontaneously

AgCl can readily be reduced by H2 to form Ag

AgCl it is a good electron acceptor or oxidizing agent

relative to SHE


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Gold (Au)Platinum (Pt)

Silver (Ag)Mercury (Hg)Copper (Cu)(Hydrogen) (H)Lead (Pb)

Tin (Sn)Nickel (Ni)Iron (Fe)Zinc (Zn)Chromium (Cr)

Aluminium (Al)Magnesium (Mg)Sodium (Na)Calcium (Ca)Potassium (K)

Lithium ( Li)

Least Active do not want to lose electrons good oxidizing agents

Most active easily lose electrons good reducing agents

unstable metals

Electrochemistry Series of Metals

stable metals


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Standard Electrode (Half) Potentials at 25C vs SHE

Reducingagents

Oxidizingagents

Li+ + e- Li -3.05 V

K+ + e- K -2.92 V

Ca2+ + 2 e- Ca -2.76 V

Na+ + e- Na -2.71 V

Ti

4+

+ 4 e- Ti -1.63 VH2O + 2 e- H2+ OH- -0.83 V

Zn2+ + 2 e- Zn -0.763 V

Cr3+ + 3 e- Cr -0.744 V

Fe2+ + 2 e- Fe -0.409 V

Cd2+

+ 2 e- Cd -0.401 VNi2+ + 2 e- Ni -0.230 V

Pb2+ + 2 e- Pb -0.126 V

H+ + 2 e- H2 0.00 V

AgCl + e- Ag + Cl- +0.223 V

Hg2Cl2 + 2 e- 2Hg + 2Cl-+0.268 VCu2+ + 2 e- Cu +0.340 V

I2(g) + 2 e- 2I- +0.536 V

Ag+ + e- Ag +0.799 V

Pt2+ + 2 e- Pt +1.188 V

Cl2(g) + 2 e- 2Cl- +1.358 VAu+ + e- Au +1.680 V


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Notation to describe Electrochemical Cells

| slash or vertical lineindicates phase boundary

, (comma) separates two

components in the samephase

|| double vertical line or

double slash indicatestwo phase boundaries(liquid-liquid junctions)designed not to addsignificant potential

difference to overall cellpotential.

dotted line indicates

these liquid-liquidpotentials are significant.

Cathode on rhsAnode on lhs

Pt|H2 | H+, Cl- || Cl-|AgCl| Ag

anode cathode


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Notation Examples

Zn|ZnSO4 CuSO4|Cu

anode cathode

Zn|ZnSO4 || CuSO4|Cu

anode cathode


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Example Calculate Eo and dGo at standard state all activities =1

AnodeZn2+(aq) + 2e Zn(s)

CathodeCu2+(aq) + 2e Cu(s)

Standard Potential of cell is

Eo=Ecathode-Eanode

From Standard Tables

=0.340 (-0.7626)= +1.103 V

2 x 96490 x 1.103= 213 x KJ

[(mole of electrons) X (coulombs/mole) XJoules/Coulomb] = Joules

E.8,,)( inTPozFEodG =

Zn | ZnS04(a=1), CuSO4(a=1) | Cu


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Calculating EMF of a cell when activities do not equal 1

ProblemCalculate Ecell for cell, where temperature isat 25 C and mean activity coefficients of HClis 0.758

Pt|H2(1.00 atm)|HCl (0.5 M)|AgCl |Ag


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Chemical Potential of Electrolyte Solutions

Dilute ionic Solutions

Ions behave ideally no ion-ion interactions or solvation

effects with solvent.

Ions in concentrated solution (> 10-3 M)

Ions interact by Coulombic forces. Thesolution is no longer ideal. The chemical

potential of ions is affected by theseinteractions. (The entropy is lowered).This is accounted for by describing theions in terms of their activity, a instead

of their concentration.

Na][Cl][RTln += oNaClNaCl

+ -

r

+ -

r


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Activities of ions

E.9RTln+

+=ClNa

aaoNaClNaCl

RTlna+++

+=Na

o

NaNa

RTlna

+= ClClCl

o

NaClClNa =+

oNaCl

oCl

oNa =+

2=+= aaaa

For infinitely dilute solutions

E.10aRTln2 += aoNaClNaCl

However cannot measure activity ofcation and anions independently. Definethe total activity for a 1.1 electrolyte,eg. NaCl in terms of the geometric

mean of the individual ionic activities

E.10bRTln2NaCl

oNaClNaCl

c+=

Therefore

NaCl Na+ + Cl-

Therefore


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Determine the geometric mean activitycoefficient

)ln()ln(2

)(2

2/1)(

+=

+=

+

=

E.12RTln2NaCl

oNaClNaCl

C+=

+ == ClNaNaCl CCC

If we also use

E.11CC

Na

+++

Clll

NaNa

Ca

Ca

RTlnC ++

+=CllNaNa

CCoNaClNaCl

Where + or - are the un-measurableactivity coefficient for the ions

Then

Mean activity coefficient of 1:1 electrolytes

NaCl Na+ + Cl-


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Back to Example calculating Ecell with Nernst Equation

ProblemCalculate Ecell for cell, where temperature isat 25 C and mean activity coefficients of HClis 0.758

Pt|H2(1.00 atm)|HCl (0.5 M)|AgCl |Ag

Write half cell reactions as reductions

Anode H+ + e- H2(g) Eo = 0.00 V

Cathode AgCl(s) + e- Ag(s) + Cl- Eo = 0.222 V

Eo =Ecathode- Eanode=0.222 V


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Example, continued

Write overall reaction

AgCl(s) +H2Ag(s) + H+

(aq) + Cl-(aq)

]HCl[lnF

2RT

ln

F

RT

aaa

aaln

zF

RT

lHa

(s)Ag-ClH

AgCl(s)2/1

2H

+

+=

o

E

oE

oEE

C

tcoefficienactivitymean

electronsofnumber:

)1-

lCoulombsmo(96490constantFaraday:

)1-

mol1-

JK(8.314constant,gas:

Kelvinre,temperatu:

z

F

R

T

Write Nernst Equation for reaction

V258.0

0361.0222.0

)]5.0*758.0[ln(96490*1

*2988.314*2222.0

=

+=

=


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Measuring the EMF of a cellor the open-circuit or zero-current cell potential

EMF is defined as the cellpotential when there is nocurrent through the cell.

The emf is sometimes coinedthe zero-current or open-circuitcell potential.

E: power supplyEs: standard cell of known potential

EX: unknown cell potential

Measuring EMF

Potentiometer slide wire isadjusted until there is no currentthrough the galvonmeter, Gwhen the switch is in position 2.

In this position R=Rs. Theprocess is repeated for switchposition 1 where R=RX.

Ex = IoRx and Es = IoRs

Ex= (Rx/Rs)Es

G

Io

Eb

Es

Ex

R

2

1

Rb

G

Io

Eb

Es

Ex

R

2

1

Rb

Poggendorf circuit


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Exchange Current Density is a function of the rate constantof the reaction (at equilibrium)

A system with a high exchangecurrent density or large rate constant,khas fast kinetics and will attainequilibrium after a short time. A

system with small kwill be sluggish.

reactionbackwardtheofconstantrate

reactionforwardtheofconstantrate

b

f

k

k

k

k

ReOf

b

+

For any redox reaction

At equilibrium when voltage, E equals the

equilibrium voltage Eeq the rate offorward reaction rate equals backwardreaction rate then

0=+ bRfo kzFmkzFm

0=+ anodecathode ii

and the net current is zero

The current at each electrode whenthe system is at equilibrium is calledthe exchange current density, jo

)mequilibriuat(

)mequilibriuat(

A

kzFm

jj

A

kzFmjj

bRanodeo

focathodeo

==

==


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Types of Cells

Galvanic cell: reactions occurspontaneously at the electrodeswhen they are connected externallyby a conductor. A battery is a

commonly used electrochemical cell.When a battery is connected to adevice it discharges its storedchemical energy providing energy to

drive the device.

Electrolytic Cell: reactions do notoccur spontaneously but are drivenby external source of current.Reactions that occur are affected byexternal voltage supply which isgreater than the open-circuit

potential of the cell.


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When Cd electrode is made more negative or more positiverelative to reference calomel electrode current will flow

Cathodic current: reduction current electronflow from electrode to species in solution.Defined as positive, but there is no strictconvention.

Anodic current: is an oxidation current electronflow from species in solution to an electrode.Defined as negative current.

reduction ofwater

0.64 -0.64 -1.1

Reductionof Cd

H20 + 2e 2H2 + 2OH-

oxidation

of Cd

(V vs. Standard Calomel Electrode)

i (A)

e

anode cathode

e

cathode anode


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Surface Potential as a Function of Distance from aNegatively Charged Electrode Surface

Distance0

o

d

Diffuse layer

Inner layer called the Stern or Helmhotz layer. Thepotential drops linearly.

-d

-bulk


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Polarization vs Nonpolarization

Ecell

Polarizable electrode: large change inpotential upon passage of smallfaradic current because of doublelayer. (e.g mercury electrode in

contact with de-aerated potassiumchloride solution)

i

E

overpotential, = E - Ecell

i

Ecell

Non-Polarizable electrode: no changein potential upon passage of smallfaradic current. (e.g. required ofreference electrode eg. Standard

Calomel electrode)


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R h d i h f


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Response the current measured is the average of manystimulus cycles

anodic current

E vs reference electrode

Current A B

C

D

F

-ve direction

cathodic current

E

Starting at an initial voltage (A), thepotential is scanned in one directionin this case in the negativedirection.

At B, a cathodic current is detectedas the analyte starts to be reduced.

The current continues to increasesas more analyte is reduced and then

peaks at (C). The current thendecays for the rest of the forwardscan.

At (D) the polarity of the voltage isreversed and the cathodic currentdecays till it reaches (E) where theanalyte starts to be oxidized. Theanodic current then peaks at F asmore analyte is re-oxidized. It then

decays as the voltage is made morepositive and the scan is complete


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Summary of lecture

Be able to calculate the cell potential of a cell from two half cells at

standard state and not at standard state

Explain what a negative or positive cell potential implies

Understand the notation to describe electrochemical cells

Explain the formation of a double layer in a electrolytic cell and explain

how it affects the cell potential

Know what is meant by cathodic and anodic current and the exchange

current density, jo of a redox reaction

Be able to interpret a cyclic voltamogram

Farrell Electrochemistry Lecture

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