ElectrochemistryProf. Dr. Sabine Prys

http://www.iccb.org/student/mod/science/mod_chem1/mod1/p1.html

@designed by ps

3.3 Normal & Standard Conditions

normal conditions:normal pressure p = 1 atm = 101,325 kPa = 1013,25 mbarnormal temperature T = 0°C = 273.15 K

 standard conditions:standard pressure p = 1 atm = 101,325 kPa = 1013,25 mbarstandard temperature T = 25°C = 298.15 K

Such definitions can vary according to different sources: IUPAC, NIST, …

3.4 Enthalpy

• Enthalpy is a measure of the total energy of a thermodynamic system including – the internal energy (energy required to create a system), – the amount of energy required to make room for it by displacing its

environment and establishing its volume and pressure.• Enthalpy is a thermodynamic potential, a state function and an extensive

quantity (i.e. depending on amount material).

VpUH

H enthalpy Uinternal energy

P pressure Vvolume

http://goldbook.iupac.org

3.8 GIBBS’ Free Energy G

Useful energy, or energy available to do work G

G = free energyH = GIBBS’ energy

(enthalpy)U = internal energy

T = Kelvin temperatureS = entropy

p= pressureV = volume

TDS is the energy not available for doing work

STVpUSTHG

3.9 Spontaneity of Redox Reactions

DH DSSpontaneity

Exothermic DH < 0 Increase DS > 0 +DG < 0

Exothermic DH < 0 Decrease DS < 0 + if|TDS| < |DH|

Endothermic DH > 0 Increase DS > 0 + ifTDS > DH

Endothermic DH > 0 Decrease DS < 0 -DG > 0

STHG

3.10 Thermodynamical Equilibrium

• Reversible processes ultimately reach a point where the rates in both directions are identical, so that the system gives the appearance of having a static composition at which the Gibbs energy G is a minimum

DG = 0

• At equilibrium the sum of the chemical potentials of the reactants equals that of the products, so that:

DG = DG298 + RT . lnK = 0 DG298 = - RT . lnK

• The equilibrium constant K is given by the mass-law effect.

http://goldbook.iupac.org

3.12 Maximum Work

Wmax = maximum workG = Gibbs free energyR = gas constantT = Kelvin temperatureK = equilibrium constantz = ion chargen = molesF = Faraday‘s constantE = galvanic cell potentialU = voltageI = currantt = time

tIUEFnzKRTGW D lnmax

4.0 Chemical Solutions

• Suspension (particle diameters 10-4 - 10-5 cm )

solid particles in homogeneous fluid• Colloid (particle diameters 10-

5 - 10-7 cm ) microscopically

dispersed particles in another substance• Solution (particle diameters 10-

7 - 10-8 cm )

Homogeneous phase with at least 2 components:

solvent and solute» gas in liquid e.g. O2 in H2O» gas in solid e.g. H2

in palladium» liquid in liquid e.g. petroleum» solid in liquid e.g. NaCl in

H2O» electrolytes in water

4.6 Ion activity

High ion concentrations in aqueous solutions ð ion – ion interactions:

pH measured < pH calculated

(1m, 0.1 m solution of acids)

ion activity:

a = activity, f = activity coefficient, c = concentrationf (HCl, 25°C): 0.001m/0.965 0.01m/0.905 0.1m/0.794 1m/0.809

cfa

4.7 Colloidal Solutions

• Larger particles in solvent, e.g. macromolecules / polymers• Properties depend on solute size and not on solute concentration !• Coagulation: growth of larger particles by smaller particles

consumption• Hydrophobe colloids: large surface, large adsorption properties• Hydrophile colloids

4.9 Electrolytes

Electrolyte: solution which conducts electrical current

Hydrated H3O+

Hydrated OH-

472

4923

32

33

3

3

OHOHOH

OHOHOH

OHOHH

COOCHHCOOHCH

ClHHCl

aqaqaq

aqaqaq

4.9.1 Electrical Conductivity in Solutions

Electrolytes• solutions which support ion transport• salts in aqueous solutions, e.g. KCl,

ZnSO4, CuCl2, etc.• molten salts

Conductivity L (resistance R)

bad electrolyte: distilled water:

0.0548 µS/cm at 25 °C. cathodecat ions

anodeanions

_ +

-

++

++++

-----

H2O

11 R

L

4.9.2 Specific Conductivity

KCl concentration [mol / l]

[1 / .m]

0°C 18°C 25°C 0 << 0,001 << 0,001 << 0,001 1 6,543 9,820 11,173

0,1 0,7154 1,1192 1,2886 0,01 0,07751 0,12227 0,14114

absolute electrolyte conductivityR = solution resistance

specific electrolyte conductivityA = electrode surface, l = electrode distance

mRAl

RL

11

11

4.9.3 Example: Proton Migration

Grotthuss Diffusion

structural defect migrationmesomeric structures between H9O4

+ and H5O2+,

5.0 Electrochemical Cells

Cl2H2

+ -Cl2H2

+ -

electrolytic cell

galvanic cell2 HCl (aq) ð H2 (g) + Cl2 (g)

H2 (g) + Cl2 (g) ð 2 HCl (aq)

electrical energy chemical energychemical energy electrical energy

5.1 Electrolysis

electrolysis: decomposing materials by electric currentH2SO4 + 2H2O ð 2H3O+ + SO4

2-

water electrolysiscathodic reduction4H3O+ + 4e- ð 2 H2 ñ + 2 H2Oanodic oxidation4 OH- ð 2 H2O + O2 ñ + 4 e-

total2 H2O (l) ð 2 H2 (g) + O2 (g)

H20 + H2SO4

1:10

electrods

batteryca. 15 V

5.1.1 Electrochemical Equivalent

eNF

EFz

M

FnQ

L

c

Q = electric charge in C

n = yield in mol

F = Faraday‘s constant

= 96485,309 As / mol

Ec = electrochemical equivalent

M = ion weight

z = ion charge

NL = Lohschmidt‘s number

e = elementary charge

5.1.2 Faraday‘s Laws

ma ,mb = mass yield in g for material a / b

Ma,Mb = molecular weight for material a / b

za, zb = chemical valency for material a / b

m = Ec . Q = Ec .I. t

m = mass yield in gEc = electrochemical

equivalent Q = electric charges

in CoulombI = current strengtht = electrolysis time

mm

Mz

zM

a

b

a

a

b

b

5.2 Galvanic Elements

Daniell Element:2 galvanic half cells + bridge

Zn / ZnSO4 // CuSO4 / Cu

electrode reactionsZn (cathode) ð Zn2+ + 2e-

Cu2+ + 2e- ð Cu (anode)

Zn metal in ionic solutionCu ions in Cu metal

electrical current results from different oxidation affinities

voltmeter ca 1,1 V

Zn Cu1 m

ZnSO4

1 mCuSO4

diaphragma(pottery)

bridge containingKCl solution

5.4 Standard Hydrogen Electrode

standard hydrogen electrode (SHE)= reference potential = E0 = 0 V

H2 ñ ð 2H+ + 2e-

p = 1,01325 barT = 25°ca(H+) = 1 mol / lc(H+) = 1,235 mol / l (HCl)

Pt electrode

H2 gas

Pt electrodeH2 gas

68

5.5 Metal Standard Potentials

standard hydrogen electrode= reference potential

E0 = 0 V

metal electrode / metal salt solutionat standard conditions= standard metal potential

M ð Mz+ + ze-

p = 1,01325 barT = 25°cc(Mz+ ) = 1 mol / l

pH < 6 precipitation prevention

5.5.1 Metal Standard Potential Tables

Red Ox z E0 [Volt] K K+ +1 - 2,93

Na Na+ +1 - 2,71 Zn Zn2+ +2 - 0,76 Fe Fe2+ +2 - 0,44 Pb Pb2+ +2 - 0,13 H2 2 H+ +2 0,00 Cu Cu2+ +2 + 0,34 Ag Ag+ +1 + 0,80 Au Au3+ +3 + 1,50

pH-dependant

Galvanic Corrosion Potential Chart K, Na, Mg, Al, Zn, Fe, Pb, Cu, Ag, Au

passivation of Al, Mg, Mn, Cralternative corrosion potential charts for industrial materials

5.5.2 Calvanic Corrosion Potential Chart

cathodeleast noble

corroded metalsstrong oxidation affinity

negative oxidation potential

anodemost nobleprotected metalsweak oxidation affinitypositive oxidation potential

5.6.3 Exercise: Gibbs Free Energy

What happens if ΔG = 0

5.7 NERNST‘s Equation 1

electrode potential dependency on temperature and concentration

E = measured cell potentialE0 = standard reaction potentialR = gas constant ( 8,3145 J . mol-1 . K-1)T = Kelvin temperaturez = chargesF = Faraday’s constant[ ] = concentration of oxidant / reductant in mol / l

][][ln0 red

oxFzTREE

5.7.1 NERNST’s Equation 2

1. type electrode ( = metal electrode in metal salt solution)

[red] = const

E = measured cell potentialE0 = standard reaction potentialR = gas constant ( 8,3145 J . mol-1 . K-1)T = Kelvin temperaturez = chargesF = Faraday’s constant[ox] = concentrationen of oxidant in mol / l

][ln05916,0:25][ln 00 oxz

EECoxFzTREE

5.7.2 Exercise: Maximum Electrical Voltage

1. Calculate the maximum electrical voltage for the Daniell element when standard conditions !

Daniell Element: Cu/Cu++//Zn++/Zn Cu/Cu++/ +0,34 V Zn++/Zn/ +0,76 V S = + 1,1 V

2. Calculate the maximum electrical voltage for a galvanic cell with Ni/Ni++//Zn++/Zn when standard conditions !

Ni/Ni++// -0,23 V Zn++/Zn/ +0,76 V S = + 0,53 V

5.7.3 Exercise: Nernst Equation

What is the electrode potential for a silver electrode at 0°C when the Ag+ concentration is 1 mol ?

][824,0024,08,0

]1[ln105,961

15,273314,88,0

:0

3

VE

E

C

][

][

][][

][ln

:

0

VsA

JV

sAKmolmolKJVV

oxFzTREE

RT

5.8 Ag / AgCl Electrode

2. type electrode = metal electrode in saturated metal salt solution= electrode with constant potential (no concentration changes)

T = 25 °C:1 m KCl E0 = + 0,220 Vsat. KCl E0 = + 0,1958 V

constAg

constLl

molClAgL

][

107,1][][ 2

210

Ag

AgClsat

K+

Ag+

Cl-

5.8.1 Concentration Cells

• Cu(s) | Cu2+ (0.05 M) || Cu2+ (2.0 M) | Cu(s)

• half cell reactions : oxidation: Cu(s) → Cu2+ (0.05 M) + 2

e– reduction: Cu2+ (2.0 M) + 2 e– → Cu(s) overall reaction: Cu2+ (2.0 M) → Cu2+ (0.05 M)

• cell's emf :

• E = E°- (0.05916\2) log [0,05/2] = 0.0474 V

• E° = 0 , (electrodes and ions are the same in both half-cells)

5.15 Dry Cells

Leclanché's cell – anode is a zinc container surrounded by a thin layer of MnO2 – Cathode a carbon bar inserted on the cell's electrolyte– moist electrolyte paste NH4Cl + ZnCl2 mixed with starch

Anode: Zn(s) → Zn2+(aq) + 2 e–

Cathode: 2 NH4+(aq) + 2 MnO2(s) + 2 e– → Mn2O3(s) + 2 NH3(aq) +

H2O(l) Overall reaction:

Zn(s) + 2 NH4+(aq) + 2 MnO2(s) → Zn2+

(aq) + Mn2O3(s) + 2 NH3(aq) + H2O(l)

E = ~ 1.5 V

moist electrolyte paste

5.16 Zn Battery

Graphics: http://en.wikipedia.org/wiki/File:Zincbattery.png

5.17 Mercury Battery

amalgamated anode of mercury and zinc surrounded by a stronger alkaline electrolyte and a paste of ZnO and HgO

Mercury battery half reactions are shown below:

Anode: Zn(Hg) + 2 OH–(aq) → ZnO(s) +

H2O(l) + 2 e–

Cathode: HgO(s) + H2O(l) + 2 e– → Hg(l) + 2 OH–

(aq)

Overall reaction: Zn(Hg) + HgO(s) → ZnO(s) + Hg(l)

no changes in the electrolyte's composition when working1.35 V of direct currentNot rechargeableGraphics: http://en.wikipedia.org/wiki/File:Mercurybattery.png

5.18 Lead-Acid battery

six identical cells assembled in series (6 x 2V ) = 12 Vlead anode lead dioxide cathode Electrolyte sulfuric acid

Anode: Pb(s) + SO42–

(aq) → PbSO4(s) + 2 e–

Cathode: PbO2(s) + 4 H+(aq) + SO4

2–(aq) + 2 e– → PbSO4(s)

+ 2 H2O(l)Overall reaction: Pb(s) + PbO2(s) + 4 H+

(aq) + 2 SO42–

(aq) → 2 PbSO4(s) + 2 H2O(l)

Rechargeable (external voltage electrolysis of the products)

http://en.wikipedia.org/wiki/Lithium-ion_battery

5.19 Lithium rechargeable battery (1)

Positive electrodesElectrode material Average potential difference Specific capacity Specific energyLiCoO2 3.7 V 140 mA·h/g 0.518 kW·h/kgLiMn2O4 4.0 V 100 mA·h/g 0.400 kW·h/kgLiNiO2 3.5 V 180 mA·h/g 0.630 kW·h/kgLiFePO4 3.3 V 150 mA·h/g 0.495 kW·h/kg Li2FePO4F 3.6 V 115 mA·h/g 0.414 kW·h/kgLiCo1/3Ni1/3Mn1/3O2 3.6 V 160 mA·h/g 0.576 kW·h/kgLi(LiaNixMnyCoz)O2 4.2 V 220 mA·h/g 0.920 kW·h/kgNegative electrodesGraphite (LiC6) 0.1-0.2 V 372 mA·h/g 0.0372-0.0744

kW·h/kgHard Carbon (LiC6) Titanate (Li4Ti5O12) 1-2 V 160 mA·h/g 0.16-0.32 kW·h/kgSi (Li4.4Si)[27] 0.5-1 V 4212 mA·h/g 2.106-4.212 kW·h/kgGe (Li4.4Ge)[28] 0.7-1.2 V 1624 mA·h/g 1.137-1.949 kW·h/kg

Lithium rechargeable battery (2)

22

22

6

212

6

CoOLiLiCoO

CoOOLiLiCoOLi

CLiCxexLi

xexLiCoOLiLiCoO

x

x

The following equations are in units of moles, making it possible to use the coefficient x.

Overdischarge supersaturates lithium cobalt oxide, leading to the production of lithium oxide

Overcharge up to 5.2 Volts leads to the synthesis of cobalt(IV) oxide

In a lithium-ion battery the lithium ions are transported to and from the cathode or anode, with the transition metal, cobalt (Co), in LixCoO2 being oxidized from Co3+ to Co4+ during charging, and reduced from Co4+ to Co3+ during discharge.

http://en.wikipedia.org/wiki/Lithium-ion_battery

Exercises 1

1. What is the internal energy of 1 mole Ar at 0°C ?2. What is the volume of 1 mole hydrogen gas at 25 °C ?3. What is the entropy change in 1 mole hydrogen gas at standard

conditions when increasing the volume to DV = 1 m3 ?4. The equilibrium constant for acetic acid in water at 25°C is 4,76.

What is Gibbs Free Energy at that temperature ?5. Calculate the maximum electrical voltage for the DANIELL element

when normal pressure and 10 °C !6. Calculate the maximum electrical voltage for a galvanic cell with

Ni/Ni++//Zn++/Zn when normal pressure and 10 °C !7. Explain the difference between a galvanic and an electrolytic cell !8. What is the standard hydrogen potential ?

Exercises 2

9. What is the standard metal potential ?10. How can you decide whether an ion will precipitated at a given electrode ?11. What is the electrode potential for a silver electrode at 10°C when the Ag+

concentration is 1 mol ?12. How can you calculate the amount of elementary metal to be formed on an

electrode ?13. How can you calculate the maximum energy which can be obtained from a

battery14. Explain the chemical potential !16. Explain the lead/acid battery !17. Explain the mercury battery !

Web Links

• http://en.wikipedia.org/wiki/Electrochemistry#Principles• http://www.jesuitnola.org/upload/clark/TeachResource.htm • http://goldbook.iupac.org/

References

• A. Burrows, A. Parsons , G. Price, J. Holman , G. Pilling; Chemistry: Introducing inorganic, organic and physical chemistry ; Oxford University Press 2009

• J. Hoinkins; E. Lindner; Chemie für Ingenieure; Verlag: Wiley-VCH Verlag GmbH & Co. KGaA, 2007

• P.W. Attkins; L. Jobnes; Chemie – einfach alles; Verlag: Wiley-VCH Verlag GmbH & Co. KGaA, 2006

• Römpp‘s Chemie Lexikon• DTV-Atlas zur Chemie