Electrochemistry
Prof. Dr. Sabine Prys
http://www.iccb.org/student/mod/science/mod_chem1/mod1/p1.html
@designed by ps
3.3 Normal & Standard Conditions
Such definitions can vary according to different sources: IUPAC, NIST, …
normal conditions:
normal pressure p = 1 atm = 101,325 kPa = 1013,25 mbar
normal temperature
T = 0°C = 273.15 K
standard conditions:
standard pressure p = 1 atm = 101,325 kPa = 1013,25 mbar
standard temperature T = 25°C = 298.15 K
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).
H  U  p V
H
P
enthalpy
pressure
U
V
internal energy
volume
http://goldbook.iupac.org
3.8 GIBBS’ Free Energy G
Useful energy, or energy available to do work G
G  H  T  S  U  p V  T  S
G
U
S
V
= free energy
= internal energy
= entropy
= volume
H
T
p
= GIBBS’ energy (enthalpy)
= Kelvin temperature
= pressure
TDS is the energy not available for doing work
3.9 Spontaneity of Redox Reactions
G  H T  S
DH
DS
Spontaneity
Exothermic
DH < 0
Increase
DS > 0
+
Exothermic
DH < 0
Decrease
DS < 0
+ if
|TDS| < |DH|
Endothermic
DH > 0
Increase
DS > 0
+ if
TDS > DH
Decrease
DS < 0
-
Endothermic DH > 0
DG < 0
DG > 0
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  DG   RT ln K   z  n  F  E  U  I  t
Wmax
G
R
T
K
z
n
F
E
U
I
t
=
=
=
=
=
=
=
=
=
=
=
=
maximum work
Gibbs free energy
gas constant
Kelvin temperature
equilibrium constant
ion charge
moles
Faraday‘s constant
galvanic cell potential
voltage
currant
time
4.0 Chemical Solutions
• Suspension
• Colloid
• Solution
(particle diameters 10-4 - 10-5 cm )
solid particles in homogeneous fluid
(particle diameters 10-5 - 10-7 cm )
microscopically dispersed particles in another substance
(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  ion – ion interactions:
pH measured < pH calculated
(1m, 0.1 m solution of acids)
ion activity:
a  f c
a = activity, f = activity coefficient, c = concentration
f (HCl, 25°C): 0.001m/0.965 0.01m/0.905 0.1m/0.794 1m/0.809
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
HClaq


H aq
 Claq
CH 3COOH aq
H   H 2O
Hydrated H3O+
Hydrated
OH-
H 3O   3H 2O
OH   3H 2O


H aq
 CH 3COOaq
H 3O 
H 9O4
H 7O4


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
_
+
H2O
Conductivity L (resistance R)
1
L
R
+
+
+
+
+
+
 
1
bad electrolyte: distilled water:
0.0548 µS/cm at 25 °C.
cathode
cat ions
anode
anions
4.9.2 Specific Conductivity
L

1 1
R   
absolute electrolyte conductivity
R = solution resistance
l 1 1 
 
A R    m 
specific electrolyte conductivity
A = electrode surface, l = electrode distance
KCl concentration
[mol / l]
0
1
0,1
0,01
0°C
<< 0,001
6,543
0,7154
0,07751

[1 / .m]
18°C
<< 0,001
9,820
1,1192
0,12227
25°C
<< 0,001
11,173
1,2886
0,14114
4.9.3 Example: Proton Migration
Grotthuss Diffusion
structural defect migration
mesomeric structures between H9O4+ and H5O2+,
5.0 Electrochemical Cells
-
+
H2
Cl2
+
H2
Cl2
electrolytic cell
galvanic cell
2 HCl (aq)  H2 (g) + Cl2 (g)
H2 (g) + Cl2 (g)  2 HCl (aq)
electrical energy  chemical energy
chemical energy  electrical energy
5.1 Electrolysis
electrolysis: decomposing materials by electric current
H2SO4 + 2H2O  2H3O+ + SO42electrods
water electrolysis
cathodic reduction
4H3O+ + 4e-  2 H2  + 2 H2O
anodic oxidation
4 OH 2 H 2 O + O2  + 4 e total
2 H2O (l)
 2 H2 (g) + O2 (g)
battery
ca. 15 V
H20 + H2SO4
1:10
5.1.1 Electrochemical Equivalent
Q
F
n
M
 Ec
zF
F
e
NL
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
m = Ec . Q = Ec .I. t
m =
Ec =
Q =
I
t
=
=
mass yield in g
electrochemical
equivalent
electric charges
in Coulomb
current strength
electrolysis time
ma
M a zb


mb
z a Mb
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
5.2 Galvanic Elements
voltmeter ca 1,1 V
Daniell Element:
2 galvanic half cells + bridge
Zn / ZnSO4 // CuSO4 / Cu
electrode reactions
Zn (cathode)
 Zn2+ + 2eCu2+ + 2e Cu (anode)
Zn
1m
ZnSO4
Cu
1m
CuSO4
diaphragma
(pottery)
Zn metal in ionic solution
Cu ions in Cu metal
electrical current results from
different oxidation affinities
bridge containing
KCl solution
5.4 Standard Hydrogen Electrode
standard hydrogen electrode (SHE)
= reference potential = E0 = 0 V
H2 2H+ + 2ep = 1,01325 bar
T = 25°c
a(H+) = 1 mol / l
c(H+) = 1,235 mol / l (HCl)
H2 gas
Pt electrode
5.5 Metal Standard Potentials
standard hydrogen electrode
= reference potential
E0 = 0 V
metal electrode / metal salt solution
at standard conditions
= standard metal potential
M
 Mz+ + ze-
p = 1,01325 bar
T = 25°c
c(Mz+ ) = 1 mol / l
H2 gas
Pt electrode
pH < 6 precipitation prevention
68
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
5.5.2 Calvanic Corrosion Potential
Chart
Galvanic Corrosion Potential Chart
K, Na, Mg, Al, Zn, Fe, Pb, Cu, Ag, Au
cathode
least noble
corroded metals
strong oxidation affinity
negative oxidation potential
anode
most noble
protected metals
weak oxidation affinity
positive oxidation potential
passivation of Al, Mg, Mn, Cr
alternative corrosion potential charts for industrial materials
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
R T
[ox]
EE0 
 ln
zF
[red ]
E
E0
R
T
z
F
[ ]
= measured cell potential
= standard reaction potential
= gas constant ( 8,3145 J . mol-1 . K-1)
= Kelvin temperature
= charges
= Faraday’s constant
= concentration of oxidant / reductant in mol / l
5.7.1 NERNST’s Equation 2
1. type electrode
( = metal electrode in metal salt solution)
[red] = const
R T
E  E0 
 ln[ox]
zF
E
E0
R
T
z
F
[ox]
0,05916
25C :E E0 
 ln[ox]
z
= measured cell potential
= standard reaction potential
= gas constant ( 8,3145 J . mol-1 . K-1)
= Kelvin temperature
= charges
= Faraday’s constant
= concentrationen of oxidant in mol / l
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/
S=
+ 1,1 V
+0,76 V
2. Calculate the maximum electrical voltage for a galvanic cell with
Ni/Ni++//Zn++/Zn when standard conditions !
Ni/Ni++//
S=
-0,23 V
+ 0,53 V
Zn++/Zn/
+0,76 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 ?
RT :
R T
 ln[ox ]
zF
 J  K  mol 
[V ]  [V ]  

 mol  K  A  s 
E  E0 
 J 
 [V ]  

 A s 
 [V ]
0C :
E0,8 
8,314  273,15
 ln[1]
1  96,5 103
E  0,8  0,024  0,824 [V ]
5.8 Ag / AgCl Electrode
2. type electrode
= metal electrode in saturated
metal salt solution
= electrode with constant potential
(no concentration changes)


L  [ Ag ]  [Cl ]1,7 10
L  const
[ Ag  ]  const
T = 25 °C:
1 m KCl E0 = + 0,220 V
sat. KCl E0 = + 0,1958 V
10
mol 2
l2
Ag
K+
Ag+
ClAgClsat
5.8.1 Concentration Cells
• Cu(s) | Cu2+ (0.05 M) || Cu2+ (2.0 M) | Cu(s)
• half cell reactions :
oxidation:
reduction:
overall reaction:
Cu(s)
Cu2+ (2.0 M) + 2 e–
Cu2+ (2.0 M)
→ Cu2+ (0.05 M) + 2 e–
→ Cu(s)
→ 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
moist electrolyte paste
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
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 working
1.35 V of direct current
Not rechargeable
Graphics: http://en.wikipedia.org/wiki/File:Mercurybattery.png
5.18 Lead-Acid battery
six identical cells assembled in series (6 x 2V ) = 12 V
lead anode
lead dioxide cathode
Electrolyte sulfuric acid
Anode:
Pb(s) + SO42–(aq) → PbSO4(s) + 2 e–
Cathode:
PbO2(s) + 4 H+(aq) + SO42–(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 electrodes
Electrode material Average potential difference
LiCoO2
3.7 V
LiMn2O4
4.0 V
LiNiO2
3.5 V
LiFePO4
3.3 V
Li2FePO4F
3.6 V
LiCo1/3Ni1/3Mn1/3O2
3.6 V
Li(LiaNixMnyCoz)O2
4.2 V
Negative electrodes
Graphite (LiC6)
0.1-0.2 V
Hard Carbon (LiC6)
Titanate (Li4Ti5O12)
1-2 V
Si (Li4.4Si)[27]
0.5-1 V
Ge (Li4.4Ge)[28]
0.7-1.2 V
Specific capacity
140 mA·h/g
100 mA·h/g
180 mA·h/g
150 mA·h/g
115 mA·h/g
160 mA·h/g
220 mA·h/g
Specific energy
0.518 kW·h/kg
0.400 kW·h/kg
0.630 kW·h/kg
0.495 kW·h/kg
0.414 kW·h/kg
0.576 kW·h/kg
0.920 kW·h/kg
372 mA·h/g
0.0372-0.0744 kW·h/kg
160 mA·h/g
4212 mA·h/g
1624 mA·h/g
0.16-0.32 kW·h/kg
2.106-4.212 kW·h/kg
1.137-1.949 kW·h/kg
Lithium rechargeable battery (2)
The following equations are in units of moles, making it possible to use the coefficient x.
LiCoO2
Li1 x CoO 2  xLi  xe
xLi  xe  6C
Lix C6
Overdischarge supersaturates lithium cobalt oxide, leading to the production of lithium oxide
Li   LiCoO2  Li2O  CoO
Overcharge up to 5.2 Volts leads to the synthesis of cobalt(IV) oxide
LiCoO2  Li   CoO2
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
battery
14. 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