book here

Outline
MAE 493R/593V- Renewable Energy Devices
• Basics of electrochemistry
• Polymer electrolyte membrane (PEM) fuel cells
Fuel Cells and Hydrogen
• Solid oxide fuel cells (SOFCs)
• Hydrogen production and storage
• Coal-fired plants and integrated gasifier fuel cell
(IGFC) systems
Basics of Electrochemistry
Why Study Electrochemistry?
• Batteries, fuel cells, and
solar cells
• Corrosion
• Industrial production of
chemicals such as Cl2,
NaOH, F2 and Al
All course notes only for class students.
The slides are modified from the original slide provided by Dr. C. S. Wang at University of Maryland
• Biological redox reactions
The heme group
Why Study Electrochemistry?
Why Study Electrochemistry?
Conventional fossil energy devices:
Renewable energy devices:
For example, fuel cells are to directly
convert chemical energy to electric work
http://www.fueleconomy.gov/feg/tech/fuelcell.gif
Anode side: 2H2 →4H+ + 4eCathode side:
O2 + 4H+ + 4e- →2H2O
Fossil fuels combustion (hydrocarbons+ oxygen)→ energy stored in the
working fluid (internal energy or enthalpy) converted to mechanical
energy by passing the working fluid to devices (such as turbines)
Net reaction:
2H2 + O2 →2H2O
Operating temp: around 80 oC
Image from: http://en.wikipedia.org/wiki/File:Fc_diagram_pem.gif
6
Basic knowledge of electrochemistry
Terminology for Redox Reactions
Table of Contents:
redox reaction
-oxidation reaction and reduction reaction
- reducing agent and oxidation agent
electrochemical cells
- electrolyte, anode, cathode
- voltaic cells, electrolytic cells
cell potential and Nernst equation
Gibbs free energy
Kinetic of electrochemical reaction
- polarization (ohmic, activation and concentration polarization)
Oxidation Reaction
Example: 2 Cu + O2 → 2 CuO
Reduction Reaction
Example: CuO + H2 → Cu + H2O
• loss of electrons
• increase in oxidation state
• addition of oxygen
• loss of hydrogen
• gain of electrons
• decrease in oxidation state
• loss of oxygen
• addition of hydrogen
copper is losing electrons
Cu 2+ in CuO is gaining electrons
voltammetry (CV)
- linear-sweep voltammetry
- cyclic voltammetry
electrochemical impedance spectroscopy (EIS)
You can’t have one… without the other!
Terminology for Redox Reactions
• Reduction (gaining electrons) can’t happen without an
oxidation to provide the electrons.
• You can’t have 2 oxidations or 2 reductions in the same
equation. Reduction has to occur at the cost of oxidation
• OXIDATION—
OXIDATION—loss of electron(s) by a species; increase in oxidation number; increase in oxygen.
• REDUCTION
REDUCTION—
—gain of electron(s); decrease in oxidation number; decrease in oxygen; increase in hydrogen.
LEO the lion says GER
GER!!
o l x
s e i
e c d
t a
r t
o i
n o
s n
• OXIDIZING AGENT—
OXIDIZING AGENT—electron acceptor; species is reduced.
a l e
i e d
n c u
t c
r t
o i
n o
s n
• REDUCING AGENT
REDUCING AGENT—
—electron donor; species is oxidized.
GER!
Review of Oxidation Numbers
Oxidation‐Reduction Reactions:
A Quick Review
The charge the atom would have in a molecule (or an
ionic compound) if electrons were completely transferred.
Cu(s) in AgNO3(aq)
1. Free elements (uncombined state) have an oxidation
number of zero.
Na Be,
Na,
Be K
K, Pb
Pb, H2, O2, P4 = 0
2. In monatomic ions, the oxidation number is equal to
the charge on the ion.
Li+ (+1); Fe3+ (+3); O2- (-2)
3. The oxidation number of oxygen is usually –2. In H2O2
and O22- it is –1.
4.4
Cu → Cu2+
QuickTime
Cu → Cu2+ + 2e–
Movie
Ag+ → Ag
Ag+ + ee– → Ag
2Ag+ + 2e– → 2Ag
Cu → Cu2+ + 2e–
Overall cell reaction:
Cu +2Ag+→2Ag + Cu2+
Cu loses e‐: oxidized
Ag+ gains e‐: reduced
Redox Reactions
• Zinc is added to a blue solution of copper(II) sulfate
Harnessing the Electricity
• Electrons flow from the zinc atoms to the copper ions During the spontaneous redox reaction.
Zn (s) + CuSO4 (aq) ' ZnSO4 (aq) + Cu (s)
• The blue colour disappears…the zinc metal “dissolves”,
metal dissolves , and and
solid copper metal precipitates on the zinc strip
• Electricity can be thought of as the “flow of electric charge”.
• The zinc is oxidized (loses electrons)
Zn (s) + Cu2+ (aq) ' Zn2+ (aq) + Cu (s)
• The copper ions are reduced (gain electrons)
• Electrochemical Cell
– a device that uses a
spontaneous redox reaction
to produce electricity
• Anode
– the electrode where
oxidation occurs
• Cathode
– the electrode where
reduction occurs
• Salt Bridge
– connects two “half-cells” to
complete the electric circuit.
– for example, a U-tube filled
with salt solution
• How to utilize the electricity: the flow of electrons from the zinc atoms to the copper ions?
Answer: Separate the Cu ions from the Zn atoms. This will force the electrons from the zinc atoms to travel through an external path to reach the copper ions.
Electrochemical Cells
Terms Used for Electrochemical Cells
Electrochemical Cells
A salt bridge has three functions:
1)
It allows electrical contact between the two
half-cells
2)
I prevents mixing
It
i i off the
h electrode
l
d solutions
l i
3)
It maintains electrical neutrality in each halfcell as ions flow into and out of the salt bridge
CHEMICAL CHANGE --->
--->
ELECTRIC CURRENT
Zn metal
With time, Cu plates out
onto Zn metal strip, and
Zn strip
p “disappears.”
pp
Cu2+ ions
•Zn is oxidized and is the reducing agent
2eZn(s) --->
---> Zn2+(aq) + 2e•Cu2+ is reduced and is the oxidizing agent
2e-- ----->
> Cu(s)
Cu2+(aq) + 2e
Electrochemical Cell:
An Atomic‐Level View
Cell potential
QuickTime
Movie
• Water only spontaneously flows one way in a waterfall.
• Likewise, electrons only spontaneously y p
y
flow one way in a redox reaction—from higher to lower potential energy.
Some Electrochemical Terms
Electrochemical Cells
e–
QuickTime
Movie
Voltaic cell
Load
• Voltaic: spontaneous chemical reaction produces
electrical energy
• Electrolytic: electrical energy forces a nonspontaneous
reaction to occur
Galvanic Cells
Cathode
Electrolyte
• Electrode: surface where redox reaction occurs
Anode: oxidation
Cathode: reduction
Active: part of redox
Inert: does not react
• Electrolyte: conducting solution (has ions)
• Electric current due to electron and ion flow
A Voltaic Cell: The Daniell (Zn
(Zn--Cu) Cell
CHEMICAL CHANGE Æ
CHEMICAL CHANGE Æ ELECTRIC CURRENT
anode
Oxidation
negative electrode
Power
Anode
Electrolyte
Voltaic
V lt i cell
ll
Electrolytic
El t l ti cell
ll
• An apparatus that allows a redox reaction to occur by transferring electrons through an external connector.
Electrolytic cell
e–
cathode
Reduction
Positive electrode
spontaneous
p
redox reaction
•To obtain a useful current, we separate the oxidizing and reducing agents
so that electron transfer occurs thru an external wire.
This is accomplished in a GALVANIC or VOLTAIC cell.
A group of such cells is called a battery
battery..
Electrolytic Cell
Battery
Anode (+):
4OH–
Electrochemistry
Two broad areas
QuickTime
Movie
Water
(aq) → O2(g) + 2H2O(l) +
4e–
Galvanic Cells Rechargeable
Electrolysis
Cells
batteries
Cathode (–
(–): 4H2O(l) + 4e
4e-- → 2H2(g) + 4OH–
Overall: 2H2O(l) → O2(g) + 2H2(g)
Voltaic Cell Diagram
Electrolytic vs Voltaic Cells
The Cu‐Ag Cell
}
• spontaneous reaction generates electricity
• Oxidation: anode
Reduction: cathode
l
d
l i
• Electrode Polarity:
Anode: negative
Cathode: positive
• e–flow: anode to cathode
• Ion flow: anions to anode; cations to cathode
}
• nonspontaneous reaction forced to occur
• Oxidation: anode
Reduction: cathode
• Electrode Polarity:
l
d
l i
Anode: positive
Cathode: negative
• e–flow: anode to cathode
• Ion flow: anions to anode; cations to cathode
The Daniell cell:
Zn(s) + Cu2+(aq) → Zn2+(aq) + Cu(s)
may be represented by a cell diagram:
Zn | Zn2+(1.0 M) || Cu2+(1.0 M) | Cu
Oxidation
half--cell
half
R d ti
Reduction
half--cell
half
¾The ANODE is described before the CATHODE.
¾Concentrations of ions are indicated in brackets.
¾A vertical line represents a phase boundary.
¾A double vertical line represents the salt bridge.
A Comparison of Cell Potentials
• Zn‐Cu cell potential: 1.10 V
Zn(s) + Cu 2+(aq) → Zn2+(aq) + Cu(s)
• Cu‐Ag cell potential: 0.46 V
Cu(s) + 2Ag+(aq) → Cu 2+(aq) + 2Ag(s)
• Oxidizing power: Ag+ > Cu 2+ > Zn 2+
• Cell potential (voltage) depends on:
nature of electrodes and ions
concentrations of ions
temperature of cell
The Cell Potential
• The magnitude of the cell potential, Ecell, is a measure of the spontaneity of a redox reaction
• The more positive the cell potential, the greater the driving force for the redox reaction to proceed as written
g
p
• The standard cell potential, Eocell, is for a cell operating under standard conditions Standard Electrode Potentials:
Standard Electrode Potentials:
• The standard electrode potential, Eohalf‐cell, is
the potential of a given half‐cell when all
components are in their standard states
• Byy convention,, the standard electrode
potential refers to a half‐reaction written as a
reduction
• The more positive the potential, the greater
the tendency for the reaction to proceed
forward
Standard Electrode Potentials
• The E°cell calculated is for the cell operating
under standard state conditions
• For electrochemical cell standard conditions are:
-solutes
l t att 1 M concentrations
n ntr ti n
- gases at 1 atm partial pressure
- solids and liquids in pure form
• The potential of a half‐cell is referenced with respect to the standard hydrogen electrode (SHE)
By convention:
• By convention:
SHE Half‐Reaction
Eohalf‐cell
H2 → 2H+ + 2e–
0.00 V
0.00 V
2H+ + 2e– → H2
• All at some specified temperature, usually 298 K
Standard Hydrogen Electrode (SHE) SHE - the reference electrode
Reference Electrode Standard ReductionPotentials
(The Electromotive Series)
Acidic Solution
Li+(aq) + e– → Li(s)
Al3+(aq) + 3e– → Al(s)
Cr2+(aq)
+ 2e– → Cr(s)
( ) + 2e
()
Zn2+(aq) + 2e– → Zn(s)
Cr3+(aq) + 3e– → Cr(s)
Cr3+(aq) + e– → Cr2+(aq)
2H+(aq) + 2e– → H2(g)
Cu2+(aq) + e– → Cu+(aq)
Cu2+(aq) + 2e– → Cu(s)
F2(aq) + 2e– → 2F–(aq)
SRP, Eo(volts)
–3.045
–1.66 –0.91
0.91 –0.763 –0.74 –0.41 0.00 0.153
0.337 2.87 Relative Oxidizing & Reducing Strengths
To determine which is a stronger oxidizing agent between Cl2 and Pb2+:
• Compare their reduction potentials
Eo = 1.360 V Cl2 + 2e– → 2Cl–
Pb2++ 2e– → Pb
Eo = –0.126 V
• The stronger oxidizing agent is more easily reduced; i.e., has more positive Eo
⇒ Cl2 is the stronger oxidizing agent
Table of Standard Reduction Potentials
Things to Remember about Eo
• The more positive the Eo, the greater the tendency for the
reaction to occur in the forward direction
• The more negative the Eo for a reaction, the greater the
tendency for the reaction to occur in the reverse direction
• If a reaction is reversed, the sign of its Eo is reversed
• If a reaction is multiplied by a factor, its potential stays the
same; Eo is not multiplied by the factor
• If half-reactions are summed up to give an overall reaction,
potentials can be summed up to give an overall cell potential
Table Of Standard Reduction Potentials
oxidizing
ability of ion
Eo (V)
Cu2+ + 2e-
Cu
+0.34
2 H+ + 2e-
H2
0.00
Zn2+ + 2e-
Zn
-0.76
To determine an oxidation
from a reduction table, just
take the opposite sign of the
reduction!
reducing ability
of element
Oxidizing and Reducing Agents
• The strongest oxidizers have the most positive reduction potentials.
• The strongest reducers have the most negative reduction potentials.
Cell Potentials
Predicting Reaction Spontaneity
• Diagonal Rule for the Electromotive Series: Any species
on the left half‐cell reaction will react spontaneously
with a species on the right half‐cell reaction located
above it
2+ + 2e
Zn2+ + 2e–→ Zn
Eo = –
= 0.76 V
0 76 V
2+ –
Cu + 2e → Cu
Eo = 0.34 V
• Spontaneous if Eocell is positive
Eo = 0 .76 V
Zn → Zn2+ + 2e–
2+ –
Eo = 0. 34 V
Cu + 2e → Cu
2+ 2+ Eo = 1.10 V
Zn + Cu → Zn + Cu
Determination of Cell Potentials
Determination of Cell Potentials
• Choose appropriate half‐reactions from the
Table of Standard Potentials
• Write half‐reaction with more positive Eohalf‐cell
as a reduction
• Write less positive half‐reaction as an oxidation;
re erse sign of Eohalf‐cell
reverse
• Balance number of electrons; do not multiply
Eohalf‐cell by factors used to multiply electrons
• Sum up reactions and potentials to give Eocell
• If Eocell > 0: reaction is spontaneous
The Cell Potential
Cr3+ (aq) + 3eAnode ((oxidation):
)
Cd (s) E0 = -0.40 V Cd is the stronger oxidizer
E0 = -0.74 V
Cr (s)
Cathode (reduction): 2e- + Cd2+ (1 M)
2Cr (s) + 3Cd2+ (1 M)
Cd will oxidize Cr
Cr3+ ((1 M)) + 3e- x 2
Cr ((s))
Cd (s)
x3
3Cd (s) + 2Cr3+ (1 M)
0 = E0
0
Ecell
cathode + Eanode
0 = -0.40 + (+0.74)
Ecell
0 = 0.34 V
Ecell
•
3Fe3+(aq) + 3e → 3Fe2+(aq);
Ered= +0.771 V
(2) Subtraction of reduction (or oxidation) potentials of half-reactions
having
g the same number of electronics.
•
Cl2(g) +2e → 2Cl-(aq); Ered= +1.36 V
•
Zn2+(aq) +2e → Zn(s);
•
•
Therefore for
Cl2(g) +Zn(s) → 2Cl-(aq) +Zn2+(aq); Ecell= +2.123
Ered= -0.763 V
Electron Transfer Reactions
What is the standard potential of an electrochemical cell made of a Cd
electrode in a 1.0 M Cd(NO3)2 solution and a Cr electrode in a 1.0 M
Cr(NO3)3 solution?
Cd2+ (aq) + 2e-
(1) A half-reaction can be multiplied through by any number without
affecting the reduction (or oxidation) potential
•
Fe3+(aq) + e → Fe2+(aq);
Ered= +0.771 V
• Electron transfer reactions are Electron transfer reactions are oxidation
oxidation‐‐reduction
or redox
or redox reactions.
• Results in the generation of an electric current ( l
(electricity) or be caused by imposing an electric i i ) b
db i
i
l
i
current. • Therefore, this field of chemistry is often called ELECTROCHEMISTRY.
Thermodynamics
Electrochemistry
The Gibbs free energy is defined as:
G = H − TS
Where
H = U + PV
• Deals with the inter‐conversion between
electrical energy and chemical energy
• Involves
oxidation‐reduction
reactions in electrochemical cells
(redox)
U is the internal energy (SI unit: J)
P is pressure (SI unit: Pa)
V is volume (SI unit: m3)
T is the temperature (SI unit: K)
S is the entropy (SI unit: J/K)
H is the enthalpy (SI unit: J)
Gibbs energy is the capacity of a system to do non-mechanical work and
ΔG measures the non-mechanical work done on it. The Gibbs free energy
is the maximum amount of non-expansion work that can be extracted from
a closed system; this maximum can be attained only in a completely
reversible process.
G is a thermodynamic properties.
G is a state function
G is NOT a path function.
http://en.wikipedia.org/wiki/Gibbs_free_energy
Thermodynamics
Thermodynamics of Chemical Reactions
The change in the Gibbs free energy of the system that occurs during a
reaction is:
Any reaction for which
If the reaction is run at constant temperature, this equation can be :
If the data are collected under standard-state conditions, the result is the
standard-state free energy of reaction,
Standard-state conditions:
• The partial pressures of any gases involved in the reaction is 0.1 MPa.
• The concentrations of all aqueous solutions are 1 M.
• Measurements are also generally taken at a temperature of 25 oC (298 K)
This equation is to determine the relative importance of the enthalpy and
entropy terms as driving forces behind a particular reaction. The change in
the free energy of the system that occurs during a reaction measures the
balance between the two driving forces that determine whether a reaction
51 is
spontaneous.
Thermodynamics of Chemical Reactions
For a chemical reaction, Standard-State Free Energy of Formation
Any reaction for which
The Gibbs free energy is the maximum amount of non-expansion work
that can be extracted from a closed system; this maximum can be attained
only in a completely reversible process.
Go < 0
is positive is therefore unfavorable.
Unfavorable or non‐spontaneous reactions:
Go > 0
Reactions can be classified according to the change in enthalpy (heat):
<0
A larger amount of the energy released in the reaction is subtracted
from a smaller amount of the energy used for the reaction.
52
Thermodynamics of Chemical Reactions
For a reaction:
aA+ bB →c C +d D
Chemical quotient (reaction quotient) is defined as:
Q=
The standard-state free energy of reaction can be calculated from the
standard-state free energies of formation as well. It is the sum of the free
energies of formation of the products minus the sum of the free energies of
formation of the reactants
is negative should be favorable, or spontaneous
Favorable, or spontaneous reactions:
[C ]c [ D] d
[ A] a [ B]b
In a chemical process, chemical equilibrium is the state in which the chemical
activities or concentrations of the reactants and products have no net change
over time.
If Q correspond
d to
t equilibrium
ilib i
concentrations,
t ti
then
th the
th above
b
expression
i iis
called the equilibrium constant and its value is denoted by K (or Kc or Kp.)
K is thus the special value that Q has when the reaction is at
equilibrium
If K > Q, a reaction will proceed forward.
If K < Q, the reaction will proceed in the reverse direction,
converting products into reactants.
If Q = K then the system is already at equilibrium
Thermodynamics of Chemical Reactions
Thermodynamics of Chemical Reactions
Example: 0.035 moles of SO2, 0.5 moles of SO2Cl2, and 0.08 moles of Cl2
are combined in an evacuated 5 L flask and heated to 100 oC. What is Q
before the reaction begins? Which direction will the reaction proceed in
order to establish equilibrium?
For any chemical process, the free-energy change under any conditions, ΔG,
is given by:
R is the ideal-gas constant, 8.314 J/mol · K; T is the absolute
temperature; and Q is the reaction quotient
When a system (a reaction) is at equilibrium: ΔG = 0, and K=Q
Thus, at equilibrium, the equation above can be rewritten as
Solution:
The relationship between ΔGo and K can be summarized as follows
<0: K>1
0.078 (K) > 0.011 (Q)
= 0: K>1
Since K >Q, the reaction will proceed in the forward direction in order to
increase the concentrations of both SO2 and Cl2 and decrease that of
55
SO2Cl2 until Q = K.
>0:
K<1
56
http://www.chem.purdue.edu/gchelp/howtosolveit/equilibrium/Reaction_Quotient.htm
Thermodynamics of Chemical Reactions
Electrolysis and Mass Changes
Thermodynamics of Electrochemical Cells
Free Energy
charge (Coulombs) = current (Amperes) x time (sec)
1 mole e- = 96,500 C = 1 Faraday
Mols of metal dissolved are obtained by dividing the mols of electron by n:
Faraday’s Law:
M =
It
(mol)
nF
ΔG for a redox reaction can be found by using the equation
ΔG = −nFE
where n is the number of moles of electrons transferred, and F
is a constant, the Faraday.
1 F = 96,485 C/mol = 96,485 J/V-mol
I –current (A); t –time (s); n- number of electrons transferred;
F –Faraday constant (96500 C)
Thermodynamics of Electrochemical Cells
Thermodynamics of Electrochemical Cells
The Cell Potential :
Work done in a redox reaction = - n FEcell
’
Nernst Equation
’
Units: Joules = moles x (coul/mole) x volts = coul x volt = J
– 1 coulomb x 1 volt = 1 joule or Joule / Coulomb = volt
– Since a spontaneous redox rxn does work on the surroundings,
the sign is “-”: W = - nFEcell = ΔG
’
Free Energy, ΔG = maximum useful work done
¾ ΔG = - nFEcell
¾ At 1M concentrations, 1 atm pressure & 25 oC: ΔG = ΔGo
¾ ΔGo = - nFEocell
• Remember that
ΔG = ΔG° + RT ln Q
• This means
−nFE = −nFE° + RT ln Q
59
Thermodynamics of Electrochemical Cells
The Nernst Equation:
• At nonstandard conditions, the cell potential may be
calculated using the Nernst equation:
S
Standard
cell
potential
Faraday,
96,500 J/Vmol e-
ΔG = -nFEcell
0
ΔG0 = -nFEcell
n = number of moles of electrons in reaction
F = 96,500
J
= 96,500 C/mol
V • mol
0
ΔG0 = -RT ln K = -nFEcell
o
E = E – 2.303 RT log Q
nF
Reaction
quotient
mol electrons
transferred
Thermodynamics of Electrochemical Cells
Absolute
temperature
0 =
Ecell
(
(8.314
J/K•mol)(298
)(
K))
RT
l K=
ln
ln K
n (96,500 J/V•mol)
nF
0
Ecell
=
0.0257 V
ln K
n
0 =
Ecell
0.0592 V
log K
n
Gas constant,
8.314 J/mol K
Thermodynamics of Electrochemical Cells
Thermodynamics of Electrochemical Cells
The Cell Potential and
the Progress of a Reaction
The Nernst Equation
• For the reaction: Zn + Cu2+ → Zn2+ + Cu
• the cell potential is given by:
• Substitution of the values for the gas constant R
and the Faraday into the Nernst equation at 25oC
gives:
0.0592
E = Eo–
n
2+
log Q
z
z
z
Thermodynamics of Electrochemical Cells
The Cell Potential and the Reaction Quotient Q
E = E o – 2.303 RT log Q
nF
0.0592
o
E =E –
log Q
n
• When:
Q < 1: [reactant] > [product], Ecell > Eocell
Q = 1: [reactant] = [product], Ecell = Eocell
Q > 1: [reactant] < [product], Ecell < Eocell
E = E o – 2.303 RT log [ Zn 2+ ]
nF
[ Cu ]
At standard conditions:
conditions: Ecell = Eocell
As cell operates
operates:: Zn2+ increases, Cu2+ decreases,
log Q increases, Ecell decreases
When Ecell = 0 (equilibrium); cell “runs down”
Thermodynamics of Electrochemical Cells
The Relationships Between
Eocell, ΔGo and Keq
• Eocell, is related to ΔGo by:
ΔGo = –nFEocell
• Since ΔGo = –2.303 RTlog K:
–nFEocell = –2.303 RTlog K • Solving for Eocell or for K:
E o = 2.303 RT log K
nF
E o = 0.0592 log K
n
nFE o
2.303 RT
nE o
log K =
0.0592
log K =
Thermodynamics of Electrochemical Cells
Thermodynamics of Electrochemical Cells
Eocell, ΔGo and K: A Summary
ΔGo
–
0
+
Forward Reaction
S
Spontaneous
t
Equilibrium Nonspontaneous
Eocell
+
0
–
K
>1
=1
<1 Calculating Equilibrium Constants
• When an electrochemical cell operates, the concentrations of the ions change until Q = K .
• When the cell reaches equilibrium, Ecell = 0.
• Combining these facts with the Nernst equation gives:
Ecell = 0 = Eo −
RT
ln (K )
nF
Alkaline Battery
• Calculate K for the reaction that occurs at 25 oC when Mg is added to a solution of AgNO3.
• The net reaction is:
Mg + 2 Ag+ ' Mg2+ + 2 Ag
RT
l (K )
ln
nF
• Rearranging, we can derive an equation to calculate the equilibrium constant for a redox reaction:
Eo =
Calculating K for a Redox Reaction
Eo =
RT
ln (K )
nF
3.17 V =
(8.314)(29 8 K)
ln (K )
(2 mol)(96500 C/mol)
247 = ln (K) so K = e247 = HUGE
QuickTime
Movie
Anode ((-): Zn + 2 OH- ----->
> ZnO + H2O + 2e
2e-2e-- ----->
> Mn2O3 + 2 OHCathode (+): 2 MnO2 + H2O + 2e
Corrosion
QuickTime
Movie
Sacrificial Anode
Corrosion Prevention
Because since is a stronger reducing agent ( i.e. more
easily oxidized) than Fe, it will act as a “sacrificial” anode
in place of Fe, therefore preventing the iron metal from
corroding.
Polarization
Faraday’s Law: M =
Kinetics of Electrochemical Reaction
I
t
n
F
It
nF
(mol)
– current (A);
– time (s);
- number of electrons transferred;
– Farady constant (96500 C)
The mass dissolution rate:
r=
Exchange Current Density
At equilibrium in a reaction such as
Electron flow must be the same in both directions (forward and reverse), i,e.,
so at equilibrium:
r f = rr =
I0
nF
where io = exchange current density, related to the current flow in an
q
situation
equilibrium
• At the equilibrium potential of a reaction, a reduction and an
oxidation reaction occur, both at the same rate.
• For example, H ions are converted gas and released from the
gas at the same rate
• The net reaction rate and net current density are zero
M
I
M =
t
nF
Polarization
exchange current density, related to the current flow in an equilibrium
situation
Polarization
Polarization
• Electrode reactions deviates from the equilibrium
state due to the flow of an electrical current through
an electrochemical cell causing a change in the
electrode potential. This electrochemical phenomenon
is referred to as polarization.
• The deviation from equilibrium causes an electrical
potential difference between the polarized and the
equilibrium (unpolarized) electrode potential known
as overpotential
Polarization
Ecorr = corrosion potential or mixed potential
corrosion rate: icorr = ia = rate of anodic dissolution in a system
equilibrium
Equilibrium potential for
cathodic reaction = Eoc
Cathodic Overpotential:
ηc = E – Eoc < 0
Real potential = E
anodic Overpotential:
Equilibrium potential for
anodic reaction = Eoa
ηa = E – Eoa > 0
Polarization
• Depending on the type of resistance that limits the reaction rate, we are talking about three different kinds of polarization
• activation polarization
• concentration polarization and • resistance (ohmic) polarization or IR Drop
Zn in acidic water
Activation Polarization
activation polarization:
• An electrochemical reaction may consist of several steps
Activation Polarization
activation polarization:
• The overpotential due to the activation polarization is determined
by Tafel equation
• The slowest step determines the rate of the reaction which requires
activation energy to proceed
• Subsequent shift in potential or polarization is termed activation
polarization
β=
2.3RT
αnF
whenever η = zero (i.e. no
polarization), i = io, exchange current
Concentration Polarization
Activation Polarization
Hydrogen Overpotential:
• Sometimes the mass transport within the solution may be rate determining – in such cases we have concentration polarization
• Hydrogen evaluation at a platinum electrode:
– H+ + e‐ → Hads
– 2Hads → H
→ H2
• Concentration
Concentration polarization polarization
implies either there is a shortage of reactants at the electrode or that an accumulation of reaction product occurs
• Step 2 is rate limiting step and its rate determines the value of hydrogen overpotential on platinum O 2 + 4H − + 4e − → 2H 2 O
Source: K. B. Kabir
Concentration Polarization
• Fick’s Law:
dc
dM
= − D ×10 −3
dt
dx
(1)
• where dM/dt is the mass transport in x direction in
mol/cm2s, D is the diffusion coefficient in cm2/s, and c
is the concentration in mol/m3
• Faraday’s law: d ’ l
M
I
i
=
=
AΔt AnF nF
(2)
• Under steady state,
mass transfer rate = reaction rate
i = DnF
C B − C0
δ
Source: K. B. Kabir
Concentration Polarization
• Maximum transport and reaction rate are attained when C0
approaches zero and the current density approaches the limiting current density:
iL = DnF
C
δ
(4)
• The most typical concentration polarization occurs when there is a lack of reactants, and (in corroding systems) therefore most
a lack of reactants, and (in corroding systems) therefore most often for reduction reactions
• This is the case because reduction usually implies that ions or molecules are transported from the bulk of the liquid to the electrode surface, while for the anodic (dissolution) reaction, mass is transported from the metal, where there is a large reservoir of the actual reactant
(3)
Where δ is the width of the depletion zone
Source: K. B. Kabir
Concentration Polarization
• Equations (1) to (4) are valid for uncharged particles, as for instance oxygen molecules
• If charged particles are considered, migration will occur in addition to the diffusion and the previous
occur in addition to the diffusion and the previous equation must be replaced by
i L = DnF
C
δN
(5)
where N is the transference number of all ions in solution except the ion getting reduced
Overpotential due to concentration polarization
• If copper is made cathode in a solution of dilute CuSO4 in which the activity of cupric ion is represented by (Cu2+ ), then the potential in absence of external current, is given by the Nernst equation:
E1 = 0.337 −
2.3RT
1
2.3RT
log
= 0.337 +
log(Cu 2 + )
nF
(Cu 2+ )
nF
• When current flows, copper is deposited on the electrode, thereby decreasing surface concentration of copper ions to a level at (Cu2+)s. The potential of the electrode becomes:
E2 = 0.337 −
2.3RT
1
2.3RT
log
= 0.337 +
log(Cu 2+ )S
nF
(Cu 2+ )S
nF
Source: K. B. Kabir
Overpotential due to concentration polarization
• Since (Cu2+ )s is less than (Cu2+ ), the potential of the polarized cathode is less noble, or more active, than in the absence of external current. The difference of potential, E2 − E1 , is the concentration polarization , equal to:
E2 − E1 =
(Cu 2+ )S
2.3RT
log
nF
(Cu 2+ )
Overpotential due to concentration polarization
i L = DnF
C
(5)
δN
( Cu 2 + ) S = ( Cu 2 + ) −
( Cu
C 2+ ) =
iδ N
DnF
iLδN
DnF
η Conc = E 2 − E 1 =
⎛
i ⎞
2 . 3 RT
log ⎜⎜ 1 − ⎟⎟
nF
iL ⎠
⎝
Source: K. B. Kabir
Source: K. B. Kabir
IR Drop
Concentration Polarization
• When polarization is measured with a potentiometer and a
reference electrode-Luggin probe combination, the measured
potential includes the potential drop due to the electrolyte
resistance and possible film formation on the electrode surface
• The drop in potential between the electrode and the tip of Luggin
probe equals iR.
• If l is the length of the electrode path of cross sectional area s, k
is the specific conductivity, and i is the current density then
resistance
l
R=
• iR drop in volts =
Combined Polarization
k
il
k
Third electrode
• Total polarization of an electrode is the sum of the individual contributions: ηT = ηa + ηc + ηr
A
voltage or
potentiostat
current source
V
RE
WE
RE
CE
ηohm
WE
ηact
WE
ηconc
RE
ηconc
RE
ηact
E − En = η = ηact + ηconc + IRu
Typical polarization curve
http://www.electrochem.org/dl/interface/fal/fal04/IF8-04-Pages17-19,45.pdf
cab
Current/A
Constant--Potential Coulometry
Constant
Time after application
of potential at which
species is electrolyzed
Voltammetry
Measurement of (Faradaic) current as a function of applied potential
Charge/C
∫ I dt
Analyte concentration is related to peak or limiting current
Linear--Sweep Voltammetry
Linear
Linear--Sweep Voltammetry
Linear
Stirred Solutions
Unstirred Solutions
EApplied > E1/2
IL ≡ Limiting Current = KCA
E1/2 ≡ Half
Half--wave Potential = E
E°°
EApplied < E1/2
Electrode surface is depleted of reactants after prolonged reaction times
(Non--Hydrodynamic) Linear(Non
Linear-Sweep Cyclic Voltammetry
For a reversible (Nernstian) couple:
Ipc = –Ipa
Epa - Epc = 0.0592/n
E° = (Epa + Epc)/2
Start
Ip = KCA
IF = IDL = Diffusion
Diffusion--limited current
For an irreversible couple:
Ipc ≠ –Ipa
Epa - Epc > 0.0592/n
E° = (Epa + Epc)/2
Voltammogram is non
non--symmetric
Used mainly for qualitative analysis
Electrochemical Impedance Spectroscopy
Electrochemical Impedance Spectroscopy
• Ohms Law:
V
R=
I
Electrochemical Impedance Spectroscopy
• Impedance is a general expression for resistance under the • Where V is the applied voltage and I is the current
• R is a resistor. It follows Ohm’s Law at all current and voltage
levels
• The resistance value is independent of frequency
• AC current and voltage signals through a resistor are in phase
with each other
L
A
A
C=ε
L
R: resistance, unit: Ω
ρ: resistivity, Ω cm
C: capacitance, F
ε: permittivity, F cm‐1
R =ρ
alternating current (AC) excitation signal
• For a sinusoidal current, the voltage is expressed by
E = E0 sin ωt
t: time
f: frequency
ω: angular frequency = 2πf
ωt: phase angle
The current is I = I0 sin (ωt + θ)
θ: phase shift
Electrochemical Impedance Spectroscopy
Electrochemical Impedance Spectroscopy
Impedance can be given with an expression analogous to Ohm's Law
as:
The expression for Z(w) is
composed of a real and an
imaginary part. If the real
part is plotted on the Z axis
and the imaginary part on
the Y axis of a chart, we get
a "Nyquist plot".
N ti that
Notice
th t in
i this
thi plot
l t the
th yaxis is negative and that
each point on the Nyquist
plot is the impedance at one
frequency.
With Eulers relationship,
Then the potential is described as
and the current response as
The impedance is then represented as a complex number,
The impedance is composed of a real and an imaginary part
Electrochemical Impedance Spectroscopy
Electrical Circuit Elements
EIS data is commonly analyzed by fitting it to an equivalent
electrical circuit model. Most of the circuit elements in the model are
common electrical elements such as resistors, capacitors, and
inductors. To be useful, the elements in the model should have a basis
in the physical electrochemistry of the system.
Component
Current Vs.
Voltage
Impedance
resistor
E= IR
Z=R
inductor
E = L dI/dt
Z = jωL
capacitor
I = C dE/dt
Z = 1/j ωC
Nyquist Plot (or Cole-Cole plot)
of Impedance
low frequency data are on the right side of the plot and higher
frequencies are on the left. This is true for EIS data where impedance
usually falls as frequency rises (this is not true of all circuits).
Electrochemical Impedance Spectroscopy
Electrical Circuit Elements
• An alternating current can be phase shifted with respect to the
voltage
• The phase shift depends on what kind of sample the current
ppasses
• To describe the response from a sample on the alternating
current, we introduce 3 passive circuit elements (R, C and L)
• The current and voltage through a resistor, R, is not phase shifted
Æ the impedance is not dependant on frequency
• A resistor only contributes to the real part of the impedance
Electrochemical Impedance Spectroscopy
• The inductor is an ideal conductor, and an ideal isolator
• The inductor only contributes to the imaginary part of the impedance
• The impedance of an inductor increases as frequency increases. An
inductor's current is phase shifted 90 degrees with respect to the voltage
0
-6
6
L = 10 H
-X / Ω
-2
Increasing
frequency
-6
2
4
6
• The capacitor (C ) can store electrical charge:
C =ε
A
A
= ε 0ε r
L
L
ε: permittivity
ε0: permittivity of free space
εr: relative dielectric e at e d e ect c
constant A capacitor only contributes
to the imaginary part of the
impedance. A capacitor's
impedance decreases as the
frequency is raised.
-4
0
Electrochemical Impedance Spectroscopy
8
a pure capacitor Nyquist plot
R/Ω
a pure inductor Nyquist plot
Souce: H. Fjeld
Electrochemical Impedance Spectroscopy
• Capacitors often do not behave ideally. Instead, they act like a
constant phase element (CPE) as defined below
[
Souce: H. Fjeld
Electrochemical Impedance Spectroscopy
Impedance of Constant Phase Element (CPE)
CPE
]
Z Q = Y ( jω)
n −1
Rct
• The
Th CPE is
i very versatile:
il
-Z”
If n = 1, CPE represents an ideal capacitor
Cdl
If n = 0, CPE represents a resistor
If n = -1, CPE represents an inductor
If n = 0.5, CPE represents a Warburg element
Bode plot
CPE
Rct
2
Rct
Z’
Electrochemical Impedance Spectroscopy
Simplified Randles Cell
The Simplified Randles cell is one of most common cell models. It includes a
solution resistance, a double layer capacitor and a charge transfer (or
polarization resistance).
Another common plot format
of impedance spectra is the
Bode plot. In general it depicts
two curves. The x-axis shows
the logarithm of the
frequency. The left axis gives
th llogarithm
the
ith off the
th
impedance, while the right
axis gives the phase angle.
equivalent circuit for a Simplified Randles Cell
Bode plots of Impedance
Source: Gamry.com
Electrochemical Impedance Spectroscopy
Simplified Randles Cell
The polarization resistance was calculated to be 250. A capacitance of 40
μF/cm2 and a solution resistance of 20 Q were also assumed
Nyquist plot of The Simplified Randles cell
Electrochemical Impedance Spectroscopy
Warburg impedance of Diffusion
Diffusion can create an impedance known as the Warburg
impedance. At high frequencies the Warburg impedance is small
since diffusing reactants don't have to move very far. At low
frequencies the reactants have to diffuse farther, thereby increasing
the Warburg impedance.
The equation for the "infinite" Warburg impedance is:
Where is the Warburg Constant.
On a Nyquist plot the infinite Warburg impedance appears as a
diagonal line with a slope of 0.5.
On a Bode plot, the Warburg impedance exhibits a phase shift of
45°.
Electrochemical Impedance Spectroscopy
Impedance of electrochemical reaction at the electrode
with infinite diffusion
Electrochemical Impedance Spectroscopy
Simplified Randles Cell
Nyquist plot of The Simplified Randles cell
Source: Gamry.com
Electrochemical Impedance Spectroscopy
Warburg impedance of Diffusion
Warburg impedance is only valid if the diffusion layer has an
infinite thickness. Quite often this is not the case. If the
diffusion layer is bounded, the impedance at lower
frequencies no longer obeys the equation above. Instead,
we get the form:
with,
δ = Nernst diffusion layer thickness
D = an average value of the diffusion coefficients of the
diffusing species
Electrochemical Impedance Spectroscopy
Impedance of electrochemical reaction at the electrode
with infinite diffusion
Or CPE
In case a charge transfer is also influenced by diffusion to and from the
electrode, the Warburg impedance will be seen in the impedance plot.
The Warburg element is easily recognized by a line with an angle of 45 °
in the lower frequency region. The equivalent
of this electrochemical cell
Or CPE
is called Randles' circuit.
circuit showing the solution resistance, double layer capacitance
(or CPE), charge transfer resistance and Warburg impedance
Complex plane plots for the circuit of Fig 5 with an ideal double layer
capacitance (which means n=1) (a) and a CPE (b) with n = 0.88.
Electrochemical Impedance Spectroscopy
Impedance of electrochemical reaction at the electrode
with infinite diffusion
Peak frequency: ω0 = (RC)-1
Electrochemical Impedance Spectroscopy