8/13/2019 Farrell Electrochemistry Lecture
1/38
8/13/2019 Farrell Electrochemistry Lecture
2/38
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.
8/13/2019 Farrell Electrochemistry Lecture
3/38
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
8/13/2019 Farrell Electrochemistry Lecture
4/38
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
8/13/2019 Farrell Electrochemistry Lecture
5/38
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
8/13/2019 Farrell Electrochemistry Lecture
6/38
8/13/2019 Farrell Electrochemistry Lecture
7/38
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
8/13/2019 Farrell Electrochemistry Lecture
8/38
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
8/13/2019 Farrell Electrochemistry Lecture
9/38
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
8/13/2019 Farrell Electrochemistry Lecture
10/38
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 =
8/13/2019 Farrell Electrochemistry Lecture
11/38
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
8/13/2019 Farrell Electrochemistry Lecture
12/38
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
8/13/2019 Farrell Electrochemistry Lecture
13/38
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
8/13/2019 Farrell Electrochemistry Lecture
14/38
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
8/13/2019 Farrell Electrochemistry Lecture
15/38
Notation Examples
Zn|ZnSO4 CuSO4|Cu
anode cathode
Zn|ZnSO4 || CuSO4|Cu
anode cathode
8/13/2019 Farrell Electrochemistry Lecture
16/38
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
8/13/2019 Farrell Electrochemistry Lecture
17/38
8/13/2019 Farrell Electrochemistry Lecture
18/38
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
8/13/2019 Farrell Electrochemistry Lecture
19/38
8/13/2019 Farrell Electrochemistry Lecture
20/38
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
8/13/2019 Farrell Electrochemistry Lecture
21/38
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
8/13/2019 Farrell Electrochemistry Lecture
22/38
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-
8/13/2019 Farrell Electrochemistry Lecture
23/38
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
8/13/2019 Farrell Electrochemistry Lecture
24/38
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
=
+=
=
8/13/2019 Farrell Electrochemistry Lecture
25/38
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
8/13/2019 Farrell Electrochemistry Lecture
26/38
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
==
==
8/13/2019 Farrell Electrochemistry Lecture
27/38
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.
8/13/2019 Farrell Electrochemistry Lecture
28/38
8/13/2019 Farrell Electrochemistry Lecture
29/38
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
8/13/2019 Farrell Electrochemistry Lecture
30/38
8/13/2019 Farrell Electrochemistry Lecture
31/38
8/13/2019 Farrell Electrochemistry Lecture
32/38
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
8/13/2019 Farrell Electrochemistry Lecture
33/38
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)
8/13/2019 Farrell Electrochemistry Lecture
34/38
8/13/2019 Farrell Electrochemistry Lecture
35/38
R h d i h f
8/13/2019 Farrell Electrochemistry Lecture
36/38
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
8/13/2019 Farrell Electrochemistry Lecture
37/38
8/13/2019 Farrell Electrochemistry Lecture
38/38
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