0581.5271 Electrochemistry for Engineers

LECTURE 2

Lecturer: Dr. Brian Rosen Office: 128 Wolfson

Office Hours: Sun 16:00

The Electrochemical CellPart II

Lower Stability of Water

Starting withH+(aq) + e- ½H2(g)

we write the Nernst equation

We set pH2 = 1 atm. Also, Gr° = 0, so E0 = 0. Thus,

we have

pHE 0592.0

H

H

a

pEE

21

2log1

0592.00

Upper Stability of Water

½O2(g) + 2e- + 2H+ H2O

but now we employ the Nernst eq.

2

0

21

2

1log

0592.0

HO apn

EE

We assume that pO2 = 1 atm. This results in

This yields a line with slope of -0.0592.

221

2log0296.023.1

HO apE

pHpE O 0592.0log0148.023.12

volts23.1)42.96)(2(

)1.237(00

n

GE r

pHE 0592.023.1

Upper Stability of Water

Recall pH = -log (aH+)

The Electrochemical Series

Pourbaix Diagram

Pourbaix Diagram of Water Stability vs. Ag/AgCl?

Recall: A Good Reference is Non-Pol.

0.00V vs. SHE +0.197V vs. SHE+0.00 vs. Ag/AgCl

Pourbaix Diagram vs Ag/AgCl

E = 1.03 V vs. Ag/AgCl

E = -.197 V vs. Ag/AgCl

Reconsider : Galvanic vs. Electrolytic

+ E- E

E° Cu/Cu+

=0.340 V vs. SHE

Cu+2 + 2e- Cu + i

- i

When the electrode is heldat its equilibrium potential,the forward and reverse current cancel and the NET current is zero

Equilibrium (Non-polarized)

+ E- E

E° Cu/Cu+

=0.340 V vs. SHE

Cu+2 + 2e- Cu + i

- i

When the electrode is negative ofits equilibrium potential, reductionis favored and there is a net flow ofelectrons consumed by the electrodefor the reduction reaction.

ΔE

Cathodic Polarization

+ E- E

E° Cu/Cu+

=0.340 V vs. SHE

Cu+2 + 2e- Cu + i

- i

When the electrode is positive ofits equilibrium potential, oxidationis favored and there is a net flow ofelectrons produced for the oxidation reaction.

ΔE

Anodic Polarization

Real Polarization of Electrodes

In reality, I-V curves for electrodestake on a variety of shapes and forms dependent on the kinetic and mass-transport parameters

1M Cd+2 1M Cu+2 CuCd

OPEN CIRCUIT POTENTIAL (OCP)

Cd+2 +2e- Cd Cu+2 +2e- Cu

+ E- E

i

E° Cd/Cd+2

-0.40 vs. SHE

+ E- E

E° Cu/Cu+2

+0.34 vs. SHE

E Cell (OCP) = 0.74 V i

1M Cd+2 1M Cu+2 CuCd

GALVANIC CELL (SPONTANEOUS)

Cd+2 +2e- Cd Cu+2 +2e- Cu

+ E- E

E° Cd/Cd+2

-0.40 vs. SHE

+ E- E

E° Cu/Cu+2

+0.34 vs. SHE

+∆E -∆E

-0.35V

+0.29V

E Cell = 0.64 V

e-

e-

+CATHODE

-ANODE

i i

1M Cd+2 1M Cu+2 CuCd

ELECTROLYTIC CELL

Cd+2 +2e- Cd Cu+2 +2e- Cu

+ E- E

E° Cu/Cu+2

+0.34 vs. SHE

+ E- E

E° Cd/Cd+2

-0.4 vs. SHE

+∆E-∆E

+0.75V

+0.29V

E Applied = 1.5 V

e-

+ANODE

-CATHODE

1.5Ve-

-0.75V ii

Summary • Galvanic (spontaneous cells) operate below their

maximum potential (OCP) due to the electrode polarization required to produce current (anode E is less negative than E°, and cathode E is less positive than E°)

• Electrolytic cells require an external voltage more than the minimum required OCP predicted by thermodynamics (anode E is more positive than E°, cathode E is more negative than E°)

η = (E - E°) = “overpotential”

Electrode Processes

KINETICS

MASS-TRANSFERdiffusion

convection migration

Electrochemical Kinetics

Electrode Processes

KINETICS

MASS-TRANSFERdiffusion

convection migration

(FAST)(SLOW)

In our modeling of kinetics, we will assumethat mass transfer to the electrode is fast

compared to the reaction rate

Our Goal

i = f(E)

How can we model the current at an electrode as a function of its potential assuming the reaction is the rate limiting step? (i.e. mass

transfer to the electrode is FAST)

Surface vs. Bulk Concentration

• Surface concentration of A

CA f(x,t)

..at surface x=0, therefore surface concentration is CA (0,t) or (CA for short here)

CA* is the symbol we will use for “bulk”

concentration

Basic Rate Laws (1st order rxn)

kf

kb

Ox + ne- Red

OxfOx

f Ckdt

dN

dRebdRe

r Ckdt

dN

dRebOxfdReOx

net CkCkdt

)NN(d

NOTE Cox is really Cox(0,t), the surface concentration of “Ox”!

Likewise Nox is the number of molsOf “Ox” on the surface

Therefore v is in units of mols/(time*area)

Measured Current

i [=] Coulombs / s

F is the “molecular weight equivalentof electrons in Coulombs / mol

dRebOxfdReOx

net CkCkdt

)NN(d

)( RedbOxfanocathnet CkCkFAiii

FA

i

dt

NNd netdOxnet

)( Rev [=] mol/(sec*cm2)

#mols Ox on surface

Hg

Na+

Mercury Drop Electrode

Na+ + 2e- Na E° = - 2.71 V vs. SHE

Na+ + 2e- Na(Hg) E° = - 2.71 V vs. SHE

Dangerous!

Solid Na is NOT stable, hence the VERY negative E°Reacts exothermically with moisture

The Energy Barrier

1. Reconfiguration of atomic position2. Repulsion forces3. Desolvation of ions in solution

Even though the reaction is favorable according to THERMODYNAMICS, it must overcome anenergy barrier.

LARGER BARRIER = SLOWER REACTION

Reasons for Energy Barriers

AB + CGib

bs F

ree

Ener

gy

+

- Energy increasesas we bring the sodium ioncloser to the Na(Hg) surfacedue to repulsion forces.Vice-versa also true for energy of amalgamated sodium atom

Changing the potential changes the energy of the participating electron

Na+ +e- Na (Hg)

The Hg drop electrode is ANODICALLY polarized by ΔE = E - E°The energy of the electrode changes by F ΔE

Na+ +e- Na (Hg)

+

-

Charge x Voltage = Energy

Na+ +e- Na (Hg)+

-

How do the anodic and cathodic activation barriers change with overpotential (η = E-E°)?

Symmetry Factor, α

• The symmetry factor, α, describes what fraction of the overpotential goes towards changing the CATHODIC barrier.

• (1-α) , same for ANODIC barrier

• For multistep/multi-electron reactions, the symmetry factor is called the transfer coefficient

+

-

Na+ +e- Na (Hg)

(1-α)F Δ E

αFΔE

R+

-

Cathodic barrier goes up by the same amount that the anodic

barrier goes downCathodic barrier goes up by less than the anodic barrier

goes downCathodic barrier goes up by

more than the anodic barrier goes down

Defining the Rate Constant

Substituting our expression for how ΔG changes with η we get

defining a standard rate constant )exp(0

0

RT

GAk

Where f = F/RTWe assume Af = Ab

Butler-Volmer Equation

)CkCk(nFAiii dRebOxfanocath

Inserting our expression for the rate constants into our expression for total current

We get:

RT

EEF

dRT

EEF

Ox eCeCFAki)()1(

Re

)(0

00

We now have our relationship for how the current at an electrode varies with overpotential!

At Equilibrium kf

Recall that at equilibrium, the kinetic model and the thermodynamic model

must match!!!

kb

Ox + ne- Red

At Equilibrium

0CkCkdt

)NN(ddRebOxf

dReOxnet

Ox

dReeq

b

f

C

CK

k

k

but….. νf and νr are NOT ZERO, rather, they cancel!

kf

kb

Ox + ne- Red

Equilibrium

At equilibrium, the surface concentration C(0,t) equals the bulk concentration in solution C*

Which is just an exponential form of the Nernst equation

Kinetic model breaks down into thermodynamic model at equilibrium

Exchange Current Density • Although the NET current is zero, the anodic and cathodic

currents still have equal but opposite values known as the exchange current density

Raise both sides to -α

Substitute into

to get

Note i0 is dependent only on kinetic parameters!

Current-Overpotential Equation

• Divide the Butler-Volmer Equation by i0 to get:

Simplifies to :

..where f = F/RT

i0 Visualized

Effect of i0 on Polarization

Effect of Symmetry Factor on Polarization

Tafel Plot

at large η either the left or the right side becomes negligible.

..where f = F/RT

What happens when we account for mass transport?

Fig.1.1 Schematic j/E plot for the electrolysis of 1.0 M solution

of KI in H2SO4, employing two Pt electrodes. The minimum

potential for dc current flow is 0.56 V.