Chapter 11

Electrochemistry

Electromotive Force (電動勢 )

(C) charge

(J)work (V) difference potentialemf

1 joule of work is produced or required when 1 coulomb of charge is transferred between two points in the circuit that differ by a potential of 1 volt.

Galvanic Cells (Voltaic Cells )

Galvanic cell - an electric cell that generates an electromotive force by an irreversible conversion of chemical to electrical energy; cannot be recharged.

The electron flow from the anode to the cathode is what creates electricity.

In a galvanic cell, the cathode is positive while the anode is negative, while in a electrolytic cell, the cathode is negative while the anode is positive.

Galvanic Cells

Standard Reduction Potentials

Standard Hydrogen Electrode

2H+(aq)+Zn(s) →Zn+2(aq)+H2(g)

Oxidation half-reaction

Zn(s) →Zn+2(aq)+2e-

Standard hydrogen electrode

2H+(aq)+2e-→H2(g)

The cathode consists of a platinum electrode in contact

with 1 M H+ ions and bath by hydrogen gas at 1 atm. We

assign the reaction having a potential of exactly 0 volts.

)(76.076.000002

2VEEE

ZnZnHHcell

Copper-Zinc Voltaic Cells

The Cell Potentials

E0cell=E0(cathode)-E0 (anode)

The value of E0 is not changed when a half reaction is multiplied by an integer.2Fe+3+2e- →2Fe+2 E0(cathode)=0.77 VCu →Cu+2+2e- -E0 (anode)=-0.34 VCu+2Fe+3 →2Fe+2+Cu+

E0cell=E0(cathode)-E0 (anode)=0.43 V

oxidationreduction

Cell Diagrams

For a copper-zinc voltaic cells

Cu’ Zn ZnSO4(aq) CuSO4(aq) Cu

1. A vertical line indicates a phase boundary.

2. A dashed vertical line indicates the phase boundary between two miscible liquid.

Dashed line

PtL| H2(g)|HCl(aq)|AgCl(s)|Ag| PtR

Anode: H2(g)=2H++2e-(PtL)

Cathode: [AgCl(s)+e-(PtR)=Ag+Cl-] ×2

Overall: 2AgCl(s)+ H2(g)=2Ag+ 2H++2Cl-

CuL|Cd(s)|CdCl2(0.1M)|AgCl(s)|Ag(s) |CuR

Anode: Cd=Cd+2+2e-

Cathode: [AgCl+e-=Ag++Cl-] ×2

Overall: Cd+2AgCl=2Ag+Cd+2+2Cl-

Nernst Equation

E0: standard reduction potentialn: moles of electronsF: Faraday constant 96485 C/mol

QnF

RTEEcell ln0

Thermodynamic-Free Energy

The maximum cell potential is directly related to the free energy difference between the reactants and the products in the cell.

max

maxmax

nFEG

nFq

qEGW

Calculation of Equilibrium Constants for Redox Reactions

0000

0000

0

ln

lnln

0

ln

KRTG-nFEG

RT

nFEKK

nF

RTE

K, Ewhen Q

QnF

RTEE

cell

cell

Reaction Quotient (Q)

Q

K

nF

RTQ

nF

RTK

nF

RTE

KnF

RT

nF

GE-nFEG

QnF

RTEE

00

00

000

0

lnlnln

ln

ln

The positive E (R>L ) means that Q<K0. As Q increases toward K0, the cell emf decreases, reaching zero when Q=K0

The Equilibrium Constant of a Cu-Zn Cell

Zn+Cu+2(aq)=Zn+2(aq)+Cu

E0=0.34V-(-0.76V)=1.10V

KJ/mol 212

101.5K

85.6K) )(298K mol J (8.314

)C J )(1.1mol C 2(96485lnK

0

370

1-1-

-1-10

G

Concentration Cells

V..

..

C

C

nF

RTEE

QnF

RTEE

R

L 0591001

10ln

964851

2983148 ln0

ln

0

0

AgL Ag+(0.1M) Ag+(1M) AgR

PtL Cl2(PL) HCl(aq) Cl2(PR) PtR

R

L

P

P

F

RTE ln

2

Liquid Junction Potential

Liquid junction: the interface between two miscible electrolyte solutions.

Liquid-junction potential: A potential difference between two solutions of different compositions separated by a membrane type separator.

The salt will diffuse from the higher concentration side to the lower concentration side.

HCl HCl

H+

Cl-

a2 < a1

＋＋＋＋＋＋＋＋＋

－－－－－－－－－－

H+

Ag+

＋＋＋＋＋＋＋＋＋

－－－－－－－－－－

AgNO3 HNO3

a2 = a1

Liquid Junction Potential The diffusion rate of the cation and the anion of the

salt will very seldom be exactly the same. Assume the cations move faster; consequently, an

excess positive charge will accumulate on the low concentration side, while an excess negative charge will accumulate on the high concentration side of the junction due to the slow moving anions.

When the cell has a liquid junction, the observed cell emf includes the additional potential difference between the two electrolyte solutions.

How to Solve the Liquid Junction Potential

Liquid junction potentials are generally small, but they certainly cannot be neglected in accurate work.

By connecting the two electrolyte solutions with a salt bridge, the junction potential can be minimized.

A salt bridge consist of a gel made by adding agar to a concentrated aqueous KCl solution.

A Cell Diagrams Containing a Salt Bridge

For a copper-zinc voltaic cells

Cu’ Zn ZnSO4(aq) CuSO4(aq) Cu

A salt bridge is symbolized by two vertical dashed lines.

Estimate the Liquid Junction Potential from EMF Measurement

Ag AgCl(s) LiCl(m) NaCl(m) AgCl(s) Ag

m(LiCl)=m(NaCl), E0=0

Anode: Ag+Cl- (in LiCl(aq))=AgCl+e-

Cathode: AgCl+e-=Ag+Cl- (in NaCl(aq))

Estimate the Liquid Junction Potential from EMF Measurement

J

J

EE

l in aq.LiCCll in aq.NaCCl

alities At low mol

l in aq.LiCCl

l in aq.NaCCl

nF

RTEEE

][][

][

][ln0

Applications of Electrochemistry

pH meterATP SynthasePotential for a resting nerve cell

Determination of pH

Pt H2(g) soln. X KCl(sat.) Hg2Cl2(s) Hg Pt’

1/2H2(g)+1/2Hg2Cl2=Hg(l)+H+(aq,X)+Cl-(aq)The cell reaction and emf Ex:

2/100

, )/(

)()(ln

PP

ClaHa

F

RTEEE X

XJX

Junction potential between X and the saturated KCl solution

If a second cell is set up to except that solution

X is replaced by solution S, the emf Es of this

cell will be:

2/100

, )/(

)()(ln

PP

ClaHa

F

RTEEE S

SJS

)( 10ln

)()(

10ln10ln)()(

)](log)(log[10ln

)()()(

)(ln

)(

)(ln

,,1

1,,

1

,,

,,

,,

XJSJSX

XJSJSXSX

XJSJSXSX

SXSJXJS

X

S

XSJXJSX

EERTF

EESpHXpH

RTF

EE

RTF

EEHpaHpa

EEEEHaHaF

RT

EEEEHa

Ha

F

RT

Ha

Ha

F

RTEEEE

Reference electrode:saturated calomel electrode (SCE)

Hg2Cl2(s)+2e- 2Hg(l)+2Cl-

Sensing electrode:Ion Selective Electrode (ISE)

Pt Ag AgCl(s) HCl(aq) glass soln. X KCl(sat.) Hg2Cl2(s) Hg Pt’

Ag(s)+Cl- AgCl(s)+e-

Determine the pH of a Solution by a pH Meter

When the glass electrode is immersed in solution X, an equilibrium between H+ ions in solution and H+ ions in the glass surface is set up.

This charge transfer between glass and solution produces a potential difference between the glass and solution.

Ion Selective Electrodes (ISE) for PH Meter An ion selective electrode contains a glass,

crystalline, or liquid membrane whose nature is such that the potential difference between the membrane and an electrolyte solution it is in contact with is determined by the activity of one particular ion.

It is dependent on the concentration of an ionic species in the test solution and is used for electro-analysis.

Marcus theory for Electron transfer reactionsRudolph A. Marcus was awarded the 1992 Nobel Prize in chemistry

Membrane Equilibrium

ii

ni,ionZ+

Phase α Phase β

ii

ni,ionZ+

Phase α Phase β

ii

ni,ionZ+

Phase α Phase β In a closed electrochemical system, the phase equilibrium condition for two phases and

C

C

nF

RTEEE

EquationNerst

ln

Free-energy change during proton movement across a concentration gradient

The movement of protons from the cytoplasm into the matrix of the mitochondrion.

pHRTG

pHpHRTRTG

RTRTEnFG

nF

RTEEE

outin

inout

303.2

)(303.2])Hlog[]H(log[303.2

]H[

]H[log303.2

]H[

]H[ln

]H[

]H[ln

HH

outin

out

in

out

in

out

in

inout

Proton Pumping

Proton pumping maintains a pH gradient of 1.4 units, then pH = + 1.4

G = -2.303RTΔpH =- 2.303 (8.315 × 10-3 kJ/mol)(298K)(1.4) = - 7.99 kJ/mol Proton concentration gradient

Free-energy change during solute movement across a voltage gradient

In mitochondria, electron transport drives proton pumping from the matrix into the intermembrane space.

There is no compensating movement of other charged ions, so pumping creates both a concentration gradient and a voltage gradient.

This voltage component makes the proton gradient an even more powerful energy source.

Membrane Potential

m = in – out=0.14 V

G =-nF m=-(1)(96485)(0.14 ) = - 13.5 kJ/mol

Proton-motive force

Proton-motive force (P) is a that combines the concentration and voltage effects of a proton gradient.

G=-nFP = - 2.303 RT pH + nFm

=(-7.99 kJ/mol)+( - 13.5 kJ/mol)

= -21.5 kJ/mol

ATP synthesis

Mitochondrial proton gradient as a source of energy for ATP synthesis

Estimated consumption of the proton gradient by ATP synthesis is about 3 moles protons per mole ATP.

G = 50 kJ/mol for ATP synthesis G = 50 + 3(- 21.5) = - 14.5 kJ/mol The synthesis of ATP is spontaneous under

mitochondrial conditions.

Potential for a resting nerve cell Goldman-Hodgkin-Katz equation

P: permeability (穿透率 )D: diffusion coefficient (擴散係數 ): thickness of membrane (薄膜厚度 )

τ

DP

)][ClP][NaP][KP

][ClP][NaP][KPln(

F

RTΔE

potential anetransmembr

ext

Cl

int

Na

int

K

int

Cl

ext

Na

ext

Kextint

Resting Nerve Cell of a Squid

Concentrations cell

△(K+)=-95 mV

△(Na+)=+57 mV

△(Cl-)=-67 mV

(mmol/dm3)

K+ Na+ Cl-

int 410 49 40

ext 10 460 540

P(K+) /P(Cl-)=2P(K+)/P(Na+)=25

The observed potential for a resting squid nerve cell is about-70 mV at 25oC.

Resting Nerve Cell of a Squid

The observed potential for a resting squid nerve cell is about -70 mV at 25oC.

Hence Cl- is in electrochemical equilibrium, but K+ and Na+ are not.

Na+ continuously flows spontaneously into the cell and K+ flows spontaneously out.

Na+-K+ pump

Batteries

Secondary batteries: Voltaic cells whose electrochemical reactions can be reversed by a current of electrons running through the battery after the discharge of an electrical current.

A secondary battery can be restored to nearly the same voltage after a power discharge.

Lead Storage battery

Anode reaction

Pb+HSO4-→ PbSO4+H++2e-

Cathode reaction

PbO2+HSO4-+3H++2e- → PbSO4+2H2O

Cell reaction

Pb+PbO2+ 2H++2HSO4-→ 2PbSO4+2H2O

Dry Cell Battery

Anode reaction

Zn→ Zn2++2e-

Cathode reaction

2NH4++2MnO2+2e- → Mn2O3+2NH3+H2O

Cell reaction

2MnO2+2NH4Cl+Zn→ Zn(NH3)2Cl2 + Mn2O3

+H2O

Alkaline Dry Cell

Anode reaction

Zn+2OH- → ZnO+H2O+2e-

Cathode reaction

MnO2+2H2O+2e- → Mn2O3+2OH-

Cell reaction

MnO2+H2O+Zn→ Mn2O3+ZnO

燃料電池工作原理

Anode reaction

2H2+4OH-→4H2O+4e-

Cathode reaction

4e-+O2+2H2O →4OH-

Cell reaction

2H2+O2 → 2H2O

質子交換膜燃料電池 Polymer Electrolyte

Membrane Fuel Cell (PEMFC)

Proton Exchange Membrane Fuel cell (PEFC)

Corrosion of Iron

Anodic Region

Fe→Fe+2+2e-

Cathodic Region

O2+2H2O+4e- →4OH-

Overall Reaction

4Fe+2(aq)+O2(g)+(4+2n) H2O(l)

→2Fe2O3‧nH2O(s)+8H+(aq)

Electrolysis

Electrolytic Cell: use electrical energy to produce chemical change

The process of electrolysis involves forcing a current through a cell to produce a chemical change for which the cell potential is negative.

standard galvanic cell standard electrolytic cell

Zn+Cu+2→Zn+2+Cu Zn+2+Cu→Zn+Cu+2

Electrolysis of Water

Anode reaction: 2H2O→O2+4H++4e-

Cathode reaction: 4H2O+4e-→2H2+4OH-

2H2O →2H2+O2 E0=-2.06V

Electrolysis of Mixture of Ions

A solution in an electrolytic cell contains the ions Cu+2, Ag+ and Zn+2.

The more positive the E0 value, the more the reaction has a tendency to proceed in the direction indicated.

Ag+ > Cu+2 > Zn+2

Electrolysis of NaCl/H2O System

Anode reaction:

2H2O→O2+4H++4e- -E0=-1.23 V

2Cl-→Cl2+2e- -E0=-1.36 VThe Cl- ion is first to be oxidized. A much higher potential than expected is required to oxidized water. The voltage required in excess of the excepted (overvoltage) is much greater for the

production of O2 than for Cl2.

electroplating

Electrolysis of NaCl