chapter 7 electrochemistry 7.1 thermodynamic properties of electrolyte solutions 7.1.1 electrolyte...

Chapter 7 ElectrochemistryChapter 7 Electrochemistry 7.1 Thermodynamic Properties of Electrolyte Solutions

7.1.1 Electrolyte

Strong electrolyte

Weak el ectrolyte

Real electrolyte

Potential electrolyte

zz YXYX

zz

NaNO3 z+ ＝ 1 ｜ z- ｜＝ 1 1-1 ；

BaSO4 z+ ＝ 2 ｜ z- ｜＝ 2 2-2 ；

Na2SO4 z+ ＝ 1 ｜ z- ｜＝ 2 1-2 ；Ba(NO3)2 z+ ＝ 2 ｜ z- ｜＝ 1 2-1 。

7.1.2 Chemical Potential of Electrolyte and Ions

A,,B

def solute

B,,A

defA

solvent

B

npTn

G

npTn

G

npTn

G

npTn

G

,,

def

,,

def

B = ++ +

nnnpVTSG dddddd AA

dT=0, dp=0, dnA=0

Bdd nG

A,,B npTn

G

B = ++ +

zz YXYX

BAA )d(ddd nnpVTS

7.1.3 Activity and Activity Coefficient

B*BB ln),( xRTpT ideal solution

B,B ,B

def b b

ba

b y

B B

,B,B

b 0 b 0B

lim lim 1bb

a

b b

y

B,BB ln),( baRTpT

θ

BBb,BB ln),(

b

bRTpT

real solution

B B ,B( , ) ln bT p RT a y

B B B

-

ln

ln

ln

RT a

RT a

RT a

y

y

y

aaRTaRT lnln BB

defB

aaaB

/

def

/

def bb

a

bb

a

bbbb

7.1.4 Mean Activity of Ions and Mean Activity Coefficients

/1

/1

def

defaaa

-

θ/1/1B /bbaa

θ4

14/1

B

θ3

13/1

B

θ2/1B

/27 13 ,31

/4 ,12 ,21

/ ,22 ,11

bbaa

bbaa

bbaa

Mean Activity Coefficient of Some electrolyte in water at 25℃

b/ (mol kg- 1) HCl KCl CaCl 2 LaCl 3 H2SO4 I n2(SO4) 3

0. 001 0. 005 0. 01 0. 05 0. 10 0. 50 1. 00 2. 00

0. 966 0. 930 0. 906 0. 833 0. 798 0. 769 0. 811 1. 011

0. 966 0. 927 0. 902 0. 816 0. 770 0. 652 0. 607 0. 577

0. 888 0. 798 0. 732 0. 584 0. 524 0. 510 0. 725

-

0. 853 0. 715 0. 637 0. 417 0. 356 0. 303 0. 583 0. 954

- 0. 643 0. 545 0. 341 0. 266 0. 155 0. 131 0. 125

- 0. 16 0. 11 0. 035 0. 025 0. 014

- -

7.1.5 The Debye - Hückel Limiting Law

Ionic atmosphere

，23

02 42

/*r

*A / kTeLC

2

1

2

1

kg1.171mol

CH2O

2/1ln IzzC

b<0.01 ～ 0.001mol·kg-1

I — Ionic Strength

7.1.6 Ionic Strength

2BB2

1defzbI

bzzzbzbI )(2

1

2

1 2222

zz YXYX

/constantln bI

I<0.01mol·kg-1

7.2 Conductive Properties of Electrolyte Solutions

7.2.1 Conductance

RG

1

G Conductance;unit Simens S ， 1S=1Ω-1 。

AlR

Resistivity ; Ω·m.

lAG

Conductivity ; S·m-1.

=K(l/A)G

A

lK l/A K Cell constant

7.2.2 Molar Conductance

cΛ

defm

Λm unit S · m2 · mol-1 。

Λm(K2SO4 ）＝ 0.02485 S·m2·mol-1

Λm( K2SO4 ）＝ 0.01243 S · m2 · mol-12

1

Conductivity of Standard KClSolutions/Sm-1 c/moldm-3

273.15K 291.15K 298.15K 1

0.1 0.01

6.643 0.7154 0.07751

9.820 1.1192 0.1227

11.173 1.2886 0.14114

7.2.3 Concentration dependence of and Λm

k/(Sm

-1)

H2SO4

KOH

KCl

MgSO4 CH3COOH

0 145 10

c/(moldm-3)

20

40

60

80

cm c

400

300

200

100

3B dm/mol c

m/(

Sc

m2

mol

-1)

HCl

NaOH

AgNO3

CH3COOH

0 0.5 1.0 1.5

cB =0 molar conductivity of infinite dilutionm Λ

molar conductivity of infinite dilution m(298.15K)

of some strong electrolyte

m electrolyte

Sm2mol-1 m

KCl LiCl

0.014986 0.011503

34.810-4

KClO4 LiClO4

0.014004 0.010598

35.110-4

KNO3 LiNO3

0.01450 0.01101

34.910-4

HCl HNO3

0.042616 0.04213

4.9010-4

KCl KNO3

0.014986 0.014496

4.9010-4

LiCl LiNO3

0.011503 0.01101

4.9010-4

7.2.4 Independent Migration of Ion

, , mmm

ΛΛΛ

7.2.5. Electrolytic Equilibrium of Weak Electrolytes

BA ,,,uu

def

nnpTn

G

zz YXYX

At equilibrium u

---

uuu

ln

ln

ln

aRT

aRT

aRT

Ka

aa

u

RT

K

uexpdef

m

m

Λ

Λ

u

22

1

b

K

au=ubu/b ＝（ 1-α ） u b/b

22 bbbaa

HOAc H+ + OAc-

7.3 Electrochemical system

+

+

++

+

+

+

+

+

+

Met

al

++

++

++

++

++

+

+

+

+

+

+

+

+

++

+

+

+

+

+

+

+

+

+

+Met

al

++

++

++

++

++

Metal 1 Metal 2

Contact potential

Liquid-junction potential (diffusion potential)

+

+

+

+

+

++

++

++

++

++

+

+

+

++

++

++

+

+

+

+

+

+

++

+

+

+

+ +

+

+

++

+

+

+

+

+

+

+

+

+

+

+

+

+

+

+

7.4 Equilibrium electrochemistry

7.4.1 Reversible cell

(1) Electrode reactions and cell reaction are reversible

(2) I 0 (equilibrium)

7.4.2 The Cell Potentials of Reversible Cell

0MF MMdef

ILRE

7.4.3 The Nernst Equation

'r, WG pT

'rmr WG

MF'

r zFEW

MFmr zFEG

MFmr zFEG

MFE ---Standard Cell Potentials

B

Bmrmr

Bln aRTGG

B

BMFMFBln a

zF

RTEE

B

BB

def aJ a

aJzF

RTEE lnMFMF

RTTGTK )/(exp)( mr

RT

zFEK

MFln

7.4.4 Standard Electrode Potential

Standard Hydrogen Electrode ---SHE

H+ [a(H+) =1 ] | H2 (p=100kPa) | Pt E=0

SHE electrode in question (reduction)

Table 11-1 25℃时某些电极的标准电极电势 (p ＝ 100kPa)

电极 电极反应（还原） E/V

K+K K+ + e- == K -2.924

Na+Na Na+ + e - == Na -2.7107

Mg2+Mg Mg2+ + 2e- ==Mg -2.375

Mn2+Mn Mn2+ + 2e- == Mn -1.029

Zn2+Zn Zn2+ + 2e-== Zn -0.7626

Fe2+Fe Fe2++ 2e- == Fe -0.409

Co2+Co Co2++ 2e- == Co -0.28

Ni2+Ni Ni2++ 2e-== Ni -0.23

Sn2+Sn Sn2+ +2e- == Sn -0.1362

Pb2+Pb Pb2++2e-== Pb -0.1261

H+H2Pt H+ +e-== 1/2H2 -0.0000( 定义量 )

Cu2+Cu Cu2+ +2e- == Cu +0.3402

Cu+Cu Cu+ +e- ==Cu +0.522

Hg22+Hg Hg2+ +2e- ==Hg +0.851

Ag+Ag Ag+ +e- == Ag +0.7991

OH -O2Pt 1/2O2 +H2O+2e- ==2OH- +0.401

H+O2Pt O2 +4H++ 2e- ==H2O +1.229

I -I2Pt 1/2I2 + e- == I- +0.535Br-Br2Pt 1/2Br2 + e- ==Br- +1.065Cl -Cl2Pt 1/2Cl2 + e- == Cl- +1.3586

I -AgIAg AgI + e- ==Ag+I- -0.1517Br-AgBrAg AgBr + e- ==Ag+Br- +0.0715

Cl-AgClAg AgCl + e-==Ag+Cl- +0.2225Cl-Hg2Cl2Hg Hg2Cl2 + 2e- == 2Hg+2Cl- +0.2676

OH-Ag2OAg Ag2O+2e- ==2Ag+2OH- +0.342SO4

2-Hg2SO4Hg Hg2SO4+2e- == 2Hg+2SO42- +0.6258

SO42-PbSO4Pb PbSO4 + 2e- == Pb +SO4

2- -0.356

Oxidation state + 2e- Reduction state

)reactionreduction (lnreduction)( aJzF

RTEE

EMF = E (R, Reduction)- E (L, Reduction)

212

-

)/(Cl

Cllnreductionreduction

pp

a

F

RTEE

state)oxidation (

) state (reductionlnreduction)(

a

a

zF

RTEE

Cl- -(a) ｜ Cl2 ｜ Pt ：

For example

)(Cle)(Cl2

1 -

2 ap

7.5 Application of EMF Measurements

7.5.1 Determination of thermodynamics quantities ΔrGm,Δr

Sm andΔrHm

ΔrGm= - zFEMF

pp T

zFE

T

GS

MFmrmr

Temperature coefficient of cellpT

E

MF

pT

EzFS

MFmr

mrmrmr STGH

pT

EzFTSTQ

MFmrr

pT

EzFTzFEH

MFMFmr

7.5.2 Determination of γ±

)](Cl)(Hln[MFMF

aaF

RTEE

1/2[ (H ) (Cl )]

/

a a

b b

y

222

2 )/()(Cl)(H bbaaaa

7.5.3 Determination of pH

H+ ｜ Q ， QH2 ｜ Pt

Q ［ a(Q) ］ +2H+ ［ a(H+)]+2e-QH2 ［ a(QH2) ］

H

1lnPtQHQH 2 aF

RTEE

Hlgdef

pH a

pH10ln

PtQHQH 2 F

RTEE

25℃ ， E ＝ (0.6997-0.05916pH) V

Q O O

HO- - OHQH2

QQH2

a(Q)≈a(QH2)

Pt ｜ H2(p ) ｜ solution(pH=x) ｜ KCl (a) ｜ Hg2Cl2 ｜ Hg

7.5.4 Determination of K and Ksp

MFln (298.15K)ZFE

KRT

y

y

7.5.5 Determination of reaction direction

ΔrGm=-ZFEMF< 0

7.6 kinetics of electrochemical system7.6.1 Rate of electrochemical reaction

M+ + e- M c

a

Ec

Ea

M

a

c

M++e

M

Cathode process υc ；

anode process υa ；

。，；，；，

mequilibriu

anode

cathode

ac

ca

ac

d

d1def

tAυ

v - Rate of electrochemical reaction molm-2s-1

Current density j j=ZFυ

:process anode

:process cathode

aa

cc

ZFj

ZFj

0ac

caca

acac

electrode mequilibriu

anode

cathode

j jj

j j j jj

j j j jj

j0:exchange current density

7.6.2 Polarization and Overpotential

{

a}

{ c,e}

{ a ,e}

{

c}

{

e}{ }

{

a}

{

c}

{j}

(a) electrolytic cell

{ }

{ a}

{ a,e}

{ c,e}

{ c}{

e}{ }

{j}

(b)chemical electric source

{

c}

{

a}

{ }

polarization curve

Overpotential ：

ec,c

def

c

ea,a

def

a

ηa — anode overpotential

ηc—anode overpotential

(1). Diffusion overpotential

Ag+

c0

c'

Diffusion layer

Ag

'ln cF

RT

0e ln

cF

RT

0

'

e lnc

c

F

RT

M+ + e- M

(2). Electrochemical overpotential

7.6.3 Electrolytic cell

22

22

22

21

2

222

O21

HOHreaction cell icelectrolyt

2eOHOOH reaction anode

OHHeOH reaction cathode

2

-

-

：

：.

(- ） Pt ｜ H2 ｜ OH- （ H2O ）｜ O2(p) ｜ Pt

（ + ）

H

2

O

2

H2O H2O

Pt

Pt

anode(+)

cathode(-)

+ —

I Power supply

Pt

AV

R

KOH

外电源

电阻

伏特计 电流计

+ _

KOH

Vd V

I

Decomposition voltage

Theory decomposition voltage

Real decomposition voltage

Δ (real)=Δ (theory) + (ηa+ ｜ ηc ｜ ) + IR

7.7 Power production and corrosion

7.7.1 Dry Cell

Zn ｜ NH4Cl ｜ MnO2 ｜ C

Negative electrode ： Zn + 2NH4Cl Zn(NH3)2Cl2 + 2H++ 2e-

positive electrode ： 2MnO2 + 2H+ + 2e- 2MnOOH

Cell reaction ： Zn + 2MnO2 + 2NH4Cl Zn(NH3)2Cl2 + 2MnOOH

11.7.2 Storage Cell

Pb ｜ H2SO4(ρ ＝ 1.28gcm-3) ｜ PbO2

Negative electrode ： Pb + H2SO4 PbSO4 + 2H+ + 2e-

positive electrode : PbO2 + H2SO4 + 2H+ + 2e- PbSO4 + 2H2O

Cell reaction ： PbO2 + Pb + 2H2SO4 2PbSO4 + 2H2O

11.7.3.Silver-zinc Cell

Zn ｜ KOH(ωB ＝ 0.40) ｜ Ag2O ｜ Ag

Negative electrode: 2Zn + 4OH- 2Zn(OH)2 + 4e-

positive electrode : Ag2O2 + 2H2O + 4e- 2Ag + 4OH-

Cell reaction ： 2Zn + Ag2O2 + 2H2O 2Ag + 2Zn(OH)

2

7.7.4. Fuel cell

M ｜ H2(g) ｜ KOH ｜ O2(g) ｜ M

OHO21

Hreaction cell

2OH2eOHO21

cathode

2eO2H2OHH anode

222

-22

-22

：

：

：

•Efficiency of Chemical Electric Source

defr m

maxr m

Δ

Δ

G

H

def

realr m

zF

H

7.7.5 Electrochemical corrosion

M+ 2H+

H2

2eM

M+2H+

H2

2e

M1

M2

Anode process ： FeFe2 ＋ +2e-

Cathode process ： (i)2H++2e- H2↑

(ii)O2+4H++4e- 2H2O

(i) cell reaction ： Fe+2H ＋ Fe2 ＋ +H2

(ii) cell reaction ： Fe+(1/2)O2+2H+Fe2++H2O

{ )}S

I

{ c,e}

{ a,e}