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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 。
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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 = ++ +
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nnnpVTSG dddddd AA
dT=0, dp=0, dnA=0
Bdd nG
A,,B npTn
G
B = ++ +
zz YXYX
BAA )d(ddd nnpVTS
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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
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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
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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
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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
- -
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7.1.5 The Debye - Hückel Limiting Law
Ionic atmosphere
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,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
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7.1.6 Ionic Strength
2BB2
1defzbI
bzzzbzbI )(2
1
2
1 2222
zz YXYX
/constantln bI
I<0.01mol·kg-1
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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
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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
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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
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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
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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
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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-
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7.3 Electrochemical system
+
+
++
+
+
+
+
+
+
Met
al
++
++
++
++
++
+
+
+
+
+
+
+
+
++
+
+
+
+
+
+
+
+
+
+Met
al
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++
++
++
++
++
Metal 1 Metal 2
Contact potential
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Liquid-junction potential (diffusion potential)
+
+
+
+
+
++
++
++
++
++
+
+
+
++
++
++
+
+
+
+
+
+
++
+
+
+
+ +
+
+
++
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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7.4 Equilibrium electrochemistry
7.4.1 Reversible cell
(1) Electrode reactions and cell reaction are reversible
(2) I 0 (equilibrium)
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7.4.2 The Cell Potentials of Reversible Cell
0MF MMdef
ILRE
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7.4.3 The Nernst Equation
'r, WG pT
'rmr WG
MF'
r zFEW
MFmr zFEG
MFmr zFEG
MFE ---Standard Cell Potentials
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B
Bmrmr
Bln aRTGG
B
BMFMFBln a
zF
RTEE
B
BB
def aJ a
aJzF
RTEE lnMFMF
RTTGTK )/(exp)( mr
RT
zFEK
MFln
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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)
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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
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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
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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
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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
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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
Page 30
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
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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
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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 ;
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。,;,;,
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
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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
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(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
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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
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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
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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
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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
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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
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7.7.4. Fuel cell
M | H2(g) | KOH | O2(g) | M
OHO21
Hreaction cell
2OH2eOHO21
cathode
2eO2H2OHH anode
222
-22
-22
:
:
:
Page 42
•Efficiency of Chemical Electric Source
defr m
maxr m
Δ
Δ
G
H
def
realr m
zF
H
Page 43
7.7.5 Electrochemical corrosion
Page 44
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
Page 45
{ )}S
I
{ c,e}
{ a,e}