Chapter 6
Electrochemical Analysis
Anode reaction:
Red === Ox + ne -
Cathode reaction:
Ox + ne - === Red
6.1 Introduction
1,Oxidation – reduction reaction
Cell reaction expression
Anode?solution,(?Ox)solution,(?Red)?Cathode
(6r-1)
(6r-2)
For example:
Zn?ZnSO4,(xMol)CuSO4,(yMol)? Cu
Anode,Zn Zn2+ + 2e-
Cathode,Cu2 + + 2e- Cu
(6r-3)
(6r-4)
2,Half-cell Potential
For half – cell reaction,
rAred + ne- pAOx
Nernst equation:
For a Cell:
Ecell = Ecathode - Eanode
If,Ecell > 0,Primary Cell
Ecell < 0,Electrolyic Cell
r
r ed
p
ox
nF
RTEE ln0
(6r-5)
(6-1)
(6-2)
3.The Types of Electrodes
1) A metal in Equilibrium with its ions
(Class Ⅰ electrodes)
Ag+ + e- Ag
AgF
RT
AgAgAgAg
EE?ln0
(6r-6)
(6-3)
2) A metal in equilibrium with a saturated
solution of a slightly soluble salt
(Class Ⅱ electrodes)
Ag?AgCl?Cl -,(?=1)
AgCl(s) + e- Ag + Cl –
Reference electrodes
Saturated calomel electrode (SCE)
Hg?Hg2Cl2(s)?Cl -,(sat’d KCL)
Hg2Cl2(s) + 2e- 2Hg + 2Cl –(sat’d KCL)
(6r-7)
(6r-8)
3) A metal in equilibrium with tow slightly
soluble salts with a common Anion
(Class Ⅲ electrodes)
Ag?Ag2S,CdS?Ag+,Cd2+,S2-,
Ag2S(s) 2Ag++S2-
CdS(s) Cd2++S2-
(6r-9)
(6r-10)
4,The departure of potential
1) Liquid-junction potential
HCl(0.1M)?KCl(salt bridge,xM)?KCl(0.1M)
When x>3.6 Eljp<1mV
2) Polarization
Efact ≠ENernst and Csurf ≠Cbolk
3) Over-voltage
real potential start a reaction > equilibrium potential
4) Ohm drop
Ecell = Ecathode - Eanode + IR
R,resistance of solution,I,current
(6-4)
6.2 Potentiometry
1,Principle
LJr e fi n d ic e l l EEEE
r e doxnfRTi n d ii n d i EE ln0
oxnfRTi n d ii n d i EE ln0
oxntc o n s
oxnf
RT
LJr e fi n d i
Ljr e foxnf
RT
i n d ic e l l
E
EEE
EEEE
lg
ln
ln
0 5 9 1.0
t a n
0
0
(6-5)
(6-6)
(6-7)
(6-8)
2,Ion selective Membrane Electrode
Structure of ISE
Types
Fig 6-1
(1) The Glass Electrode
Ag︱ Agcl(s) ︱ HCl(?inner) ︱ glass ︱ H+(unknown solution)
pHK
K
kE
o u t e r
f
RT
g l a s s
i n n e r
o u t e r
0591.0
lg0591.0
ln
(6-9)
Fig 6-2
pHK
pHKEE
EEEE
LjS C E
Ljg l a s sr e fc e l l
0 5 9 1.0'
0 5 9 1.0
pHK
K
kE
o u t e r
f
RT
g l a s s
i n n e r
o u t e r
0591.0
lg0591.0
ln
Glass electrode︱ unknown solution ︱ SCE
0 5 9 1.0
'KEpH c e l l
(6-10)
(6-11)
(6-12)
Selectivity of Glass electrode
H+G-+M+(sol) M+ G- + H+ (sol)
MH k
k,selectivity coefficient
)l g (05 91.0 MHg l a s s kKE
)l g (0591.0
imiHg l a s s
kKE
(6-13)
(6-14)
(6r-11)
(2) The Response Behavior of ISE
Nernst response and Detect limit
MnfRTI S EI S E EE?ln
0
(6-15)
Fig 6-3
Selectivity
Response time
)l n ( /.0 jA jj nnMp o tMAAnfRTI S EA KEE
(6-16)
Fig 6-4
(1) The Prerequisite of Experiments
Ion Intensity Buffer
3.Quantitative Analysis
i o ni o n fc
)(,t o t l ei o ncFf?
c
fcK
gKE
n
n
n
lgK'
)lg (
0,0 5 9 1
0 5 9 1.0
0 5 9 1.0
(6-17)
(6-18)
(6-19)
f_activity coefficient
If Cion,T≈constant,f ≈constant.
pH Buffer
MZ+ + xOH- M(OH)x (z-x)+
H+ + OH- H2O
Complex reagent
M Z+ + nL MLnZ+
n
Z
n
nz
Z
n
[ L ]
]ML[
L]][M[
]ML[
c x
K
(6-20)
(6r-12)
(6r-13)
(6r-14)
c
c
cc
x
x
x
K
1
)[ L ]1(
]ML[
n
Z
n0
)[ L ]1(1 nK
(6-21)
(6-22)
cffc x 0
),,( 0L0M Kf cc
(6-23)
(6-24)
(2)Standard calibration Methods
C0 / molL-1 10-3 3.16x10-4 10-4 3.16x10-5 10-5
lgc -3 -3.500 -4 -4.500 -5
standard concentration series
If?=1:
E = K + s lgC0
Fig 6-5
(3)Standard Addition Methods
XcfSKSKE 1111 lglg
X
SS
Xs
ss
V
VC
VV
VCC?
CC
VV
VCVCC
X
SX
SSXX
SX
)(lg
lg
22
22
ccfSK
cfSKE
x
SXSX
(6-25)
(6-26)
(6-27)
(6-28)
X
X
SX cf
ccf
SEEE
11
22
1
)(
lg
X
X
c
cc
SE
)(
lg
CC S EX )110(
assume,f1=f2,?1=?2,S = 0.0591/n
(6-29)
(6-30)
(6-31)
6.3 Polarography
1,Introduction
(1) Electrolytic cell
Cathode,
M+ + e- →M
Hg(l) ∣ M+(C)︱ SCE
Wkg,Working Electrode
Ref:Reference Electrode(SCE)
(2) Polarization
M +(Bulk) → M +(Cathode)
Fig 6-7
2,The Dropping Mercury Electrode(DME)
(1) Structure of DME
Fig 6-8
(2)Electrolytic current and current density
Fig 6-9
3,Quantitative Analysis
(1) Ilkovic Equation
ctmDni d 6/13/22/10.6 0 7?
id
m ____rate of mercury flow
D ____diffusion coefficient
cki d?
____Average diffusion current
(6-32)
(6-33)
(2)The factor of affect diffusion current
Residual current
Changing current
Migrating current
Maximum phenomenon
Oxygen interference
4,Qualitative Analysis
Half wave potential
i
ii
nf
RT
ed
cdEE )(
2/1,ln
2/1
2/1ln0
2/1 sa
as
Df
Df
nf
RTEE
(6-34)
(6-35)
Electrochemical Analysis
Anode reaction:
Red === Ox + ne -
Cathode reaction:
Ox + ne - === Red
6.1 Introduction
1,Oxidation – reduction reaction
Cell reaction expression
Anode?solution,(?Ox)solution,(?Red)?Cathode
(6r-1)
(6r-2)
For example:
Zn?ZnSO4,(xMol)CuSO4,(yMol)? Cu
Anode,Zn Zn2+ + 2e-
Cathode,Cu2 + + 2e- Cu
(6r-3)
(6r-4)
2,Half-cell Potential
For half – cell reaction,
rAred + ne- pAOx
Nernst equation:
For a Cell:
Ecell = Ecathode - Eanode
If,Ecell > 0,Primary Cell
Ecell < 0,Electrolyic Cell
r
r ed
p
ox
nF
RTEE ln0
(6r-5)
(6-1)
(6-2)
3.The Types of Electrodes
1) A metal in Equilibrium with its ions
(Class Ⅰ electrodes)
Ag+ + e- Ag
AgF
RT
AgAgAgAg
EE?ln0
(6r-6)
(6-3)
2) A metal in equilibrium with a saturated
solution of a slightly soluble salt
(Class Ⅱ electrodes)
Ag?AgCl?Cl -,(?=1)
AgCl(s) + e- Ag + Cl –
Reference electrodes
Saturated calomel electrode (SCE)
Hg?Hg2Cl2(s)?Cl -,(sat’d KCL)
Hg2Cl2(s) + 2e- 2Hg + 2Cl –(sat’d KCL)
(6r-7)
(6r-8)
3) A metal in equilibrium with tow slightly
soluble salts with a common Anion
(Class Ⅲ electrodes)
Ag?Ag2S,CdS?Ag+,Cd2+,S2-,
Ag2S(s) 2Ag++S2-
CdS(s) Cd2++S2-
(6r-9)
(6r-10)
4,The departure of potential
1) Liquid-junction potential
HCl(0.1M)?KCl(salt bridge,xM)?KCl(0.1M)
When x>3.6 Eljp<1mV
2) Polarization
Efact ≠ENernst and Csurf ≠Cbolk
3) Over-voltage
real potential start a reaction > equilibrium potential
4) Ohm drop
Ecell = Ecathode - Eanode + IR
R,resistance of solution,I,current
(6-4)
6.2 Potentiometry
1,Principle
LJr e fi n d ic e l l EEEE
r e doxnfRTi n d ii n d i EE ln0
oxnfRTi n d ii n d i EE ln0
oxntc o n s
oxnf
RT
LJr e fi n d i
Ljr e foxnf
RT
i n d ic e l l
E
EEE
EEEE
lg
ln
ln
0 5 9 1.0
t a n
0
0
(6-5)
(6-6)
(6-7)
(6-8)
2,Ion selective Membrane Electrode
Structure of ISE
Types
Fig 6-1
(1) The Glass Electrode
Ag︱ Agcl(s) ︱ HCl(?inner) ︱ glass ︱ H+(unknown solution)
pHK
K
kE
o u t e r
f
RT
g l a s s
i n n e r
o u t e r
0591.0
lg0591.0
ln
(6-9)
Fig 6-2
pHK
pHKEE
EEEE
LjS C E
Ljg l a s sr e fc e l l
0 5 9 1.0'
0 5 9 1.0
pHK
K
kE
o u t e r
f
RT
g l a s s
i n n e r
o u t e r
0591.0
lg0591.0
ln
Glass electrode︱ unknown solution ︱ SCE
0 5 9 1.0
'KEpH c e l l
(6-10)
(6-11)
(6-12)
Selectivity of Glass electrode
H+G-+M+(sol) M+ G- + H+ (sol)
MH k
k,selectivity coefficient
)l g (05 91.0 MHg l a s s kKE
)l g (0591.0
imiHg l a s s
kKE
(6-13)
(6-14)
(6r-11)
(2) The Response Behavior of ISE
Nernst response and Detect limit
MnfRTI S EI S E EE?ln
0
(6-15)
Fig 6-3
Selectivity
Response time
)l n ( /.0 jA jj nnMp o tMAAnfRTI S EA KEE
(6-16)
Fig 6-4
(1) The Prerequisite of Experiments
Ion Intensity Buffer
3.Quantitative Analysis
i o ni o n fc
)(,t o t l ei o ncFf?
c
fcK
gKE
n
n
n
lgK'
)lg (
0,0 5 9 1
0 5 9 1.0
0 5 9 1.0
(6-17)
(6-18)
(6-19)
f_activity coefficient
If Cion,T≈constant,f ≈constant.
pH Buffer
MZ+ + xOH- M(OH)x (z-x)+
H+ + OH- H2O
Complex reagent
M Z+ + nL MLnZ+
n
Z
n
nz
Z
n
[ L ]
]ML[
L]][M[
]ML[
c x
K
(6-20)
(6r-12)
(6r-13)
(6r-14)
c
c
cc
x
x
x
K
1
)[ L ]1(
]ML[
n
Z
n0
)[ L ]1(1 nK
(6-21)
(6-22)
cffc x 0
),,( 0L0M Kf cc
(6-23)
(6-24)
(2)Standard calibration Methods
C0 / molL-1 10-3 3.16x10-4 10-4 3.16x10-5 10-5
lgc -3 -3.500 -4 -4.500 -5
standard concentration series
If?=1:
E = K + s lgC0
Fig 6-5
(3)Standard Addition Methods
XcfSKSKE 1111 lglg
X
SS
Xs
ss
V
VC
VV
VCC?
CC
VV
VCVCC
X
SX
SSXX
SX
)(lg
lg
22
22
ccfSK
cfSKE
x
SXSX
(6-25)
(6-26)
(6-27)
(6-28)
X
X
SX cf
ccf
SEEE
11
22
1
)(
lg
X
X
c
cc
SE
)(
lg
CC S EX )110(
assume,f1=f2,?1=?2,S = 0.0591/n
(6-29)
(6-30)
(6-31)
6.3 Polarography
1,Introduction
(1) Electrolytic cell
Cathode,
M+ + e- →M
Hg(l) ∣ M+(C)︱ SCE
Wkg,Working Electrode
Ref:Reference Electrode(SCE)
(2) Polarization
M +(Bulk) → M +(Cathode)
Fig 6-7
2,The Dropping Mercury Electrode(DME)
(1) Structure of DME
Fig 6-8
(2)Electrolytic current and current density
Fig 6-9
3,Quantitative Analysis
(1) Ilkovic Equation
ctmDni d 6/13/22/10.6 0 7?
id
m ____rate of mercury flow
D ____diffusion coefficient
cki d?
____Average diffusion current
(6-32)
(6-33)
(2)The factor of affect diffusion current
Residual current
Changing current
Migrating current
Maximum phenomenon
Oxygen interference
4,Qualitative Analysis
Half wave potential
i
ii
nf
RT
ed
cdEE )(
2/1,ln
2/1
2/1ln0
2/1 sa
as
Df
Df
nf
RTEE
(6-34)
(6-35)
