Harris Quantitative Analysis, Instrumental Analysis

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Chapter 6
Electrochemical Analysis

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Anode reaction:
Red === Ox + ne -
Cathode reaction:
Ox + ne -
=== Red
6.1 Introduction
1. Oxidation – reduction reaction
Cell reaction expression
Anodesolution,(αOx)solution, (αRed) Cathode
(6r-1)
(6r-2)

3. www.theme
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Zn ZnSO4,(xMol)  CuSO4, (yMol)  Cu
Anode: Zn Zn2+
+ 2e-
Cathode: Cu2+
+ 2e-
Cu
(6r-3)
(6r-4)

4. www.theme
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For half – cell reaction :
rAred + ne-
pAOx
Nernst equation:
For a Cell:
Ecell = Ecathode - Eanode
If, Ecell> 0: Primary Cell
Ecell< 0: Electrolyic Cell
α
α
r
red
p
ox
nF
RT
EE ln0
+=
(6r-5)
(6-1)
(6-2)

5. www.theme
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1) A metal in Equilibrium with its ions
(Class electrodes)Ⅰ
Ag+
+ e
-
Ag
+++ += AgF
RT
Ag
Ag
Ag
Ag
EE αln0
(6r-6)
(6-3)

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2) A metal in equilibrium with a saturated solution of a
slightly soluble salt
(Class electrodes)Ⅱ
AgAgCl Cl
-
,(α=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)

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3) A metal in equilibrium with tow slightly soluble salts
with a common Anion
(Class electrodes)Ⅲ
AgAg2S,CdSAg+
,Cd2+
,S2-
,
Ag2S(s) 2Ag+
+S2-
CdS(s) Cd2+
+S2-
(6r-9)
(6r-10)

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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)

9. www.theme
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1. Principle
LJrefindicell EEEE +−=
α
α
red
ox
nf
RT
indiindi EE ln0
+=
αoxnf
RT
indiindi EE ln0
+=
oxntcons
oxnf
RT
LJrefindi
Ljrefoxnf
RT
indicell
E
EEE
EEEE
α
α
α
lg
ln
ln
0591.0
tan
0
0
+=
++−=
+−+=
(6-5)
(6-6)
(6-7)
(6-8)

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2. Ion selective Membrane Electrode
 Structure of ISE
 Types Fig 6-1

11. www.theme
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Ag ︱ Agcl(s) ︱ HCl(αinner) ︱ glass ︱ H+
(unknown solution)
pHK
K
kE
outer
f
RT
glass
inner
outer
0591.0
lg0591.0
ln
−=
+=
+=
α
α
α
(6-9)
Fig 6-2

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pHK
pHKEE
EEEE
LjSCE
Ljglassrefcell
0591.0'
0591.0
+=
+−+=
+−=
pHK
K
kE
outer
f
RT
glass
inner
outer
0591.0
lg0591.0
ln
−=
+=
+=
α
α
α
Glass electrode ︱ unknown solution ︱ SCE
0591.0
'KE
pH cell −
=
(6-10)
(6-11)
(6-12)

13. www.theme
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H+
G-
+M+
(sol) M+
G-
+H+
(sol)
++ =∆ MH
kαα
k: selectivity coefficient
)lg(0591.0 ++ ++= MHglass kKE αα
)lg(0591.0 ++ ∑++=
imiHglass kKE αα
(6-13)
(6-14)
(6r-11)

14. www.theme
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 Nernst response and Detect limit
Mnf
RT
ISEISE EE αln0
±= (6-15)
Fig 6-3

15. www.theme
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 Response time
)ln(
/
.
0 jA
jj
nn
M
pot
MAAnf
RT
ISEA KEE αα ∑+±=
(6-16)
Fig 6-4

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(1) The Prerequisite of Experiments
 Ion Intensity Buffer
3.Quantitative Analysis
ionion fc=α
)( ,totleioncFf =
c
fcK
gKE
n
n
n
lgK'
)lg(
0.0591
0591.0
0591.0
±=
±=
±=
(6-17)
(6-18)
(6-19)
f_activity coefficient
If Cion,T≈constant, f ≈constant.

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 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[
cx
K
+
+
+
== (6-20)
(6r-12)
(6r-13)
(6r-14)

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c
c
cc
x
x
x
K
χ
1
)[L]1(
]ML[
n
Z
n0
=
+=
+= +
)[L]1(
1 n
K+=
χ
(6-21)
(6-22)
cffcx 0
χα ==
),,( 0L0M
Kf cc=χ (6-23)
(6-24)

19. www.theme
gallery.com(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 χ=1:
E = K + s lgC0
Fig 6-5

20. www.theme
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XcfSKSKE 1111 lglg χα +=+=
X
SS
Xs
ss
V
VC
VV
VC
C ≈
+
=∆
CC
VV
VCVC
C X
SX
SSXX
SX ∆+≈
+
+
=+
)(lg
lg
22
22
ccfSK
cfSKE
x
SXSX
∆++=
+= ++
χ
χ
(6-25)
(6-26)
(6-27)
(6-28)

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X
X
SX
cf
ccf
SEEE
11
22
1
)(
lg
χ
χ ∆+
=−=∆ +
X
X
c
cc
SE
)(
lg
∆+
=∆
CC S
E
X ∆−=
∆
)110(
assume: f1=f2 , χ1=χ2 , S = 0.0591/n
(6-29)
(6-30)
(6-31)

22. www.theme
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1. Introduction
(1) Electrolytic cell
Cathode:
M+
+ e-
→M
Hg(l) M∣ +
(C) ︱ SCE
Wkg: Working Electrode
Ref:Reference Electrode(SCE)

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(2) Polarization
M +
(Bulk) → M +
(Cathode)
Fig 6-7

24. www.theme
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(1) Structure of DME
Fig 6-8

25. www.theme
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Fig 6-9

26. www.theme
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(1) Ilkovic Equation
ctmDnid
6/13/22/1
0.607=
id
m ____rate of mercury flow
D ____diffusion coefficient
ckid
=
____Average diffusion current
(6-32)
(6-33)

27. www.theme
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 Residual current
• Changing current
• Migrating current
• Maximum phenomenon
• Oxygen interference

28. www.theme
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Half wave potential
i
ii
nf
RT
ed
cd
EE −
+= )(
2/1. ln
2/1
2/1
ln0
2/1
sa
as
Df
Df
nf
RT
EE +=
(6-34)
(6-35)