Download I. Introduction. In this section we consider "simple" electrochemistry

CHAPTER 2:
INORGANIC ELECTROCHEMISTRY (l)
A. TRANSITION METAL COMPLEX REDOX RATES
I.
Introduction.
In
this
section
we
inorganic compounds.
consider
"simple"
electrochemistry
of
We will concentrate on systems where the
electron transfer event is rapid and uncomplicated by associated
chemical reactions:
Classification
E=electrochemical step
C= chemical step
Reaction
E,
[2 . 1 ]
CE
[2. 2 ]
EC
[2. 3]
but not:
A+ + e = A
Or:
-+
B
slow
A+ + e = A
[2 . 4 ]
where E, refers to a
reversible electron transfer event and
refers to a quasi-reversible electron transfer event.
E~,
By confining
our attention to a rapid, reversible, simple E, reaction we hope to
see which system is amenable to analytical applications based on
DP
(differential
pulse),
SW
(square
wave),
and/or
CV
(cyclic
show
plot
voltammetric) analysis.
As
an
example,
dimensionless
in
Figure
2.1
(2),
we
(normalized) current function
~
a
of
a
for a linear sweep
experiment:
[2 •5]
The different lines on the plot illustrate the effect of relative
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
•
a= 0.5
0.4
~-----,#--;a~:---I-----i-----t----j
0.3
~
0.2
1----J.-/-l.:---,~-_+-+--_+_----+_-_1
0.1
I--~t+---t+-----T~----+-----t-----j
__-+--+_ _
~+-
~e.-_+_----+_ ---- j
'¥(E)
o
-128
128
-n(E-E,I2)'
2.1
variation
of
quasi-reversible
different values of
Q
following values of
A:
IV,
1jl(E)
). =
=
).
=
10.
2
•
(0.7,
I,
A
kOjD'I2(nFjRT)'I2T)'/2.
2.)
current
0.5,
=
10;
0.3,
II,
385
function,
tP (E),
as indicated)
A
=
1;
III,
for
and the
A
= 0.1;
Dashed curve is for a reversible reaction.
ijnFAC o *D o 'l2(nFjRT) 1 12 T)1/2
(From Re f.
257
mV (25°)
magnitude of the electron transfer rate constant (k,)
to the time
scale of the experiment established by the scan rate of the
linea~
sweep experiment (v).
=
k
-Y,­
v
50.68
'it:.
where the constant 50.68 arises when we assume 0
nF/RT is 38.92
=
10
,5
2
cm Is,
V".
Note from Figure 2.1 that a
A
full reversible linear sweep scan.
of 10 is required to achieve the
The advantage of a reversible
easil~,
system is that one gets the maximuD peak height that is
related to the bulk solution concentration.
values of
A
an:::
and k" as a
In Table 2.1
variou~
function of scan rate are shown.
Fro:­
Table 2.1 we note that we need electron transfer rate constants
the order of 0.05 cmls or more depending upon the scan rate,
0:
whic~
controls the time scale of the experinent.
Reversibility
and
fast
electron
transfer
are
related
solvent structural changes and to structural changes expected
the
complex.
We
predict
that
systems
reorganization should be the fastest.
involving
the
t:
i~
leas:
In order to have aver',
basic understanding of structural changes in inorganic
complexe~
we turn our attention to crystal field theory.
II.
Crystal Field theory
The ease of electron transfer in metal complexes proceeds, , ­
one part,
results
from the spreading of charge over a large volume.
in a
low
charge
density
reorganization around the complex.
which
If,
requires
little
at the same time,
Thi~
solven:
littl~
I
I
I
I
I
I
I
I
~
TABLE 2.1: Values of >. as a function of
T)
and k o •
k o cm/s
A
0.05
0.5
.2-
50
1.0
4.4x10· 2
1.39xl0'
4.4Xl0·'
1. 39
1
4.4XI0· 3
1.29xIO<
4.4X10
0.1
4.4xl0·4
1.29xIO"
4.4xl0· 3
v(V/s):
2
1.39xIO·'
1.39xl0· 2
change in internal bond structure occurs (little lability causir:
bond
length
changes
and/or
ligand
replacement),
the
electrc­
transfer reaction should be rapid and reversible.
Crystal
field
theory
presumes
that
the
main
interactic­
between the metal ion and the ligands is electrostatic in nature
Assuming
an
octahedral
complex
(6
coordinate),
incoming
1 igan::: ~
c
approach along the x, y and z axis (Figure 2.2), perturbing the
y2
and the d z 2 (Figure 2.3) ra is ing them in energy (Figure 2.4)
Orbitals lying off axis
and
are
lowered,
orbi tals
into
3
(d xy '
resul ting
degenerate
d xz '
in
dyJ
are less perturbed in ener::
splitting
t2~
(J,
(d,y'
of
d,z'
the
d\,z)
5
degenerate
orbitals
and
The total energy splitting between orbitals is arbitrarily
at 10Dq.
The absolute value of this energy difference is
S'C°
relat~
to the charge transfer bands observed'spectrochemically in the 4C:­
700 nm region.
lowered t
that
the
2g
e~
By noting that the sum of the
orbitals must equal zero,
energy
is
divided
between
2g
t~
simple arithmetic thus she.
the
eg
orbitals
orbitals as weighted values of +6Dq and -4Dq,
x = the t
orbitals with
and
the
respectively.
:
L,,'
orbi ta 1 energy and y the e] orb i tal energy:
=
30 - 3x
2x = 3y
2x
x + Y = 10
30
Y = 10 -x
x
=
6 so
3y = 30 - 3x
Y
=
4
5x
As an example, let us examine chromium.
.
.
conf1.gurat1.on
0
f 3 d 5 4s , 4p 0 .
Cr has an
electro~.
Notice that the electronic conf igurat:..:
x
y
)'
..r:y
:
z
/
/
x
x
y
.v
xz
2.2
Complete set of d
orbitals
orbitals are shaded and the
in an octahedral
t2~
vz
field.
The e g
orbitals are unshaded.
The
(From
torus of the d: 2 orbital has been omitted for clarity.
Re f. 3.)
~3
I
- 2; ....{. "0
!--/?
......
I\j
.
It
•
I
•
I \
2.3
Spatial arrangement of the five d orbitals.
(From Ref. 3.)
fie,
j
_~
_ _ eg
1
1
/
/
/
6Dq
/
/
/
----I
IODq=Ll
---\-"---­
\
4Dq
\
\
1
\
\----(2g
2.4
Splitting
of
the
degeneracy
octahedral ligand field.
of
the
(From Ref.
five
3.)
d
orbitals
by
an
1S written to imply that the 4s orbitals are higher in energy than
the 3d orbitals,
from
the
4s
therefore electrons
orbital.
The
orbital
removed
from Cr come
configuration
is
first
obtained by
placing the d electrons in the lowest possible orbitals shown in
Figure
2.5.
Two
examples
are
diagrammed.
That
in
which
the
incoming ligand greatly perturbs the d orbitals (high field ligand)
and
that
which
only
weakly
total
energy
perturbs
the
d
orbitals
(low
field
crystal
fielc
ligand) .
The
of
the
stabilization energy, CFSE.
splitting between the t
29
two
states
is
the
Note that for the low field case, the
and e g orbital levels is less and it is
energetically more favorable to fill the upper e g orbital for the
d 4 complex than to pair up the electrons in the lower t
The low field complex for Cr 2 •
field
(d
J
)
orbital.
29
has higher spin than the hig:-.
(more unpaired electrons).
The energy for the high ligand field Cr 2• complex 1S compute::
from four t
electrons
29
electrons minus the energy,
wi thin
the
same
orbit.
The
P,
required to pair u:=
energ ies
of
the
varies
electronic configurations can be calculated as shown in Table 2.2.
Similar analysis can be made of other metal ions.
work through C0 2 +/ ]+ (F igure 2. 6) and Fe 2 >J+ (Figure 2. 7).
electronic
3d 6 4so.
Fe]·
have
configuration
of
3d 7 4s",
so
Co 2 •
is
3d 7 4So
Fe has the electronic configuration of 3d6 4s 2 ,
the
configurations
of
3d"
and
3d 5 •
The
electronic configurations are shown in Table 2.3.
We
shal~
Co has tr.·
and
Co]·
i::
so Fe 2• ai.::
correspondii.::­
....
I
I
I
I
I
I
I
I
~
~
FIGURE 2.5
-
i
--
- i
i
- - i
- -
t6Dq
J.4Dq
- t -­
- t -­
- -- it J.
i
2.5
i
Diagram of Cr
of
a
high
represents
ligands.
I
LOW FIELD LIGAND
HIGH FIELD LIGAND
2
+
and Cr3+ d orbital spl i tting of in the presence
field
the
and
low
degenerate
field
energy
1 igand.
level
The
of
the
dotted
1 ine
unperturbed
it
TABLE 2.2
Crystal Field Stabilization Energies in Dq units
a)
4
high field Cr 2 + ( d )
4 (-4 Dq)
+
o (+6Dq)
+
IP
b)
high field cr)+ (d j )
] (-4Dq)
+
o (+6Dq)
+
OP
c)
low field cr 2 + (d 4 )
] (-4 Dq)
+
1 (+6Dq)
+ OP
d)
j
low field Cr J + (d
] (-4 Dq)
+
O(+6Dq)
+ OP
)
/
>
,
L·
=
-16Dq+P
-12Dq
=
-6Dq
-12Dq
--
I
I
I
,
I
I
~
,
HIGH FIELD LIGAND
~
- -­
FIGURE 2.6
LOW FIELD LIGAND
I
t
--­
I
----­
--­
-t - ­
t
t
t
t
t
2.6
-it - ­
t
t
~
t
i
i
~
~
---------­
~
~
--­
-i - ­
i
- -­
i
~
~
~
~
Diagram of Co 2 , and Co J • d orbital splitting in the presence of
a
high and low field
level
of
the
perturbation.
five
ligand.
degene=ate
ener~y
Dotted line marks
the
orbitals
absence
in
the
of
.......
FIGURE 2.7
LOW FIELD LIGAND
HIGH FIELD LIGAND
i
i
-i - ­
-i - ­
--­
--­
- - - - ­ -i - ­
i
--­
i ~
i
i
i
2.7
~
- i -­
~
i
i
~
Diagram of Fe
a
2
+
~
~
and Fe). d orbital spl i tting in the presence
high and low field ligand.
level
- - - - - - - - - ­ -i - ­
-i - ­
i
of
the
five
degenerate
Dotted 1 ine marks the
orbitals
in
the
0:
energ~·
absence
0:
perturbation.
~L
./ --­
,.
I~
30
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
I
III.
Ease of oxidation/Reduction from CFSE theory
t-ie may make some inferences
::::nsider
~~esence
the
reduction/oxidation
of
First,
(Cr N3 +).
chromium
let's
In
the
of a high field ligand there is little major change in the
electronic
configuration,
change in the complex,
reactions.
so,
in
the
absence
of
other
we might expect that there is little structural
considerations,
~n
from Table 2.3.
thus facilitating rapid electron transfer
This, of course, presumes that the CFSE energy shown
Table 2.3 is of a similar order of magnitude for. the divalent
and trivalent complexes (Dq similar).
quite
always
a
electrostatic
complexes
lot
larger
for
considerations.
should
be
more
the
In fact,
trivalent
This
stable
compared to divalent complexes.
to
the Dq values are
suggests
complex
that
sUbstitution
Figure 2.8
(4)
due
to
trivalent
reactions
as
confirms these
expectations by showing that the on/off rate of inner sphere water
molecules is much slower for trivalent complexes than for divalent
complexes.
Thus, reduction of a trivalent complex to a divalent
complex should always be checked for lability and attack of the
reduced complex.
Such attack would convert our simple E reaction
to an EC reaction (see equation 2.3).
This analysis holds up even more when looking at a complex in
which the ligand produces a weak interacting field with Cr
Table 2.3).
Here we see that a change in orbital configuration
accompanies a change in the redox state.
orbital
field
(see
state are noted
complexes,
Similar changes in the
for the oxidation/reduction of Co high
as compared to
-1.7
./ I
Fe or Ru high field complexes.
TABLE 2.3
Table of Electronic Configurations and CFSE
For Several Metal Ions
Cr
'-"-.)
"1-'
electronic
configuration
Jd 5 4s'4p(J
#d e
High Field
Electronic Config
Low Field
Energy
Electronic Config
-lGDq+P
t g) e g1
-120q
t,u
-180q+JP
t'Q ell
-24Dq+JP
t 29 e g
cr 2 '
Jd 4 4So Jp o
d4
t 2g 4
Cr]'
3d)4So Jp O
d)
t,u
Co
Jd 7 4S'
Cot.
3d 7 4S°
d
Co]'
3do 4S°
db
t
Fe
3do4 S°
Fe"
3do4 S°
d6
t 29°
-240q+JP
t
Fe)'
3d 5 4so
d5
t y5
-200q+2P
t 2g ) e g 2
Ru
55'4d 7
Ru 2 '
5s o4d 6
dO
t 296
R,,/'
5s 0 4d 5
d5
t 2g 5
l
t
l
b
2tl
2g
e g1
h
29
~
-6Dq
)
-12Dq
5
2
-BD:}~2P
4
,
-4cqtP
4
e g2
-4D:J+P
OOq
'--
Na+ K+Cs+
u+
Be 2 +
~!' ~Rb~
Ca 2 + s,-2 + Ba 2 +
Mg2+
f
i"
c~+
Ru3+
,
Fe 3 + a3+
/V 3+
A1 3 +
\_,,)
3
Ti 3 + In +
Yb 3 +_ 03+- Gd 3+
"I~
,-
0~
V2 +
Ru 2 +
~
Pt 2 +
10- 6
10- 4
Ni 2 +
,
Co2 + Fe 2 + Cu 2 + c,-2 +
2
" 1 Mn +
Zn 2 + Cd 2 + Hi+
Pd 2 +
10- 2
100
102
104
106
loS
---...
-.:\
1'\.[\
~
,:./\.
2.8
Characteristic rate constants (s") for sUbstitution of inner­
sphere water molecules on various metal ions.
(From Ref. 4.)
10 10
Recall
that the e" orbital
is most directly
in the path of the
oncoming ligands and so we might expect large differences in bond
lengths in going from the d 4 to the d 3 complexes of Cr when in the
low field system.
Consequently, we might also expect that the rate
of electron transfer should be low.
Marcus theory
(5,
6,
7,
8)
predicts that the rate of a self exchange reaction, k,,:
A + A
k"
=
A + A"
[2 •7 J
should relate to the rate of electron transfer at an electrode,
heterogeneous electron transfer, k o :
[2.8:
via the relationship:
k" ==
Zel
(
~,,_
) '/2
Zsoin
where
and
Zel
Z'OII1
are the collisional frequency factors generall::o
taken to be 10 3 to 10 4 cm/s and
10~'
M·'s·'.
The frequency factors
tell you how many times the reactants collide at the electrodE
surface or together in solution before an electron transfer even:
occurs.
Zsoln
is estimated from the thermal velocity of the react in:::
molecules:
ZSOln
-
(kT/27Tm)
[2.1C
1/2
where k is the gas constant,
T is the temperature,
and m is
t~~
effective mass of molecules (9).
From equation [2.9J we note tha:
the
will
rate
constant.
of
electron
transfer
mirror
the
self
exchans::
Table 2.4 (4) and Appendix 8.1 show some data for
of self exchange for several metal complexes.
rate~
Note that the sel:
I
I
I
I
I
I
,
,
I
Some Outer-Sphere Electron-Exchange Reactions
Reacting pair
Electron configuration
Rate
(L mol-I S-I at 2SOC)
[Fe(bi py )3]2 + 13 +
Difference in M-L
bond lengths (A)
0.00 ± 0.01
[Mn(CN)6]~-/3­
[Mo(CN)s]~-/3­
"
"
[W(CN)S]"-/3­
[IrCI 6P-/2­
Very small
t~g/ t~g
[Os(bipy) ]2+/3+
t~g/tig
[Fe(CN)6]~-/3­
t~g/ tig
[Ru( en)3]H /3.+
t~g/ ti g
4 x Hr'
[Ru(NH3)6]2+f3+
[Ru(H 20)6]2+/3+
[Fe(H 20)6]2+f3+
tt/d g
4 x 1()3
t 2geg t 2g eg
[MnO~J2-/I­
"
[C oen 3J2+/3+
[CO(NH 3)6]2+f3+
-lOS
.
t~g / t~g
4
2/ 3
20C
2
4
>1()3
0.04 ± 0.01
0.09 ± 0.02
0.14 ± 0.02
}
-10- 4
0.18 :±: 0.02
[CO(~O~)3]4-/3­
aNot octahedral, but the change in electronic configuration occurs in a nonbonding orbital.
exchange rate of the cobalt complexes is a good deal slower
t~
that of the Fe and Ru complexes which involve only a
tha~
electron~
(orbitals out of the path of the incoming ligand).
From Table 2.4 we can also observe the effect of moving
the periodic table.
same group,
do~~
Note that even though Fe and Ru are in
tt~
their electronic configurations In the presence of
low field ligand (water) are different.
~
Fe behaves as a low fiel:
complex with electrons in the e g orbitals while Ru behaves as a hig.­
field complex with electrons conf ined to the t?_ orbitals.
This':'"
,~
because size and electron cloud density effects change as one
down the periodic chart.
The
l~lger
mOVE~
d orbitals of Ru are
greatly perturbed by the incoming ligand and greater
mo~~
stabilizatic~
results.
The magnitude of Dq increases down the periodic
char~
Complexes
of the
almos~
2nd
exclusively low spin
and
3rd
row
(high field)
transition
series
in nature (3).
are
Because Fe hc.'
a low field configuration with electron density in the e g orbitals
the bond length changes
in the oxidation/reduction reaction
greater and,
the self exchange rates are much
therefore,
a~·:
slo~E~
than for the aquo complex of ruthenium.
IV.
Summary - reversibility in Metal Complexes
We
look
for
reversible
electron
transfer
events
complexes lower in the periodic chart and in which
t~
in
met:::.
electrons a=,
removed exclusively (Fe, Os, Ru).
B. TRANSITION METAL REDOX POTENTIALS
Having looked at the complexes and gained some rough feel
their
reversibility,
can
we
also
get
a
feel
for
the
fc~
absolu:·
~
I
I
,
,
e~ergetics
required to cause the electron transfer to occur?
:s, can we get a feel for the redox potentials?
Let's consider some redox potentials for
~rite
That
The answer is yes.
CoJ~'.
We can first
the Nernst equation for simple reduction of trivalent Co to
divalent Co:
E = EO - RT ln [Co 2,]
[2.11]
[Coo.]
nF
Next we note the complex formation reactions for both the di- and
tri-valent complexes:
Co J+ + 6L
:=
CoL/·
Kill
C0 2 + + 6L
:=
coLt
1\1
-w'here
Kill
r <;:0 L,~~""l
[Co'""] [Lf
[2.12]
[COL)~_
[2.13]
:=
=
[Co""] [L]"
and K I are the formation constants reactions
[2.13].
By
combining equations
[2.11-2.13]
and
[2.12]
and
separating out
constants:
E
= {
EO -
RT ln K II
}
-
~I
nF
RT ln ~ ~
[ C0 4'·]
[2.14]
The term in the {} on the right hand side of equation [2,14] is the
formal
potential,
trivalent
species
potential will
simple cation.
EO',
for
is
more
the Co complex.
strongly
shift negative
Note that when
complexed
from the
formal
(stabilized)
the
the
potential of the
These trends are observed for the cobalt metal
complexes as shown in Table 2.5.
Dq is a measure of the strength
of the ligand in creating the ligand field,
of ligand strength.
as is If', a ranking
In general ligands follow the order of:
TABLE 2.5
Formal Potential,
CFSE,
and
f,
ligand strength
factors
3
for Co ' Complexes
EC
Reaction
Co 3+ + e
= Co 2 ,
Co (ox) /
+e = Co (ox) 3 ­
e
= Co (phen) 32+
e = Co(bpy)/+
Co(bpy)/+ +
3
Co(NH 3)6 + + e
2
= Co(NH 3)6 +
2
co(en)/+ +
e
= Co(en)3 +
Co (CN) /
e
=
+
D9(3+) IkJ-mol-
1
.f
1.808
4
Co (phen) /+ +
(vs NHE)
Co (CN)
5
3
­
0.57
.99
0.37 to 0.42
1.
0.31 to 0.37
1. 3 =
3~
0.1
278
1. 2::
-0.26
278
1. 2::
-0.83
401
1. 7
•
•
•
•
•
•
•
•
•,
•
~here
ox is oxalate, en is
is phenanthroline.
ethylenedia~ine,
bpy is bipyridine, phen
Similar trends can be cODpiled from Appendix
B.2.
From the EO' values for Co we see that in the absence of any
ligand and for the oxalate complex, the divalent state is preferred
over
the
trivalent
complex.
This
might
be
expected
from
the
relative second and third ionization potentials of cobalt which
increase indicating the greater difficulty in removing a second or
third electron from the atom.
ammonia,
and
cyano
As the ligand strength increases to
complexes,
the
trivalent
complex
can
stabilized in solution (oxidation potentials shift negative).
be
The
chelate complexes of bipyridine and phenanthroline do not follow
the sequence perfectly due to the unique structural effects of the
chelating ligand.
The reason the trivalent complex can be favored is related to
the large energy gain from the complex in the trivalent state (from
-18Dq to -24Dq for the high field complexes) .
C. ANALYTICAL APPLICATIONS: STRIPPING ANALYSIS
The aquated complexes of the metal ions lie between high and
low field complexes.
divalent
That is,
we can not assume that both the
and trivalent complex of the
aquated specie should be
particularly well stabilized in a similar electronic configuration
involving only a transfer of a
t;~
electron.
Thus we might infer
that the reversible reduction of the aquated metal ions would be
poor and not a good candidate for electrochemistry as an analytical
method.
Tables
2.6
(3)
and
2.7
(6)
(
.
)1
show
the
data
for
aquo
TABLE 2.6:
Electron configuration and CFSE for Aqua Complexes
Of Some Metal Ions
Ion
Electrons 10Dg/em
Cr 3 +
t
2Q
Cr 2 •
t
2g3
eg
Mn 3 +
t
2g3
eg
Mn 2 +
t
2g
Fe 3 +
t 2g 3 e g 2
1400
Fe 2 +
t
4
2g
e g2
1000
Co 3 +
t
2g
Co 2 +
t
2g
e g2
1000
3
3
1760
,
,
e g2
1400
2100
750
6
5
.,
I
I
. self-exchange reactions
Calculated values of .1G:~ Ao and AI for some .Inorgamc
solution
L1G*o
A. o IJI
A.I~ 1
e
kcal rno\-I kcal mol-I kcal mol-I
r I'.'A
r/A
Co(HP)~"
3.56
3.40
3.6
26.3
Fe(HP)~"
3.59
3.43
3.6
Mn(Hp)~.j.
3.66
3.46
Cr(Hp)~~
3.58
V(HP)~'
Ti(/lP)~~
Reduced form
(CO'IIW 11 0
40
r­
/Ru.,O(CH)COOMpY)J l~
In
t
.dG*·
d
cole
L1G~bS
48.4
22.3
14.3
26.1
48.4
22.2
14.2
3.6
25.7
75.2
28.8
19.8
3.40
3.6
26.2
60.4
25.3
~21.4
3.56
3.41
3.7
26.2
12.0
13.3
17.6
3.56
3.45
3.6
26.1
22.8
15.8
17.7
5.0
5.0
12.7
18.3
11.0
20.0
16.7
7.0
7.0
0
a
2.3
4.0
'-I
I
9.0
I
aqueous
complexes.
From Table 2.6 again note the consistently greater stability
(large 10Dq values)
of the trivalent complex.
note that
reduction
only the
electrons,
thus
we
might
of
Fe"" to
predict
that
Fe 2 '
More importantly,
involves
the
solely t;o;
remaining
aquated
complexes would be sluggish at an electrode and not amenable to the
assumption of reversibility at the electrode surface, hindering the
analysis of currents in sweep methods.
This
is true.
We can beat this problem by taking another
Many metal
tack.
metallic state.
ions
form
Hg
analgams
\·;hen
reduced
to
their
The amalgam formation depends upon the metallic
solubility of the compound in liquid Hg.
Since Hg is large and
polarizable we would expect similarly large and polarizable metals
to be soluble within Hg.
metals in mercury (10).
Table 2.8 shows the solubility of various
Those metals grouped on the left-hand side
have larger solubilities than those on the right-hand side.
In
general,
those with larger solubilities fall to the right of the
periodic
chart
and
transition metal
solubility in Hg,
almost
series.
all
are
in
Nearly all
the
2nd
those
and
Jrd
row
ions exhibit ing
of
low
are first row transition metals, which will be
smaller and less polarizable.
Metal
ions
which
can
preconcentration in Hg are:
be
Bi J. ,
determined
CU
t.
,
Ga
by
analytically
3·
,
Ge 4 +
,
I n
3+
,
·2.
N1
,
The metals are determined via a method
termed anodic stripping voltammetry (ASV).
to the. electrode surface which
A potential is applied
reduces the metals
resul ting
in
I
I
I
I
I
I
I
~
I
TABLE 2.8
SolUbility of Metals in Mercury
Metal
Solubility (wt%)
Metal
Solubility (wt%)
In
68.3
Cu
8xlO- J
Th
42.4
Mn
6.6xlO- J
Cd
5
Sb
3.8xlO·
Zn
5.6
Ni
2.1X1O- J
Sn
1.3
Co
3xlO· 4
Pb
1.2
Bi
1.2
4
metal-mercury amalgam
formation.
This process concentrates the
metal ions in the small mercury drop
n
\.
(Figure 2.
( 2) •
After a
loading period, the electrode potential is swept positive, causing
the oxidation of the metals and their
drop.
removal
from the mercury
The resulting anodic stripping current is large due to the
preceding concentration period (Figure 2.S; (10))
2.9
are
some
Voltammetry
typical
(ASV)
detection
limits
for
Listed in Table
Anodic
Stripping
utilizing either Differential Pulse
or Linear
Sweep techniques (see Introduction) (10) and also typical detection
1
imi ts
(11)
for spectroscopic methods
flame atomic absorption spectrosccpic,
atomic absorption specroscopy and
0
f
anal ys is,
where AAS
is
GFAAS is graphite furnace
ICPAES
is
inductively coupled
plasma atomic emission spectroscopy.
Note that GFAA has the lowest detection limits, but is useful
for analysis of single components only.
ICPAES is a
multicomponen~
spectroscopic technique but does not have the detection limits of
ASV with
DP detection.
ASV can analyze
simul taneously (Figure 2 ./~ .
for several components
Stripping
M(Hg) -. M+ 11 + Hg + ne
(e)
(10-100 sec)
- - - - - - k - - - - - - - 's------=·t~---_;~_
t
2.9
Principle of anodic stripping experiment.
typical
analysis.
ones
(a)
used;
potentials
and
Ep
typical
of
Preelectrolysis at E,,; stirred solution.
Rest period, stirrer off. (c) Anodic scan
(From Re f. 2.)
are
Values shown are
(ry = 10-100
cu
2
•
(b)
mV/sec).
Table 2.9 Detection Limits (DL) in
Anodic Stripping Voltamrnetry (ASV)
DP = Differential Pulse, LS = Linear Swee~
and Spectroscopy
AAS = Atomic Absorption Spectroscopy
GFAA = Graphite Furnace Atomic Absorption Spect~:
ICPAES = Inductively Coupled Plasma Atomic Emission Spe:'
Spectroscopy
Anodic stripping
ion
ng/ml (ppb)
DP
LS
AAS
GFAAS
ICPAES
10~
2
.01
Bi
Cd
0.005
0.01
1
Cu
0.005
0.01
2
0.1
Ga
0.4
In
0.1
Pb
0.01
0.02
10
2
10
Rh
Sn
2
Tl
0.01
0.04
Zn
0.04
0.04
20
0.1
30
2
5x10-5
2
I
I
I
I
<!
:J.
-
Z
to-
lJJ
c::
a::
u
:::>
Zn
Cd
+0.25
0
-0.25
-0.50
-0.75
-1.00
-1.25
POTENTIAL (V vs Ag/AgCU
2.10 Current-sampled
polarogram
(top)
and
anodic
stripping
vol tammogram (bottom) of 2.5 ppm cu;', Zn 2. , and 5 ppm Pb 2 . , Cd 2•
in 0.1 M sodium acetate.
rs~' Ie
CHAPTER 2: PROBLEMS
2.1
a)
Work out the electron configuration for
OS2'
and
OS3'
i;:
the presence of CN- and in the presence of Cl-.
B)
Would you expect the sel f exchange rate for
rapid as a CN or as a Cl complex?
2.2
a)
to be
OS2o(3.
Justify your answer.
Work out the electron con f igura t ion for Cu 2 ' and Cu"
ir.
the presence of CN- and in the presence of Cl-.
b)
Would you expect the self exchange rate for CU 2 • 11 - to be
rapid as a CN or as a Cl
2.3
Would
2.4
expect
cyclic
voltammetry for RU(en)/- at a scan rate of 5,000, 500,
50, c:::­
Assume 0
Buttrey and Anson
a
•
IS
peak
Justify your answer.
in
5 Vis?
you
co~plex?
.~
splitting .tiL of
2
5x10· cm /s.
(12)
59
Assume no iR error.
ion exchanged Co(bpy)/' into a Nafio:­
ion exchange polymer modifying a Pt electrode.
the scan
rate they
mV
found
differential
heights for the 3+/2+ vs the 2+/1+ peaks.
As they varie=
changes
in the pea:-:
The current of one
of the redox couples was dependent upon physical diffusion
the complex within the Nafion to the electrode surface.
0:
The
second redox couple was found to be dependent upon the rate
of self-exchange of electrons between couples immobilized i:­
the Nafion.
Which couple was which?
I
I
2.5
I
You
are
Ru (bpy)
performing
t
in
an
cycl ic
aqueous
vol tammetry
of
Cr (bpy) /.
med ia
a
small
with
phenanthroline present at a fairly slow scan rate
and
amount
(5 mV/s).
Sketch the cyclic voltammograms that you might expect to see
for the two different couples.
2.6
a)
Jorgensen
(13)
has
Justify your sketches.
estimated
10Dq
values
from
the
formula:
10Dq = f"gano
If
X
Co(II)
g,en'
and
respectively,
Co(phen)6 J "
b)
Co(III)
compute
have
the
g
10Dq
values
values
of
for
9
and
18.2,
Co(phen)6;'
and
respectively.
Using these values make some predictions as to the EO
val ue of the Co (phen) 53.;;. coupl e as compared to the EO val ue of
the straight
2.7
C03~'
reduction at +1.8 V vs NHE.
(From Bard and Faulkner (2).)
a)
An analysis for lead at the HMDE gives rise to a peak
current of 1
~A
under conditions in which the deposition time
is held constant at 5 min and s'tleep rate is 5 OmV Is.
What
currents would be observed for sweep rates of 25 and 100 mV/s?
You may consider the peak current in the linear sweep to be
roughly described by equation (14)
b)
in Chap. 1.
The same solution gives a peak current of
A thick
25~A
at a 100
mercury film electrode (MFE) on glassy carbon when the
deposition time is 1 min, the electrode rotation rate is 2000
rpm,
and the sweep rate is 50mV/s.
What currents would t"
observed for sweep rates of 25 and 100 mV/s under otherwis­
unchanged conditions?
where
CR
mol/cm 3 ,
c)
is
the
(The peak current in a MFE is (10):
concentration of
the
metal
in the
.­
e is the thickness of the HME.
Why does the current follow a direct
MFE in (b), but a
v
1a
v
dependence for
(2), Kissinger and Heineman (10)
Compare
deposition
this
time
situation
of
1
min,
Faulkne~
rotation rate of 4000 rpm?
or Reiger (14).
to
a
the
sHeep
(C~
t~"
(Hint.
dependence for the HMDE in (a)?
Refer to technique oriented textbooks like Bard and
d)
MFE
one
rate
observed
of
for
50mV/s
and
is related to the depositic­
time and the rotation rate of the electrode.
The rotatic­
rate sets the diffusion layer, and hence current, for
moveme~~
of the ion from the bulk solution to the mercury electrode
The limiting current of a rotating disk electrode is (14):
= 0 62 nFAC Oulk 0 Ox 2/3 1/ -1/6 W 1;2
l' L ·
where,
in
this
case,
1/
is
the
kinematic
viscosi ty
of
solution and w is the rotation rate of the electrode in
(rad=27THz) .
A typical kinematic viscosity is
amount of charge deposited is Q
lO~ m~s.
tr.-::
rad!~
T:--.­
= nFN where N is the numbe:
of moles deposited, and q is the integrated current fidt.)
e)
Suppose
the
film
thickness were varied by the use c:
different concentrations of the mercuric ion in the analyte
What effect would one see on the peak current under otherwis"
2~_
I
I
~
constant conditions?
2.8
Films
of
Pb0 2
Suggest
an
can
be
analytical
deposited
oxidatively
determination
on
Sn0 2
Pb
based
your
bulk
of
on
( 15) .
this
phenomena.
2.9
Your
electrode
area
is
0.05
cm<
and
solution
concentration of co(en)/· 5 mM in 0.01 M NaCl (K. :::: 11.85xl0··
n·'cm·').
Assuming that the solution res istance measured at a
disk electrode is p/4a can you attribute peak splitting in
cyclic voltammetry
at
500
mV/s
to
slow
electron
transfer
kinetics?
(Hint: you will need to compute the extent of iR error at the
peak current, you may wish to refer to Bard and Faulkner (2)
or Reiger (14) for more detail on iR error.)
LITERATURE CITED
1.
For
an
early
review
see:
H.
Electron
Taube,
Transfe~
Reactions of Complex Ions in Solution, Academic Press, 1970.
2.
Bard, A. J. and Faulkner, L. R. 1980, Electrochemical Methods,
Wiley and Sons, p.
225.
3.
Huheey, J. E. 1978, Inorg. Chem., Chap. 9.
4.
Cotton,
F.
A.
and
Wilkinson,
G.
1988,
Advanced
Inorganic:
Chemistry, 5th Ed., Chap. 29.
5.
Marcus, R. A. Electrochim.
6.
Eberson, L., Electron-Transfer Reactions in Organic Chemistr;
7.
Hush,
8.
Kojima and A. J.
9.
Marcus, R. A., J.
Chem. Phys.,
10.
Heineman,
Mark,
N. S., Electrochim.
Roston,
W.
in
R.,
Bard, J.
Laboratory
H.
Acta, 1968, 13, 995.
Acta., 1968, 113, 13, 1005.
Am. Chern. Soc., 1985, 97,
B.,
6317.
1965, 28: 962.
Jr.,
Techniques
J.
in
A.
Wise,
and
D.
A.
Electroanalytica~
Chemistry, 1984, Marcel Dekker.
11.
Skoog,
D.A.,
Principles of Instrumental
1985, Saunders.
Analysis,
3rd Ed.,
12.
Buttry, D. A. and Anson, F. C. J. Amer. Chern. Soc., 1983, 105,
685.
13.
Jorgensen,
1969,
C.
K.,
Oxidation
Numbers
and Oxidation States,
Springer, N.Y.
14.
Rieger, P.H., Electrochemistry, 1987, Prentice Hall.
15.
Laitinen,
H.
A.
and Watkins,
1352.
-" ,-,"
N.
H.
Anal.
Chern.,
1975,
47,