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1-1-1979
A Survey of Ligand E(ects Upon the Reaction
Entropies of Some Transition Metal Redox
Couples
Edmund L. Yee
Michigan State University
Robert J. Cave
Harvey Mudd College
Kendall L. Guyer
Michigan State University
Paul D. Tyma
Michigan State University
Michael J. Weaver
Michigan State University
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Recommended Citation
Yee, E.L.; Cave, R. J.; Guyer, K.L.; Tyma, P.D.; Weaver, M.J. “A Survey of Ligand E=ects Upon the Reaction Entropies of Some
Transition Metal Redox Couples," J. Am. Chem. Soc., 1979, 101, 1131. DOI: 10.1021/ja00499a013
Weauer et
al.
/
Reaction Entropies
of
Transition Metal Redox Couples
1131
A
Survey
of
Ligand Effects upon the Reaction
Entropies
of
Some Transition Metal Redox Couples
Edmund
L.
Yee, Robert
J.
Cave, Kendall
L.
Guyer, Paul
D.
Tyma, and
Michael
J.
Weaver*
Contribution from the Department of Chemistry, Michigan State Unicersity,
East Lansing, Michigan
48824.
Receiced
July
20,
1978
Abstract: The reaction entropies
lSo,,
of
a
number of transition metal redox couples of the form
M(III)/(
11)
in aqueous
solu-
tion have bcen determined using nonisothermal electrochemical cells
in
order to explore the effect of varying the ligand struc-
ture upon the nature of the ion-solvent interactions. Examination of six
aquo
couples of the form
M(OHZ),,~+'~+
with varying
metal
M
yielded
ASo,,
values
in
the range 36-49 eu.
In
order
to
scrutinize the effect of replacing aquo with ammine and simple
anionic ligands,
Ru(l
I
I)/(
II)
couples were employed since the relativc substitution inertness of both oxidation states allowed
AS',,
to be determined using cyclic voltammetry. The stepwise replacement of aquo by ammine ligands results
in
substantial
reductions in
ASo,,
which are attributed to the smaller extent of ligand-solvent hydrogen bonding for ammine compared with
aquo ligands. Substitution of both aquo and ammine by anionic ligands also resulis
in
substantial reductions in
ASo,,.
A
num-
ber of
M(III)/(II)
couples containing chelating ligands were
also
examined. Sizable differcnces
in
ASo,,
were found between
Co(lll)/(ll)
couples and the corresponding Ru(lll)/(ll) and
Fe(lll)/(ll)
couples. Suggested explanations are differences
in ligand conformation and electron delocalization effects. The possible contribution of outer-sphere solvent structuring effects
to the large reorganization energies observed for electron exchange of aquo complexes is noted. The validity
of
the assumptions
required for the estimation of
ASo,,
from nonisothermal cell measurements is discussed.
Introduction
The entropies of transition-metal ions in aqueous solutions
have long been known to be strongly dependent upon their
charge and the nature of the coordinated ligands.'-3 These wide
variations are undoubtedly due to differences in specific solvent
structure surrounding the ions, such as "structure-making"
and "structure-breaking" as well as
to
classical
electrostatic Besides their intrinsic interest, a
knowledge of partial molal ionic entropies,
or
at least the en-
tropy difference
AS",,
between the ions that form redox cou-
ples, also allows the entropic driving forces for redox reactions
to be computed. The acquisition of such information should
allow the achievement of a deeper understanding of the
structural factors that influence the thermodynamics of redox
processes than is possible from
a
knowledge of free energies
alone.
Of
particular interest in this connection is the effect upon
AS",,
of varying the nature of the coordinated ligands for
a
given pair of oxidation states. Since
AS",,
is often large, this
term can provide the dominant component of the free-energy
driving force in electrode reactions.* The entropy driving force
for homogeneous redox reactions
ASohoin
will tend to be
smaller owing to
a
partial cancellation of
AS",,
for
the two
constituent redox couples, although
AS",,
and consequently
ASohom
can be strongly dependent upon the nature of the
coordinated ligands. However, the available data are relatively
sparse and sometimes contradictory. The entropies of simple
aquo cations are known to become markedly more negative
with increasing positive charge'.5,6
so
that
AS",,
for
a
one-
electron redox couple is expected to be
in
the range
40-50
eu
(when written conventionally
as
a
reduction). The substitution
of coordinated water by large organic ligands has been found
to result
in
much smaller values of
AS",,
which have been
ascribed to the increased shielding of the metal cation from the
surrounding water.9 However, few
AS",,
data exist for other
types
of
metal-complex couples.
A
major reason for this state
of affairs
is
that
most
unidentate ligands do not form complexes
in aqueous solution that are sufficiently stable with respect to
dissociation, chemical oxidation, etc.,
in
both oxidation states
to allow
AS",,
to be obtained directly from the temperature
dependence of the equilibrium electrode potential. However,
a number of ruthenium(
Ill)/(
11)
couples have recently been
shown to exhibit substitution ineriness not only
in
the trivalent
0002-7863/79/
I501
-
1
I3
1$01
.OO/O
but
also
in the reduced state, at leastson the time scale of
electrochemical perturbation techniques such as cyclic volt-
ammetry.'0-14 Similar behavior is also exhibited by some
os-
mium(III)/(II) ammine couples.15 Since these couples also
exhibit complete electrochemical reversibility (i.e., rapid
heterogeneous electron transfer) under these conditions, cyclic
voltammetry can be used to obtain accurate values of the re-
versible cell potentials for these systems.lO-'s
We have used this technique to determine
So,,
for a series
of
Ru(III)/(II)
couples containing aquo, ammine, halide, and
other simple unidentate ligands. These choices of systems were
initially motivated by the desire to obtain values of
AS",,
for
mixed aquo and ammine complexes which might be used to
estimate
AS',,
for the corresponding
Cr(lIl)/(II)
and
Co(
I
I
I)/(II)
reactions for comparison with the corresponding
activation entropies for the heterogeneous reduction of these
latter complexes.I6 There is evidence from empirical entropy
to indicate that
AS",,
values for simple redox
couples are primarily dependent on the nature of the coordi-
nated ligands and
on
the charges on, rather than the nature
of,
the central metal ions.
If
this is the case, then
AS",,
values for
the large majority of redox systems for which such data are
unobtainable could be inferred from the values for measurable
systems with the same ligand constitution and charges. Such
a
rule is not unexpected, since the major contribution to
ASo,-,
aside from dielectric polarization should arise from specific
interactions such
as
hydrogen bonding between the ligands and
the solvating water molecules. However, tests of this supposi-
tion are rare. We have therefore measured
AS",,
for
a
number
of
M3+/'+
aquo couples for which the electronic structure
of
the central metal ion can be systematically varied.
In
addition, we have determined
Sorc
for
a
number of more
intricate
M(III)/(II)
redox couples containing various che-
lating ligands. The high stability of these complexes allows the
effect of varying the nature of the central metal ions to be
further explored and enables the influence
of
specific solvation
factors to be examined for couples containing large hydro-
phobic ligands which are
of
relevance to larger redox systems
such
as
metalloproteins.
Experimental Section
mine
the rcxtion entropy
AS",,
for the redox couples
Experimental Tactics. Yonisotherrnal Cells.
It
19
desired
to
deter-
0
1979 American Chemical
Society
1132
Journal
of
the American Chemical Society
/
101:5
/
February
28,
1979
M1I1L,’L,,”
+
e- (metal electrode)
~i
MI1L,,’L,”
(I)
in aqueous media, where
I-’
and
L”
are neutral or anionic ligands.
Since reaction
I
is only one-half
of
a complete electrochemical cell
reaction, its equlibrium properties cannot be determined without resort
to
extrathermodynamic assumptions. Indeed, the determination of
individual ion free energies has been the subject of much debate over
the
year^.'^.'^
Fortunately, however, there are
a
number of reliable
routes to the quantitative estimation of individual ionic entropies, and
especially
So,,.
A
useful summary of these methods has been given
by Criss and Sal~rnon.~~ For the present purposes, the most convenient
method involves the use of nonisothermal electrochemical cells.20,21
In this arrangement, the temperature of the half-cell containing the
redox couple
of
interest is varied while the temperature of the other
half-cell consisting of some convenient reference electrode is held
constant.*’ One such cell arrangement that was commonly used in the
present work can be written
as
The measured temperature coefficient dEpi/dT of the overall (for-
mal) potential
Epi
across such a nonisothermal cell which is reversible
to
the couple
M1I1/l1
can be separated into various components as in
the equation
@,I,
is
the Galvani potential difference across the thermal liquid
junction within the KCI salt bridge,
4Jtc
is the “thermocouple” potential
difference between the hot and cold regions of the mercury working
electrode,
E?’
is the formal potential of the redox couple measured
across the nonisothermal cell, and
@p
is
the corresponding Galvani
metal-solution potential difference
at
the working electrode. Since
F
-
=
AS”,,
E;)
(3)
then
if
dg,,/dT and d&lj/dT are known or can be estimated,
AS”,,
can be obtained from measurements of dEp/dT. Absolute values
of
the Thomsun coefficient d&/dT are known for a number of metals;
in
most cases they amount only to a few microvolts per degree.20 For
mercury and platinum that we used
in
the present work over the
temperature range
0-
100
“C, d&/dT is equal to about
14
and
6
pV
deg-’, These values are essentially negligible in coni-
parison with the measured values of dEfn’/dT and w.ill be neglected.
Although only relative rather than absolute values of d&lj,/dT are
thermodynamically accessible, there is ample evidence that indicates
that for most aqueous electrolytes, d@,i,/dT
5
50
qV
deg-l
20.21
For
strongly acidic or alkaline media, markedly larger values of d@tl,/dT
are obtained2Ib which recall the large isothermal liquid junction po-
tentials which can be generated
in
media containing H+ or OH- ions.
DeBethune ct
al.
have suggested2Ib that d+,l,/dT can be minimized
by the use of concentrated aqueous potassium chloride in the region
where the thermal gradient occurs (the so-called “nonisothermal salt
bridge”). While the exact validity
of
this assumption has been ques-
tioncd,*I‘ there is little doubt that d+,lJ/dT for this arrangement is
no
greater than ca. 20
pV
dcg-I, and probably much smaller.*’
AI-
though such uncertainties in d@,l,/dT are a serious concern for ex-
tremely accurate detcrminations of
AS”,,,
they are essentially neg-
ligible in the present cxpcriments where a precision of only
f
50
~IV
de!-’ could be reliably achieved for most systems. Since this uncer-
tainty in d@,lj/dT corresponds to an uncertainty in
AS”,,
of
fl
eu,
and variations in
AS’,,
of
up
to
50
eu were observed between the
various redox systems rcported here, such considerations are not of
serious concern in the present study.
(Also
the
relatice
values of
,1s”,,
for various systems
will
be unal‘fected by such considerations, as are
the values of
AS”
for homogeneous reactions that are obtained from
the difference
in
So,,
for the appropriate pair of redox couples.) Such
experiments therefore yield “absolute” entropy differences for redox
couples which should be carefully distinguished from reaction en-
tropies for complete electrochemical cells that are obtained from
isothermal cell
measurement^,^^
as well as those that have been
computcd by arbitrarily assigning the entropy of the hydrogen ion
a
value of ~r0.1~.*3
M’c chose to employ
3.5
M KCI
in
the nonisotherrnal salt bridge
since the solubility of KCI is slightly greater than
3.5
M
cvcn at thc
lowest temperature
(2
“C) that was employed in our measurements.
For experiments involving neutral supporting electrolytes, the sub-
stitution of
3.5
M KCI instead
of
the electrolyte in the salt bridge re-
sulted in small and usually negligible changes in dEpi/dT, as ex-
pected. However, for supporting electrolytes where protons made a
significant (>5?6).contribution to the total ionic strength, the sub-
stitution of these electrolytes by 3.5
M
KCI in the salt bridge yicldcd
appreciable differences
in
dEpi/dT. Therefore,
3.5
M
KCI
was cm-
ployed with these systems \*hich served to minimize the isothermal
liquid junction potentials between the salt bridge and the supporting
electrolytes.
For
some experiments in concentrated perchlorate media,
3
M NHdCI was used
in
the salt bridge in place of KCI to avoid the
generation of spurious potentials from the precipitation of potassium
perchlorate
in
the liquid junction. The electrochemical cell was con-
structed
so
that the temperature drop within the nonisothermal salt
bridge occurred over a short distance
(<1
cm) within glass tubing of
internal diameter
-0.8
cm. These conditions ensured that there was
only a negligible development of concentration polarization due to
thermal diffusion (Soret effect), the presence of which could lead to
larger values
of
d4J,lj/dT.20.21b The absence of this effect, at least to
a significant extent, was confirmed by the observed stability of the cell
potentials within ca.
I
mV for several hours under nonisothermal
conditions.
The temperature dependence
of
the reversible potential (dEpi/dT)
could therefore be identified with the coefficient (d4p/dT), which
yields
AS”,,
from eq
3.
As
mentioned above,
Ef
was determined for
most systems using cyclic voltammetry rather than potentiometry
because of the frequent instability
of
the reduced half of the redox
couple. By working under the appropriate conditions, most of these
couples could be made to exhibit reversible behavior. Then the elec-
trode potential
Ell2
that
is
the average of the cathodic and anodic peak
potentials
is
related to
Er
by
Elp
=
Ef
+
(RT/F)
In
(D~~/Dlll)1~2,
where
Dll
and
Dlll
are thediffusion coefficientsof MI1 and MI1’, re-
~pectively.~~ Fortunately the ratio
Dll/Dlll
is usually close to unity
so
that
El/*
is within
2-3
mV
of
E,-.
For the present purposes, it
is
only
required that the temperature dependence of the term
(RT/F)
In
(D~l/D~~l)1/2
be negligible
so
that dEl,p/dT
*
dE,-“/dT. This as-
sumption was confirmed by determining
Dll
and
Dlll
as a function
of temperature for the representative systems Eu(OH~)~~+/~+ and
Ru(NH3)b3+12+ from the limiting polarographic and cyclic voltam-
metric peak currents for the appropriate reduced and oxidized species.
Estimated errors of less than
0.5-1
eu
in
So,,
resulted by equating
dEl,pi/dT with dEf“’/dT.
Apparatus.
Conventional two-compartment glass cells (solution
volume ca.
IO
mL) were emploled for the electrochemical measure-
ments. The liquid junction between the working compartment and the
salt bridge was formed using glass frits of “very fine” or “ultrafine”
grade manufactured by Corning. Inc. (average porosity
1-3
pn),
which prevented significant mixing of the two solutions
on
the time
scale of each experiment (2--3 h). The working compartment, the
liquid junction, and a portion of the salt bridge were surrounded by
a cemmon jacket through which was circulated water from
a
Braun
Melsiingen circulating thermostat. The temperature of the
cell
solu-
tions could be controlled within
f0.05
“C. The temperature of the
reference electrode (saturated calomel electrode) that was immersed
in the salt bridge solution was held at a fixed, ambient temperature
along with the remaining portion of the salt bridge by means of a
separate water jacket and circulator. For redox couples that exhibit
formal potentials that are sufficiently negative to be examined at
mercury clectrodcs, a commercial (Brinkniann Instruments) hanging
mercury drop electrode (HMDE) was used. The other redox couples
were examined using a platinum “flag” electrode consisting
of
a
small
(2-mm square) sheet of platinum spot-welded to fine platinum wire.
The design of both these electrodes ensured that rapid thermal equi-
librium was achieved when the electrode was immersed
in
the solution.
Dc polarograms were obtained using a capillary with a natural drop
time
of
ca.
6
s.
Essentially complete thermal equilibrium at the
growing drop was obtained under these conditions as evidenced by the
identical kinetic parameters that were obtained over a range
of
tem-
peratures at the dropping mercury electrode (DME) and the HMDE
for the irreversible reductions of Cr7+ and
Eu3+.
Ik
polarograms, as well as cyclic voltammograms with sweep rates
in
the region
5O-~lOOO
mV
s-I
were obtained using
a
PAR
I74
po-
larographic analyzer (Princeton Applied Research) coupled with
a
Hewlett-Packard Model
7045A
fast
X-Y
recorder. This arrangement
Weauer et al.
/
Reaction Entropies
of
Transition Metal Redox
Couples
Table
1.
Reaction Entropies
So,,
for Various M(OH2),,3+12+ Redox Couples
1133
E
IJP,~
temp
ASOrcrd
mV vs. range, cal
K-'
mol-I,
coude electrolvte SCE "C at 25 "C
C~(OHZ)~)+/~+
f
Fe(OH2)b3+/*+
R
v(oH~)~~+/~+
J
Eu(OH~)~~+/~+~
1
M NaC104 (pH 2)
0.2
M LiC104 (pH
1-1.8)
0.2
M
LiC104 (pH
1-1.8)
0.02 M NapTS, (pH
3)?
0.1
M
NapTS, (pH
3)'
1
M NaC104 (pH
3)?
Y b(OH2)n3+/'+
f
0.1
M KPF6 (pH
-5)'
Ru(OH~)~~+/~+
J
0.3 M HpTS,
-660
500
-475
-628
-626
-620
-
1423
-16
3-60 496
3-60 431' (48h)
3-60
3IL
3-60 48.5"
4gC
45.5b.C
3-60 48"
3-50 36' (-33')
Reversible "half-wave" potential determined
in
appropriate electrolyte, at 25 "C against a SCE held at ambient temperature (23
f
0.3
"C); related to formal potential
Ef
by
E1/22s
=
E$s
+
(RT/F)
In
(D~~/D~~~)~~~,
where
DII
and
Dlll
are the diffusion coefficients
of
the reduced
and oxidized species, respectively. For most systems
Ef
=
El/2
-
2
(k
I)
mV.
h
Determined using combination
of
potentiometry and dc polar-
ography.
<
Determined using cyclic voltammetry (sweep rates
50-500
mV
s-1).
Reaction entropy of redox couple (eq
I),
defined as
AS",,
=
S"II
-
SOlll,
where
SO11
and
Solll
are the "absolute" partial molal entropies of the reduced and oxidized species, respectively; determined
from
AS",,
=
F(dE Ipni'/dT) for
T
=
25
"C. (For most systems
AS",,
varied by less than
f2
eu over the temperature range studied.) Experi-
mental precision estimated to be
fl
eu, accuracy within
1-2
eu (see text). Values
in
parentheses are from literature sources; see footnotes
h
and
i.
El,!
found to be unaffected by pH variations
of
at least one unit around pH valuegiven.
f
Determined using HMDE
R
Determined
using Pt electrode. Calculated from ionic entropy data given
in
ref
1
by assuming that
SOH+
=
-5
eu.19
i
Calculated from isothermal cell
data given
in
ref 30 by noting that
AS",,
for the reaction H+
+
e-
s
I/2H2 equals
21
eu.19323
J
pTS
=
p-toluenesulfonate.
allowed peak potentials, etc., to be recorded with a precision
of
fl-2
mV. For faster voltammetric sweep rates
(1
-
100
V
s-l),
a PAR I73
potentiostat driven by a digitally controlled sweep generator that was
constructed
in
this department was employed along with a Tektronix
Model 7623A storage oscilloscope. These latter results were recorded
using Polaroid film which resulted
in
a somewhat lower precision
(f2-3 mV). All electrode potentials are quoted vs. a saturated calomel
electrode (SCE) situated within the reference compartment which
was thermostated close to ambient temperature (23
&
0.3
"C).
Materials and Syntheses.
Most analytical grade reagents were used
without further purification. Solutions for electrochemical experi-
ments were prepared using water purified by double distillation from
alkaline, permanganate followed by "pyrodistillation", which consisted
of
repeatedly passing a mixture of steam and oxygen through a silica
tube network held
at
750
"C.
The ruthenium complexes employed
in
the present study were
synthesized as
follows.
Ru(NH3)&13 (Matthey Bishop, Inc.) was
used as the starting material for the preparation of Ru(N H3)sCI.C12.25
RU(NH~)~CI.CI~ in turn was used to prepare RU(NH~)~OH:~+,I*
RU(NH~)~NCS.(CIO~)~,~~ and RU(NH~)~CI~.CI.~~ RuC13.I -3H20
(Alfa Products) was used
to
prepare solutions
of
Ru(OH1)5C12+ and
Ru(OH2)4C12+ by refluxing
in
0.
I
M p-toluenesulfonic acid over
mercury
in
a nitrogen atmosphere for several hours, followed by cation
exchange separation using Dowex
50W-XI2
resin. Solutions of
Ru(OH~)~~+ were prepared by electrolyzing Ru(OH?)5C12+
in
0.
I
M p-toluenesulfonic acid using a stirred mercury pool at -300 mV
vs. SCE, adding a slight excess
of
Ag+ to precipitate free chloride ions,
filtering, and further electrolyzing at
+IO0
mV vs. SCE to reoxidize
RU(OH~)~?+
to
Ru(OH2)h3+ and to electrodeposit the excess A&+.
Samples
of
Ru(en)3.Br3,
ei.~-Ru(NH3)4(0Hr)*.(CF3S0,)3,
and
Ru(bpy)zC03*2HzO were kindly supplied by Dr. Gilbert Brown of
Brookhavcn National Laboratory. Solutions of eis-Ru(bpy)z-
(OH?)z'+
were generated by dissolving Ru(bpy)zC03.2HzO in per-
chloric acid.
Os(N
H3)(,13
was prepared from N~~OSCI~~' (Matthey Bishop,
Inc.). Solutions
of
Cr3+ were prepared by reducing Cr03 with H202
in
excess perchloric acid. Solutions
of
V3+
were prepared by dissolving
V?Os
in
excess perchloric acid, clectroreducing to
V2+
at a stirred
mercury pool held at
-I
100
mV vs. SCE, and reoxidizing to
V3+
at
-300
mV vs. SCE. Solutions
of
Eu3+ and Yb3+ were prepared by
dissolving Eu@3 and Yb203
in
a slight excess
of
perchloric acid.
Co(en)3.C13 was prepared as
in
ref 28. Solutions
of
Fe(b~y)~z+, Fe-
(phen)3?+, Co(bpy)32+, and Co(phen)?'+ were prepared by adding
an
CXC~SS
of the appropriate ligand to a solution of the given metal
ion.
The various Co(
I I I)
macrocycle complexes scrutinized here were
kindly provided by Professor John Endicott
of
Wayne State Univer-
sity.
Results
1.
Aquo Couples.
The reaction entropy
AS',,
of six aquo
couples of the type
M(OH2)n3+/2+
were studied: Cr-
(OH2)63+/2+, Eu(OH~)~~+/~+, and Yb(OH2)n3+/2+. These
systems were chosen because their formal potentials allow them
to be conveniently studied at mercury
or
platinum electrodes,
and they exhibit substantial variations in electronic structure
of
the central metal ions. Previous determinations of
AS",,
for
these couples are sparse. The absolute ionic entropies
of
Fe3+
and Fe2+ have been determined,Z9 and an estimate of
AS",,
for Ru(OH~)~~+/~+ has been reported from electrochemical
measurements.30
Most data for the Cr3+l2+ and
Eu3+I2+
couples in per-
chlorate media were obtained using potentiometry because the
small heterogeneous electron transfer rates for these systems
resulted in distinctly irreversible cyclic voltammograms.
However, by working in sodium p-toluenesulfonate (NapTS)
media, the strong specific adsorption of p-toluenesulfonate
anions resulted in almost reversible cyclic voltammograms for
the
Eu3+/'+
couple. Accurate values of
El/1
could still be
obtained from such "quasi-reversible" voltammograms in the
usual way provided that the cathodic-anodic peak separation
lies in the range
57
to ca.
90
mV.'jb
For
the remaining aquo
couples, essentially reversible
or
quasi-reversible cyclic volt-
ammograms were obtained, at least after the addition of small
quantities of NapTS. The resulting values of
AS",,
are listed
in Table
I,
together with other pertinent information. It is seen
that some limited dependence of
AS",,
upon the nature
of
the
metal ion is obtained. The dependence of
AS",,
upon ionic
strength was investigated for
Eu3+l2+
and was found to be
small (Table
I).
Good agreement between the earlier and
present determinations is found for Fe(OH1)63+/'+ (Table
I),
but
a
large qualitative discrepancy is seen for
Ru-
A
possible reason for this discrepancy
is
that the
isothermal cell measurements of ref
30
were complicated by
an unknown temperature dependence of the electrode potential
of the glass reference electrode used in that
study.
2.
Ruthenium(III)/(II)
and
Osmium(III)/(II) Couples.
The
reaction entropies of
12
Ru(IIL)/(II)
couples containing
ammine, aquo, and simple anionic ligands were evaluated.
These systems were selected
in
order to scrutinize the effects
(OH2)63+/2+, V(OH2)63+/2+, Fe(OH2)63+/2+, RU-
1134
Table
11.
Reaction Entropies
-lSo,,
for Various Rulll/ll and
Journal
of
the American Chemical Society
1
101:5
/
February
28,
1979
Redox Couples
temp
-1s
"
rc,h
-El
,225,o
range,
caI
K-I
mol-',
couple electrolyte
mV
vs.SCE "C at 25 "C
RU(NH~)~~+/~+ 0.02
M
KPF6
175
3-60
19
f
O.Sc
0.25 M KPF6 183 (1931°,
18712)
15-60
17
f
0.5r
0.1
M
NaC104
I78
15-60 19
f
0.5"
(7-")
0.2
M
CF3COONa
180
3-60 16.5
f
0.5'
0.8
M
CF3COONa
188
3-60
14
f
0.5"
O~(N
~~)~3+/2+ 0.05
M
CF3COONa
990
(1010~4) 3-65
18
f
0.5'
R~(en)j~+/~+
0.1
M
KPF6 60 3-60 13
f
0.5(
(I
I3l)
Ru(N H3)SOH23+/2+ 0.2 M CF3COOH 162 (178,'O 17412) 3-60 25
f
2"
(1
7.531)
cis
-
R
u
(
N H
3)
4
(
0
H
2)
23
+/
*+
Ru(
N
ti
3)5NCS2+/+ 0.02
M
KPFb I30 3-60
I5
f
0.5''
0.4
M
KPF6
140
(1
I I
10)
3-60 15
f
0.5"
0.1
M HpTS'
135
(144,'O
14012)
3-60 26
f
2'
Ru(N H3)50H2+/+
0.2
M
NaOH
653 (664'O) 5-50
0
f
3'
Ru(N ti3)5Cl2+/+ 0.5 M NaC104
295 (286'O) 2-45
IO
f
2d
cis-Ru(N H3)4CI2+/O
I
M
NaC104 350 (344,1° 32612) 2-28
IO
f
4"
RU(OH*)~~+/'+ 0.3
M
HpTSe 16 (3030) 3-50 38
f
3"
(-3330)
Ru( OH z)sCI2+/+
I
M
HpTS'
165
3-40 28
f
3'
cis-R~(OH2)4C12+/~
0.1
M HpTSe 268
4-35 25
f
2''
Reversible "hulf-wave" potential determined by cyclic voltammetry at
a
HMDE
(see
notes
for Table
I).
Values
in
parentheses are from
indicated literature sources and correspond to comparable experimental conditions. Reaction entropy
of
redox couple (see notes for Table
I).
Stated precision was estimated from scatter
of
experimental points
in
the vicinity of 25 "C. Values
in
parentheses are from indicated literature
sources.
'
Determined using cyclic voltammetric sweep rates
in
the range 50-500 mV
s-l.
Determined using sweep rates
in
the range
1
--
100
V
s-l,
<'
pTS
=
p-toluenesulfonate.
Table
111.
Reaction Entropies
AS",,
for Various
M1ll/ll
Couples Containing Chelating Ligands
tetnp
ASQrc,h
E
I
/225,rr
range, cal K-I
mol-',
cou131e electrolyte
mV
vs.SCE "C at 25 "C
0
I
M
KPF6
I
M
NaC104
+
50
mM
en
0
05
M
KCI
+
25
mM
phen
0
05
M
KCI
t
25
mM
bpy
0
I
M
HpTS
0
05 M KCI
+
25
mMphen
0
05
M
KCI
t
25 niM bpq
0
I
M
NaCIOj
0
1
M
HClOj
0
I
M HClOj
-60
-460
(-448,
p
=
03?)
870
(865.
p
=
0.0533)
845 (845,
p
=
0.0513)
652
I45
70
--540
(-5403j)
315 (31535b)
3
I5
(
300jSb)
3-60
3-60
4-45
4-45
3-60
3-45
3-40
3
-50
3-55
3-55
13
k
0.5
(I
I3l)
37
f
2
(40,32
p
=
0)
3
f
2
(0,p
=
09.33)
2
f
2 (2,
=
09.33)
2f2
22*3(18')
22
f
3
(21C)
19
f
2
45
f
2
23
f
5
Reversible "half-uave"
potential
determined b] cyclic voltammetr! using
sivccp
rates
of
50-500
mV
5-l
(5ce
notes for
Tablc
I).
Values
in
parenthese9 are taken from indicated literature sourccc.
p
is
ionic strength. Reaction cntropq of redox
couple
(for details
scc
note\
for Tables
I
and
11).
Determined using Pt electrode.
('
Nomenclature
as
in
ref
35.
r-[13]
diene
=
5.7.7.IZ.lJ.IJ-hcxa-
nicth)I-1.4.8.1
I
-tetraazac~clotetradec~1-4,1
1
-diene; TIM
=
2,3,9, IO-tetramethyl-
I
,J.8,
I I
-tctraazacqclotctrndcca-
l.3,8.
IO-tctracnc.
'
Noin-
cnclature
as
in
ref
34.
R
Calculated from isothermal cell data
[A.
Ciann
and
V.
Cresccn7i. quoted
by
21.
Chou.
C.
Crcuu. and
U.
Sutiii,
.I.
.4~1.
Chrnr.
Soc..
99,
5616
(1977),
Table
VI
by assuming that
-1S",,
for H+
+
e-
--
I/?H? equals
21
CU.~').~~
Determined
using
HVDE.
of replacing ammine by aquo ligands and of changing the
charge type of the couple resulting from substitution of the
ammine and
aquo
ligands by simple anions. The results are
summarized in Table
11.
For
all these systems, the heteroge-
neous electron transfer rates were sufficiently rapid
so
that the
cyclic voltammograms were essentially reversible even at the
highest sweep rates
(100
V
s-'),
However, the relative lability
of the Ru1I state for the Ru(NH3)5CI2+/+ and Ru(NH3)4-
CIZ+/~)
couples necessitated the use of large sweep rates
(1
-
100
V
S-I)
in
order
to
avoid significant aquation of Rull during the
potential scan. Estimates of
AS",,
have previously been ob-
tained for RU(NH~)~~+/?+, Ru(NHJ)~OH~~+/?+, and
Ru(en)j3++/'+ from the temperature dependence of the equi-
librium constants for reduction of the Ru(lI1) complexes by
Np3+
coupled with an estimate of
AS",,
for the Np+'++/'+
couple.?' While reasonable agreement between the present and
earlier determinations is found for R~(en),3+;~+, substantial
differences are seen for the other two systems (Table
[I).
These
discrepancies may arise from systematic errors
in
the kinetic
analysis employed to determine the equilibrium constants
in
ref
3
1
when these quantities are much larger than unity. Sig-
nificant differences are also seen between present and earlier
determinations of
Ell,
for
some
Ru(lIl)/(Il)
couples (Table
11).
In view of the care taken to minimize liquid junction po-
tentials
in
the present work, these differences probably arise
chiefly from the presence of such potentials in the earlicr work
combined with the slightly different thermal conditions
em-
ployed here.