Salt and solvent effects on the kinetics of the oxidation of the excited state of the [Ru(bpy)3]2+ complex by S2O 82-

Article abstract of DOI:10.1021/jp055189l

The title reaction was studied in different reaction media: aqueous salt solutions (NaNO₃) and water-cosolvent (methanol) mixtures. The observed rate constants, k_obs, show normal behavior in the solutions containing the electrolyte, that is, a negative salt effect. However, the solvent effect is abnormal, because a decrease of the rate constant is observed when the dielectric constant of the reaction medium decreases. These effects (the normal and the abnormal) can be explained using the Marcus-Hush treatment for electron transfer reactions. To apply this treatment, the true, unimolecular, electron-transfer rate constants, k_et, have been obtained from k_obs after calculation of the rate constants corresponding to the formation of the encounter complex from the separate reactants, k_D, and the dissociation of this complex, k_-D. This calculation has been carried out using an exponential mean spherical approach (EMSA).

Full text of DOI:10.1021/jp055189l

4196
J. Phys. Chem. A 2006, 110, 4196-4201
Salt and Solvent Effects on the Kinetics of the Oxidation of the Excited State of the
2-
[Ru(bpy)3]2+ Complex by S2O8
T. Lopes-Costa, P. Lopez-Cornejo, I. Villa, P. Perez-Tejeda, R. Prado-Gotor, and F. Sanchez*
Contribution from: Departamento de Qu´ımica F´ısica, Facultad de Qu´ımica, UniVersidad de SeVilla, c/
Profesor Garc´ıa Gonza´lez s/n, 41012 SeVilla, Spain
ReceiVed: September 14, 2005; In Final Form: NoVember 17, 2005
The title reaction was studied in different reaction media: aqueous salt solutions (NaNO3) and water-cosolvent
(methanol) mixtures. The observed rate constants, kobs, show normal behavior in the solutions containing the
electrolyte, that is, a negative salt effect. However, the solvent effect is abnormal, because a decrease of the
rate constant is observed when the dielectric constant of the reaction medium decreases. These effects (the
normal and the abnormal) can be explained using the Marcus-Hush treatment for electron transfer reactions.
To apply this treatment, the true, unimolecular, electron-transfer rate constants, ket, have been obtained from
kobs after calculation of the rate constants corresponding to the formation of the encounter complex from the
separate reactants, kD, and the dissociation of this complex, k-D. This calculation has been carried out using
an exponential mean spherical approach (EMSA).
Introduction
Under the circumstances prevailing in this work, it can be
shown that:
Electron-transfer reactions are seen often in chemistry,
biology, as well as in industrial fields. They are unique in the
sense that, since the pioneering work of Marcus1 and Hush,2
there is a quantitative theoretical framework that allows a deeper
insight in the factors controlling the rate of this kind of reaction.
Thus, it is well-known that the rate constant for electron-transfer
reactions, ket, as given by:3
kDket
kobs
)
(3)
k-D + ket
where kD and k-D are the rate constants of the forward and
backward processes, respectively, in the formation of the
precursor complex from the separate reactants.
Consequently, ket can be obtained from kobs after calculations
of kD and k-D. Once ket is separated from kobs, ∆Gq is easily
obtained. In this way, λ can be calculated, provided that ∆G°′
is known (see eq 2).
ket ) κelνn e-∆Gq/RT
(1)
is controlled by an electronic factor, κel, a nuclear frequency
factor, νn, and the activation free energy, ∆Gq. This free energy
can be written as:1-3
Our selection of the reaction studied here was based on the
ideas described in the preceding paragraphs: first of all, the
free energy for this reaction is very favorable so that eq 3 can
be safely applied. Second, as was recently shown by Simonin
and Hendrawan,6 kD (and k-D) can be calculated to a reasonable
accuracy by employing an exponential mean spherical approach
(EMSA). Third, redox potentials of the S2O82-/3- couple in the
reaction media studied here are available7,8 so that by measuring
the redox potentials of the [Ru(bpy)3]3+/2+ couple in these media,
the reaction free energy can be calculated.
The results presented here can be considered normal in the
case of salt solutions: kobs decreases when the concentration of
the salt increases. However, the results obtained in the water-
methanol mixtures are abnormal according to the conventional
theory of solvent effects,9 which predicts an increase of the rate
constant, kobs, when the dielectric constant of the reaction
medium is lowered, whereas here a decrease of kobs is seen.
This abnormal effect can be easily rationalized from the data
(λ and ∆G′) obtained for the water-methanol mixtures as
described previously.
(λ + ∆G′)2
∆Gq )
(2)
4λ
In this equation, λ is the reorganization free energy and ∆G′ is
the free-energy change for the electron-transfer step.
For a given electron-transfer reaction, κel and νn are practically
fixed so that control on the rate can be achieved through
modulation, by the reaction medium, of λ and ∆G′. Conse-
quently, knowledge of how these parameters change when the
reaction is carried out in different solvents is important in an
understanding of how to control the rate of the reaction. First,
it is therefore necessary to obtain ket in different reaction media.
It is important to note that for bimolecular electron-transfer
reactions, like the one studied here, ket is not the datum obtained
in a kinetic experiment, kobs. In fact, ket corresponds to the
unimolecular electron-transfer step, once the donor and the
acceptor have formed the precursor complex4 (S2O82-/Ru-
(bpy)32+* f S2O83-/Ru(bpy)33+, in this case), and kobs corre-
2-
3-
sponds to the process S2O8 + Ru(bpy)32+* f S2O8
+
Experimental Section
3+
Ru(bpy)3 (see ref 5).
Materials. Tris (2,2′-bipyridine) ruthenium (III) chloride
([Ru(bpy)3]Cl2) from Biomedicals Inc., sodium peroxodisulfate
(Na2S2O8) from Fluka, NaNO3 from Merck, and methanol from
* To whom correspondence should be addressed. E-mail: gcjrv@us.es;
Tel. +34-954557175; Fax. +34-954557174.
10.1021/jp055189l CCC: $33.50 © 2006 American Chemical Society
Published on Web 03/04/2006

Oxidation of [Ru(bpy)3]2+ Complex by S2O8
J. Phys. Chem. A, Vol. 110, No. 12, 2006 4197
2-
TABLE 1: Stern-Volmer Constants (Ksv), Lifetime in the
Absence of the Quencher (τ0), and Observed Rate Constants
2-
(kobs) of the Reaction [Ru(bpy)3]2+ + S2O8 in NaNO3 Salt
Solutions at 298.2 K
[NaNO3]
10-2Ksv
τ0
(ns)
10-9kobs
(mol dm-3
)
(mol dm-3
)
(mol-1s-1dm3)
0.009
36.8
7.88
3.87
1.82
1.46
1.27
1.19
1.10
0.97
603.6
603.4
603.6
603.5
603.9
603.6
603.7
603.5
603.4
6.10
1.31
0.64
0.30
0.24
0.21
0.20
0.18
0.16
0.2
0.5
1
2
3
4
5
6
TABLE 2: Stern-Volmer Constants (Ksv), Lifetime in the
Absence of the Quencher (τ0), and Observed Rate Constants
2-
(kobs) of the Reaction [Ru(bpy)3]2+ + S2O8 in
Water-Methanol Mixtures at 298.2 K
% weight
(methanol)
10-3Ksv
τ0
(ns)
10-9kobs
(mol-1 dm3)
(mol-1 s-1 dm3)
5.68
10.20
18.37
26.53
30.64
39.15
1.18
1.04
0.85
0.67
0.58
0.40
531.2
528.8
525.7
522.1
520.6
518.4
2.22
1.96
1.62
1.28
1.11
0.78
Figure 1. Decay of the excited state of [Ru(bpy)3]2+ in salt solution
([NaNO3] ) 5 mol dm-3) at 298.2 K.
Merck were used as received. All the solutions were prepared
with deionized water from a Millipore Milli-Q system, having
cyclic voltammetry technique as described in ref 11. γox and
γred in eq 4 represent the activity coefficients of oxidized and
reduced species of the ruthenium complex, respectively. A
vitreous carbon working electrode, a saturated calomel reference
electrode, and a platinum auxiliary electrode were used in these
measurements. A sweep rate of 0.2 V s-1 was employed.
In the electrochemical measurements, the concentration of
[Ru(bpy)3]2+ was ranged from 10-3 to 1.8 × 10-3 mol dm-3
for salt solutions. In the case of methanol-water mixtures, a
concentration of the ruthenium complex equal to 10-3 mol dm-3
was used. For the mixtures, NaNO3 at concentration 0.1 mol
dm-3 was added.
a conductivity <10-6 S m-1
.
Fluorescence Measurements. (a) Intensity measurements
were carried out in a spectrofluorimeter (Hitachi f-2500)
interfaced to a PC for the reading and handling of the spectra
at 298.2 K. Intensity measurements were performed in the
absence of the quencher (I0) at [Ru(bpy)3]2+ ) 5 × 10-6 mol
2-
dm-3 and in the presence of different quencher (S2O8
)
.
concentrations ranging from 5 × 10-4 to 3 × 10-3 mol dm-3
In the case of measurements in the presence of the quencher,
for water-methanol mixtures, a constant Na+ concentration was
maintained by adding an inert salt (NaNO3).
All the measurements were carried out at 298.2 K.
(b) Fluorescence lifetimes of the excited state of the
ruthenium complex were measured with a FL920 fluorescence
lifetime spectrometer from Edinburgh Instruments using the time
correlated single-photon counting technique at 298 K. Fluores-
cence decays were obtained up to 104 counts in the peak and
were analyzed by an iterative deconvolution procedure based
on the Marquardt algorithm.10 The goodness of the fit was
Results
Table 1 contains the Stern-Volmer constants, KSV, for the
salt solutions obtained from:12
I
0 ) 1 + KSV[S2O8
]
(5)
2-
2
measured by the magnitude ø2 (ø2 ) ∑i|Fi - fi| , where Fi is
I
the value of the ith data point and fi is the value obtained from
the fit) and the shape functions of the weighted residuals.
Before lifetime measurements, the solutions were deoxygen-
ated by bubbling argon through them for at least 30 min.
Emission and excitation wavelengths were 597 and 452 nm for
salt solutions and 594 and 452 nm for cosolvent mixtures. The
excitation and emission wavelengths were those that cor-
responded to the maxima of the absorption and emission spectra,
respectively, in the different reaction media.
The table also contains the lifetimes, τ0, in the absence of
the quencher, obtained as previously described. From KSV and
τ0, the observed rate constants, kobs, were obtained (kobs ) KSV
/
τ0).
Table 2 contains the same data as Table 1 but refers to water-
methanol mixtures.
In the Stern-Volmer representations, good linear plots were
obtained in all cases. As an example, Figure 2 gives the plot
corresponding to a water-methanol mixture with a % of weight
of methanol of 18.36.
Figure 1 shows an example of the decay of the excited
ruthenium complex and the residuals obtained.
The standard formal redox potentials for the [Ru(bpy)3]3+
/
Electrochemistry. Standard formal redox potentials, E°′, for
the [Ru(bpy)3]3+/2+ couple:
3-
[Ru(bpy)3]2+ and the S2O82-/S2O8 (from ref 7) and the [Ru-
(bpy)3]3+/[Ru(bpy)3]2+* couples in salt solutions appear in Table
3. The latter redox potentials were calculated through the
equation:13
γox
E°′ ) E° + RT ln
(4)
γred
E°′Ru(bpy)
2+* ) E°′
2+ - E(0-0) (6)
Ru(bpy)3 /Ru(bpy)3
3+
3+
/Ru(bpy)3
in the different reaction media were obtained following the
3

4198 J. Phys. Chem. A, Vol. 110, No. 12, 2006
Lopes-Costa et al.
6 that the slow rate for the thermal process comes from the
high reorganization free energy. This circumstance has also been
noted by other authors.25
Calculations
To know the electron-transfer rate constant, ket, that is the
rate constant corresponding to process 3b, the value of kD and
k-D (eq 3a) need to be calculated.
The calculations of these diffusion rate constants have been
obtained by using the EMSA, following the procedure described
in ref 6. In this approach, the ions (reactants and background
electrolyte) are characterized by their charges and diameters.
kD is given by:
kD ) 4π(DA + DD)L
(7)
Figure 2. Plot of I0/I versus the quencher concentration, [S2O82-], in
water-methanol mixture (% weight of methanol ) 18.37) at 298.2 K.
where DA and DD represent the diffusion coefficients of the
acceptor (S2O82-) and donor ([Ru(bpy)3]2+*), respectively.
Parameter L is given by:
TABLE 3: Standard Formal Redox Potential (E°′/V) Values
of the S2O82-/S2O83-, [Ru(bpy)3]3+/[Ru(bpy)3]2+, and the
Excited [Ru(bpy)3]3+/[Ru(bpy)3]2+* Couples (vs NHE) at
Different NaNO3 Concentrations at 298.2 K
L-1
)
∞r-2 exp[âVEMSA(r)]dr
(8)
∫
AD
σr
2-
[NaNO3]
S2O8
S2O8
/
[Ru(bpy)3]3+
/
[Ru(bpy)3]3+
/
where σr is the reaction distance and VEMSA(r) is the mean
(mol dm-3
)
[Ru(bpy)3]2+
[Ru(bpy)3]2+*
3-a
AD
force potential, as given by the EMSA:
0.009
1.32
1.34
1.28
1.28
1.25
1.23
1.23
1.23
1.22
1.22
-0.74
-0.80
-0.81
-0.83
-0.85
-0.85
-0.86
-0.86
-0.86
0.2
0.5
1
2
3
4
5
6
1.44
1.48
1.50
1.53
1.55
1.56
1.57
1.57
G(r)
EMSA
AD
âV
(r) ) -
)
r
∞
RAD
1
G (X )H(r - r ) (9a)
∑
n
n
σ
(
)
r
(1 + ΓrA)(1 + ΓrD)n)1
R
AD ) ZAZDR
(9b)
(9c)
a Data taken from ref 7.
âe2
R )
TABLE 4: Standard Formal Redox Potential (E°′/V) Values
of the S2O82-/S2O83-, [Ru(bpy)3]3+/[Ru(bpy)3]2+, and the
Excited [Ru(bpy)3]3+/[Ru(bpy)3]2+* Couples (vs NHE) in
Different Water-Methanol Mixtures at 298.2 K
4πꢀ0ꢀ
In eq 9a, H is the HeaViside and G(r) is defined as:
2-
% weight
(methanol)
S2O8
S2O8
/
[Ru(bpy)3]3+
/
[Ru(bpy)3]3+
/
3-a
[Ru(bpy)3]2+
[Ru(bpy)3]2+*
el
G(r) ≡ rg (r)
(10)
AD
5.68
10.20
18.37
26.53
30.64
39.15
1.40
1.30
1.32
1.35
1.36
1.37
1.39
-0.80
-0.78
-0.76
-0.75
-0.74
-0.73
el
AD
1.40
1.39
1.38
1.38
1.37
with g being the electrostatic contribution of the (gAD) radial
distribution function. For a more detailed explanation, see refs
6 and 15.
On the other hand, KIP ) kD/k-D, which is the equilibrium
constant in absence of the quenching reaction, has been
a Data taken from ref 8.
EMSA
AD
calculated from V
(σr), the potential at contact, through:
where E(0-0) corresponds to the 0-0 emission energy. All
these potentials are referred to as NHE.
EMSA
AD
KIP ) exp(-âV
(σr))
(11)
Table 4 contains the standard formal redox potentials in the
methanol-water mixtures. Those of the S2O82-/S2O83- couple
where σr is taken as the contact distance, that is, σr ) rA + rB.
Once one has KIP and kD, it is possible to obtain k-D as:
3-
were from ref 8. As the S2O82-/S2O8 in the table contains
the correction of the liquid junction potentials, a similar
correction was carried out in the case of [Ru(bpy)3]3+/[Ru-
(bpy)3]2+ potentials. To perform this correction, the redox
potentials of the Fe(µ5-Cp)2+/Fe(µ5-Cp)2° couple (taken from
KIP
k-D
)
(12)
kD
ref 14) were employed.
The values of kD, k-D, KIP, and ket (this latter from eq 3) are
given in Tables 5 and 6 for the salt solutions and the water-
methanol mixtures, respectively. The value of KIP corresponding
to a solution containing NaNO3 0.009 mol dm-3 is similar to
2-/3-
The redox potentials of the S2O8
couple are close to or
higher than those of Ru(bpy)33+/2+; that is, the thermal electron-
transfer reaction is allowed from a thermodynamic point of view.
However, this reaction is very slow, as we checked in
preliminary experiments. Thus, the half-life of this process is
≈ 24 h. As our experiments were carried out in a few seconds,
no detectable decrease of the Ru(bpy)32+ is expected during the
time of measurements. It is clear from the data in Tables 5 and
the reported value for the reaction Ru(NH3)5pz2+ + S2O8 in
2-
water by Fu¨rholz and Haim.25 This latter reaction also involves
a Ru2+ charged complex and S2O8
.
2-
A final comment before closing this section. To calculate ket,
we have not used the experimental (KSV/τ0) values of kobs but

Oxidation of [Ru(bpy)3]2+ Complex by S2O8
TABLE 5: Values of kD, k-D, KIP, ket, ∆G′, and λ Obtained for Different NaNO3 Concentrations
J. Phys. Chem. A, Vol. 110, No. 12, 2006 4199
2-
[NaNO3]
10-9kD
10-9k-D
KIP
10-7ket
∆G′
λ
(mol dm-3
)
(mol-1 s-1 dm3)
(s-1
)
(mol-1 dm3)
(s-1
)
(kJ mol-1
)
(kJ mol-1
)
0.009
16.2
10.7
9.65
8.87
7.79
6.80
5.89
5.05
4.25
0.73
1.31
1.56
1.69
1.69
1.57
1.41
1.24
1.07
22
44
18
11
7.6
5.5
4.7
4.3
4.1
4.0
-218
-225
-228
-233
-235
-237
-238
-238
-238
418
439
450
465
469
472
474
475
476
0.2
0.5
1
2
3
4
5
6
8.2
6.2
5.2
4.6
4.3
4.2
4.1
4.0
TABLE 6: Values of kD, k-D, KIP, kEt, ∆G′, and λ Obtained for Different Water-Methanol Mixtures.
% weight
(methanol)
10-9kD
10-8k-D
KIP
10-7ket
∆G′
λ
(mol-1 s-1 dm3)
(s-1
)
(mol-1 dm3)
(s-1
)
(kJ mol-1
)
(kJ mol-1
)
5.68
10.20
18.37
26.53
30.64
39.15
12.2
11.4
9.47
8.66
8.48
8.51
5.09
4.52
3.39
2.75
2.52
2.19
24
25
28
32
34
39
11
-222
-220
-218
-216
-215
-214
440
441
442
445
447
451
9.5
6.7
4.6
3.8
2.5
the values of this rate constant resulting from the fit of these
experimental values to (see Figures 3 and 4):16
However, ∆G′ and ∆G°′ are related through:
∆G′ ) ∆G°′ + wp - wr
(16)
k0 + Kk1[NaNO3]
kobs
)
(13)
Here, wr and wp are the free energies corresponding to the
formation of the precursor complex from the separate reactants
and the formation of the successor complex from the separate
products.
1 + K[NaNO3]
for salt solutions, and to eq 14 for water-methanol mixtures:
17
wr was calculated as:
k0 + Kk1x
1 + Kx
wr ) -RT ln KIP
(17)
kobs
)
(14)
from the values of KIP appearing in Table 5. As for the wp values,
wp ) (9/4)wr was used, taking into account that the product of
where x represents the ratio between the mole fractions of the
methanol and water.
3-
the charges of the ions forming the successor complex (S2O8
and [Ru(bpy)3]3+) is 9/4 of the product of the charges of the
reactants. In this way, the values of ∆G′ and λ given in Table
5 were obtained.
Discussion
(a) Salt Effects. According to the data in Table 1, the
expected negative salt effect was observed for the reaction
studied here, taking into account that the reactants are ions of
opposite charge. Moreover, according to data in Table 5, ket
decreases with the salt concentration. That is, a negative salt
effect on ket is observed so that the negative (global) salt effect
arises from the effect of the salt on the diffusion step (kD) and
on the electron-transfer step.
It is clear that the negative salt effect on ket arises from the
fact that although the electron-transfer step becomes more
favorable from a thermodynamic point of view when the
concentration of the salt increases, this is not enough to
compensate for the increase of λ. The fact that the reaction
becomes more favorable thermodynamically speaking is a
2-
consequence of S2O8 being a more powerful oxidant in the
To take a deeper insight into the negative salt effect on ket,
the Marcus-Hush formulation for electron-transfer reactions,
as given in eq 1, was used. In this equation, the pre-exponential
term, κel νn, can be considered independent of the reaction
medium. This term, except for strongly nonadiabatic processes,
is of the order of the (average) vibratory frequency promoting
the activation of the precursor complex. Thus, a value of 1012-
1013 s-1 seems reasonable. In the calculations, we used a value
of 6.62 × 1012 s-1. This value corresponds to the value of the
pre-exponential factor in the expression of the rate constant
given by the classical transition state theory (kBT/h) at the
working temperature. In this way, ∆Gq can be obtained from
ket (see eq 1).
presence of the salt and [Ru(bpy)3]2+* a more reductant species.
This is clearly seen in eq 4, which gives the standard formal
redox potential of a given couple. For the S2O82-/S2O83- couple,
both γox and γred decrease with increasing salt concentration.
However, the decrease in γred is more marked because of the
higher (absolute) charge of the reduced form of this couple.
Thus, E°′ increases as the salt concentration does. The opposite
is true for the cationic, Ru(bpy)33+/Ru(bpy)32+*, couple. Con-
sequently, the reaction becomes more favorable thermodynami-
cally. Notice that parameter λ causes the negative salt effect on
ket, as this parameter increases as the concentration of the salt
is increased, in agreement with the theoretical treatment of the
salts effects on this reorganization free energy.18
(b) Solvent Effects. In many ways, the results obtained for
the water-methanol mixtures are the most interesting results
of this work. They correspond to an unexpected solvent effect,
as kobs decreases when the content of methanol increases. To a
small extent, this is due to a decrease in the rate of the diffusion
step (kD). However, the main cause is the diminution of the ket.
Once ∆Gq has been calculated, it is possible to obtain the
two parameters, λ and ∆G′, which, according to eq 2, appear
in ∆Gq. It is important to realize that ∆G′ is not the standard
formal reaction free energy, ∆G°′, of the reaction:
∆G°′ ) -nF(E°′S O 2-/3- - E°′
)
(15)
3+/2+*
Ru(bpy)3
2
8

4200 J. Phys. Chem. A, Vol. 110, No. 12, 2006
Lopes-Costa et al.
Figure 4. Plot of the rate constant kobs versus the relative molar fraction
x (see text in Calculations Section) at 298.2 K.
Figure 3. Plot of the rate constant kobs versus the NaNO3 concentration
at 298.2 K.
solvent (and not only the solvent polarization) will be intermedi-
ate between the positions corresponding to the (preferential)
solvation of the precursor and successor complexes. The cause
of the extra component in λ is not the preferential solvation
itself but the changes in this preferential solvation in the
activation process, which implies a movement of solvent
molecules in the activation step.
This component of the reorganization energy has been
observed by some of the present authors in previous works19
as well as by other authors. Thus, Curtis et al.20 suggested this
extra contribution from the results obtained through thermody-
namic (redox) measurements corresponding to some inorganic
complexes in solvent mixtures. A similar conclusion was
reached by Hupp et al.21 from the study of the spectra of some
complexes in solvent mixtures. Moreover, the existence of this
extra component of the solvent reorganization energy in solvent
mixtures has been predicted theoretically by Matyushov22 and
corroborated through simulations.23
This diminution can be considered in detail using the same
approach as in the case of salt effects. Thus, we calculated the
values of ∆G′ and λ in the water-methanol mixtures. They
appear in Table 6.
It can be clearly seen from this table that both the variation
of the free energy of the electron-transfer step and the
reorganization energy of this step produce a diminution of ket,
because both of them increase when the reaction medium
becomes richer in methanol content.
The increase of ∆G′ can again be explained using eq 4: when
the dielectric constant of the reaction medium decreases, both
γox and γred will increase. For the S2O82-/S2O8 couple, γox
3-
will increase less than γred because the oxidized form of this
couple bears a lower (absolute) charge. In this way, the S2O8
2-
becomes a less powerful oxidant when the methanol content is
increased. The ruthenium complex becomes less reductant in
this case. Thus, a less favorable ∆G′ is seen when the amount
of the alcohol in the reaction medium increases.
The increase of λ in water-methanol mixtures is somewhat
unexpected. This reorganization free energy contains an internal
contribution, λin, arising from the internal reorganization of the
bonds of the donor and the acceptor, and a solvent contribution,
λs, arising from the solvent reorganization. The internal con-
tribution can be considered as independent of the reaction
medium. However, λs depends on the solvent:1,2
According to the previous interpretation, in solvent mixtures,
a component of the reorganization energy, not included in eq
20, must exist to produce an increase in λ when the amount of
the alcohol increases and, thus, the Pekar’s factor decreases.
This component can be estimated as follows; assigning λex as
this extra component of the reorganization free energy, it can
thus be written for the water-methanol mixtures:
λex ) λ - λin - λs
(20)
1
1
1
λs ) NAe2
+
-
γ ) Aγ
(18)
Thus, according to previous arguments, this component does
not exist in pure solvents, in water for example, and it can be
written:
(
)
2rA 2rD dr
As the Pekar’s factor, γ, given by:
λin ) λH O - (λs)H O
(21)
2
2
1
1
ꢀ
γ )
-
(19)
In principle, λs for water would be calculated from eq 18.
However, this equation has been questioned because it over-
estimates λs.24 For this reason, we preferred to estimate λin using
published data. Thus, λin for S2O82- was established to be about
n2
decreases when the content of methanol increases, λs and, thus,
λ should decrease. However, the opposite trend is observed in
Table 6.
660 kJ mol-1 25
. For the ruthenium complex, a value of λin of 2
kJ mol-1 was used.26 Consequently, a value of 331 kJ mol-1 is
obtained. Using this value, λs for water is calculated as 87.7 kJ
mol-1. Thus, the effective value of parameter A in eq 18 is:
To explain the increase of λ, it is important to realize that
our data correspond to solvent mixtures instead of neat solvents.
In these mixtures, when the electron transfer happens, both
reactants change their charges, and consequently, a modification
of the composition of their solvations shells is expected (this
modification, of course, is absent in neat solvents). This change
in the composition of the solvation shells will produce an extra
reorganization of the solvent, caused by a translational move-
ment of some solvent molecules, because in the transition state,
the position of the molecules of the two components of the
(λ )
s H2O
A )
) 159.4 kJ mol-1
(22)
γ
H2O
Using this value of A to calculate λs in eq 20, as well as the
value of λin previously estimated, the values of λex appearing
in Table 7 are obtained.

Oxidation of [Ru(bpy)3]2+ Complex by S2O8
J. Phys. Chem. A, Vol. 110, No. 12, 2006 4201
2-
point is now included in the general plot. This supports our
estimation of λex.
Conclusions
In this work we have studied the oxidation of [Ru(bpy)3]2+
*
2-
by S2O8 in salt solutions and in water-methanol mixtures.
Using an extended mean spherical approach (EMSA) and the
Marcus-Hush formulation for electron-transfer reactions, it was
possible to explain the normal salt effects and the abnormal
solvent effects. The latter is a consequence of the fact that: (i)
in water-methanol mixtures, the reaction becomes less favor-
able thermodynamically speaking and (ii) in these mixtures, an
extra contribution of the solvent reorganization free energy
appears.
Acknowledgment. This work was financed by the D.G.I-
.C.Y.T. (BQU 2002-01063) and the Consejer´ıa de Educacio´n y
Ciencia de la Junta de Andaluc´ıa. Two of the authors thank
Ministerio de Ciencia y Tecnolog´ıa (MCYT) and Ministerio de
Educacio´n y Ciencia (MEC) for their financial support through
Grants BES-2003-1219 and AP 2003-1155.
Figure 5. Plot of ln ket versus the Grunwald-Winstein polarity
parameter, YGW, in water-methanol mixtures.
References and Notes
(1) Marcus, R. A. Annu. ReV. Phys. Chem. 1964, 15, 155, and references
therein.
(2) Hush, N. S. J. Chem. Phys. 1958, 28, 962.
(3) Marcus, R. A.; Sutin, N. Biochim. Biophis. Acta 1985, 811, 265.
(4) Sanchez Burgos, F.; Moya´, M. L.; Gala´n, M. Prog. React. Kinet.
1994, 19, 1.
3-
(5) After this rate-determinating step, S2O8 descomposes and pro-
duces SO42- + SO4-•. The SO4-• radical anion oxidizes a second ruthenium
complex in a rapid (non-rate-determining) step.
(6) Simonin, J. P.; Hendrawan, H. PCCP, 2001, 3, 4286.
(7) Rodriguez, A.; Lo´pez-Cornejo, P.; Muriel, F.; Sa´nchez, F.; Burgess,
J. Int. J. Chem. Kinet. 1999, 31, 485.
Figure 6. Plot of ln k′ versus the Grunwald-Winstein polarity
et
parameter, YGW, in water-methanol mixtures.
(8) Sa´nchez, F.; Rodriguez, A.; Muriel, F.; Burgess, J.; Lo´pez-Cornejo,
P. Chem. Phys. 1999, 243, 159.
(9) Laidler, K. J. Chemical Kinetics, 2nd ed.; McGraw-Hill: London,
1965; pp 202 ff.
(10) Marquardt, D. W. J. J. Soc. Pure Appl. Math. 1963, 11, 431.
(11) Roldan, E.; Dominguez, M.; Gonzalez-Arjona, D. Comput. Chem.
1986, 10, 187.
(12) Rodr´ıguez, A.; de la Rosa, F.; Gala´n, M.; Sa´nchez, F.; Moya´, M.
L. Photochem. Photobiol. 1992, 55, 367.
TABLE 7: Values of λex and k′ Obtained for Different
et
Water-Methanol Mixtures
% weight (methanol)
λ
ex (kJ mol-1
)
10-8k′ (s-1
)
et
5.68
10.20
18.37
26.53
30.64
39.15
22
23
25
27
29
34
5.5
4.8
4.1
3.5
3.3
2.8
(13) Berg-Brennan, C.; Subramanian, P.; Absi, M.; Stern, C.; Hupp, J.
T. Inorg. Chem. 1996, 35, 3719.
(14) Matamoros-Fontela, M. S.; Perez, P.; Lo´pez, P.; Prado-Gotor, R.;
De la Vega, R.; Sa´nchez, F. Ber. Bunsen-Ges. Phys. Chem. 1997, 101, 1452.
(15) Blum, L.; Hoye, J. S. J. Phys. Chem. 1977, 81, 1311.
(16) Olson, A. R.; Simonson, T. R. J. Chem. Phys. 1949, 17, 1167.
(17) Perez-Tejeda, P.; Franco, F. J.; Sa´nchez, A.; Morillo, M.; Denk,
C.; Sa´nchez, F. PCCP 2001, 3, 1271.
To have an idea of the accuracy of this estimation of λex,
consider Figure 5. In this figure, ln ket has been plotted versus
the Grunwald-Winstein polarity parameter, YGW, corresponding
to the water-methanol mixtures.27 A good linear plot is obtained
if the water point is excluded.
(18) Pe´rez-Tejeda, P.; Jime´nez Sindreu, R.; Lo´pez-Cornejo, P.; Sa´nchez
Burgos, F. Curr. Top. Solution Chem. 1997, 2, 49.
This behavior could be due to two reasons: the values of ket
corresponding to the mixtures are too low, or the value of ket
corresponding to the water must be lower than the value
obtained experimentally. Next, we can calculate the electron-
transfer constant of this process without the extra component
of the reorganization free energy for the water-methanol
mixtures. This electron-transfer constant, ket′, can be calculated
using the eq 23:
(19) Morillo, M.; Denk, C.; Perez, P.; Lopez, M.; Sa´nchez, A.; Prado,
R.; Sa´nchez, F. Coord. Chem. ReV. 2000, 204, 173 and references therein.
(20) Curtis, J. C.; Blackbourn, R. L.; Ennix, K. S.; Roberts, J. A.; Hupp,
J. J. Inorg. Chem. 1989, 28, 3791.
(21) (a) Hupp, J. T. Inorg. Chem. 1987, 26, 2657. (b) Blackbourn, R.
L.; Doorn, S. K.; Roberts, J. A.; Hupp, J. T. Langmuir 1989, 5, 696.
(22) (a) Matyushov, D. V. Mol. Phys. 1993, 79, 795. (b) Karasevskii,
A. I.; Matyushov, D. V.; Gorodyskii, A. V. Chem. Phys. 1990, 142, 1.
(23) Denk, C.; Morillo, M.; Sa´nchez-Burgos, F.; Sa´nchez, A. J. Chem.
Phys. 1999, 110, 473.
(24) Karki, L.; Lu, M. P.; Hupp, J. T. J. Phys. Chem. 1996, 100, 15637.
(25) Fu¨rholz, U.; Haim, A. Inorg. Chem. 1987, 26, 3243.
(26) In fact, the value corresponds to the Fe(bpy)32+. However, as this
value is small, its contribution to the total value of λin is not significant
(Terrettaz, S.; Becka, A. M.; Traub, M. J.; Fetlinger, J. C.; Miller, C. J. J.
Phys. Chem. 1995, 99, 11216).
kBT
h
(λ - λex + ∆G′)2
4(λ - λex)RT
k′ )
exp
(23)
et
(
)
The values of ket′ are given in Table 7, and plotted versus
YGW in Figure 6. It can be seen in this figure that the water
(27) Moya´, M. L.; Sa´nchez, F.; Burgess, J. Intl. J. Chem. Kinet. 1993,
25, 891 and references therein.