Reaction of copper(II) with ferrocene and 1,1′-dimethylferrocene in aqueoys acetonitrile: The copper(II/I) self-exchange rate

Article abstract of DOI:10.1021/ic048614i

The kinetics of the reactions of copper(II) with ferrocene (Fc) and 1,1′-dimethylferrocene (Dmfc) have been studied at 25°C in aqueous acetonitrile (AN) containing 50-97.5 vol % AN. With increasing % AN, the rate constant increases along with the driving-force for the reaction. The results are analyzed in terms of Marcus theory to estimate the Cu(II/I) electron self-exchange rate constant (K₁₁) for the system. Over the solvent range studied, the calculated k₁₁ changes from 1.1 × 10 ^-9 to 17 × 10^-9 M^-1 s^-1, with an average value of 5 × 10^-9. In addition, the structures of the trifluoromethanesulfonate salts of [Cu(AN)₄]⁺, [Cu(OH₂)₂(AN)₂]²⁺, and [Cu(AN) ₄]²⁺ are reported. It is found that the Cu-NCCH ₃ bond-length difference between the Cu(I) and Cu(II) oxidation states is only ～0.02 A.

Full text of DOI:10.1021/ic048614i

Inorg. Chem. 2005, 44, 1619−1625
Reaction of Copper(II) with Ferrocene and 1,1′-Dimethylferrocene in
Aqueous Acetonitrile: The Copper(II/I) Self-Exchange Rate
Japhet Irangu,† Michael J. Ferguson,‡ and Robert B. Jordan*,†
Department of Chemistry, and X-ray Crystallography SerVice Laboratory, UniVersity of Alberta,
Edmonton, Alberta, Canada T6G 2G2
Received October 5, 2004
The kinetics of the reactions of copper(II) with ferrocene (Fc) and 1,1
′-dimethylferrocene (Dmfc) have been studied
at 25 C in aqueous acetonitrile (AN) containing 50 97.5 vol % AN. With increasing % AN, the rate constant in-
°
−
creases along with the driving-force for the reaction. The results are analyzed in terms of Marcus theory to estimate
the Cu(II/I) electron self-exchange rate constant (k11) for the system. Over the solvent range studied, the calculated
10- to 17
9
×
10- M- s- , with an average value of 5
9
1
1
×
10- . In addition, the structures
9
k
11 changes from 1.1
×
]+, [Cu(OH
(AN)
]2 , and [Cu(AN)
+
]2+ are reported. It is found
of the trifluoromethanesulfonate salts of [Cu(AN)
that the Cu NCCH
4
2
)
2
2
4
−
3
bond-length difference between the Cu(I) and Cu(II) oxidation states is only
∼
0.02 Å.
Introduction
plexes and obtained an estimate of ∼2 × 10 M-1 s-1. More
-
4
5
1
recently, Sisley and Jordan studied the reduction of Cu(II)
Since the introduction of Marcus theory in the 1960s, it
has been recognized that knowledge of the rates of electron
self-exchange reactions is fundamental to understanding and
predicting the rates of outer-sphere electron-transfer reactions.
Consequently, the self-exchange rates have been measured
by direct methods for many solvated transition metal ions
and their complexes. For the first transition metal series, the
exchange rates in water are known for the common oxidation
states, with the glaring exception of the Cu(II/I) system.
Unless the rate is moderately fast, it is unlikely that this
system will ever be studied in water because of the instability
of aqueous Cu(I) with respect to disproportionation.
by Co(II)(sep) and found a self-exchange rate constant of
-7
-1 -1
∼
5 × 10
M
s
(sep ) 1,3,6,8,10,13,16,19-octaazabicyclo-
[
6.6.6]eicosane). These authors also corrected the E° values
for ionic strength effects and applied these to the results of
4
Davies to obtained self-exchange rate constants in the range
-
7
-1 -1
6
of (2-9) × 10
M
s . Espenson and co-workers studied
the oxidation of aqueous V(II) and Cr(II) by aqueous Cu-
II), and obtained rate constants of 26.6 and 0.17 M s ,
-
1
-1
(
respectively. These give self-exchange rate constants of 3
-
2
-6
-1 -1
×
10 and 7 × 10
M
s , respectively, from the Marcus
cross-relationship. The latter value is reasonably consistent
with the range calculated by Sisley and Jordan, whereas
5
The general area of Cu(II/I) redox chemistry has been
the V(II)/Cu(II) system would appear to be using an inner-
2
reviewed recently by Rorabacher. There have been several
7
sphere mechanism. Rorabacher and co-workers also con-
applications of the Marcus cross-relationship to estimate the
Cu(II/I) electron self-exchange rate in water. Sutin and co-
3+
cluded that the oxidation of Cu(I) by Co(TIM)(OH
2,3,9,10-tetramethyl-1,4,8,11-tetraazacyclotetradeca-1,3,8,-
0-tetraene) proceeds by an inner-sphere mechanism because
)
2 2
(TIM
)
3
workers studied the reaction of Cu(I) with various Ru(III)
1
polypyridyl complexes and estimated a rate constant of ∼1
5
it yields a large self-exchange rate constant of ∼2 × 10
for aqueous Cu(II/I). It would appear that the
aqueous Cu(II/I) self-exchange rate constant is in the range
-
5
-1 -1
4
×
10
M
s . Shortly thereafter, Davies measured the
-
1
-1
M
s
rates for Cu(I) reacting with several Ru(III) ammine com-
-
6
-7
-1 -1
of 10 -10
M
s , and the rate would not be competitive
*
Author to whom correspondence should be addressed. E-mail:
with disproportionation of aqueous Cu(I).
bob.jordan@ualberta.ca.
†
Department of Chemistry.
X-ray Crystallography Service Laboratory.
The situation is different in acetonitrile (AN), where Cu-
‡
8
(
I) is quite stable. Therefore, it is at least chemically feasible
(
1) Marcus, R. A. Annu. ReV. Phys. Chem. 1964, 15, 15. Marcus, R. A.
J. Chem. Phys. 1965, 43, 679. Marcus, R. A.; Sutin, N. Biochim.
Biophys. Acta 1985, 811, 265.
(5) Sisley, M. J.; Jordan, R. B. Inorg. Chem. 1992, 31, 2880.
(6) Parker, O. J.; Espenson, J. H. Inorg. Chem. 1969, 8, 185. Shaw, K.;
Espenson, J. H. Inorg. Chem. 1968, 7, 1619.
(7) Martin, M. J.; Endicott, J. F.; Ochrymowycz, L. A.; Rorabacher, D.
B. Inorg. Chem. 1987, 26, 3012.
(
(
2) Rorabacher, D. B. Chem. ReV. 2004, 104, 651.
3) Hoselton, M. A.; Lin, C.-T.; Schwartz, H. A.; Sutin, N. J. Am. Chem.
Soc. 1978, 100, 2383.
(4) Davies, K. M. Inorg. Chem. 1983, 22, 615.
1
0.1021/ic048614i CCC: $30.25
© 2005 American Chemical Society
Inorganic Chemistry, Vol. 44, No. 5, 2005 1619
Published on Web 01/26/2005

Irangu et al.
to measure directly the Cu(II/I) self-exchange rate in AN.
ylferrocene (Alfa Inorganics) were used as supplied. Ferrocene
9
(
Strem Chemicals) was purified by sublimation. The copper content
of the various products was determined by iodimetry.
Tetraaquacopper(II) triflate [Cu(OH (F CSO ] (I) was pre-
In fact, Manahan reported in 1967 that radiochemical tracer
-
1
methods gave a self-exchange rate constant of g0.3 M
s
-1
2
)
4
3
3 2
)
in AN. This value seems anomalously large as compared
pared typically by adding 5.0 mL (26.5 mmol) of 5.3 M triflic acid
to a slurry of 1.04 g (13.0 mmol) of cupric oxide in 25 mL of
water. The mixture was heated at ∼60 °C until the solid had
dissolved, and then filtered and evaporated to dryness on a steam
bath. The blue, crystalline product was redissolved in a minimum
volume of water on the steam bath and recrystallized by cooling.
This product was dissolved in acetonitrile (∼10 mL) and precipi-
tated with ether, filtered, and washed with ether and dried in air.
to more recent estimates in water, and this was confirmed
in our preliminary experiments which failed to detect any
Cu(I) NMR line broadening in the presence of Cu(II).
However, before attempting any direct measurements, it
obviously would be helpful to have some idea of the
magnitude of the rate of Cu(II/I) exchange to choose the
appropriate experimental method and time scale.
6
3
The present work describes experiments to estimate the
Cu(II/I) electron exchange rate in AN by applying the Marcus
cross-relationship to the reduction of Cu(II) with ferrocene
2 6 8 10 2
Anal. Calcd for CuC F H O S : Cu, 14.65; C, 5.54; H, 1.86.
Found: Cu, 14.50; C, 5.20; H, 1.67.
1
Anhydrous Cu(II) triflate, Cu(F CSO ) (II), was obtained as a
3
3 2
fine, white hygroscopic powder by heating the tetrahydrate salt in
(Fc) and 1,1′-dimethylferrocene (Dmfc) in AN/water mix-
air at ∼100 °C. This solid was stored in a vial with a plastic cap
tures. Reactions of ferrocenes are generally thought to be
outer-sphere, and necessary background information is
in a desiccator. Anal. Calcd for CuC
Found: Cu, 17.6; C, 6.30.
2 6 6 2
F O S : Cu, 17.5; C, 6.64.
+
available from studies of the Cu(II) and ferrocinium ion (Fc )
3 4 3 3
Tetraacetonitrilecopper(I) triflate [Cu(NCCH ) ](F CSO ) (III)
reduction potentials in AN/water mixtures by Cox and co-
17
was prepared by a modification of the methods by Ogura and
workers10 and the electron self-exchange studies in AN of
18
Jenkins and Kochi. A mixture containing 50 mL of acetonitrile,
+
11-13
+ 11
the Fc/Fc
and Dmfc/Dmfc
couples. In the present
1.0 g (2.3 mmol) of I, and 0.3 g (4.7 mmol) of copper foil was
stirred in a capped parafilm-sealed Erlenmeyer flask until the
solution turned colorless. Filtration on a 4-8 µ sintered glass frit
gave a clear solution. Addition of anhydrous ether produced a white
powder, which was collected by filtration under argon. Argon was
sucked through the product until it looked reasonably dry, and then
study, the driving force for the reaction is varied by changing
the reductant, but primarily by changing the AN/water
composition, and the variation of the rate will be analyzed
in terms of Marcus theory to obtain an estimate of the Cu-
(II/I) self-exchange rate constant.
it was sealed under argon. Anal. Calcd for CuC
9 3 12 4 3
F H N O S: Cu,
The speciation of solvated Cu(II) ions in AN/water solu-
16.86; N, 14.87; C, 28.69; H, 3.21. Found: Cu, 17.10; N, 14.18;
tions was studied by Funahashi and co-workers14 for [H
O]
between 0 and 0.84 M (98.5% AN), and they reported for-
2
C, 27.64; H, 2.98.
The Cu(II) solvates, [Cu(H O) (NCCH ) ](F CSO ) (IV) and
2 2 3 2 3 3 2
2
+
mation of [Cu(OH
2
)
n
+
(NCCH
3
)
6-n
]
(n ) 0-3) with
3 4 3 3 2
[Cu(NCCH ) (F CSO ) ] (V), were obtained as blue crystals by
[
Cu(OH
2
)
2
(NCCH
3
)
4
]2 as the dominant species for [H
2
O]
slow evaporation of acetonitrile solutions of the tetrahydrate (I)
and the anhydrous (II) Cu(II) triflates, respectively. The crystals
from the solution of the tetrahydrate were obtained in an air
atmosphere, whereas those from the solution of the anhydrous salt
were obtained under an argon atmosphere. Single crystals for the
structure determination were selected from the solution-crystal
mixture in the X-ray crystallography laboratory.
The AN/water solvent was made by transferring an appropriate
volume of doubly distilled water, and sometimes standardized aque-
ous perchloric or triflic acid, to a 500 mL or 1.00 L volumetric flask
and diluting to volume with AN (99.7% or 99.5%). Therefore, the
as low as 0.5 M (∼99% AN). For Cu(I), the formation
15
constants determined by Kamau and Jordan suggest that
+
Cu(OH
2
)(NCCH
3
)
3
is the dominant species for >50% AN,
+
but the point at which this converts to Cu(NCCH
)
3 4
is uncer-
16
63
tain. Our study of Cu(I) NMR line widths in AN revealed
that there is significant line broadening for >0.5 M H
gesting the formation of at least some Cu(OH
2
O, sug-
)(NCCH )
3 3
+
2
at this point, and that the latter is the dominant species for
the 50-97.5% AN of this study. The electrochemical studies
of Cox and co-workers10 show that the Cu(II/I) reduction
potential increases smoothly with increasing % AN (50-
%
AN refers to volume percentage. The acid added was prepared by
diluting the concentrated acid with doubly distilled water and analy-
zed by titration with 0.100 M NaOH. The mixed solvents were
stored in volumetric flasks and used within 2 days. The densities
and molarities as a function of volume % AN are given in the
Supporting Information.
100%) and do not suggest any abrupt change in species.
Experimental Section
Materials. Acetonitrile (Caledon, Fisher or BDH), perchloric
acid (Fisher), trifluoromethanesulfonic acid (triflic acid, Aldrich),
copper(II) nitrate trihydrate (Allied Chemicals), and l,1′-dimeth-
For kinetic studies, stock solutions of Cu(II) were prepared by
dissolving ∼1.0 g (∼2.3 mmol) of (I) or ∼0.6 g (∼2.5 mmol) of
Cu(NO
3
)
2
2
‚3H O in 50.0 mL of the appropriate solvent. The Cu(II)
(
8) Ahrland, S.; Nilsson, K.; Tagesson, B. Acta Chem. Scand. 1983, 37A,
93.
9) Manahan, S. E. Can. J. Chem. 1967, 45, 2451.
1
content was determined by standard iodimetry. Aliquots from these
solutions were diluted to 25.0 mL with the solvent and used for
the kinetic runs.
(
(
10) Cox, B. G.; Jedral, W.; Palou, J. J. Chem. Soc., Dalton Trans. 1988,
733.
Solutions of Fc and Dmfc were prepared by dissolving weighed
amounts of Fc (∼10 mg) or Dmfc (∼11 mg) in the appropriate
solvent in 25.0 mL volumetric flasks. Next, 10.0 mL aliquots of
these solutions were diluted in 50.0 mL with the same solvent to
give stock solutions for the kinetic runs.
(
(
11) Yang, E. S.; Chan, M.-S.; Wahl, A. C. J. Phys. Chem. 1980, 84, 3094.
12) Kirchner, K.; Dang, S.-Q.; Stebler, M.; Dodgen, H. W.; Wherland,
S.; Hunt, J. P. Inorg. Chem. 1989, 28, 3604.
(13) McManis, G. E.; Nielson, R. M.; Gochev, A.; Weaver, M. J. J. Am.
Chem. Soc. 1989, 111, 5533 and references there in.
(14) Inamo, M.; Kamiya, N.; Inada, Y.; Nomura, M.; Funahashi, S. Inorg.
Chem. 2001, 40, 5636.
(
(
15) Kamau, P.; Jordan, R. B. Inorg. Chem. 2001, 40, 3879.
16) Irangu, J.; Jordan, R. B. Inorg. Chem. 2003, 42, 3934.
(17) Ogura, T. Transition Met. Chem. 1976, 1, 179.
(18) Jenkins, C. L.; Kochi, J. K. J. Am. Chem. Soc. 1972, 94, 843.
1620 Inorganic Chemistry, Vol. 44, No. 5, 2005

The Copper(II/I) Self-Exchange Rate
Table 1. Summary of Crystallographic Data for [Cu(NCCH3)4](F3CSO3) (III), [Cu(H2O)2(NCCH3)2](F3CSO3)2 (IV), and [Cu(NCCH3)4](F3CSO3)2 (V)
III
IV
V
empirical formula
molecular mass
temp (K)
cryst syst
space group
a (Å)
C9H12CuF3N4O3S
376.83
193
monoclinic
P21/c (No. 14)
15.2062 (14)
14.1400 (13)
22.399 (2)
CuC6F6H10N2O8S2
479.82
193
CuC10F6H12N4O6S2
525.90
193
orthorhombic
Pbca (No. 61)
13.5406 (17)
10.8441 (14)
27.725 (4)
triclinic
P 1h (No. 2)
5.7426 (9)
7.2723 (11)
10.5221 (16)
79.855 (3)
84.183 (3)
78.537 (3)
422.92 (11)
1
b (Å)
c (Å)
R (deg)
â (deg)
94.527 (2)
γ (deg)
3
V (Å )
4801.2 (8)
12
4071.1 (9)
8
Z
Fcalcd (g cm-3)
cryst size, mm
collecn 2θ limit (deg)
wavelength (Å)
reflns collected
indep reflns
1.564
1.884
1.716
0.81 × 0.69 × 0.58
0.40 × 0.25 × 0.07
0.46 × 0.41 × 0.27
52.76°
52.84°
52.82°
0.71073
9759
6972
0.71073
1710
1523
0.71073
4170
3565
a
final R indices
2
2
R1 [Fo g 2σ(Fo )]
0.0827
0.2706
0.0420
0.1236
0.0391
0.1083
2
2
wR2 [Fo g -3σ(Fo )]
a
R1 ) ∑||Fo| - |Fc||/∑|Fo|; wR2 ) [∑w(Fo - Fc ) /∑w(Fo )]1/2.
2
2 2
4
Kinetic Measurements. Runs under pseudo-first-order, and a
reveal that the reactants Fc and Dmfc have maxima at 440
-
1
few under second-order, conditions were done in 50%, 80%, 90%,
and 432 nm, with extinction coefficients of 95 and 102 M
95%, or 97.5% AN. The rates were too fast in 99.5% AN to give
-1
cm , respectively, while the corresponding values for the
reliable data. Measurements were done on a Tritech Dynamic
Instruments stopped-flow spectrophotometer, in which the storage
and drive syringes, the observation cell, and all connecting tubing
are in a circulating, thermostated water bath at 25 ( 0.5 °C. The
temperature was monitored via a Fluke 2180A digital thermometer.
Most runs were under pseudo-first-order conditions with [Cu(II)]
-1
-1
oxidized forms are 616 and 644 nm, 482 and 357 M cm .
-1
The extinction coefficients show minor variations ((10 M
cm ) with the % AN in 80%, 90%, and 95% AN. For Cu-
-
1
(
II) triflate, the extinction coefficients at 616 and 644 nm
-1
-1
are 3.65 and 6.81 M cm , respectively. The latter decrease
significantly with decreasing % AN. These observations for
Cu(II) agree well with those of Funahashi and co-workers.14
Cu(I) is essentially transparent in the visible region. Overall,
these results led to the selection of 616 nm for observation
of the oxidation of Fc and Dmfc by Cu(II) for conditions of
>
10 [Fc] or [Dmfc].
The rate of formation of the Fc+ or Dmfc+ product was
monitored by measuring the change in absorbance with time at 616
nm. The voltage/time data from the photomultiplier were stored
on a transient recorder and transferred to a 486 PC using the
manufacturer’s software and stored as a text file. A locally
developed program read this file, converted the data to absorbance/
time, and fitted it by iterative least-squares to a first-order, or
second-order when appropriate, rate law to obtain the rate constants.
At least 120 points were used in the analysis of each run, and the
rate constants are the average of 8-12 kinetic runs.
[
Cu(II)] . [Fc] or [Dmfc].
It has been shown by Kratochvil and co-workers20 that
the reaction of Cu(II) with Fc in AN proceeds with 1:1
stoichiometry. For [Cu(II)] . [Fc] or [Dmfc], it is shown
here that the rate is first-order in [Cu(II)], and a few runs
under second-order conditions indicate that the rate is also
first-order in Fc.
X-ray Structures. The crystal data are summarized in Table 1.
For Cu(NCCH
3 2 2 2 3 3 2 3 4 3 3 2
) (OH ) (F CSO ) (IV) and Cu(NCCH ) (F CSO )
(
V), crystals were obtained by slow evaporation of acetonitrile
Although plots of the pseudo-first-order rate constant
versus [Cu(II)] were always linear, they sometimes showed
a significant intercept. It was found that this intercept could
be greatly reduced if g0.2 mM perchloric or triflic acids
were present. The effect is illustrated in Figures 1 and 2
for reactions in 80% and 95% AN, respectively.
Analogous plots for other runs are given in the Supporting
Information. The second-order rate constants (k12) reported
in Table 2 were obtained by least-squares fitting of the
pseudo-first-order rate constants (kobs) to eq 1.
solutions of I in air and of II under argon, respectively. A sample
of III was dissolved in acetonitrile, concentrated under argon, and
cooled at ∼5 °C to yield a white, crystalline product. In each case,
a crystal was selected for the structure determination. Data were
collected at -80 °C on a Bruker PLATFORM/SMART 1000 CCD
diffractometer using graphite-monochromated Mo KR (λ ) 0.71073
Å) radiation using 0.2° ω scans of 20 or 25 s exposures.19 Empirical
or multiscan (SADABS) methods were used to correct the intensity
data for decay and absorption. A summary of the crystal and
refinement data for all of these crystals is given in the Supporting
Information. Hydrogen atoms were not apparent in the electron
density maps and thus were not included in the fitting models.
21
kobs ) k + k [Cu(II)]
(1)
0
12
Results
It is important to note that the slopes (k12) of plots such as
those in Figures 1 and 2 are not affected by the addition or
The electronic spectra of the reactants and products in
acetonitrile (AN) (see details in the Supporting Information)
(
19) Programs for diffractometer operation, data collection, data reduction,
(20) Quirk, P. F.; Kratochvil, B. Anal. Chem. 1970, 42, 492. Kratochvil,
B.; Al-Daher, I. M. Talanta 1980, 27, 989.
and absorption correction were those supplied by Bruker.
Inorganic Chemistry, Vol. 44, No. 5, 2005 1621

Irangu et al.
the Cu(II/I) and Fc(+/0) or Dmfc(+/0) systems, and K12 is
the equilibrium constant for the redox reaction. The correc-
tion factor f12 is given by eq 3,
2
(
ln K + (w - w )/RT)
12 12 21
ln f )
(3)
1
2
2
4
ln (k k /Z ) + (w + w )/RT
11 22 11 22
where Z is the collision number (∼10 M-1 s-1), and the
individual work term corrections (wij) at 25 °C are given by
eq 4,
11
3
31.7zizj
w )
(4)
ij
ꢀsr(1 + r 8.50µ/ꢀ )
x
s
Figure 1. Variation of kobs with [Cu(II)] for reactions of Cu(II) triflate in
where r is the sum of the radii (Å) of the reaction partners,
+
8
(
0% AN at 25 °C with: Fc, no H added (b); Fc and 0.202 mM HClO4
s
µ is the ionic strength (M), and ꢀ is the dielectric constant
of the solvent. The overall work term correction in eq 2 is
given by eq 5,
+
O); Dmfc, no H added (9); Dmfc and 0.202 mM HClO4 (0).
-
(w + w - w - w )
12 21 11 22
W ) exp
(5)
1
2
(
)
2
RT
For the present system, it should be noted that w12 ) w22
)
0
because one of the reaction partners has z ) 0.
To estimate k11, known or good estimates of k22 and K12
will be used in eq 2, and the correction factors f12 and W12
will be calculated to give a best estimate of k11. The dominant
factor determining the variation of k12 with solvent composi-
tion is K12, and this can be obtained from the electrochemical
1
0
measurements of Cox and co-workers for the Cu(II/I) and
Fc(+/0) couples over the range of solvent compositions used
here. The same information is not available for Dmfc, but it
Figure 2. Variation of kobs with [Cu(II)] for reactions of Cu(II) triflate in
2
2
+
is known to have a reduction potential ∼0.10 V more
positive than Fc in acetonitrile, and that the difference in
reduction potential for several methyl-substituted ferrocenes
9
5% AN at 25 °C with Fc: no H added (O); 0.285 mM HClO4 (b); 0.423
mM triflic acid (9).
nature of the acid. This also is true if the acid is varied within
a particular set of runs, as can be seen from the results in
Table 2 in both 90% and 95% AN.
23
is the same in many solvents. Therefore, it will be assumed
that a difference of 0.10 V is maintained for the AN/water
solutions.
Although the ionic strength (µ) was not controlled, the
values of k12 in 80% AN (see Table 2) suggest that there is
no significant difference between 1.2 or 1.8 mM and 8-50
mM µ, as might be expected because one of the reactants is
uncharged. The values of k12 do change substantially with
The self-exchange rate constant (k22) for Fc(+/0) in aceto-
nitrile has been the subject of several recent studies; the
1
2
6
-1 -1
values of Kirchner et al. (k22 ) 9.3 × 10 M s , µ ) 0)
1
3
6
-1 -1
and McManis et al. (k22 ) 9.1 × 10 M s , µ ) 0.65
2
M) are in excellent agreement and show very little ionic
the solvent composition, increasing by a factor of ∼5 × 10
11
strength effect on k22. Earlier, Yang, Chan, and Wahl re-
ported values of 5.3 × 10 M
between 50% and 97.5% AN. This variation will be the
subject of the following discussion.
6
-1 -1
s
(µ ) 0.035 M) for
Discussion
(21) The source of the k0 term has not been exhaustively investigated. It is
not due to an impurity introduced with the Cu(II), because then it
would be proportional to [Cu(II)] and would simply make the rate
faster than the true Cu(II) oxidation rate. The latter possibility has
been checked by showing that a number of different preparations of
copper(II) triflate and copper(II) nitrate give the same values for k2.
Different sources and resublimation of Fc have no effect. The fact
It will now be shown that the variation of k12 with solvent
composition can be reasonably understood in terms of
Marcus theory and can be used to estimate the Cu(II/I)
electron-exchange rate for AN/water solvates. Some struc-
tural parameters for these solvates also are discussed with
regard to the inner-sphere reorganization energy for such
systems.
+
that k0 is supressed by H at first seems to suggest proton equilibria
+
of the reactants (protonation of Fc or formation of Cu(OH) ), but these
should be rapidly established equilibria and would not lead to eq 1.
Dioxygen is a possible oxidant for Fc, but the reaction is quite slow
in aqueous AN. The O2/Fc reaction would need to be activated by
some species in solution whose concentration either does not directly
affect the rate or is not proportional to the Cu(II) concentration.
(22) Nelsen, S. F.; Chen, L.-J.; Ramm, M. T.; Voy, G. T.; Powell, D. R.;
Accola, M. A.; Seehafer, T. R.; Sabelko, J. J.; Pladziewicz, J. R. J.
Org. Chem. 1996, 61, 1405.
1
The theory predicts that k12 is given by eq 2,
1/2
k ) (k k K f ) W
(2)
12
11 22 12 12
12
where k11 and k22 are the self-exchange rate constants for
1622 Inorganic Chemistry, Vol. 44, No. 5, 2005

The Copper(II/I) Self-Exchange Rate
Table 2. Kinetic Results for the Reaction of Cu(II) with Ferrocene (Fc) and 1,1′-Dimethylferrocene (Dmfc) in Aqueous Acetonitrile (AN) at 25 °C and
Variable Ionic Strength (µ)
k12, M- s-1 c
1
[
Cu(II)], mMa
range
µ, mM
range
+
[H ], mMb
%
AN
Fc
Dmfc
5
5
8
8
8
8
8
8
9
9
9
9
9
9
9
9
9
9
9
0
0
0
0
0
0
0
0
0
0
0
5
5
5
5
5
2.19-14.6
0
0
6.6-44
7.8-52
7.6-50
9.3-47
1.2
4.34 ( 0.07
3.95 ( 0.18
6.14 ( 0.40
6.84 ( 0.09
17.1 ( 0.6
15.0 ( 0.4
26.3 ( 0.9
26.4 ( 1.3
28.5 ( 0.5
d
2.61-17.4
2.48-16.5
3.09-15.6
0.385
0.202
0
0
0.254
0.254
0
0.096 × [Cu(II)]
0.103 × [Cu(II)]
0.0208 × [Cu(II)]
0
0.285
0.423
e
0.505
2.52-15.0
2.85-9.96
1.8
6.22 ( 0.15
5.63 ( 0.26
25.6 ( 0.5f
21.2 ( 0.4
24.2 ( 1.4
110 ( 3
d
7.8-45
8.6-30
7.8-52
7.3-48
7.5-50
6.6-47
7.7-50
8.0-51
8.1-54
7.6-51
8.1-61
6.3-25
5.9-24
d
2.51-16.7
2.34-15.6
2.33-15.7
2.21-1.6
2.46-16.4
2.52-16.8
2.68-17.9
2.52-16.8
2.64-19.8
2.04-8.15
1.98-7.91
23.8 ( 1.0
21.4 ( 2.4
21.3 ( 1.8
207 ( 17
203 ( 5
98.4 ( 3
101 ( 2
829 ( 33
872 ( 9
794 ( 21
795 ( 24
842 ( 19
7780 ( 380
8070 ( 260
g
185 ( 4
g
0.0095 × [Cu(II)]
178 ( 13
185 ( 3
g
0.025 × [Cu(II)]
5
7.5
7.5
0.071 × [Cu(II)]
195 ( 9
0.202
0
1970 ( 50
1790 ( 70
a
Triflate salt unless otherwise indicated. b Perchloric acid unless otherwise indicated. c Errors are one standard deviation from fitting kobs to eq 1. d Nitrate
salt. e With [Dmfc] ) 0.208 mM and analyzed by a second-order rate law. With [Fc] ) 0.266 mM and [Dmfc] ) 0.297 mM and analyzed by a second-
order rate law. Triflic acid.
f
g
Fc(+/0) and 8.3 × 10 M s-1 (µ ) 0.016 M) for Dmfc-
6
-1
(+/0). McManis et al. also found that k22 for Fc(+/0) has
only a ∼3-fold variation in a range of organic solvents.
22
Nelsen et al. have reported quite similar values for Fc(+/0),
Dmfc(+/0), and pentamethylferrocene(+/0) in AN. For the
present purpose of estimating k11 for Cu(II/I), we will assume
6
that Fc and Dmfc have the same value of k22 ) 9.3 × 10
-
1 -1
M
s
and that it is independent of the solvent composition.
It is now possible to determine if Marcus theory will even
approximately describe these systems. For this, it is conve-
nient to use the logarithmic form of eq 2 and substitute the
usual thermodynamic relationship between log(K12) and ∆E°
to obtain eq 6.
log(k ) )
1
2
0
.5 log(k k ) + 8.45∆E° + 0.5 log(f ) + log(W ) (6)
Figure 3. Variation of Log(k12) with DE for the reaction of Cu(II) in
aqueous acetonitrile (50-97.5%) with Fc (O) and Dmfc (b).
1
1
22
12
12
If one assumes, as a first approximation, that the f12 and W12
terms are insignificant, then eq 6 predicts that a plot of log-
(k12) versus ∆E° should be linear with a slope of 8.45, and
with k22 known, the intercept gives an estimate of k11. Such
Ideally, the values of k11 from Fc and Dmfc should be the
same, and they do agree to within a factor of <3; this
difference could be removed by decreasing the E° for Dmfc
by only 0.015 V. There does seem to be a persistent increase
in k11 with increasing % AN which might be attributed to
a plot is shown in Figure 3, and it is linear with a slope of
8
.7 ( 0.3, quite close to the theoretical prediction. The
2
replacement of coordinated H O by AN on Cu(II) and/or
Cu(I), but the differences are within the uncertainties usually
-
9
-1 -1
intercept of -0.93 ( 0.09 gives k11 ≈ 1.4 × 10
M
s .
The apparent close agreement of the plot in Figure 3 to
the theoretical prediction may be somewhat accidental,
because the nature of the Cu(II) solvate probably is changing
with the solvent composition. The simplest explanation for
this agreement would seem to be that the various Cu(II)
solvates have similar self-exchange rate constants. In any
case, the approximate analysis has been extended to include
the f12 and W12 factors. The w11 and w12 were calculated using
radii for the Cu(II) and Cu(I) solvates based on crystal
structures reported here, and estimates of Murguia and
ascribed to the theory. Overall, the k11 values have a range
-
9
-9
-1 -1
of (1.1-17) × 10 , with an average of 5 × 10
M
s .
The correlation in Figure 3 can be used to estimate that
4
-1 -1
k
12 ≈ 4.8 × 10 M
s
for the reaction of Cu(II) with Fc
1
0
in 100% AN (∆E° ) 0.646 V). This value can be used to
estimate that k11 ≈ 4 × 10 M-1
-
8
s
-1
in 100% AN. The
-1
-1
9
value of g0.3 M
s
in AN determined by Manahan seems
to have been affected by separation-induced exchange. For
(
23) Noviandri, I.; Brown, K. N.; Fleming, D. S.; Gulyas, P. T.; Lay, P.
A.; Masters, A. F.; Phillips, L. J. Phys. Chem. B 1999, 103, 6713.
24) Murguia, M. A.; Wherland, S. Inorg. Chem. 1991, 30, 139.
25) Venables, D. S.; Schmuttenmaer, C. A. J. Chem. Phys. 1998, 108,
4935.
2
4
+
+
Wherland for Fc and Dmfc ; dielectric constants were
(
(
25
taken from Venables and Schmuttenmaer. The results are
summarized in Table 3.
Inorganic Chemistry, Vol. 44, No. 5, 2005 1623

Irangu et al.
Table 3. Summary of Kinetic and Thermodynamic Data for the Reactions of Cu(II) with Ferrocene (Fc) and 1,1′-Dimethylferrocene (Dmfc) in
Aqueous Acetonitrile (AN)
k12, M- s-1
1
∆E°, V
log(K12)
Dmfc
log(f12)d
10 × k11, M s-1
9
-1
e
Dmfce
%
AN
Fca
Dmfca
Fcb
Dmfcc
Fc
Fc
Dmfc
Fc
5
0
4.15
6.21
22.2
194
16.1
25.4
103
826
7930
0.164
0.197
0.242
0.348
0.460
0.264
0.297
0.342
0.448
0.560
2.77
3.33
4.09
5.88
7.78
4.46
5.02
5.78
7.57
9.47
-0.068
-0.10
-0.15
-0.34
-0.62
-0.19
-0.24
-0.32
-0.57
-0.93
2.7
1.7
4.1
7.7
17
1.1
0.76
2.5
4.6
12
8
9
9
9
0
0
5
7.5
1880
a
b
Values are averages of those in Table 2 for each % AN. Values from ref 10 at 25 °C in 0.10 M NaClO4; the value at 97.5% AN has been obtained
c
d
by interpolation. Values assume a 0.10 V difference from Fc, based on ref 20. Calculated including w11 and w21 at µ ) 0.03 M with radii of 6.00, 6.02,
.75, and 4.25 Å for Cu(AN)x(OH2)y , Cu(AN)m(OH2)n , Fc , and Dmfc , respectively, and dielectric constants from ref 25. Calculated including the
2
+
+
+
+
e
3
log(W12) term, although it is small and relatively constant, varying from 0.064 to 0.088 for Fc, and 0.073 to 0.10 for Dmfc.
attainable conditions with triflate salts of [Cu(II)] ) [Cu(I)]
)
0.1 M, the estimated value of k11 predicts a half-time for
exchange of nearly 8 years, and it seems unlikely that anyone
will have the patience to directly measure the Cu(II/I) self-
exchange rate in acetontrile.
There have been many studies of the Cu(II/I) electron
exchange in various types of multidentate ligand complexes,
2
as reviewed recently by Rorabacher. For these systems, k11
-
2
5
-1 -1
ranges widely between 2 × 10 and 8 × 10 M s , but
none are nearly as small as the solvated aqueous and AN
systems. It was originally suggested by Vallee and Williams
26
that Cu(II/I) electron exchange normally should be slow
because of the much different coordination geometries of
the two oxidation states, tetragonally distorted octahedral for
Cu(II) and tetrahedral for Cu(I). A significant amount of the
work on model systems has been devoted to designing
ligands that would constrain the two oxidation states to have
similar geometries and therefore faster electron exchange
rates. It is somewhat ironic that some systems that seem to
2
7,28
most nearly meet this goal have the smallest k11 values,
and the largest k11 is for a system in which the geometries
are much different.29
Figure 4. Perspective drawing based on the X-ray crystal structure of the
trifluoromethanesulfonate salt of [Cu(OH2)2(NCCH3)2] (IV).
2+
Notwithstanding the difficulties encountered in structure-
rate correlations for Cu(II/I) electron exchange, the structures
above. The AN in III is typically not linearly coordinated,
with Cu-N-C angles ranging from 170.1° to 179.1° and
averaging 173.8°. Full details are given in the Supporting
Information.
The structures of the Cu(II) species, IV and V, provide
bond lengths that are helpful in assessing the inner-sphere
ligand reorganization involved in the electron-exchange
of several species relevant to the present study have been
+
determined. The structure of the triflate salt of Cu(AN)
4
(
III) is generally similar to the previously determined
30
31
structures of the perchlorate, hexafluorophosphate, and
tetrafluoroborate salts. All have three independent Cu-
32
+
(AN)
4
ions showing somewhat different degrees of distor-
process. In IV, one obtains Cu-NCCH
3
2
and Cu-OH bond
tion from a tetrahedral arrangement of the AN ligands. In
the triflate salt, the N-Cu-N angles range from 102.0° to
lengths in the same ion, and both IV and V provide Cu-N
+
bond lengths for comparison to Cu(AN)
4
(III). The
1
16.3° but average to the ideal tetrahedral angle of 109.4°.
The Cu-NCCH bond lengths range from 1.980 to 2.022 Å
with an average of 2.002 Å, which is close to the average of
.996 Å from the structures of the other salts mentioned
perspective views and bond lengths of the structures of IV
and V are shown in Figures 4 and 5, respectively.
In both structures, the bond angles at Cu are within 90 (
3
1
2°, and the average Cu-O bond length to triflate in V (2.391
Å) is similar to that in IV (2.395 Å). In IV, the AN is close
to linearly coordinated with Cu-N-C angles of 175.8°, but
in V, this angle varies between 161.9° and 177.0°, with an
(
26) Vallee, B. L.; Williams, R. J. P. Proc. Natl. Acad. Sci. U.S.A. 1968,
9, 498.
27) Xie, B.; Elder, T.; Wilson, L. J.; Stanbury, D. M. Inorg. Chem. 1999,
8, 12.
5
(
3
(
(
28) Xie, B.; Wilson, L. J.; Stanbury, D. M. Inorg. Chem. 2001, 40, 3606.
29) Krylova, K.; Kulatilleke, C. P.; Heeg, M. J.; Salhi, C. A.; Ochry-
mowycz, L. A.; Rorabacher, D. B. Inorg. Chem. 1999, 38, 4322.
30) Csoregh, I.; Kierkegaard, P.; Norrestam, R. Acta Crystallogr. 1975,
B31, 314.
2
average of 170.0°. In IV, the Cu-OH bond length (1.966
Å) is slightly shorter than the Cu-N bond length (1.975 Å),
and in V, the latter is slightly longer with an average of 1.989
Å. Full details are given in the Supporting Information.
(
(
(
31) Black, J. R.; Levason, W.; Webster, M. Acta Crystallogr. 1995, C51,
The Cu(II)-NCCH
reported by Torrelli et al. for two dimeric Cu(II) complexes
3
bond lengths are similar to those
623.
33
32) Jones, P. G.; Crespo, O. Acta Crystallogr. 1998, C54, 18.
1624 Inorganic Chemistry, Vol. 44, No. 5, 2005

The Copper(II/I) Self-Exchange Rate
π-back-bonding in the system. However, the C-N bond
lengths in Cu(I)-AN complexes show no evidence of
+
lengthening. In various Cu(AN)
4
salts, the average C-N
]-
). In the Cu(II) complexes, IV and V, where no
bond length is 1.13 Å, and the same is found for [Cu(AN)
2
3
4
(B(C
6
F
5
)
4
π-back-bonding is expected, the average length is 1.129 Å.
With regard to the Cu(II/I) electron self-exchange kinetics,
the theory suggests that one important consideration is the
change in Cu-N bond length between the two oxidation
states. The structures determined here indicate that this
change will be ∼0.02 Å (1.98 (Cu(II)) vs 2.00 (Cu(I))), so
that simple bond stretching and compression should not be
important factors in making this exchange so slow in AN,
and probably also in water. The model system studies
described above, and the ease of tetrahedral-octahedral
3
5
isomerization of Ni(II) complexes, also suggest that
coordination geometry differences between Cu(I) and Cu-
(II) may not be the controlling factors. Perhaps symmetry
differences in the model systems affect electronic factors,
which make electron exchange in the models so much faster
and seemingly unrelated to the ligand geometry.
Figure 5. Perspective drawing based on the X-ray crystal structure of the
trifluoromethanesulfonate salt of [Cu(NCCH3)4]2+ (V).
Acknowledgment. We are pleased to acknowledge the
financial support of the Natural Sciences and Engineering
Research Council of Canada, and the assistance of M. Wang
with one crystal structure determination.
in which the average equatorial Cu-NCCH
Å. There is longer distance of 2.355 Å to an axial NCCH
The Cu-N-C angle for the latter is 159.0°, while it ranges
between 164.3° and 175.3° for the equatorial NCCH ligands.
3
distance is 2.00
3
.
3
Supporting Information Available: X-ray crystallographic
details of the three compounds in CIF format, densities, mole
fractions and molarities of solvent mixtures, electronic spectra
(molar extinction coefficients), and dependence of kobs on [Cu(II)].
This material is available free of charge via the Internet at
http://pubs.acs.org.
These systems contain both 5- and 6-coordinate Cu(II), and
the other equatorial ligands are N-donors (pyridine, tertiary
amine), while the axial ligands are O-donors (phenol, THF,
perchlorate). It appears that the equatorial Cu(II)-NCCH
3
bond length is not very sensitive to the other donor types.
The relatively strong complexation of Cu(I) by AN in
water, and the stability of Cu(I) in pure acetonitrile, suggest
IC048614I
15
(34) Liang, H.-C.; Kim, E.; Incarvito, C. D.; Rheingold, A. L.; Karlin, K.
(
33) Torelli, S.; Belle, C.; Gautier-Luneau, I.; Pierre, J. L.; Saint-Aman,
D. Inorg. Chem. 2002, 41, 2209.
(35) Knoch, R.; Elias, H.; Paulus, H. Inorg. Chem. 1995, 34, 4032 and
E.; Latour, J. M.; Le Pape, L.; Luneau, D. Inorg. Chem. 2000, 39,
326.
references therein.
Inorganic Chemistry, Vol. 44, No. 5, 2005 1625