Kinetics and mechanism of the reduction of the molybdatopentaamminecobalt(III) ion by aqueous sulfite and aqueous potassium hexacyanoferrate(II)

Article abstract of DOI:10.1016/S0020-1693(02)00686-2

A detailed investigation on the oxidation of aqueous sulfite and aqueous potassium hexacyanoferrate(II) by the title complex ion has been carried out using the stopped-flow technique over the ranges, 0.01≤[S(IV)]_T≤0.05 mol dm^-3, 4.47≤pH≤5.12, and 24.9≤θ≤37.6°C and at ionic strength 1.0 mol dm^-3 (NaNO₃) for aqueous sulfite and 0.01≤[Fe(CN)₆^4-]≤0.11 mol dm^-3, 4.54≤pH≤5.63, and 25.0≤θ≤35.3°C and at ionic strength 1.0 or 3.0 mol dm^-3 (NaNO₃) for the hexacyanoferrate(II) ion. Both redox processes are dependent on pH and reductant concentration in a complex manner, that is, for the reaction with aqueous sulfite, k_obs={(k₁K₁K₂K₃+k ₂K₁K₄[H⁺])[S(IV)]_T]/ ([H⁺]²+K₁[H⁺]+K₁K ₂) and for the hexacyanoferrate(II) ion, k_obs={(k₁K₃K₄K₅+k ₂K₃K₆[H⁺])[Fe(CN)₆ ^4-]_T)/([H⁺]²+K₃[H ⁺]+K₃K₄). At 25.0°C, the value of k′₁ (the composite of k₁K₃) is 0.77±0.07 mol^-1 dm³ s^-1, while the value of k′₂ (the composite of k₂K₄) is (3.78±0.17)×10^-2 mol^-1 dm³ s^-1 for aqueous sulfite. For the hexacyanoferrate(II) ion, k′₁ (the composite of k₁K₅) is 1.13±0.01 mol^-1 dm³ s^-1, while the value of k′₂ (the composite of k₂K₆) is 2.36±0.05 mol^-1 dm³ s^-1 at 25.0°C. In both cases there was reduction of the cobalt(III) centre to cobalt(II), but there was no reduction of the molybdenum(VI) centre. k₂₂, the self-exchange rate constant, for aqueous sulfite (as SO₃^2-) was calculated to be 5.37×10^-12 mol^-1 dm³ s^-1, while for Fe(CN)₆^4-, it was calculated to be 1.10×10⁹ mol^-1 dm³ s^-1 from the Marcus equations.

Full text of DOI:10.1016/S0020-1693(02)00686-2

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Inorganica Chimica Acta 331 (2002) 279–289
Kinetics and mechanism of the reduction of the
molybdatopentaamminecobalt(III) ion by aqueous sulfite and
aqueous potassium hexacyanoferrate(II)
Alvin A. Holder a, Tara P. Dasgupta b,*
a Department of Biological and Chemical Sciences, Uni6ersity of the West Indies, Ca6e Hill Campus, PO Box 64, Bridgetown,
St. Michael, Barbados
b Department of Chemistry, Uni6ersity of the West Indies, Mona Campus, Mona, Kingston 7, Jamaica
Received 22 June 2001; accepted 12 November 2001
Dedicated to Professor A.G. Sykes
Abstract
A detailed investigation on the oxidation of aqueous sulfite and aqueous potassium hexacyanoferrate(II) by the title complex
ion has been carried out using the stopped-flow technique over the ranges, 0.015[S(IV)]T50.05 mol dm−3, 4.475pH55.12,
and 24.95q537.6 °C and at ionic strength 1.0 mol dm−3 (NaNO3) for aqueous sulfite and 0.015[Fe(CN)64−]50.11 mol
dm−3, 4.545pH55.63, and 25.05q535.3 °C and at ionic strength 1.0 or 3.0 mol dm−3 (NaNO3) for the hexacyanoferrate(II)
ion. Both redox processes are dependent on pH and reductant concentration in a complex manner, that is, for the reaction with
aqueous sulfite, kobs={(k1K1K2K3+k2K1K4[H+])[S(IV)]T]/([H+]2+K1[H+]+K1K2) and for the hexacyanoferrate(II) ion, kobs
=
{(k1K3K4K5+k2K3K6[H+])[Fe(CN)64−]T)/([H+]2+K3[H+]+K3K4). At 25.0 °C, the value of k% (the composite of k1K3) is
1
0.7790.07 mol−1 dm3 s−1, while the value of k% (the composite of k2K4) is (3.7890.17)×10−2 mol−1 dm3 s−1 for aqueous
2
sulfite. For the hexacyanoferrate(II) ion, k% (the composite of k1K5) is 1.1390.01 mol−1 dm3 s−1, while the value of k% (the
1
2
composite of k2K6) is 2.3690.05 mol−1 dm3 s−1 at 25.0 °C. In both cases there was reduction of the cobalt(III) centre to
cobalt(II), but there was no reduction of the molybdenum(VI) centre. k22, the self-exchange rate constant, for aqueous sulfite (as
SO32−) was calculated to be 5.37×10−12 mol−1 dm3 s−1, while for Fe(CN)64−, it was calculated to be 1.10×109 mol−1 dm3
s−1 from the Marcus equations. © 2002 Elsevier Science B.V. All rights reserved.
Keywords: Redox; Ferrocyanide; Molybdenum(VI); Aqueous sulfite; Cobalt(III)
1. Introduction
ligand hydroxide on dissolved SO2 to form an O-
bonded sulfito complex, a reaction which is readily
reversed by immediate acidification [1–5]. Metal-to-
oxygen bonding is not involved in this reversible pro-
cess as confirmed by NMR measurements [6].
Subsequent reactions in the cobalt(III) systems com-
prise O-bonded to S-bonded isomerisation, internal re-
dox, sulfite ion addition, or a combination of these
processes depending on the pH and the nature of the
N4 or N5 ligand grouping [1].
The hexacyanoferrate(II) anion on the other hand
can reduce some pentaamminecobalt(III) complexes to
Co(II) via an outer-sphere electron transfer step [7]. In
the past, the reductions of a series of substituted (pyri-
dine)pentaamminecobalt(III) complexes by hexacyano-
ferrate(II) proceed via the formation of an ion-pair,
Over the past 2 decades a number of systems have
been studied in our laboratory and by collaborators
elsewhere that involve the reactions of various aqua
transition metal complex ions with ‘free’ sulfite in
aqueous solution. The studies reported include the reac-
tions of the aquapentaammine complexes of cobalt(III)
[1–3], rhodium(III) [4], platinum(IV) [5], and chromiu-
m(III) [4], along with (tren)Co(OH2)23+ (tren=2, 2%,
2¦-triaminotriethylamine) [3]. The kinetic data show
that in each instance the most significant first step in
the overall process is very rapid nucleophilic attack by
* Corresponding author. Fax: +1-876-977 1835.
E-mail address: tara@uwimona.edu.jm (T.P. Dasgupta).
0020-1693/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved.
PII: S0020-1693(02)00686-2

280
A.A. Holder, T.P. Dasgupta / Inorganica Chimica Acta 331 (2002) 279–289
followed by internal electron transfer within the ion-
pair [8]. It is postulated that the ion-pairs feature
approach by Fe(CN)64− on the ammonia side of the
cobalt(III) complexes [8]. The electron transfer process
is assumed to be adiabatic and the variations in rate are
associated with changes in the reduction potentials
and/or rate constants for self-exchange of the
cobalt(III) complexes [8].
of the complex of known concentration were prepared
in volumetric flasks (10 cm3). The ionic strength of each
solution was adjusted to the required value with appro-
priate amounts of NaNO3 and the flasks were ther-
mostatted for 10 min before introducing the solutions
into the syringes of the stopped-flow apparatus. The
apparatus was equilibrated at the reaction temperature
for at least 0.5 h prior to use and the solutions were
kept in one of the thermostatted drive syringes for 5
min before each experiment.
The title complex {[(H3N)5CoOMoO3]+} is binuclear
with a cobalt(III) centre and a molybdenum(VI) centre,
so it is possible that one or both metal centres can be
reduced by both reductants, that is, Co(III) to Co(II),
Mo(VI) to Mo(V) (or even lower oxidation states). Also
it is possible that there could be anation by the aqueous
sulfite followed by internal redox depending on the pH.
Clearly both reactions with aqueous sulfite and the
hexacyanoferrate(II) (ferrocyanide) anion are of vital
importance.
The other syringe contained the respective reducing
agent, buffer (potassium hydrogen phthalate–NaOH or
CH3CO2Na–CH3CO2H), and supporting electrolyte
(NaNO3). This syringe with its contents was also pre-
thermostatted at the desired temperature. Both reac-
tants were then mixed in the stopped-flow
spectrophotometer after triggering. Na2H2EDTA (with
the reductant, supporting electrolyte, and buffer) was
used in the reaction involving Fe(CN)64− so as to
2+
(aq)
sequester the Co
formed [7]. Constant ionic strength
was maintained at 1.0 mol dm−3 (NaNO3) in all cases
(or 3.0 mol dm−3 in one case for the reaction with the
ferrocyanide anion). The NaNO3 solution was stan-
dardised by an ion-exchange method using Dowex 50
W-X8 (50 mesh, H+ form) resin. The redox processes
were followed at 524 nm, where the largest absorbance
change occurred. An excess of reductant was used in all
cases to ensure pseudo-first order conditions.
The kinetic data were collected and processed with a
Hi-Tech Scientific IS-1 software suite V 1.0a. The
pseudo-first order rate constants (kobs) were determined
by a non-linear least squares regression to fit the curve
of the photomultiplier voltage versus time. The re-
ported rate constants are an average of at least three
kinetic runs. The standard deviation for each kobs is
95%. The pH of each solution was measured on an
Orion Research EA 920 Expandable Ion Analyser,
fitted with a Cole Partner combination electrode.
2. Experimental
2.1. Materials
All reagents were of analytical grade (BDH). Ultra-
pure water, obtained by deionising distilled water using
a Milli-Q Reagent Grade water system, was used for
preparative work and to make up solutions for all
physical measurements. Solid Na2S2O5 (BDH) was the
source of aqueous sulfite; this salt is very stable in the
solid form but hydrates rapidly and completely when
dissolved in water to yield aqueous sulfite [1].
2.2. Preparation of the complex
[(H3N)5CoOMoO3]ClO4 was prepared by the method
outlined previously [9]. Visible spectrum: umax (nm (0.1
mol dm−3 Na2MoO4) 360 and 526 (m (dm3 mol−1
cm−1) 61 and 92). Lit. [9]: umax (nm (0.1 mol dm−3
Na2MoO4) 360 and 526 (m (dm3 mol−1 cm−1) 61.3 and
91.7).
2.4. Stoichiometry
The redox stoichiometry [reductant: complex] was
determined by measuring the absorbance at 416 nm (for
Fe(CN)64−) and 524 nm (for aqueous sulfite) of
buffered solutions containing the complex at a fixed
concentration while varying added reductant, then de-
termining the break in the plot of absorbance versus the
ratio, [complex]: [reductant].
2.3. Kinetic measurements
All visible and ultraviolet spectra were recorded with
either a Pye Unicam Model PU 8800 or a Hewlett–
Packard 8452A diode array spectrophotometer. All ki-
netic measurements were made using a Hi-Tech SF-51
stopped-flow spectrophotometer interfaced with a com-
puter. The spectrophotometer syringes were immersed
in a water-bath linked to a thermostat system (Haake
D8) capable of maintaining temperatures within 9
0.02 °C.
3. Results and discussions
3.1. Reduction with aqueous sulfite
For the electron transfer reactions involving aqueous
sulfite solution or K4Fe(CN)6 (potassium hexacyanofer-
rate(II)) the following was carried out: Stock solutions
3.1.1. Nature of the reaction
On reacting [(H3N)5CoOMoO3]+ in aqueous sulfite
solutions at pH 5.29 (potassium hydrogen phthalate–

A.A. Holder, T.P. Dasgupta / Inorganica Chimica Acta 331 (2002) 279–289
281
Fig. 1. Repetitive scan for the reduction of [(H3N5)CoOMoO3]+ by aqueous sulfite at 23.8 °C. [complex]=1×10−3 mol dm−3, [S(IV)]=0.05
mol dm−3, I=1.0 mol dm−3 (NaNO3), pH 5.66 (buffer=CH3CO2H–CH3CO2Na), cycle time=25 s.
sodium hydroxide buffer) there was an immediate yel-
low coloration, which slowly got paler with time. At the
We favour direct reduction by the SO32− ligand (Eq.
−
’
(2)), with the formation of the radical anion [13], SO3
2+
−
’
end of the reaction a pale pink solution left behind. The
and Co(aq) . The SO3 radical anion is then scavenged
pale pink solution was due to the formation of Co
,
by the [(H3N)5CoOSO2]+ ion. Analyses of the final
reaction mixture confirmed the presence [10] of Co
2+
(aq)
2+
(aq)
which was identified by the thiocyanate–acetone test
[10]. Molybdate(VI) was tested in the solution by using
the molybdyl ‘oxinate’ method [11]; this proved positive
for molybdate(VI). Fig. 1 shows a repetitive scan of the
reaction over the wavelength range. Preliminary studies
of the reaction of aqueous sulfite with the title complex
ion indicate that there is a uniphasic reaction at 524
at concentrations exactly equal to the initial concentra-
tions of the Co(III) complex, and this finding was
independent of reaction conditions. The identity of the
sulfur-containing reaction product with aqueous BaCl2
Table 1
nm, resulting in the reduction of [(H3N)5CoOMoO3]+
Stoichiometry of the reaction between [(H3N)5CoOMoO3]+ and
aqueous sulphite at 25.0 °C, pH 5.64 (CH3CO2Na–CH3CO2H
2+
(aq)
to Co
.
buffer), I=1.0 mol dm−3 (NaNO3), [complex]=2×10−3 mol dm−3
u=524 nm, cell path length=1.00 cm
,
3.2. Stoichiometry of the reaction
[S(IV)]T/[complex]
Absorbance
The stoichiometric data in Table 1 are consistent
with the reaction summarised in the following
equations:
0.0625
0.125
0.250
0.375
0.148
0.123
0.100
0.065
0.025
0.024
0.025
0.023
0.024
0.023
0.028
0.026
0.026
0.024
0.030
2[(H3N)5CoOMoO3]+ +2H2O+2SO2
a
0.500
X 2[(H3N)5CoOSO2]++4H++2MoO4
(1)
(2)
2−
1.000
1.500
2.000
2.500
3.000
3.500
4.000
4.500
5.000
5.500
[(H3N)5CoOSO2]+“Co(aq) 2+ +5NH3+SO3
−
−
’
[(H3N)5CoOSO2]++SO3
’
2−
“Co(aq) 2+ +5NH3+SO2+SO4
(3)
(4)
Overall:
2[(H3N)5CoOMoO3]++2H2O+SO2“2Co(aq)
2+
+6NH3+4NH4 ++2MoO4 2− +SO4
a Break point occurs at [S(IV)]T/[complex]=0.50.
2−

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A.A. Holder, T.P. Dasgupta / Inorganica Chimica Acta 331 (2002) 279–289
Table 2
Pseudo-first order rate constants for the reaction between
[(H3N)5CoOMoO3]+ and aqueous sulfite
[S(IV)]T (mol
q=24.9 °C
q=31.8 °C
103 kobs (s−1
q=37.6 °C
102 kobs (s−1
)
dm−3
)
103 kobs (s−1
)
)
0.01
0.02
0.025
0.03
0.035
0.04
–
3.25
–
–
8.22
–
9.31
–
0.915
1.60
–
2.11
–
2.34
–
2.68
1.76 (2.93) a
– (3.17)
2.39 (3.47)
– (3.60)
2.84 (3.78)
– (3.98)
0.045
0.05
3.35 (4.13)
10.3
Scheme 1.
Variation in [S(IV)]T, u=524 nm, [complex]=0.5×10−3 mol dm−3
,
I=1.0 mol dm−3 (NaNO3), pH 4.88 (potassium hydrogen phthalate–
NaOH buffer).
a Values in parentheses are at pH 5.34.
2+
(aq)
was inconclusive as Ba
and also MoO42− [12].
precipitates SO42−, SO32−
It is quite interesting to note that only the cobalt(III)
centre of the binuclear title complex ion was reduced to
cobalt(II) by aqueous sulfite during the redox process.
3.3. Aqueous sulfite, temperature and pH dependence of
the reaction
Kinetic runs were carried out over the ranges, 0.015
[S(IV)]T50.05 mol dm−3
,
4.475pH55.12, and
Fig. 2. A plot of kobs vs. [S(IV)] for the reduction of [(H3N)5-
CoOMoO3]+ by aqueous sulfite at 37.6 °C.
24.95q537.6 °C ranges, and at ionic strength 1.0 mol
dm−3 (NaNO3). Individual kinetic runs showed first-
order kinetics in [complex] for the uniphasic reaction.
The pseudo-first order rate constants (kobs) for the
reaction at the various [S(IV)]T, temperatures, and pH
are shown in Tables 2 and 3. The rate of the reaction
increases with increasing [S(IV)]T and tends to reach a
saturation point at high [S(IV)]T. A behaviour such as
this, is indicative of an ion-pair formation as shown in
Scheme 1, where
kobs=k2K4[S(IV)]/(1+K4[S(IV)])
(5)
A plot showing the saturation behaviour is shown in
Fig. 2, from which k2=(5.2990.32)×10−2 s−1 and
K4=21.191.8 mol−1 dm3 s−1 are calculated (data in
Table 2 at 37.6 °C) after carrying out linear regression
on the inverse of Eq. (5), where the slope, 1/(k2K4) and
the intercept, 1/k2. Over the pH range the main existing
Table 3
Pseudo-first order rate constants for the reaction between [(H3N)5CoOMoO3]+ and aqueous sulfite
pH
q=25.0 °C
103 kobs (s−1
pH
q=31.2 °C
103 kobs (s−1
pH
q=36.4 °C
102 kobs (s−1
)
)
)
–
–
–
–
4.65
4.74
4.83
4.92
–
–
4.47
1.28
1.39
1.58
1.72
1.87
1.99
2.15
2.34
4.50
4.60
4.71
4.82
4.92
5.03
5.07
2.08
2.25
2.54
2.79
2.95
3.12
13.32
4.53
4.64
4.75
4.82
4.94
5.01
15.12
5.56
6.14
6.83
7.93
8.73
9.72
5.02
15.10
Variation in pH and temperature, u=524 nm, [complex]=0.5×10−3 mol dm3, I=1.0 mol dm−3 (NaNO3), [S(IV)]T=0.045 mol dm−3
Buffer=potassium hydrogen phthalate–NaOH.
,

A.A. Holder, T.P. Dasgupta / Inorganica Chimica Acta 331 (2002) 279–289
283
sulfite species are the HSO3− and SO32− ions, while
[(H3N)5CoOMoO3]+ and [(H3N)5CoOMoO2(OH)]2+
where [S(IV)]T represents the total sulfite concentration.
The expression can be rearranged to give:
,
exist in equilibrium [9], but since the pK1 of
[(H3N)5CoOMoO2(OH)]2+ is 2.09; the deprotonated
species, [(H3N)5CoOMoO3]+, is the reactive species in
the reaction as over the pH range and it exists in
\99% as the predominant cobalt(III) species. The ob-
served pseudo-first order rate constants, kobs, increase
with an increase in pH (Table 3), and this observation
may be interpreted in terms of the reactive species via
the proposed mechanism in Scheme 1 where K1=
1.26×10−2 mol dm−3 and K2=5.01×10−7 mol
dm−3 at 25 °C [2]. Based on the increase of kobs with
pH it can be deduced that SO32− is the more reactive
species in the electron transfer reaction; so the k1 path
is the main contributing path over the pH range.
The proposed mechanism given in Scheme 1 leads to
the expression:
{kobs([H+]2+K1[H+]+K1K2)[S(IV)]T−1
=k1K1K2K3+k2K1K4[H+]
}
(7)
A plot of the left hand side of Eq. (7) versus [H+] is
linear in the pH range 4.475pH55.12, the slope being
k2K1K4 and intercept being k1K1K2K3. A plot at 25.0 °C
shown in Fig. 3 is linear over the pH range. A linear
regressional analysis was carried out and due to the
inability to separate k1 from K3 and k2 from K4, it was
necessary to combine k1 and K3 to give k%, and to
1
combine k2 and K4 to give k%. The rate and activation
2
parameters, along with the pK1 and pK2 values are [2]
shown in Table 4.
In our work the separation of the equilibrium con-
stant and the rate constant for the electron transfer has
proven to be difficult. This is due to the equilibrium of
the two reactive species, namely, HSO3− and SO32−. It
would not be correct to neglect the contribution from
HSO3− in the k2 path (see Scheme 1).
k
obs={(k1K1K2K3+k2K1K4[H+])[S(IV)]T}
/([H+]2+K1[H+]+K1K2)
(6)
At 25.0 °C the value of k% is 0.7790.07 mol−1 dm3
1
s
−1, while the value of k% is (3.6090.18)×10−2
2
mol−1 dm3 s−1; so one can see that SO32− reacts about
21 times faster than HSO3−. The transition state in-
volving HSO3− is more ordered than that involving
SO32− as can be seen from the respective values for
entropy of activation, the values being DS"2 =116988
J mol−1 K−1 and DS"1 =204927 J mol−1 K−1
respectively.
,
We can compare our studies with electron transfer
reactions involving sulfite and other Co(III) complexes.
What is noticeable is that after the formation of the
ion-pair in Scheme 1 there is intermolecular electron
transfer. The rate constant for the intramolecular elec-
tron transfer [1] of the complex, [(H3N)5CoOSO2]+,
after SO2 addition to [(H3N)5CoOH2]3+, within the pH
range 3–7, is 1.4×10−2 −1. The activation parame-
s
ters are DH" =112.5 kJ mol−1 and DS" is 96.7 J
mol−1 K−1 at 25 °C. For [(H3N)5CoSO3]+, the rate [5]
constant is ꢀ1×10−4 −1. Our rate of electron trans-
s
Fig. 3. A plot of [kobs([H+]2+K1[H+]+K1K2][S(IV)]T−1] vs. [H+
]
fer by SO32− occurs at a rate of 0.77 mol−1 dm3 s−1 at
25.0 °C, which is faster than either of the electron
transfer reaction involving either Co(III) complex. The
for the reduction of [(H3N)5CoOMoO3]+ by aqueous sulfite at
25.0 °C.
activation parameters (DH" and DS") for the SO32−
,
Table 4
Rate parameters and pK values a for the reaction between
[(H3N)5CoOMoO3]+ and aqueous sulfite
term (k%) during the electron transfer process is com-
1
parable with those for the [(H3N)5CoSO3]+ system.
The [(tren)Co(OH2)(OSO2)]+ complex undergoes
[2,5,13] only a redox reaction for pHB5 but at higher
pH values shows evidence for the disappearance of the
redox reaction, while addition of a second sulfite anion
yields a stable complex of stoichiometry [(tren)Co-
(SO3)2]−, which predominates at a pH of 7.2 or higher
[13].Similarly, the bis(ethylenediamine) species, cis-
[(en)2Co(OSO2)]+ exhibits [14] redox over the pH
ranges 3–7 as the only observable secondary process.
q (°C)
k% (mol−1 dm3
102 k% (mol−1 dm3
pK1 pK2
1
2
s−1
)
s−1
)
25.0
31.2
36.4
0.7790.07
2.6390.10
5.8590.52
3.6090.18
6.8590.33
21.5491.28
1.90 6.30
1.98 6.30
2.03 6.30
DH"1 =13498 kJ mol−1; DH"2 =116927 kJ mol−1; DS"1 =2049
27 J mol−1
a Ref. [2].
K .
−1; DS"2 =116988 J mol−1 K−1

284
A.A. Holder, T.P. Dasgupta / Inorganica Chimica Acta 331 (2002) 279–289
Table 5
transfer between the cobalt(III) centre and the sulfito
ligand.
The activation parameters in Table 5 are very similar
and can be used in an isokinetic plot of DH" versus
DS" since
Summary of the activation parameters for various redox reactions
involving some cobalt(III) complexes and sulfite (‘free’ and co-ordi-
nated) in aqueous solution
a
Complex
DH"
DS"
Reference
(kJ mol−1
)
(J mol−1 K−1
)
DH" =DG"o +ioDS"
(8)
[(H3N)5CoOSoO2]+ (1)
112.590.8 96.79117.6 [2]
where io is the isokinetic temperature and DG"o is the
intrinsic free energy of activation. Fig. 4 shows such a
plot where the linearity proves that a common mecha-
nism exists 15 for the sulfito cobalt(III) complexes and
the reaction involving aqueous sulfite and the title
complex ion, with DG"o =10495 kJ mol−1 and io=
144951 K.
[(tren)Co(OH2)(OSO2)]+ (2) 101.3934.3 34.3927.6
[5]
[(phen)2Co(SO3H)SO3] (3) 104.699.6
4.6929.3
[16]
[16]
[16]
[(bpy)2Co(SO3H)SO3] (4)
[(phen)2Co(SO3H)-
(OH2)]2+ (5)
132.692.1 91.696.7
118.497.9 51.5924.3
[(H3N)5CoOMoO3]+ (6)
[(H3N)5CoOMoO3]+ (6)
A (7)
13498
116927
117.695.9 117.690.4
204927
116988
this work
this work
[17]
A, [(H3N)3Co(m-OH)2(m-SO3)Co(NH3)3]2+
.
3.4. Reduction with hexacyanoferrate(II)
a Each complex is numbered in Fig. 4.
3.4.1. Nature of the reaction
On mixing Fe(CN)64− and [(H3N)5CoOMoO3]+ in
aqueous solution a precipitate (presumably cobalt(II)
hexacyanoferrate(II) and/or cobalt(II) hexacyanofer-
rate(III)) was formed, and, therefore, homogeneous
kinetic measurements were precluded. However, when
disodium
dihydrogen
ethylenediaminetetraacetate
(Na2H2EDTA) was added to the solution to complex
the cobalt(II) formed, no precipitate was produced [7].
A repetitive scan for the reaction at 25.0 °C is shown in
Fig. 5, where an increase in absorbance is observed.
3.5. Stoichiometry of the reaction
The stoichiometric data in Table 6 are consistent
with the reaction summarised in the following equation:
Fe(CN)6 4− +[(H3N)5CoOMoO3]++H2EDTA2−
Fig. 4. An isokinetic plot of the activation parameters for various
redox reactions involving some cobalt(III) complexes and sulfite
(‘free’ and co-ordinated) in aqueous solution.
+3H+“Fe(CN)6 3− +CoEDTA2− +5NH+4
2−
+MoO4
(9)
Meanwhile, the long chain tetraethylenepentaammine
(tetren) analogue of ab S-[(tetren)Co(OSO2)]+, under-
goes a slow internal rearrangement to the S-bonded
form with no evidence for redox even at elevated
temperatures [3]. There is evidence of a complex ana-
tion reaction by aqueous sulfite at much higher pH with
the title complex ion, with the production of yellow
cobalt(III) complex [15].
A summary of data concerning the redox reactions of
a selection of sulfito cobalt(III) complexes is shown in
Table 5. As depicted in Table 5 the activation parame-
ters found for the m-sulfito species compares reasonably
well with those of the mononuclear systems implying a
similarity in nature of the mechanisms. However, it is
believed that the m-sulfito species undergoes a two
electron transfer process with the reduction of the two
cobalt(III) centres and the simultaneous oxidation of
S(IV) to S(VI). This contrasts with the mononuclear
cobalt(III) sulfito species which involves one-electron
Eventually a reddish purple colour is produced over
a period of hours. The formation of the reddish purple
colour is straightforward. The Fe(CN)63− and
CoEDTA2− produced in Eq. (9) undergo an electron
transfer reaction [8] that produces purple CoEDTA−.
This reaction is very slow and does not interfere with
the reaction of interest, Eq. (9).
Fe(CN)6 2− +CoEDTA2−
“CoEDTA−+Fe(CN)6
(10)
4−
The purple product of CoEDTA− was identified
spectrophotometrically.
3.6. Aqueous potassium hexacyanoferrate,
temperature and pH dependence of the reaction
Kinetic runs were carried out over the ranges, 0.015
[Fe(CN)64−]50.11 mol dm−3, 4.545pH55.63, and

A.A. Holder, T.P. Dasgupta / Inorganica Chimica Acta 331 (2002) 279–289
285
Fig. 5. Repetitive scan for the reduction of [(H3N)5CoOMoO3]+ by Fe(CN)64− at 25.0 °C. [complex]=0.5×10−3 mol dm−3, [Fe(CN)64−]=
0.025 mol dm−3, I=1.40 mol dm−3 (NaNO3), pH 5.51 (buffer=CH3CO2H–CH3CO2Na), cycle time, 25 s.
25.05q535.3 °C and at ionic strength 1.0 or 3.0 mol
dm−3 (NaNO3). Tables 7 and 8 summarise the results
obtained for kobs at the various pH values, [Fe(CN)64−],
and temperatures. From the tables one can see that kobs
is dependent on both pH and [Fe(CN)64−]. kobs in-
creases with increasing [Fe(CN)64−] and tends to reach
a saturation point at high [Fe(CN)64−]. This implies
that there is ion-pair formation (as shown in Scheme 2)
from which Eq. (11) is derived:
solution are H2Fe(CN)62−, HFe(CN)63−, Fe(CN)64−
and [(H3N)5CoOMoO3]+.
The kobs values decrease with an increase in pH
(Table 8); so based the trend the mechanism in Scheme
2 is proposed, where K3=6.0×10−3 mol dm−3 and
K4=6.7×10−5 mol dm−3 at 25 °C [19].
Based on the decrease of kobs with pH it can be
deduced that HFe(CN)63− is the more reactive ferro-
cyanide species in the electron transfer reaction; so k2 is
the main contributing path over the pH range.
,
k
obs=k1K5[Fe(CN)6 4−]/(1+K5[Fe(CN)6 4−])
(11)
Eq. (11) can be rearranged to form
Table 6
Stoichiometry of the reaction between [(H3N)5CoOMoO3]+ and
Fe(CN)64− at 25.0 °C, pH 5.56 (CH3CO2Na–CH3CO2H buffer),
[complex]=1×10−3 mol dm3, I=1.0 mol dm−3 (Na2NO3),
[Na2H2EDTA]=3×10−3 mol dm−3, u=416 nm, cell path length=
1.00 cm
1/kobs=1/k1+(k1K5[Fe(CN)6 4−])
(12)
A plot of the left hand side of Eq. (12) versus
1/[Fe(CN)64−] is shown in Fig. 6, from which k1=
(2.5290.54)×10−1 s−1 and K=5.1591.26 mol−1
dm3 s−1 at 35.3 °C, after carrying out linear regression
on Eq. (12).
[Fe(CN)6 4−]/[complex]
Absorbance
0.125
0.250
0.500
0.750
0.126
0.150
0.192
0.223
0.251
0.343
0.409
0.477
0.536
0.600
There is evidence [18] that the ferrocyanide anion
may exhibit, in principle, the behaviour of a quadriva-
lent Bro¨nsted base. The corresponding base strengths
can be expressed conveniently in terms of the successive
ionisation constants of the respective conjugate acids
[19], viz. by Scheme 3. At 25 °C [19], K1\K2\0.1 mol
dm−3, K3=(6.092.0)×10−3 mol dm−3, and K4=
(6.790.3)×10−5 mol dm−3. Fig. 7 shows the varia-
tion of the ferrocyanide species with pH. Over the pH
range of the reaction, the main species in aqueous
a
1.000
2.000
3.000
4.000
5.000
6.000
a Break point occurs at [Fe(CN)64−]/[complex]=1.00.

286
A.A. Holder, T.P. Dasgupta / Inorganica Chimica Acta 331 (2002) 279–289
Table 7
The proposed mechanism given in Scheme 2 leads to
the expression:
Pseudo-first order rate constants for the reaction between
[(H3N)5CoOMoO3]+ and Fe(CN)64−
k
obs={(k1K3K4K5+k2K3K6[H+])[Fe(CN)6 4−]T}
/([H+]2+K3[H+]+K3K4)
[Fe(CN)6 4−] (mol dm−3
)
102 kobs (s−1
)
(13)
0.01
0.02
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
1.27
2.10
3.30
4.31
5.17
6.08
6.98
7.60
8.32
9.07
9.57
where [Fe(CN)64−
concentration.
The expression can be rearranged to give:
]
represents the total ferrocyanide
T
{kobs([H+]2+K3[H+]+K3K4[Fe(CN)6
=k1K3K4K5+k2K3K6[H+]
]
}
4− −1
T
(14)
A plot of the left hand side of Eq. (14) versus [H+] is
linear in the range 4.535pH55.63, the slope being
k2K3K6 and the intercept being k1K3K4K5 A plot at
25.0 °C shown in Fig. 8 is linear over the pH range. A
linear regressional analysis was carried out and due to
the inability to separate k1 from K5 and k2 from K6, it
Variation in [Fe(CN)64−], [complex]=0.5×10−3 mol dm−3
,
[Na2H2EDTA]=1.5×10−3 mol dm−3
, u=524 nm, I=3.0 mol
dm−3 (NaNO3), pH 5.59 (CH3CO2Na–CH3CO2H buffer), q=
35.3 °C.
was necessary to combine k1 and K5 to give k%, and to
1
combine k2 and K6 to give k%. K3 and K4 are indepen-
2
dent of temperature as deduced from literature [19].
Table 8
The rate and activation parameters are shown in Table
9.
Pseudo-first order rate constants for the reaction between
[(H3N)5CoOMoO3]+ and Fe(CN)64−
At 25.0 °C the value of k% is 1.1390.01 mol−1 dm3
1
pH
q=25.0 °C
102 kobs (s−1
pH
q=30.4 °C
102 kobs (s−1
pH
q=35.3 °C
101 kobs(s−1
)
s
−1, while the value of k% is 2.3690.05 mol−1 dm3; so
2
one can see that HFe(CN)63− reacts with
)
)
4.54
4.62
4.72
4.82
5.04
5.16
5.27
5.38
5.62
–
3.79
3.61
3.46
3.36
3.13
3.10
3.06
3.01
2.98
–
4.54
4.63
4.73
4.83
4.94
5.05
5.16
5.27
5.40
5.63
8.73
8.47
8.29
7.93
7.71
7.55
7.35
7.16
6.96
6.86
4.53
4.63
4.72
4.83
4.94
5.05
5.17
5.27
5.41
–
1.59
1.54
1.47
1.44
1.38
1.33
1.30
1.24
1.21
–
Variation in pH and temperature, u=524 nm, [complex]=0.5×10−3
mol dm−3, I=1.0 mol dm−3 (NaNO3), [Fe(CN)64−]=0.025 mol
dm−3, Buffer=CH3CO2Na–CH3CO2H, [Na2H2EDTA]=1.5×10−3
mol dm−3
.
−1
obs
−1
Fig. 6. A plot of k
vs. [Fe(CN)64−
]
for the reduction of
[(H3N)5CoOMoO3]+ by Fe(CN)64− at 35.3 °C.
Scheme 3.
Scheme 2.

A.A. Holder, T.P. Dasgupta / Inorganica Chimica Acta 331 (2002) 279–289
287
k1=(2.5290.54)×10−1 s−1 and that K5=5.1591.26
mol−1 dm3 at 35.3 °, I=3.0 mol dm−3 (NaNO3), and
pH 5.59; from Eq. (12), k% =1.3090.60 mol−1 dm3
1
s
−1. This value of k% =1.3090.60 mol−1 dm3 s−1 is
1
less than the value k% =4.6090.06 mol−1 dm3 s−1 at
1
35.3 °C and I=1.0 mol dm−3 (NaNO3) from Table 9.
This shows that k% decreases with an increase in ionic
1
strength, a clear indication that the effect of ionic
strength on rates of ionic reactions is well established
[20]. For species of like charges, the rate increases with
an increase in ionic strength, while for species of oppo-
site charges, the rate decreases as the ionic strength
increases. The rate is unaffected by ionic strength for
uncharged species. From our decrease in k% with an
1
increase in ionic strength from 1.0 to 3.0 mol dm−3, it
shows that species of unlike charges due to
[(H3N)5CoOMoO3]+ and Fe(CN)64− reacting to form
the ion-pair in Scheme 2.
We
now
compare
our
reaction
between
[(H3N)5CoOMoO3]+ and Fe(CN)64− with other reac-
tions involving Fe(CN)64− and other cobalt(III) com-
plexes. Our value of K5=5.1591.26 mol−1 dm3 is less
(1/55 of the value) than that of 3.0×102 mol−1 dm3
from the reaction [21] of [(H3N)5Co(OAc)]2+ and
Fe(CN)64−, while k1 for the acetate complex is 3.7×
10−4
[(H3N)5CoOH2)]3+ and Fe(CN)64− [7], K=15009100
mol−1 dm3 and k1=(1.990.1)×10−1 −1, which
s−1
.
For
the
reaction
involving
Fig. 7. A plot showing the percent speciation of Fe(CN)64− (A),
HFe(CN)63− (B), and H2Fe(CN)62− (C), with variation in pH.
s
shows that the two values of k1 are very similar under
experimental errors. The value of K5 for our system is
much lower than for [(H3N)5Co(OAc)]2+ and
[(H3N)5CoOH2]3+
.
The value of k1 for our system is slightly higher than
the system reported by Miralles et al. [8] for reductions
of various substituted (pyridine)pentaamminecobalt(III)
complexes by Fe(CN)64−. Their k1 values ranged from
1.51×10−2 to 76×10−2 −1, while their K5 values
s
were much higher than ours, clearly due to the +3
charge on the cobalt(III) complexes. Miralles et al.
[8] concluded that internal, outer-sphere electron
transfer process occur within the ion-pair containing a
pyridine bound to the cobalt(III) centre. Based on this
fact, we can conclude that an internal, outer-sphere
electron transfer process has occurred within the ion-
Fig. 8. A plot of {kobs([H+]2+K3[H+]+K3K4][Fe(CN)64− −1} vs.
]
T
[H+] for the reduction of [(H3N)5CoOMoO3]+ by Fe(CN)64− at
25.0 °C.
Table 9
Rate parameters for the reduction of [(H3N)5CoOMoO3]+ by
Fe(CN)64−
[(H3N)5CoOMoO3]+ about two times faster than
Fe(CN)64−. The transition state involving Fe(CN)64− is
more ordered than that involving HFe(CN)63− as can
be seen from the respective values for the entropy of
activation, the values being DS"1 =99931 J mol−1
q (°C)
k% (mol−1 dm3 s−1
)
k% (mol−1 dm3 s−1
)
1
2
25.0
30.4
35.3
1.1390.01
2.6690.01
4.6090.06
2.3690.05
5.5590.07
10.590.2
K−1 and DS"2 =126917 J mol−1
K
−1, respectively.
k% =4.6090.06 mol−1 dm3 s−1 at 35.3 °C from
DH"1 =10298 kJ mol−1; DH"2 =10894 kJ mol−1; DS"1 =99931
J mol−1 −1; DS2" =126917 J mol−1 K−1
1
Table 9 and given the fact that k% =k1K5 and that
K
.
1

288
A.A. Holder, T.P. Dasgupta / Inorganica Chimica Acta 331 (2002) 279–289
Table 10
Summary of the activation parameters for the reduction of [(H3N)5CoOMoO3]+ by some reducing agents
a
Reductant
DH"1 (kJ mol−1
)
DS"1 (J mol−1 K−1
)
DH"2 (kJ mol−1
)
DS"2 (J mol−1 K−1
)
Ascorbate (1) b
2997
10298
13498
−124930
99931
204927
9999
10894
116927
67935
126917
116988
Fe(CN)64− (2) c
Aqueous sulfite (3) c
a Each reductant is numbered in Fig. 9.
b [22].
c This work.
pair formed between [(H3N)5CoOMoO3]+ and
Fe(CN)64−
equations [23–25] on knowing the self-exchange rates
of both reductants and oxidants, in order to calculate
k12 and compare it with the observed k12, but in our
case, k22 for aqueous sulfite (as SO32−) is not known so
we need to calculate it. The self-exchange rate constant,
k22, for Fe(CN)64− has been reported as (0.1–9)×104
mol−1 dm3 s−1 in water at various ionic strengths
[26,27]. The self-exchange rate constant, k11, for
[(H3N)5CoOMoO3]+, is 2.32×10−5 mol−1 dm3 s−1
.
The rate constants and thermodynamic parameters
for the reduction of [(H3N)5CoOMoO3]+ by some re-
ductants, viz.
L
-ascorbic acid [22], Fe(CN)64−, and
aqueous sulfite, are summarised in Table 10. The acti-
vation parameters for the reactions are very similar and
can be used in an isokinetic plot of DH" versus DS".
The isokinetic plot is shown in Fig. 9. It is concluded
that a common mechanism exists, with DG"o =7293
kJ mol−1 and io=324922 K. Below this temperature
the reactions are controlled by DH", that is, the lower
the DH" value, the higher the rate constant; and above
this temperature by DS" values. It was evident that
from the studies carried out on this work, that an
[22], k12 (k%) (0.77 mol−1 dm3 s−1 at 25.0 °C for the
1
cross reaction involving SO32−) is the cross-reaction
rate constant, E2°2, −0.93 V [28] for the SO42−, H2O/
SO32−,OH− couple, while E° for [(H3N)5CoOMoO3]+,
11
+0.12 V [22]. K12 is the equilibrium constant (5.67×
1017), and k22 is the self-exchange rate constant for
aqueous sulfite as SO32−, which is unknown. From the
rate constant for the aqueous sulfite (as SO32−) reduc-
tion of [(H3N)5CoOMoO3]+ (k12=0.77 mol−1 dm3
outer-sphere electron transfer took place with the re-
2+
(aq)
duction of the Co(III) centre to Co
when reductants
such as L
-ascorbic acid [22], Fe(CN)64−, and aqueous
sulfite are used. The molybdenum(VI) centre, however,
remains unaffected.
s
−1), the self-exchange rate constant, k22, for aqueous
sulfite (as SO32−) was calculated to be 5.37×10−12
3.7. Calculation of self-exchange rate constants for
mol−1 dm3 s−1
.
both aqueous sulfite (as SO32−) and Fe(CN)64−
For the reaction involving Fe(CN)64−, where k12 (k%)
1
(1.13 mol−1 dm3 s−1 at 25.0 °C) is the cross-reaction
rate constant, k11, the self-exchange rate constant for
[(H3N)5CoOMoO3]+, is 2.32×10−5 mol−1 dm3 s−1
[22], k22 is the self-exchange rate constant for
Redox reactions involving cobalt(III) complexes are
often viewed as outer-sphere electron transfer reactions
[22]. The equations from the Marcus theory [23–25] are
used in predicting rate constants for heteronuclear
outer-sphere redox reactions from the self-exchange
rate constants for each partner and the overall equi-
librium constant:
k12=(k11k22k12 f12)1/2
(15)
(16)
(log K12)2
log f12=
k k
ꢀ ꢁ
11 22
4 log
1022
nF(E° −E° )
11
22
ln K12=
(17)
RT
where k22, the self-exchange rate constant for either
reductant, k11, the self-exchange rate constant for the
oxidant, E° , redox potential for the oxidant
11
{[(H3N)5CoOMoO3]+}, E° , redox potential for the
22
reductant, K12, the equilibrium constant for the cross
reaction, and k12, the second order rate constant for the
cross reaction. Normally one would use the Marcus
Fig. 9. An isokinetic plot of the activation parameters for the
reduction of [(H3N)5CoOMoO3]+by some reducing agents.

A.A. Holder, T.P. Dasgupta / Inorganica Chimica Acta 331 (2002) 279–289
289
Fe(CN)64−, E° , +0.36 V at zero ionic strength [29] for
[3] A.C. Dash, A.A. El-Awady, G.M. Harris, Inorg. Chem. 20
(1981) 3160.
[4] R. van Eldik, Inorg. Chim. Acta 42 (1980) 49.
[5] K.C. Koshy, G.M. Harris, Inorg. Chem. 22 (1983) 2947.
[6] R. van Eldik, J. von Jouanne, H. Kelm, Inorg. Chem. 21 (1982)
2818.
[7] D. Gaswick, A. Haim, J. Am. Chem. Soc. 93 (1971) 7347.
[8] A.J. Miralles, A.P. Szecsy, A. Haim, Inorg. Chem. 21 (1982) 697.
[9] A.A. Holder, T.P. Dasgupta, J. Chem. Soc., Dalton Trans.
(1996) 2637.
[10] R.G. Hughes, J.F. Endicott, M.Z. Hoffman, D.A. House, J.
Chem. Edu. 46 (1969) 440.
[11] Vogel’s Textbook of Quantitative Inorganic Analysis, ELBS, 4th
ed., p. 472.
[12] Vogel’s Textbook of Quantitative Inorganic Analysis, ELBS, 4th
ed., p. 452.
[13] A.A. El-Awady, G.M. Harris, Inorg. Chem. 20 (1981) 4251.
[14] T.P. Dasgupta, G.M. Harris, Inorg. Chem. 23 (1984) 4399.
[15] A.A. Holder, T.P. Dasgupta, unpublished work.
[16] V.K. Joshi, R. van Eldik, G.M. Harris, Inorg. Chem. 25 (1986)
2229.
22
the Fe(CN)63−/Fe(CN)64− couple, while E° for
11
[(H3N)5CoOMoO3]+, +0.12 V [22]. We calculated k22
for Fe(CN)64− as 1.10×109 mol−1 dm3 s−1 from the
Marcus equations [23–25], which is much higher than
the reported value of (0.1–9)×104 mol−1 dm3 s−1 in
water at various ionic strengths [26]. This discrepancy
probably is due to the method carried out and the
approximations used in the calculations by the authors
[27] in determining k22 for Fe(CN)64−. We believe that
our k22 value is correct under the controlled conditions
carried out for the cross reaction.
In summary, k22, the self-exchange rate constant, for
aqueous sulfite (as SO32−) was calculated to be 5.37×
10−12 mol−1 dm3
s
−1, while for Fe(CN)64−, it was
calculated to be 1.10×109 mol−1 dm3 s−1 from the
Marcus equations [23–25].
[17] G. Powell, M.Ph. Thesis, University of the West Indies, Jamaica,
1988.
[18] L.M. Kolthoff, Z. Anorg. Allg. Chem. 110 (1920) 143.
[19] J. Jordan, G.J. Ewing, Inorg. Chem. 1 (1962) 586.
[20] J.N. Bro¨nsted, Z. Phys. Chem. 102 (1922) 169.
[21] A. Miralles, A. Haim, R.E. Armstrong, J. Am. Chem. Soc. 99
(1977) 1416.
Acknowledgements
Funding for this work was provided by the Depart-
ment of Chemistry, and a Postgraduate Award by the
Board of Graduate Studies, University of the West
Indies, Mona Campus, Jamaica (to A.A.H.) is grate-
fully acknowledged.
[22] A.A. Holder, T.P. Dasgupta, S.-C. Im, Transition Met. Chem.
22 (1997) 135.
[23] R.A. Marcus, Discuss. Faraday Soc. 29 (1960) 21.
[24] R.A. Marcus, Can. J. Chem. 55 (1959) 37.
[25] R.A. Marcus, J. Phys. Chem. 853 (1963) 67.
[26] K.S. Alleman, K. Weber, S.E. Creager, J. Phys. Chem. 100
(1996) 17050.
[27] M. Shpoer, G. Ron, A. Lowenstein, Inorg. Chem. 4 (1965) 361.
[28] F.A. Cotton, G. Wilkinson, Advanced Inorganic Chemistry, 4th
ed., Wiley, USA, p. 532.
References
[1] R. van Eldik, G.M. Harris, Inorg. Chem. 19 (1980) 880.
[2] A.A. El-Awady, G.M. Harris, Inorg. Chem. 20 (1981)
1660.
[29] A.G. Sharpe, The Chemistry of Cyano Complexes of the Transi-
tion Metals, Academic Press, 1976, p. 106.