Tellurium(V). A pulse radiolysis study

Article abstract of DOI:10.1021/jp010577i

Four different tellurium(V) oxoradicals, assumed to be H₂TeO^4-, TeO₃^-, HTeO₄^2-, and TeO₄^3-, were detected by the pulse radiolysis technique. H₂TeO₄^- is the product of the reaction of OH with HTeO₃^-, whereas HTeO₄^2- and TeO₄^3- arise by reactions of OH and O^- with the TeO₃^2-. TeO₃^- is a secondary product formed by dehydration of H₂TeO₄^-, a process catalyzed by HTeO₃^-. The same tellurium(V) species except H₂TeO₄^- are formed by reaction of the hydrated electron with H₆TeO₆, H₅TeO₆^-, and H₄TeO₆^2-. The spectra, kinetics of the reactions of the tellurium(V) species, the acidity constant of HTeO₄^2- (～10^-13), and the apparent acidity constant of TeO₃^- (10^-10) have been measured. The standard Gibbs energies of formation Δ_fG_ao°(TeO₃^-) = -214 kJ/mol, Δ_fG_ao°(HTeO₄^2-) = -394 kJ/mol, and Δ_fG_ao°(TeO₄^3-) = -319 kJ/mol were determined from the rate constants for the forward and reverse reactions TeO₃^2- + O^- ? TeO₄^3- and TeO₃^2- + OH ? HTeO₄^2-, combined with the acidity constants of TeO₃^- and HTeO₄^2- and the standard Gibbs energy of formation of OH, O^-, and TeO₃^2-. TeO₃^- is a strong reducing agent (E_o(red) = -0.40 V), which appears to reduce O₂, as well as a strong oxidant (E_o(ox) = 1.74 V), oxidizing CO₃^2- to CO₃^-.

Full text of DOI:10.1021/jp010577i

J. Phys. Chem. A 2001, 105, 6637-6645
6637
Tellurium(V). A Pulse Radiolysis Study
U. K. Kla1ning*,†
Chemistry Department, UniVersity of Aarhus, DK-8000 Aarhus C, Denmark
K. Sehested‡
Risø National laboratory, DK-4000 Roskilde, Denmark
ReceiVed: February 14, 2001; In Final Form: April 16, 2001
Four different tellurium(V) oxoradicals, assumed to be H2TeO4 , TeO3 , HTeO42-, and TeO43-, were detected
-
-
-
-
by the pulse radiolysis technique. H2TeO4 is the product of the reaction of OH with HTeO3 , whereas
HTeO42- and TeO43- arise by reactions of OH and O- with the TeO32-. TeO3- is a secondary product formed
-
-
-
by dehydration of H2TeO4 , a process catalyzed by HTeO3 . The same tellurium(V) species except H2TeO4
are formed by reaction of the hydrated electron with H6TeO6, H5TeO6 , and H4TeO62-. The spectra, kinetics
-
2-
of the reactions of the tellurium(V) species, the acidity constant of HTeO4 (∼10-13), and the apparent
acidity constant of TeO3- (10-10) have been measured. The standard Gibbs energies of formation ∆fGaoo(TeO3 )
-
) -214 kJ/mol, ∆fGaoo(HTeO42-) ) -394 kJ/mol, and ∆fGaoo(TeO43-) ) -319 kJ/mol were determined
from the rate constants for the forward and reverse reactions TeO32- + O- / TeO43- and TeO32- + OH /
HTeO42-, combined with the acidity constants of TeO3 and HTeO4 and the standard Gibbs energy of
-
2-
formation of OH, O-, and TeO32-. TeO3 is a strong reducing agent (Eo(red) ) -0.40 V), which appears to
-
2-
-
reduce O2, as well as a strong oxidant (Eo(ox) ) 1.74 V), oxidizing CO3 to CO3 .
Introduction
absorbances that arise in aqueous solution by the reaction of
OH and O- with tellurous acid, and of those that arise by the
Oxoradicals of the group six elements sulfur, selenium, and
tellurium in the oxidation state V may be formed in aqueous
solution.1-6 The only S(V) radical observed is SO3-; selenium
-
reaction of eaq with telluric acid. On the basis of these
measurements we assign the absorbances to four Te(V) species
of definite composition, and their evolution in time to reactions
among these species. We have determined rate constants for
the reactions and constants for the observed equilibria involving
Te(V) species, and estimated the standard free energy of
formation of these species. Moreover, we have measured the
kinetics of the reactions of the Te(V) species with molecular
oxygen and with hydrogen carbonate and carbonate. The
properties of Te(V) oxoradicals are compared to those of the
corresponding S(V) and Se(V) oxoradicals.
-
similarly forms SeO3 and, in strongly alkaline solution also,
HSeO42-. Whereas the S(V) and Se(V) radicals have been
characterized in detail, little is known about the properties of
the corresponding oxoradicals of tellurium. However, it has been
shown previously that Te(V), like S(V) and Se(V), is amenable
to study in aqueous solution by the pulse radiolysis technique.7-9
Here Te(V) species may be formed by reduction of telluric acid
(H6TeO6) and the tellurates (H5TeO6-, H4TeO62-) with the
hydrated electron, eaq-, as well as by oxidation of hydrogen
tellurite (HTeO3-) and tellurite (TeO32-) with OH or O-. A
transient absorbance detected in an O2-containing tellurite
solution after irradiation was assigned to TeO3- 9, a species
Experimental Section
Pulse radiolysis was made at ambient temperature (21 ( 1
°C) with the HCR linac at Risø delivering 10 MeV in single
square pulses. The pulse length was varied between 0.1 and 1
µs. The dose, ranging from 2.5 to 20 Gy, was measured with
the ferrocyanide dosimeter13 taking the extinction coefficient
of ferricyanide at 420 nm equal to 1000 cm-1 M-1 and the
G-value (molecules/100 eV) for formation of ferricyanide equal
to 5.9. Yields of products were calculated from the measured
dose using published G-values14 corrected for spur reactions.15
The experimental setup for irradiation and for kinetic spectros-
copy measurements were as previously described.6 Chemicals
were reagent grade or of higher purity. Solutions were prepared
with triply distilled water. Nitrous oxide, N48 (purity 99.998%),
was ALPHAGAZ. Argon, oxygen, and nitrogen, all N40 (purity
99.99%), were supplied by Dansk Ilt og Brint.
-
1-5
- 6,10
similar to SO3
and SeO3
.
This assignment was
-
substantiated by the detection of TeO3 in tellurite crystals
irradiated with X-rays.11 TeO3- has in the solid matrix the same
symmetry (C3V) as TeO3 .
2- 12 Also reactions of eaq- with telluric
acid and tellurate have been studied, but no transient absorbance
was assigned to Te(V) species.7,8
Since not only SeO3- but also HSeO42- are observed by pulse
radiolysis of aqueous selenite and selenate solutions6 a more
comprehensive pulse radiolysis study of aqueous tellurite and
tellurate may be expected similarly to reveal the formation of
tellurium(V) species other than TeO3-. In the present study,
we have measured the spectra and kinetics of the transient
* Author to whom correspondence should be addressed.
† Present address: Møllegaarden, Obstrupvej 12 M, DK-8320 Maarslet,
Denmark.
Solutions were purged of oxygen by bubbling-through with
Ar or N2O at 0.1 MPa. In studies of reactions of eaq-, Ar was
‡ Strandhøjen 5, Himmelev, DK-4000 Roskilde, Denmark.
10.1021/jp010577i CCC: $20.00 © 2001 American Chemical Society
Published on Web 06/14/2001

6638 J. Phys. Chem. A, Vol. 105, No. 27, 2001
Kla¨ning and Sehested
Figure 2. Absorbance at 300 and 380 nm as a function of time
measured in 2 × 10-4 M hydrogen tellurite at pH 8.15 after irradiation
(dose 19.8 Gy).
Figure 1. Transient absorption spectra measured 2 µs and 50 µs after
irradiation (dose 19.8 Gy) of 2 × 10-4 M tellurite/hydrogen tellurite
solutions at pH 8.15, 10.6, and 13.5.
-
used. N2O was used when interference from reactions of eaq
were to be avoided. N2O converts eaq- into O- in a fast reaction,
16
N2O + eaq- f N2 + O- k1 ) 9.1 × 109 M-1 s-1
(1)
pH was adjusted by addition of sodium hydroxide and perchloric
acid and was, for pH < 12, measured with a pH-meter
(Radiometer pH M 64). For pH > 12, pH was taken equal to
14 + log[NaOH]. The pK-values for the dissociations of
tellurous and telluric acid were determined by pH-metric titration
of 10-3 M sodium tellurite and telluric acid with perchloric acid
and sodium hydroxide, respectively, using a Radiometer titrator
TTT 60 fitted with a Radiometer autoburette ABU (volume 0.25
mL). For H2TeO3 we found pK1 ) 6.3 and pK2 ) 9.6, and for
H6TeO6 pK1 ) 7.8 and pK2 ) 11.0, in agreement with recently
recommended values.17
Simulation of kinetic data was performed using the computer
package “Gepasi” equipped with the optimization module
Multistart (Levenberg-Marquardt) Version 1.00.18-20
Figure 3. Absorbance at 380 nm as a function of time measured in 2
× 10-4 M tellurite/hydrogen tellurite solutions at various pH values
after irradiation (dose19.8 Gy). The smooth curves are simulations
calculated with the Gepasi package21-23 (see text).
Results and Discussion
the spectrum recorded at pH 8.15 2 µs after the irradiation is
very different from that recorded after 50 µs, the initial
maximum at 355 nm giving way to a shoulder at ∼340 nm.
Figure 2, showing the absorbance change at 300 and 380 nm
during the first 50 µs after the irradiation, illustrates this process.
After a fast increase at both wavelengths owing to the reaction
of HTeO3- with OH, the absorbance at 300 nm further increases
for the next 10 µs, while the absorbance at 380 nm suffers a
decrease on the same time scale. Figures 1 and 2 suggest the
formation of four species, of which three, displaying a maximum
absorbance at 325-350 nm, are Te(V) species formed in
primary reactions of OH and O- with Te(IV), and the fourth,
associated with the shoulder at 345 nm and also assumed to be
a Te(V) species, is formed from the primary Te(V) species that
predominates at pH 8.15. Further measurements have shown
that the absorbance change associated with the formation of
the fourth species is independent of pH in the range from 6.6
(the lowest pH used) to 8.5 and is of first order with a rate
constant that increases linearly with the total concentration of
Te(IV).
Reaction of H2TeO3 and HTeO3- with OH, and Reactions
of TeO3 with OH and O-. The measurements were made
2-
with 10-4-10-2 M solutions prepared from sodium tellurite at
pH ranging from 6.6 to 13.5. Measurements at pH < 6 proved
unreliable since such solutions became turbid on standing. Upon
irradiation of N2O-saturated tellurous solutions, a transient
absorbance was observed to grow-in at λ < 430 nm in a pseudo
first-order reaction with a rate constant proportional to the
concentration of tellurous acid. We ascribe the transient absor-
bance to formation of Te(V) species by reactions of OH and
O-. (Absorbance changes owing to removal of Te(IV) by the
irradiation were neglected throughout.) The spectrum and the
time evolution of the transient absorbance depend on pH. Figures
1, 2, and 3, illustrate the absorbance changes observed after
irradiation of 2 × 10-4 M Te(IV) solutions with a dose of 19.8
Gy. Figure 1 shows the spectrum of the transient absorbance
measured 2 µs and 50 µs after the irradiation at pH 8.15, 10.6,
and pH 13.5. The three spectra are clearly distinct initially (at
2 µs), and they evolve differently in time. At pH 13.5, no time
evolution is detected. At pH 10.6, the absorbance decreases only
slightly with time while the spectrum is unchanged. In contrast,
Figure 3 shows the pH-dependence of the transient absorbance
at 380 nm. The absorbance increases with increasing pH and

Tellurium(V). A Pulse Radiolysis Study
J. Phys. Chem. A, Vol. 105, No. 27, 2001 6639
-
2-
the fast decay associated with the formation of the fourth
(secondary) Te(V) species decreases steadily, indicating the
appearance and growing importance of a new Te(V) species
that is stable on the 10 µs time scale. Between pH 11 and 12
no further change of absorbance with pH was observed,
suggesting that one Te(V) species predominates in this pH
interval. At pH > 12 the absorbance increases further with
increasing pH, while the maximum absorbance shifts toward
shorter wavelengths, indicating the formation of yet another
Te(V) species. The eventual decay of the transient absorbance
is a second-order process with a rate constant that decreases
with increasing pH.
or by reaction of H2TeO4 with TeO3
H2TeO4- + TeO32- f HTeO3- + HTeO4
2-
k7 (7)
We point out that a dehydration taking place by reactions similar
to reactions 6 and 6a were previously observed by pulse
radiolysis of solutions of arsenite.23 Here the As(IV) species
As(OH)4 and As(OH)3O- formed by addition of OH to H3AsO3
-
and H2AsO3 dehydrate subsequently to yield H2AsO3 and
HAsO3-, respectively.
The Te(V) species participate in the protolytic equilibria
TeO3- + H2O / H2TeO4- / HTeO42- + H+ K8,9
(8),(-8),(9),(-9)
The spectra of the primary Te(V) species are alike, in the
sense that they all display a maximum in the region from 325
nm to 360 nm, whereas the secondary formed species has a
quite different spectrum. We take this to suggest that the three
primary Te(V) species have the same coordination at the
tellurium atom and that the formation of the secondary species
involves a change of coordination at the tellurium atom.
A consistent interpretation of these observations may be
achieved by assigning the three primary transient spectra to the
four-coordinated Te(V) oxoanions H2TeO4-, HTeO42-, and
HTeO42- / TeO43- + H+ K10
(10),(-10)
The second-order decay of absorbance observed at pH < 12
is ascribed to the reactions
TeO3- + TeO3- + 3H2O f HTeO3- + H5TeO6
k11
(11)
-
-
TeO43-. In neutral and slightly alkaline solutions H2TeO4 is
HTeO42- + TeO3- + 2H2O f TeO32- + H5TeO6
k12
-
-
formed by addition of OH to H2TeO3 and HTeO3
,
(12)
H2TeO3 + OH f H2TeO4- + H+ k2
(2)
(3)
2-
HTeO42- + HTeO42- + H2O f TeO32- + H4TeO6
k13
(13)
HTeO3- + OH f H2TeO4
k3
-
An additional reaction is suggested to be important at pH >
We note that the same Te(V) species appears to be formed
at pH 6.6 and at pH 8.5, despite the fact that at pH 6.6 around
30% of Te(IV) is present as H2TeO3 whereas HTeO3 pre-
12
-
3-
HTeO42- + TeO4 + 2H2O f
dominates at pH 8.15. Hence, one might expect to observe the
formation of H3TeO4 as well as of H2TeO4- at pH 6.6. However,
using Pauling’s rule for the strength of oxoacids,21 which
suggests a dissociation constant of the order of 10-3 for the
acid H3TeO4, and the commonly accepted estimate (1010-1011
TeO32- + H4TeO62- + OH- k14 (14)
-
2-
Reaction of eaq with H6TeO6, H5TeO6-, and H4TeO6
.
Transient absorbances in O2-free 10-3-10-2 M telluric acid
solutions saturated with Ar were measured in the pH-range from
5.5 to 13.5. Here the formation of Te(V) species in the reactions
of eaq- with H6TeO6, H5TeO6-, and H4TeO62- can be studied.
Interfering reactions of OH and O- with telluric acid and
tellurate may conceivably occur in such solutions. However,
M-1 s-1) for the rate constant of a reaction such as that of H+
- 22
with H2TeO4
,
we find a rate constant for the protolysis of
the order of 107-108 s-1, in keeping with the absence of a
transient assignable to H3TeO4.
With increasing pH, the composition of the Te(IV) substrate
2-
shifts toward TeO32-; HTeO4 formed by
-
no transient absorption was observed if eaq was quenched by
N2O (reaction 1), suggesting that reactions of OH with telluric
acid and of O- and OH with tellurate are slow compared to
other reactions that remove O- and OH. (This observation also
indicates that reactions of H atoms with Te(VI) can be
neglected).
2-
TeO32- + OH f HTeO4
k4
(4)
therefore gains importance and dominates at 11 < pH < 12.
At pH > 12, OH gives way to O- and TeO4 formed by
3-
2-
addition of O- to TeO3
The transient absorption spectra that arise in tellurate solutions
at pH > 11 are similar to those observed at the same pH in
TeO32- + O- f TeO4
k5
(5)
3-
2-
N2O-saturated tellurite solutions and assigned above to HTeO4
and TeO43-. This indicates the occurrence of the reactions
becomes important.
We assign the secondary, transient spectrum that dominates
after 50 µs at low pH to TeO3-. Hence we ascribe the spectral
evolution seen at 8.15 < pH < 10 (Figure 1) to a transformation
H5TeO6- + eaq- f HTeO42- + 2H2O
(4a)
(5a)
and
-
of H2TeO4 into TeO3-, occurring either by a dehydration
H4TeO62- + eaq- f TeO43- + 2H2O
H2TeO4- f TeO3- + H2O k6
(6)
In the pH range 11 < pH < 12, where the Te(V) species
HTeO4 dominates, the absorbance decays somewhat faster
than in tellurite solutions. The process seems to be of mixed
first and second order. In solutions at pH > 12, the absorbance
decays in a first-order process rather than the second-order
process observed in tellurite solutions. However, in an Ar-
2-
-
catalyzed equally by H2TeO3 and HTeO3
H2TeO4- + HTeO3 /H2TeO3 f
-
TeO3- + H2O + HTeO3 /H2TeO3 k6a (6a)
-

6640 J. Phys. Chem. A, Vol. 105, No. 27, 2001
Kla¨ning and Sehested
ionic strength/M
TABLE 1: Summary of Reactions and Constants
reaction/equilibrium
rate constant/M-1 s-1; pK-values
k1 ) 9.1 × 109 a
N2O + eaq- f N2 + O-
H2TeO3 + OH f H2TeO4- + H+
k2 ) (6 × 109)-(8 × 109) b
k3 ) (6.2 ( 0.6) × 109 c
k4 ) (4.8 ( 0.5)b × 109;c k-4 ) (1.3 ( 0.4) × 103 c,d
k5 ) (1.0 ( 0.10) × 109;c k-5 ) 3.7 ( 0.4 × 103 c,d
k6 ∼ 104 b,c,d
<10-3
HTeO3- + OH f H2TeO4
<10-3
-
2-
TeO32- + OH / HTeO4
<10-3; 10-2-0.3
0.1; 10-2-0.3
<5 × 10-3
<5 × 10-3
<10-3
TeO32- + O- / TeO4
3-
H2TeO4- f TeO3- + H2O
H2TeO4- + HTeO3- f TeO3- + H2O + HTeO3
k6a ) (8.6 ( 0.8) × 108 c
k7 ∼ 108 b
-
H2TeO4- + TeO32- f HTeO42- + HTeO3
-
TeO3- + H2O / H2TeO4- / HTeO42- + H+
HTeO42- / TeO43- + H+
pK8,9 ) 9.96 ( 0.15 c
10-2-3 × 10-2
10-2-0.3
<10-2
pK10 ) 13.2 ( 0.2
TeO3- + TeO3- + 3H2O f HTeO3- + H5TeO6
k11 ) (4.7 ( 0.8) × 108 c
k12 ) (1.1 ( 0.2) × 109 c
k13 ) (1.2 ( 0.4) × 107 c
k15 ) 3.2 × 1010 e
-
HTeO42- + TeO3- + 2H2O f TeO32- + H5TeO6
<10-2
-
HTeO42- + HTeO42- + H2O f TeO32- + H4TeO6
<10-2
2-
H6TeO6 + eaq- f TeO3- + 3H2O
OH + OH f H2O2
k17 ) 5.5 × 1010 a
OH + H f H2O
k18 ) 7 × 109 a
TeO3- + O2 f TeO5
k33 ) (6.8 ( 0.7) × 108 c
k34 ) (2.9 ( 0.17) × 108 c
k35 ) (2.5 ( 0.3) × 108 c
k37 ) (1.6 ( 0.5) × 106 c
k38 ) (1.7 ( 0.5) × 107 c
<10-3
-
HTeO42- + O2 f TeO5- + OH-
<10-2
TeO43- + O2 + H2O f TeO5- + 2OH-
0.2
HCO3- + TeO3- f CO3- + HTeO3
2 × 10-2-0.2
2 × 10-2-0.2
-
CO32-+ TeO3- f CO3- + TeO3
2-
a Ref 16. b Value estimated. c This work. d s-1 e Ref 7.
.
saturated solution containing both tellurite and tellurate in equal
concentrations, where OH and O- react with tellurite and eaq
-
reacts with tellurate, the decay of absorbance was of second
order with a rate constant similar to that measured in N2O-
saturated tellurite solutions at the same pH. These observations
suggest that HTeO42- and TeO43- may disappear by the reverse
of reactions 4 and 5
HTeO42- f TeO32- + OH k-4
TeO43- f TeO32- + O- k-5
(-4)
(-5)
as well as by the reactions 13 and 14. The reactions -4 and
-5 parallel the thermal split-off of O- or OH from the electron
adducts of selenate,6 periodate,24 and perxenate.25
At pH < 11, the transient absorption spectrum is similar to
that observed in tellurite solutions after the transient ascribed
to H2TeO4 has decayed. Moreover, the absorbance decays
Figure 4. Spectra of TeO3-, H2TeO4-, HTeO42-, and TeO43- calculated
from measurements (see text).
-
without change of spectrum in a second-order process that
-
matches the decay of TeO3
.
-
3-
These observations indicate that TeO3 is formed directly
by reaction of eaq with H6TeO6
Owing its large base strength, TeO4 cannot be made the
-
3-
predominant Te(V) solute. ꢀTeO (λ) was obtained from eq 16
4
H6TeO6 + eaq- f TeO3- + 3H2O k15
(15)
ꢀTeO 3-(λ) ) (ꢀ(λ) - ꢀ
2-(λ) (1 - x 3-))/x
3-
TeO4
(16)
HTeO4
TeO4
4
-
3-
rather than via H2TeO4 as is the case in the reaction of OH
where ꢀ(λ) is the spectrum of the equilibrium mixture of TeO4
-
2-
with HTeO3
.
3-
and HTeO4 in 0.3 M NaOH, and xTeO is the fraction of
4
Te(V) present as TeO43-, found to be 0.63 in 0.3 M NaOH
The reactions and equilibria discussed above are summarized
in Table 1.
(see eq 25 below).
Determination of the Spectra of TeO3-, H2TeO4-, HTeO42-
,
The overlap of reactions 2 and 3 with reactions 6 and 6a
and TeO43-. The spectra of TeO3-, H2TeO4-, HTeO42-, and
precludes a direct determination of the spectrum of H2TeO4
.
-
TeO43-, represented as the extinction coefficients versus
ꢀH TeO (λ) shown in Figure 4 was calculated from absorbances
measured 2 µs after the irradiation of a tellurite solution at pH
8 (where Te(V) species other than TeO3 and H2TeO4 may
-
2
4
-
-
2-
3-
wavelength, ꢀTeO (λ), ꢀH TeO (λ), ꢀHTeO (λ), and ꢀTeO (λ), are
3
2
4
4
4
-
-
-
2-
3-
shown in Figure 4. ꢀTeO (λ), ꢀHTeO (λ), and ꢀTeO (λ), were
3
4
4
-
obtained from transient absorbances measured in 2 × 10-3
M
be neglected) and the concentrations at that time of H2TeO4
telluric acid 2 µs after the irradiation at pH 8, 11.4, and 13.48,
and TeO3-. These concentrations were obtained as a function
of time from a simulation of the absorbance at 350 nm during
the first 5 µs after the irradiation. The simulation was based on
the reactions 3, 6 and 6a, accounting for the formation of
-
respectively. At that time the primary reaction of eaq as well
as the subsequent protolytic reactions are completed whereas,
on the other hand, the slow second-order decay of the absor-
bance may be neglected.
H2TeO4 and its transformation into TeO3-, respectively,
-

Tellurium(V). A Pulse Radiolysis Study
J. Phys. Chem. A, Vol. 105, No. 27, 2001 6641
k6 and k6a shown in Table 1 were obtained from a fit of a linear
function to the plot, k6 as the constant term, and k6a as the
coefficient to [HTeO3-]. We note that the data do not allow an
accurate determination of k6. We find k6 to be around 104 s-1
,
which is the same order of magnitude as found for the
uncatalyzed dehydration of the As(IV) species As(OH)3O-.23
Reaction 7 between H2TeO4- and TeO32- was not observed
directly. A value of ∼108 M-1 s-1 was estimated for the rate
constant, k7.
The rate constants k11, k12, and k13 for the reactions 11-13,
by which TeO3- and HTeO42- disappear, were determined from
k22, the second-order rate constant for the decay of the
absorbance OD(t) at 350 nm measured at pH values between
8.15 and 11.76. Since in the actual experiments pH remains
-
2-
constant and equilibrium between TeO3 and HTeO4 is
Figure 5. Dehydration of H2TeO4-. The pseudo first-order rate constant
kobs at pH 8 for the dehydration of H2TeO4- (reactions 6 and 6a) plotted
against the concentration of HTeO3-. × represents experimental points;
the straight line is a linear least-squares fit to the experimental points.
The slope is k6a (Table 1).
-
maintained during the decay, the fraction xTeO of the total
concentration c(t) of Te(V) that is present as TeO3 remains
3
-
constant. Consequently, the integrated rate equation for the
simultaneous disappearance of TeO3 and HTeO4 may be
expressed by
-
2-
supplemented by the competing removal of OH by reactions
17 and 18
c(t)-1 - c(t ) 0)-1 ) (2k11 × x2 - + k
×
TeO3
12
xTeO - (1 - x -) + 2k13 × (1 - xTeO -)2) × t (20)
TeO3
3
3
OH + OH f H2O2
H + OH f H2O
(17)
(18)
where xTeO ) (1 + K8,9 × 10pH
)
-1; (K8,9 ) 1.1 × 10-10, see
-
3
below).
The integrated rate equation for disappearance of the absor-
bance may be expressed by
-
The value of ꢀTeO at 350 nm and the values of the rate constants
3
k3, k6 and k6a used in the simulation were as determined (Table
1). The rate constants of reactions 17 and 18 were taken to be
, respectively. Fitting
the calculated absorbance to the measured by adjusting the value
OD(t)-1 - OD(t ) 0)-1 ) k22 × t ) (c(t)-1 - c(t ) 0)-1)/
5.5 × 109 M-1 s-1 16 and 7 × 109 M-1 s-1 16
(l × ꢀTeO - × x - + l × ꢀ
2- × (1 - x -)) (21)
TeO3
HTeO4
TeO3
3
-
of ꢀH TeO at 350 nm, we then obtained the concentrations of
2
4
-
-
where l is the length of the optical cell (5.5 cm).
From eqs 20 and 21 we find
H2TeO4 and TeO3 2 µs after the irradiation. With these
concentrations and ꢀTeO (λ), we obtained ꢀH TeO (λ) shown in
-
-
3
2
4
Figure 4 from the measured absorbance.
k22 ) (2k11 × x2 - + k12 × xTeO - (1 - x -) + 2k
×
Determination of Rate Constants for Reactions of H2TeO4-,
TeO3-, HTeO42-, and TeO43-. Rate constants determined
below are shown in Table 1. Throughout the analysis we neglect
possible reactions of hydrogen tellurite and tellurite with the
hydrogen atom formed in the primary radiolytic process.
Recalling that the observed kinetics of absorbance change
was independent of pH in the region from 6 to 8.5, we may
assume that the rate constants k2 and k3 for the reactions of OH
with H2TeO3 and HTeO3- are similar. k3 and the rate constants
for the reactions of OH and O- with TeO32-, k4 and k5, were
determined from the rate of growing-in of the absorbance at
350 nm after irradiation of 10-4 M hydrogen tellurite and
tellurite solutions with 2.5 Gy (Table 1). The values of k3 and
k5 were determined from the rate observed in solutions at pH 8
and at pH 13.3, respectively. Then, k4 was determined from
the relation
TeO3
TeO3
13
3
(1 - xTeO -)2)/(l × ꢀ - × x - + l × ꢀ
×
2-
HTeO4
TeO3
TeO3
3
(1 - xTeO -)) (22)
3
-
-
3
Figure 6 shows a plot of k22 × (l × ꢀTeO × xTeO + l ×
3
2-
-
-
3
ꢀHTeO × (1 - xTeO )) against xTeO together with the least-
4
3
squares fit of a quadratic function to the experimental points.
-
By equating coefficients to like powers of xTeO in eq 20 and
3
in the quadratic function, we find the values for k11, k12, and
k13, shown in Table 1.
The rate constants k-4 and k-5 were determined from the first-
order rate constant, k23, for the decay of absorbance at 325 nm,
measured at pH varying between 12.19 and 13.48. k23 may be
expressed by
k23 ) k-5 × xTeO 3- + k-4 × (1 - xTeO
)
3-
4
(23)
4
k19 ) k4 × xOH + k5 × (1 - xOH
)
(19)
where xTeO ) K10 × 10pH/(1 + K10 × 10pH ) is the fraction
3-
4
where k19 ) 4.4 × 109 M-1 s-1 is the rate constant for formation
of the total Te(V) concentration that is present as TeO4 in
3-
of tellurium(V) at pH 10.9 and xOH is given by xOH ) (1 +
equilibrium with HTeO42-. Figure 7 shows a plot of k23 against
KOH × 10pH -1
)
, under the assumption that the equilibrium
xTeO . k-4 and k-5 were found by fitting a linear function to
3-
4
between OH and O- is maintained during the reaction (KOH
)
the experimental points (Table 1).
10-11.9).16
Test of the Mechanism. The rate constants of the mechanism
proposed above were determined under the assumption that
overlap among the individual reactions could be neglected.
However, a test performed without this assumption by simulat-
ing the time evolution of the absorbance measured at 380 nm
in N2O-saturated 2 × 10-4 M tellurite solutions at pH 8.15,
The rate constants k6 and k6a for the uncatalyzed and the
catalyzed dehydration of H2TeO4- were obtained from measure-
ments of the rate constant kobs for the decrease of absorbance
-
at 350 nm in solutions at pH 8 containing HTeO3 in varying
concentration. Figure 5 shows a plot of kobs against [HTeO3-].

6642 J. Phys. Chem. A, Vol. 105, No. 27, 2001
Kla¨ning and Sehested
Figure 6. Determination of the second-order rate constants, k11, k12,
Figure 8. pK8,9, the apparent acid dissociation constant of TeO3-, and
pK10, the acid dissociation constant of HTeO42-, determined from plots
of the quantity log(ꢀ - ꢀA)/(ꢀB - ꢀ) against pH. In the left curve A
and B stand for TeO3- and HTeO42-, and in the right curve for HTeO42-
and TeO43-, respectively. ∆, 0, ×, and ∇, are experimental points, ∆
measured at 350 nm, 0 at 400 nm, × at 425 nm, and ∇ at 325 nm.
Straight lines are linear least-squares fits to the experimental points.
and k13, for the disappearance of TeO3- and HTeO42-. k22 × (l × ꢀTeO
-
3
-
2-
-
3
-
× xTeO + l × ꢀHTeO × (1 - xTeO )) is plotted against xTeO . k22 is
3
4
the rate constant of the second-order decay of absorbance at 3350 nm
-
-
(see text). xTeO is the fraction of TeO3 present in the equilibrium
3
mixture of TeO3 and HTeO42-. Concentration of tellurite/hydrogen
-
tellurite: 2 × 10-4 M; dose 19.8 Gy; pH varies between 8 and 11. ×
represents experimental points, the full line represents a least-squares
-
fit of a quadratic function of xTeO to the experimental points.
3
where (B- ) TeO32- and OH-), involving the species HTeO4
,
2-
become important. Here the test was performed by fitting
calculated absorbances to the measured absorbances by adjusting
three parameters: the dose, again only within (4% of the
nominal value, and the pseudo first-order rate constants k24 [B-]
and k-24 [HB]. The rate constants of reactions 3, 4, 6, 7, 11,
12, 13, 17, and 18, were taken from Table 1 and the extinction
2-
coefficients of H2TeO4-, TeO3-, and HTeO4 were as mea-
sured (Figure 4).
From pH and the corresponding values obtained for k24 [B-]
and k-24 [HB] in the four solutions we find
pK ) pH + log(k-24 [HB]/k24 [B-]) ) 9.94 ( 0.13 (25)
in agreement with the value for pK (pK8,9) ) 9.96 ( 0.15
determined by the equilibrium measurements described below
and therefore indicating the consistency of the mechanism for
these four solutions also.
Figure 7. Determination of the rate constants k-4 and k-5 for the
dissociation of HTeO4 into TeO3 and OH and the dissociation of
2-
2-
Equilibrium Constants, Standard Gibbs Energy of For-
-
3-
TeO43- into TeO32- and O-, respectively. k23 ) k-5 × ꢀTeO × xTeO
3-
mation, and Standard Electrode Potentials of TeO3
,
+ k-4 × ꢀHTeO × (1 - xTeO ) is plotted against xTeO × xTeO 4is
4
H2TeO4-, HTeO42-, and TeO43-. The values of pK for the
apparent acid dissociation of TeO3-, pK8,9 ) 9.96 ( 0.15, and
for the acid dissociation of HTeO42-, pK10 ) 13.2 ( 0.1, were
found from plots against pH of the left side of the equations
2-
3-
3-
3-
4
4
4
4
3-
3-
the fraction of TeO4 present in the equilibrium mixture of TeO4
and HTeO42-. k23 is the first-order rate constant for the decay of
absorbance at 325 nm. The straight line shows of a linear least-squares
fit to the experimental points (×).
log(ꢀ - ꢀTeO -)/(ꢀ
2- - ꢀ) ) pH - pK8.9
(26)
HTeO4
3
9.27, 9.62, 9.92, and 10.6, showed that the mechanism is
consistent with this set of data (Figure 3). At pH 8.15, where
and
-
-
the species H2TeO4 and TeO3 dominate, the important
reactions of the mechanism are 3, 6, 6a, 11, 17, and 18. Here
the calculated absorbance was fitted to the measured absorbance
by adjusting the dose, allowing it to vary within (4% of the
nominal value, whereas the rate constants had the values given
log(ꢀ - ꢀHTeO 2-)/(ꢀ 3- - ꢀ) ) pH - pK10
(27)
TeO4
4
(Figure 8). ꢀ is the extinction coefficient measured at varying
-
2-
3-
pH. ꢀTeO , ꢀHTeO , and ꢀTeO , stand for the extinction
-
3
4
4
in Table 1, and the extinction coefficients of H2TeO4 and
coefficients of TeO3-, HTeO42-, and TeO43-, respectively. pK8,9
was determined from measurements of ꢀ at the wavelengths 325,
350, 375, 400, and 425 nm, pK10 from measurements of ꢀ at
-
TeO3 at 380 nm were those shown in Figure 4.
At pH 9.27, 9.62, 9.92, and 10.6, the additional reactions 4,
7, 12, 13, as well as
3-
325 nm. Since the large base strength of TeO4 precludes a
3-
direct determination of ꢀTeO , pK10 was determined from eq
4
TeO3- + B- + H2O a HTeO42- + HB (24),(-24)
27 by adjusting ꢀTeO to ꢀTeO ) 6400 M-1 cm-1 by trial
3-
3-
4
4

Tellurium(V). A Pulse Radiolysis Study
J. Phys. Chem. A, Vol. 105, No. 27, 2001 6643
TABLE 2: Standard Electrode Potentials
the reaction between Te(V) and O2 is very fast, which we take
-
-
to suggest that TeO5 rather than O2 is the product.
electrode process
E°/Volta
The reactions of the Te(V) species H2TeO4-, TeO3-, HTeO42-
,
2-
TeO3- + e- ) TeO3
1.74
2.31
1.50
3-
and TeO4 with O2 may be
TeO3- + H+ + e- ) HTeO3
-
HTeO42- + e- ) TeO3
2-
H2TeO4- + O2 f TeO5- + H2O
(32)
(33)
(34)
TeO43- + H2O + e- ) TeO32- + OH-
H6TeO6 + e- ) TeO3- + 3H2O
1.45
-0.40
-0.52
-0.66
H5TeO6- + e- ) HTeO42- + 2H2O
H4TeO62- + e- ) TeO43- + 3H2O
-
TeO3- + O2 f TeO5
a Estimated error ( 0.01 V.
HTeO42- + O2 f TeO5- + OH-
and error until the required linear dependence on pH was
obtained.
The determination of the rate constants for both pairs of
and
TeO43- + O2 + H2O f TeO5- + 2OH-
(35)
forward and the reverse reactions 4, -4, and 5, -5 allows us
3-
to determine the standard Gibbs energy of formation of TeO4
,
The rate constants k33, k34, and k35, for reactions 33, 34, and
35, were determined from measurements of the first-order rate
constants for disappearance of Te(V) in N2O-saturated 5 × 10-4
M tellurite solutions containing oxygen in the concentrations
1.9 × 10-4 M, 2.5 × 10-4 M, and 3.8 × 10-4 M O2. At pH 7.9
the first-order rate constant for disappearance of Te(V) was
found to be (1.7 ( 0.2) × 105 s-1 at 2.5 × 10-4 M O2. Since
HTeO42-, and TeO3-. These may be calculated from
∆fGaoo(TeO43-) ) RT ln(k-5/k5) +
∆fGaoo(TeO32-) + ∆fGaoo(O-) (28)
∆fGaoo(HTeO42-) ) RT ln(k-4/k4) +
∆fGaoo(TeO32-) + ∆fGaoo(OH) (29)
-
the rate constant for the dehydration of H2TeO4 in 5 × 10-4
M tellurite is three times larger, we assume that the value
measured pertains to the pseudo first-order constant of reaction
33. With this assumption we find k33 ) (6.8 ( 0.8) × 108 M-1
s-1. k34 () 3.1 ( 0.17 × 108 M-1 s-1) was determined from
measurements in solutions containing 1.9 × 10-4 M, 2.5 × 10-4
M, and 3.8 × 10-4 M O2 at pH 11.1, at which pH HTeO42- is
and
-
∆fGaoo(TeO3 ) ) RT ln K8,9 + ∆fGaoo(HTeO42-) -
∆fGaoo(H2O) (30)
the predominant species. k35 () (2.5 ( 0.3) × 108 M-1 s-1
)
was determined from the value of k34 and the rate constant k
() (2.8 ( 0.3) × 108 M-1 s-1) for disappearance of Te(V)
determined in a solution containing 2.5 × 10-4 M O2 at pH
13.3, where HTeO42- and TeO43- are present in approximately
equal concentrations.
-
The standard Gibbs energy of formation of H2TeO4 may
be estimated from
-
∆fGaoo(H2TeO4 ) ) ∆fGaoo(HTeO42-) + RT ln K
-
H2TeO4
Pseudo first-order rate constants for the disappearance of
Te(V) in solutions containing CO32- and HCO3- were measured
in N2O-saturated 10-2 M tellurite solutions and in 10-2 M O2-
free tellurate solutions. The product of the reaction was identified
(31)
Taking ∆fGaoo(TeO32-) ) -383.4 kJ/mol,17 ∆fGaoo(O-) )
95 kJ/mol,26 ∆fGaoo(OH) ) 27 kJ/mol,26 and ∆fGaoo(H2O) )
by its spectrum as CO3 .
- 30 The total concentration of carbonate,
[CO32-] + [HCO3-], was varied between 10-2 M and 6 × 10-4
22
-237.13 kJ/mol,27 and estimating KH TeO = 10-7
for the
-
2
4
M. The fractions xHCO ) [HCO3-]/([CO32-] + [HCO3-]) and
dissociation of H2TeO4-, we find ∆fGaoo(TeO43-) ) -319 kJ/
mol, ∆fGaoo(HTeO42-) ) -394 kJ/mol, ∆fGaoo(TeO3-) ) -214
kJ/mol, and ∆fGaoo(H2TeO4-) = -434 kJ/mol.
-
3
xTeO ) [TeO3-]/([HTeO42-] + [TeO3-]) were calculated from
-
3
-
pH of the solutions and the pK values of HCO3 and
TeO3-, taken as the values pertaining to infinite dilute solution
These results lead to ∆G° ) 17 kJ/mol for the hydration of
TeO3- and, hence, to the estimate K8 = 10-3 for the equilibrium
8, -8, a value in agreement with the fact that reaction 8 was
not observed.
The standard electrode potentials shown in Table 2 are
calculated from the values of ∆fGaoo for the four Te(V) species
and from published values of ∆fGaoo for the Te(IV) and Te(VI)
species.17
- 27
(10.34 for HCO3
and 9.97 for TeO3-) corrected by
means of Gu¨ntelberg’s formula for the activity coefficients of
ions.31
In strongly alkaline solution (pH g 13), where the dominant
Te(V) species are HTeO4 and TeO43-, no reaction was
2-
observed, indicating that CO32- does not react at a measurable
rate with HTeO42- and TeO43-, in accordance with the fact that
∆G° for these reactions are positive.
Reactions of Te(V) with O2 and HCO3-. Te(V) species
were found to react with O2 under formation of a product having
an absorption that increases with decreasing wavelength without
reaching a maximum in the range (>250 nm) accessible with
-
Measurements in less alkaline solutions show that TeO3 is
the only Te(V) species that reacts at a measurable rate with
HCO3 and CO32-. We find that the decay of the absorbance
-
at 350 nm is of pseudo first order with a rate constant that for
our instrument. The observable part of this spectrum resembles
fixed xHCO (and xTeO ) is proportional to [CO32-] + [HCO3-].
-
-
that of O2- 28 as well as those of SO5
,
- 29 the O2-adduct of SO3
,
-
3
3
Further we find that the second-order constant, k36, for the
and the O2-adduct of As(IV).23 Hence, with the reasonable
assumption that an O2-adduct of TeO3- () TeO5-) would also
have a spectrum similar to that of O2-, the observed spectrum
suggests that the product is either O2- or TeO5-, the reduction
of O2 implied by both assignments being consistent with the
high reduction power of the Te(V) species (Table 2). However,
2-
-
reaction of Te(V) with total carbonate (CO3 + HCO3
divided by xTeO varies linearly with xHCO , indicating that k36/
xTeO may be expressed by
)
-
-
3
3
-
3
k36/xTeO - ) k x
- + k38(1 - x
)
-
HCO3
(36)
37 HCO3
3

6644 J. Phys. Chem. A, Vol. 105, No. 27, 2001
Kla¨ning and Sehested
-
TABLE 3: Standard Electrode Potentials of SO3-, SeO3
,
-
and TeO3
electrode process
Eo/Volt
ref
SO3- + e- ) SO3
0.73 ( 0.01
1.68 ( 0.01
1
6
2-
SeO3- + e- ) SeO3
2-
2-
TeO3- + e- ) TeO3
1.74 ( 0.02 this work
SO42- + 2H+ + e- ) SO3- + H2O
SeO42- + 2H+ + e- ) SeO3- + H2O
-0.91 ( 0.01
-0.03 ( 0.01
1
6
H4TeO62- + 2H+ + e- ) TeO3- + 3H2O -0.70 ( 0.02 this work
reactions by ∆G° (8,9) and ∆G° (39,40), respectively, we have
∆G°(39,40) - ∆G°(8,9) ) - RT ln K39,40 + RT ln K8,9
(41)
-
Taking the acid constants K41 and K9 of H2SeO4- and H2TeO4
to be equal and assuming, moreover, that the rate constant of
-
-
the uncatalyzed hydration of SeO3 is equal to that of TeO3
,
Figure 9. Determination of the rate constants k37 and k38 for oxidation
i.e., k39 ) k8 we find
HCO3- and CO32- by TeO3-. k36/xTeO ) k37‚xHCO + k38(1 - xHCO
)
-
-
-
3
3
3
-
is plotted against xHCO . k36 is the pseudo-first-order rate constant for
-RT ln K39,40 + RT ln K8,9 ) ∆G°(39) - ∆G°(8) )
3
-
decay of absorbance at 350 nm in solutions containing HCO3 and
RT ln k-39/k-8 (42)
-
CO32- multiplied by ([HCO3-] + [CO32-]). xTeO ) [TeO3-]/([TeO3
]
-
3
+ [HTeO42-]), xHCO ) [HCO3-]/([HCO3-] + [CO32-]). 0 and × are
experimental points3and the straight line is a linear least-squares fit to
the experimental points. The points 0 were measured in N2O-saturated
solutions containing HTeO3- and TeO32- in the total concentration 10-2
M, and in which the total concentration of HCO3- and CO32- was varied
between 5 × 10-3 M and 6 × 10-2 M. The points × were measured
-
for the difference between the standard Gibbs energy of
-
-
hydration of SeO3 and of TeO3
.
Setting K39,40 ) 10-14,6 K8,9 ) 10-10, and k-8 ) k6 ∼ 104
s-1 as determined above for the uncatalyzed dehydration of
H2TeO4-, we find k-39 ∼ 107 s-1 for the uncatalyzed dehydra-
tion of H2SeO4-, a value that would make H2SeO4- impossible
to detect with the apparatus used.6
2-
in Ar-saturated solutions containing H6TeO6, H5TeO6-, and H4TeO6
in the total concentration 10-2 M, and in which the total concentration
-
2-
of HCO3 and CO3 was varied between 10-2 M and 2 × 10-2 M.
In contrast to Se(V) and Te(V), S(V) apparently cannot form
four-coordinated oxoradicals. Thus the species SO43- is inher-
where k37 and k38 are the rate constants of
2-
ently unstable: electron attatchment to SO4 in solid K2SO4
leads to immediate dissociation into O- and SO3 even at
2-
-
HCO3- + TeO3- f CO3- + HTeO3
cryogenic temperatures.33 Moreover, the fact that sulfate in
contrast to selenate and tellurate is inert toward reduction by
the hydrated electron16 suggests that this dissociative state
(SO43-) lies high in energy. Consequently, whereas the oxidation
of selenite and tellurite by O-/OH seems to take place by
addition to the selenium or tellurium atom, this type of process
does not appear feasible for sulfite.
∆G° ) -11 kJ/mol (37)
and
2-
CO32- + TeO3- ) CO3- + TeO3
∆G° ) -15 kJ/mol
(38)
The standard electrode potentials of SO3-, SeO3-, and TeO3
are compiled in Table 3. As apparent from the table, the redox
-
respectively. ∆G° for reactions are calculated taking the standard
electrode potential of CO3-/CO3 equals 1.59 V.32
2-
-
properties do not change smoothly on going from SO3 to
-
-
Figure 9 shows a plot of k36/xTeO against xHCO . From a
3
3
TeO3-. Thus, as oxidants, SeO3- and TeO3- are equally strong
and much stronger than SO3-. On the other hand, as reducing
linear least-squares fit to the experimental points we find k37
)
1.6 × 106 M-1 s-1 and k38 ) 1.7 × 107 M-1 s-1. We note that
-
-
agents, SO3 and TeO3 are of similar strength and much
k38 is much larger than k37, reflecting that reaction 37 takes place
stronger than SeO3-. These differences are reflected in the
by hydrogen atom transfer, and reaction 38 by electron transfer.
Comparison of the Oxoradicals of S(V), Se(V), and
Te(V). The only four-coordinated Se(V) oxoradical observed
in aqueous solution is HSeO42-.6 This species is detected only
in strongly alkaline solution (pH > 13) indicating an extremely
low acid strength, which of cause precludes the detection in
aqueous solution of its corresponding base, SeO43-. This species,
reactions with O2 and with HCO3 and CO32-: SeO3 and
-
-
-
2-
-
TeO3 both oxidize HCO3-/CO3 to CO3-, SO3 does not;
-
-
SO3 and TeO3 both reduce O2, whereas no reaction of O2
-
with SeO3 has been observed.6
Acknowledgment. We thank Dr. Igor Plesner for making
the Gepasi method of modeling chemical kinetics available to
us and for the instruction in the use of this method. Dr. Jørgen
R. Byberg is thanked for improving the manuscript by construc-
tive criticism and valuable suggestions. Hanne Corfitsen and
Torben Johansen are thanked for technical assistence. We are
grateful to a referee for suggesting that the reaction of Te(V)
with O2 leads to O2-adducts.
however, has been observed in X-ray-irradiated crystals contain-
2- 10
ing SeO4
.
2-
The low acid strength of HSeO4 as compared to that of
-
HTeO42-, and the fact that H2TeO4 is observed whereas
-
H2SeO4 is not, may be rationalized by comparing the set of
reactions 8, -8, 9, and -9 with the corresponding set
SeO3- + H2O / H2SeO4- / HSeO42- + H+
(39),(-39),(40),(-40)
References and Notes
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Tellurium(V). A Pulse Radiolysis Study
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