A mathematical model for oxygen exchange out of labeled
(e.g., 17O) Na2CrO4 into
solvent H2O according
to the dimerization reaction
2CrO4
2- + 2H+ ⇌
(1/K
a(HCrO
4
−
))
2HCrO4
- ⇌ (α/β)
Cr2O7
2- +
H2O is described. Two
rates of isotopic change are identified: (1) a rapid change
intimately associated with the attainment of chemical
equilibrium, but not identical with it (rate constants ν1
and ν2, respectively), in which the fractional label in
monomeric
HCrO4
- +
CrO4
2- (p) decreases
more rapidly than that in the dimer
Cr2O7
2-
(q), i.e. ṗ > q̇, followed
by (2) a
slower decrease in both (q̇ > ṗ)
until isotopic equilibrium with the solvent is established,
p = q = r (rate
constant
ν3). Visible−UV and 17O NMR spectra
have been used to characterize the elusive
HCrO4
- ion. Vibrational
fine
structure is seen in the visible spectrum
(C
3
v
symmetry), and
integration of the monomeric (HCrO4
- +
CrO4
2-)
17O
absorption agrees with only four O atoms in
HCrO4
-. A pH-dependent shift to higher
frequency
(δCrO
4
2−
= 812
ppm;
δHCrO
4
−
= 860 ppm) is used to give
pK
a(HCrO
4
−
)
= 5.80 (I = 1.0 M, 25 °C), and comparisons with the
integrated
Cr2O7
2- signal
(δCr
2
O
7
2−
= 1115 ppm) give K
d's for dimerization (=
α/β) of 81 M-1 (I = 1.0 M)
and 132 M-1 (I =
6.0 M), at 25 °C. Dimerization and hydrolytic rate constants
(α and β) have been obtained under the conditions of
the 17O exchange experiments; they are shown to contain
spontaneous, buffer, and [H+] and [OH-]
contributions in
agreement with earlier investigations. 17O exchange
out of enriched Na2CrO4 has been followed
in aqueous solutions
over the concentration range 0.01−2.0 M and over the pH range
6.38−13.0 at 25 °C and constant ionic strength
(I
= 1.0, 6.0). The dimerization reaction (eq 1) contributes only
at the highest Cr(VI) concentration (2.0 M), and then
only slightly (i.e., ∼10% at pH 7.3). The rate data have been
interpreted in terms of the direct exchange paths
Cr17O4
2- +
H2O → (k
1)
Cr17O3O2- +
H2
17O;
HCr17O4
- + H2O →
(k
2)
HCr17O3O- +
H2
17O;
H2Cr17O4 + H2O
→
(k
3)
H2Cr17O3O +
H2
17O;
Cr2
17O7
2-
+ H2O → (k
4)
Cr2
17O6O2-
+ H2
17O, with rate constants
k
1 = 7.2 × 10-8
M-1
s-1, k
2 = 7.6 ×
10-4 M-1
s-1, k
3 = 1.7 ×
105 M-1
s-1 (I = 1.0 M, 25 °C), and
k
4 = 4.1 × 10-3
M-1 s-1
(I = 6.0
M, 25 °C). The monomeric paths (but not the rate constants)
agree with those found in an earlier study, but that
involving Cr2O7
2- is
new. Rate constants for 17O exchange are compared with
those of other substitution reactions
of HCrO4
- and
Cr2O7
2-.