4002 J. Phys. Chem. B, Vol. 102, No. 20, 1998
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Emerging Technologies in Hazardous Waste Management.; Tedder, D. W.,
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pp 35-76.
Table 2). However, the equilibrium constant obtained from the
experiment performed at 360 °C with the solution acidified with
3.83 × 10-3 m HClO4 deviated strongly from the model,
indicating that perchloric acid was not fully dissociated under
these conditions. The model was further used to calculate the
dissociation constants of chromic acid at temperatures higher
than 340 °C.
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(iii) Errors in Density. The accuracy of the normalized
absorbance depends on the uncertainty in the solution density.
We have utilized density data for NaCl solutions to estimate
-
the effect of solution density on mHCrO . The density of a 0.2%
4
NaCl (approximately 3.4 × 10-2 mol kg-1) solution at 396 °C
and 271 atm pressure, i.e., under conditions very similar to our
experiments, is around 7% higher than the pure steam density
under identical conditions.77 At lower temperatures this dif-
ference is smaller. Consequently, the absorbance measured at
400 °C and 27.6 MPa for our more dilute solutions may be
overestimated by approximately 7%, whereas the observed
increase in the normalized absorbance is much higher (Figure
4). In addition, the absorbance increase is accompanied by a
spectral shift indicating a change in equilibrium, not just a
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Society: Washington, DC, 1989; pp 276-286.
-
change in mHCrO (Figures 4 and 5). Clearly, the density effect
4
on the normalized absorbances is minor compared with the
change in chemical equilibrium.
(iv) Other Sources of Error. A 1% uncertainty in KOH
concentration produces an uncertainty of 0.1 in pKa2 at 160 °C
for the lowest KOH concentration (2.91 × 10-4 m) and 0.03
for the highest concentration. At 180 °C the corresponding
numbers are 0.05 and 0.03, while for other temperatures they
usually do not exceed 0.03. The uncertainty due to uncertainties
in band areas strongly depends on the chromate/bichromate ratio
and may be as high as 0.15 for a 2% uncertainty in the measured
area at 160 °C, but it quickly drops to around 0.05 at higher
temperatures.
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Conclusions
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Acid-base equilibria of Cr(VI) may be measured directly
by UV-vis spectroscopy up to 400 °C. The deprotonation of
-
the HCrO4 becomes less favorable as the temperature of
alkaline solutions (m0
g 5.81 × 10-4 mol kg-1) of Cr(VI)
KOH
is raised from 20 to 260 °C. Bichromate is a sufficiently strong
acid such that deprotonation is exothermic. At higher temper-
atures, Ka2 decreases faster than at lower temperatures due to
an isobaric decrease in density. From 380 to 400 °C, the
-
HCrO4 concentration decreases unlike the case at lower
temperatures. Ion pair formation of (K+)(CrO42-) becomes very
favorable even in weakly alkaline solutions. Also pronounced
2-
electrostriction of water about CrO4 and nonspecific effects
of activity coefficients (ionic strength) can contribute to the
decreased stability of HCrO4- in the supercritical region. These
effects are best understood by examining the relative acidity of
-
bichromate versus water, described by the reaction HCrO4
+
OH- ) CrO4 + H2O, rather than Ka2. Progressive ionic
association eventually leads to K2CrO4 precipitation at 420 °C.
2-
(36) Sasaki, Y. Acta Chem. Scand. 1962, 16, 719.
Acknowledgment. We gratefully acknowledge support from
the Department of Energy (DE-FG07-96ER14687), from the
U.S. Army for a University Research Initiative Grant (30374-
CH-URI), from the R.A.Welch Foundation, and from the
Separations Research Program at the University of Texas, a
consortium of over 30 companies. We thank Steve Buelow and
Kirk Ziegler for useful discussions.
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References and Notes
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