Correspondence pubs.acs.org/IECR
Comments on “Mechanism and Kinetics of Sulfite Oxidation in the Presence of Ethanol”: Corrected Rate Law for Sulfite Oxidation Mechanism with Ethanol Inhibition David A. Rockstraw New Mexico State University, Box 30001, MSC 3805, S. Horseshoe Oval, Jett Hall 259, Las Cruces, New Mexico 88003, United States Sir: The rate law proposed by Wang et al.1 is not consistent with the proposed mechanism. Wang et al. proposed the following mechanism of elementary steps to describe the oxidation of sulfite inhibited by the presence of ethanol:
[*SO−3 ] =
=
k1
HSO−3 + O2 → (*SO−3 ) + (*HOO)
(1)
k2
(*SO−3 ) + O2 → (*SO−5 ) k3
⎛k K ⎞ r = k 2⎜ 1 a ⎟[O2 ]3/2 ⎝ k5 ⎠
(3)
k4
SO52 − + SO32 − → 2SO24 −
(4)
k5
2(*SO−3 ) + C2H5OH → C2H5OSO−2 + SO24 −
It was assumed that the rate-controlling step was eq 2; thus, the rate law can be written as (6)
Applying the pseudo-steady-state hypothesis to the radical concentrations, r*SO−3 = k1[HSO−3 ][O2 ] − k 2[*SO−3 ][O2 ] + k 3[SO32 −] [*SO−5 ] − k5[*SO−3 ]2 [C2H5OH] =0 (7)
■ ■ ■
r*SO−5 = k 2[*SO−3 ][O2 ] − k 3[SO32 −][*SO−5 ] =0
(8)
=
k1[HSO−3 ][O2 ]
k5[*SO−3 ]2 [C2H5OH] = k1K a[SO32 −][H+][O2 ]
(11)
REFERENCES
(1) Wang, L. D.; Ma, Y. L.; Hao, J. M.; Zhao, Y. Mechanism and Kinetics of Sulfite Oxidation in the Presence of Ethanol. Ind. Eng. Chem. Res. 2009, 48, 4307.
Solving eq 11 for the radical concentration yields eq 12: © 2012 American Chemical Society
AUTHOR INFORMATION
ACKNOWLEDGMENTS Thank you to Dr. H. Scott Fogler for reviewing the derivation in this correspondence prior to submission.
The bisulfite concentration can be eliminated by substitution of the equilibrium constant defined by Wang et al.,1 as shown by substituting eq 10 into eq 9 to yield 11: (10)
(13)
The authors declare no competing financial interest.
(9)
[HSO−3 ] = K a[SO32 −][H+]
[SO32 −][H+] [C2H5OH]
Notes
Substituting eq 8 into eq 7 to eliminate the terms containing k2 and k3 yields k5[*SO−3 ]2 [C2H5OH]
(12)
As such, the effect of the oxygen concentration on the reaction rate based on the proposed mechanism is 1.5-order, rather than second order as stated in the article. An attempt to check the goodness of fit to this model was unsuccessful and led to the identification of inconsistencies in the data. There are five data points in Table 2 of the original article1 for which temperature, pH, sulfite concentration, and ethanol concentration are constant (see data points 4, 9, 12, 13, and 14). Data points 4 and 9 are for identical reaction conditions, but report reaction rates that differ by a factor of 2. On the other hand, data points 12 and 13 represent rates for which oxygen concentrations differ by a factor of greater than two, but the reaction rates of the two conditions are identical. The rate data presented in Table 2 of the original article1 does not support the regression results presented in the article, nor can they be used to fit the 1.5-order oxygen concentration model derived above.
(5)
r = k 2[*SO−3 ][O2 ]
k1K a[SO32 −][H+][O2 ] k5[C2H5OH]
Substitution of the radical concentration in eq 12 into the rate law described by eq 6 leads to the final result for the proposed mechanism given in eq 13:
(2)
(*SO−5 ) + SO32 − → SO52 − + (*SO−3 )
k1[HSO−3 ][O2 ] k5[C2H5OH]
Published: August 22, 2012 11587
dx.doi.org/10.1021/ie3014583 | Ind. Eng. Chem. Res. 2012, 51, 11587−11587
