344
Ind. Eng. Chem. Fundam. 1982, 27, 344-352
Kinetics of Sulfite Oxidation Reaction K. Slvajl' and 0. S. R. N. Murty' Department of Chemical Engineering, Indian Institute of Technology, Bombay 400 076, India
A single liquid droplet of sodium sulfite solution, mixed with cobaltous sulfate catalyst, is suspended aerodynamically in air and used as a means of contacting oxygen in air to study the kinetics of the sulfite oxidation reaction. For the two sulfite concentrations studied, 0.39 and 0.15 mol L-', the reaction is found to be independent of sulfite concentration in the former case, while in the latter concentration the reaction is first order in both the solute gas and the reacting species. Overall, the process is fast second order and the order in the catalyst is unity. No previous experimental work was reported making use of this technique and system.
Introduction The absorption of oxygen in sodium sulfite solution in the presence of cobaltous sulfate has been used for determination of interfacial area in different gas-liquid contacting devices such as agitated vessels, packed columns, and bubble columns. This method requires knowledge of the kinetics of the homogeneous reaction of dissolved oxygen with sulfite ions. The kinetics of this reaction has been studied by many workers (e.g., Fuller and Christ, 1930; Onken and Schalk, 1978). However, there is a wide disagreement in the reported data, and the kinetics of the reaction are still not well understood as the reaction is extremely complex in nature. Also, in several cases, the results of different workers appear to contradict one another. The most significant feature of the reaction is its marked sensitivity to catalysts of both positive and negative ion species. Further, experimental results seem to depend upon the type of equipment used to study the reaction, purity of sulfite used, the pH of solution, and concentrations of oxygen and sulfite solution (Yagi and Inoue, 1962; De Waal and Okeson, 1966). Linek and Mayrhoferovii (1970) explained the influences of impurities, pH, and the presence of inert gas on the rate of absorption. The reaction rate has been found to be increasing with increasing pH up to 9.1 (Chen and Barron, 1972; Srivastava et al., 1968; Linek and Mayrhoferovi, 19701, but beyond this pH value the studies are limited. Review of Literature A detailed review on sulfite oxidation is given by Danckwerts (1970), Sherwood et al. (1975), Sivaji (1977), and Linek and Vacek (1981). The order of reaction with respect to oxygen changes with sulfite concentration and also with oxygen partial pressure (Linek and Mayrhoferovii, 1970). Linek and Mayrhoferovii(l970) have observed the order of reaction to be one or two in oxygen and zero in sulfite for the concentration range of oxygen and sulfite studied. Barron and O'Hern (1966) and Chen and Barron (1972) have employed the rapid mixing technique for studying the kinetics of this reaction in the presence of copper and cobalt catalysts. In both these cases, the reaction is zero order in oxygen and 1.5 order in sulfite, and rate is proportional to square root of catalyst concentration. Kinetic studies with the thermal flow *Department of Chemical Engineering, Indian Institute of Science, Bangalore 560012, India. Retired Professor, 105A-Prashant Appartments, Opposite to I.I.T. Main Gate, Powai, Bombay 400 076, India.
method (Srivastava et al., 1968) show that the reaction is first order in oxygen and 1.5 order in sulfite, and the rate is proportional to the square root of catalyst concentration. Kinetic studies with the thermal flow method show that the reaction is first order in oxygen and variable order in sulfite concentration. Experiments with agitated vessels and laminar jet apparatus (Bengtsson and Bjerle, 1975) show that the orders are zero, 1.5, and 0.5 with respect to oxygen, sulfite, and cobalt concentrations, respectively. Yagi and Inoue (1962) used very dilute solutions and reported a first-order reaction in oxygen, but their results differ considerably with those of Barron and O'Hern (1966). The findings of Trushanov et al. (1975) deviate from others regarding the order of reaction with respect to sulfite concentration: when sulfite concentration is below 0.2 mol L-l, the order is unity in sulfite and zero order above 0.2 mol L-' concentration. Studies of Sawicki and Barron (1973) with wetted-wall columns indicate that the reaction is second order in oxygen and 0.5 order in cobalt concentration. However, he reported zero order in oxygen under homogeneous conditions. The difference in reaction orders can be attributed to the observed variation in activation energies for the two systems. Linek (1966) extensively investigated the reaction in a stirred cell and found that the reaction is between first and second order in oxygen. Wesselingh and Van't Hoog (1970) reported, from their experiments on wetted-wall columns and a laminar jet, that the order is two in oxygen. Their results on absorption rates are in good agreement with those of Reith (1966),but for the wetted-wall column, De Waal and Okeson (1966) mistakenly reported the reaction to be first order in oxygen. Since the reaction of oxygen with sodium sulfite is complex and the reaction depends on several unavoidable factors, we have studied the kinetics of this reaction in an entirely different type of contactor. In the present work, a liquid droplet of sodium sulfite solution (mixed with catalyst) suspended freely in air was used to study the kinetics of this reaction. This technique eliminates the use of any external agitator or a metallic moving device. Due to constant partial pressure all along the interface, the absorption rates are uniform at all places on the droplet surface. Any liquid element on the surface will have a longer contact time than in a laminar-jet apparatus. Some of the inherent experimental constraints present in a wetted-wall apparatus, such as the occurrence of ripples of the liquid surface, may be eliminated in the proposed arrangement. Since the size of the droplet in the present work is large compared with the boundary layer thickness, the effect of curvature is negligible. No experimental data were reported earlier with such a contactor.
0196-4313/82/1021-0344$01.25/0 0 1982 American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 21, No. 4, 1982
Theoretical Treatment Very extensive treatment of absorption aecornpanied by chemical reaction is given by Danckwerts (1970) and Astarita (1967). However, expressions used in the present work are briefly discussed here. Consider a reaction A, + zB1 products (1)
-
The reaction is irreversible and mth order in A and nth order in B. Gaseous species A dissolving in liquid undergoes a chemical reaction with species B present in the liquid phase. 2 is the stoichiometric coefficient. If the solubility of A in the liquid phase is limited, then the gas-side resistance is negligible and all the resistance to mass transfer is confined to the liquid phase. Further, on assuming that the reacting species B and the product are nonvolatile, the following dimensionless terms are defined (Danckwerts, 1970) &p12=-
[-
11 2
DA~,,(A*)~-'(&)"]
kL m + l
(2)
Table Ia
t, s 0 60 90 120
The term hPI2gives a ratio of A reacting in the film to that going unreacted in the bulk B phase according to Chhabria and Sharma (1974). The reaction represented by eq 1can be considered as a "fast" reaction if
Wf2 > 1.0 (4) On the other hand, if the value of MI2is less than 1, then the reaction is termed a "slow" one. Reaction 1is a fast pseudo-mth order reaction provided the following two conditions are fulfilled M
> 3.0
R
lo6,
X
mol/ cm2 s
K2,n x mL/cm3 s
-
iW2
-
0.150 0.140 0.144
2.35 2.04 2.17 av K2,n 2.19
4.41 4.03 4.12
qA
862 669 634 584
Table IIa
Bo x lo6, a , t, s mol/mL cm-I 0 60 120 240
(3)
Bo X lo6, a, mol/mL cm-l 387.10 6.12 300.45 4.81 285.12 4.06 262.29 3.60
mol L-l; reaca Concentration of catalyst = 7.11 X mol/mL; D A tion temperature = 28 "C; A* = 1.79 x = 2.51 X cm2/s;D B = 1.59 x cm2/s.
180
and
345
151.03 48.26 27.83 25.68 7.10
4.85 3.93 3.43 3.05 2.49
R
X
lo6,
mol/ Kl,, x l o - * , cm2 s mL/mol s
0.218 0.150 0.114 0.120
3.89 2.20 1.31 1.97 av K l , l 2.34
M1'*
qA
-
226 72 41 38 10
60 34 35 16
a Concentration of catalyst = 7.11 x mol L-l; reaction temperature = 25 "C; A* = 2.38 x mol/mL; DA = 2.33 x cm2/s;Dg= 1.19 X cmz/s.
Using eq 7 to integrate eq 9, we get for a second-order reaction in the gaseous solute 3(Bi - Bf)2 k2,o = 8 a 2 D ~ ( A * ) 3 t 2 (10) Similarly, for a reaction which is first order in both the solute gas and the reacting species, the second-order rate constant is given by
(5)
and
