36
Ind. Eng.
Chem. Fundam. 1980, 19, 36-39
McKoy, V., Sinanoglu, O.,J. Chem. Phys., 38, 2946 (1963). Ng, H.J., Robinson, D. B., Ind. €ng. Chem. Fundam., 15, 293 (1976). Ng, H.J., Robinson, D. B., AIChEJ., 23, 477 (1977). Parrish, W. R., Prausnitz, J. M., Ind. fng. Chem. Process Des. Dev., 11, 26 (1972). Peng, D.-Y., Robinson, D. B., Ind. Eng. Chem. Fundam., 15, 59 (1976). Sloan, E. D., Khoury, F. M., Kobayashi, R., Ind. Eng. c&m. Fundam., 15,318 (1976).
van der Waals, J. H., Platteeuw, J. C., Adv. Chem. Phys., 2, 1 (1959).
Received f o r review January 8, 1979 Accepted October 24, 1979 The financid support received from the Alberta Research council for this work is sincerely appreciated.
Kinetics of Absorption of Oxygen in Aqueous Solutions of Ammonium Sulfite K. Neelakantan and J. K. Gehlawat" Department of Chemical Engineering, Indian Institute of Technology, Kanpur, Kanpur-2080 16, India
The reaction between oxygen and ammonium sulfite is industrially important. The kinetics of absorption of oxygen in aqueous solutions of ammonium sulfite was studied in stirred cells. Cobaltous sulfate was used as the soluble catalyst. The absorption of oxygen in ammonium sulfite solutions was found to conform to the fast pseudenth-order mechanism. In the range of the reactant concentrations of 0.045to 0.45g-mol/L the reaction was found to be first order with respect to oxygen and second order with respect to ammonium sulfite. The third-order reaction rate constant at 30 OC was found to be 2.70 X IO4 [L/g-molI2 s-' and the energy of activation was found to be 14.5 kcal/g-mol.
Introduction Aqueous solutions of ammonia are used to absorb the lean mixtures of waste sulfur dioxide to control atmospheric pollution in several fertilizer plants producing SO2 and ammonia. Ammonium sulfite is thus obtained as a byproduct. It can be easily oxidized to ammonium sulfate, which is used as a fertilizer. In the chemical engineering literature the problem of oxidation of aqueous sodium sulfite has been studied exhaustively. On the other hand, the oxidation of ammonium sulfite has received very little attention. Some preliminary studies have been reported by Young (19021, Vorlander and Lainau (1929),and Hori (1937). Recently Grigorayan (1968) investigated the oxidation of ammonium sulfite by atmospheric oxygen in the presence of nitrogen oxides. Matsuura et al. (1969) studied this reaction in a batch reactor without catalysts. Mishra and Srivastava (1975, 1976) conducted a study for the homogeneous and heterogeneous liquid phase oxidation of ammonium sulfite by the Hatridge and Roughton method of rapid mixing. A mechanism of the reaction was proposed. It may be noted that detailed information on the kinetics of the heterogeneous reaction between oxygen and ammonium sulfite under conditions of industrial importance is not available in the literature. According to the theory of absorption with chemical reaction, this system is likely to conform to the fast reaction regime. It may be erroneous to infer anything about the kinetics of absorption of oxygen in ammonium sulfite solutions based on the controversial information available on the sodium sulfite-oxygen system. An independent study is needed. The present work was therefore undertaken to make a systematic study of the kinetics of reaction between dissolved oxygen and ammonium sulfite. An apparatus 00 19-78741801 1019-0036$0 1.OO/O
of well-defined interface geometry has been used. The theory of absorption accompanied by chemical reaction has been used to interpret the results obtained. Experimental Section Absorption experiments were carried out in stirred cells of various dimensions. The design features of the apparatus were similar to those employed by Gehlawat and Sharma (1968). Figure 1shows the schematic diagram for the experimental setup. A known amount of solution was added to the stirred cell which was installed in a constant-temperature bath. The absorption of oxygen was measured by the volumetric uptake method similar to that employed by Gehlawat and Sharma (1968) and the analytical method described by Jhaveri and Sharma (1967). In the volumetric uptake method, pure oxygen was placed in a balloon which was connected to the stirred cell. The volumetric uptake of oxygen was measured by a soap-film meter. In a few experiments the partial pressure of oxygen was varied from 12.5% to 99% by using nitrogen as the diluent. The mixture of oxygen and nitrogen in the desired proportion was passed through the apparatus for sufficient time so that the partial pressure of oxygen in the apparatus was the same as that in the incoming stream. The gas phase in the stirred cell was also agitated by another stirrer kept a t about 0.5 cm above the gas-liquid interface. A known amount of solution of known concentration was then introduced in the cell, the gas flow was stopped, and the unit was connected to a balloon containing pure oxygen at essentially atmospheric pressure. After several minutes the volumetric uptake of oxygen was noted. In the analytical technique oxygen or mixtures of oxygen and nitrogen were passed through the apparatus containing a known amount of solution of prefixed concentration for 0
1980
American Chemical Society
Ind. Eng. Chem. Fundam., Vol. 19, No. 1, 1980
37
P
q t,
1 Gas c y mdvl
3 63
2 Bubtisr
i 5oaa
5 ittrrcc ccl
103"
1 1 1 ' 1rnefai
5 5t
rror
10
M a - c ~ r )i e r i i
3'occs
Figure 1. Flow diagram for a stirred cell.
E 'L
3
Reaction
Gas l l q u l l inter l a w
153
IZG
233
250
cm2
Figure 3. Effect of interfacial area on the specific rate of absorption in stirred cells at 30 OC.
Eulg liquid
Gas phase
[ A IC
50
Ettective intzrtciial area s t tne st rred c e I
6
5:
I
Figure 2. Concentration profiles of reactant [B] and dissolved solute [A] for a fast reaction conforming to pseudo-nth-order mechanism. The film thickness is 6.
a known period of time and the progress of reaction was determined by analyzing the solution for the sulfite content before and a t the end of the run. The ammonium sulfite was analyzed according to the method suggested by Vogel (1951). A known amount of ammonium sulfite was titrated against standard iodineiodide solution using starch as indicator.
Theory of Fast Reactions The reaction between dissolved oxygen and ammonium sulfite is likely to be a fast reaction. Hence the theory of absorption accompanied by a fast reaction is discussed briefly. Consider the reaction A(g) + ZB(1) products (1) where A is the dissolved gas reacting with a nonvolatile reactant B and 2 is the number of moles of reactant B reacting with one mole of solute A. If the solubility of the solute gas in the liquid is very low, the gas-side resistance will have a negligible effect. For a fast reaction, the reaction between dissolved solute gas A and the reactant B occurs entirely in the film.Under certain conditions the concentration of the reactant B in the neighborhood of the gas-liquid interface is very little different from that in the bulk of the liquid. Further, if its numerical value is much larger than the concentration of the dissolved gas A, the reactant concentration does not drop appreciably within the film. Under these conditions the solute gas A undergoes a pseudo-nth-order reaction mechanism. Figure 2 shows the concentration profiles for a fast pseudo-nth-order reaction. Brian (1964) has discussed the appropriate theory. The following equation for the specific rate of absorption was derived on the basis of the penetration theory.
-
[
R = [A] --D n t 1
A k m+*
[B]"[A]"-'
]1'2
(2)
where R = specific rate of absorption, g-mol/cm2 s; [A] = solubility of solute gas (species A) in the liquid, g-mol/cm3; DA = diffusivity of the solute gas (species A) in liquid, cm2/s; k,+, = reaction rate constant (cm3/g-mol)m+n-1 s-l; [B] = concentration of the reactant (species B), g-mol/cm3; m = order of reaction with respect to the reactant (species
1
c
13 ;ata1,st
20 Car-C"
3c
GC
ic
I
grnolollxlCJ
Figure 4. Effect of catalyst concentration on the specific rate of absorption in a stirred cell at 30 "C.
B); and n = order of reaction with respect to the solute gas (species A). The necessary physical conditions to be satisfied for the occurrence of the mechanism are
and
Results and Discussion Absorption in Different Stirred Cells. The data obtained on the absorption of oxygen in aqueous solutions of ammonium sulfite in different stirred cells using cobalt sulfate as the catalyst are shown in Figure 3. Note that the specific rate of absorption, R , g-mol/cm2s is the same for an eightfold variation in interfacial area. Further, the specific rate of absorption of oxygen in ammonium sulfite solutions was noted at different volumes of the reactant taken in the same stirred cell. It was found that for about threefold variation in the volume of reactant the specific rate of absorption was independent of the volume of the reactant. This means that the reaction is fast and takes place a t the interface. Effect of Catalyst Concentration, The absorption of oxygen in aqueous solutions of ammonium sulfite was carried out using different concentrations of cobaltous sulfate as catalyst. The results are shown in Figure 4. It
38
Ind. Eng. Chem. Fundam., Vol. 19, No. 1, 1980 I
0
-
00
20
IC
50
80
I
01
12
03
3 L
05
:E1 o r n o l e i l
100
Figure 7. Effect of ammonium sulfite concentration on the specific rate of absorption at 30 O C .
Speed o t agitation,rev lrcln
Figure 5. Effect of speed of agitation on the specific rate of absorption in a stirred cell at 30 O C .
I 0
0
20
LO
E0
80
sx.,j' 1-3 1CC
-lo x y g e r p c r t i a l 3ressu'o
Figure 6. Effect of partial pressure of oxygen on the specific rate of absorption at 30 "C.
is observed that the specific rate of absorption increases with an increase of catalyst concentration up to about 4.70 X g-mol/L; thereafter it tended to level off with the catalyst concentration. Hence additional experiments were carried out a t this optimum catalyst concentration. Effect of Speed of Agitation. Figure 5 shows a plot of the speed of agitation vs. the specific rate of absorption. Note that the rate does not vary with speed of agitation in the speed range used in this study. The hydrodynamic factors are therefore unimportant. Absorption in a Jet Apparatus. A few runs were carried out in a laminar jet apparatus for the absorption of pure oxygen in aqueous solutions of ammonium sulfite. The principal design features of the jet apparatus were akin to those employed by Gehlawat and Sharma (1968). The specific rate of absorption remained practically constant when the time of contact was varied from 0.016 to 0.09 s. This confirms that hydrodynamic factors are unimportant under the conditions of this study. Effect of Partial Pressure of Oxygen. The effect of partial pressure of oxygen on the absorption of oxygen in aqueous ammonium sulfite solutions was studied by the analytical method as well as by the volumetric uptake method. The data are shown in Figure 6. The specific rate of absorption is found to vary linearly with partial pressure of oxygen, which shows that the reaction is first order with respect to oxygen. This is in agreement with the observations of Mishra and Srivastava (1976). Effect of Concentration of Ammonium Sulfite. The reactant, concentration [B] was varied from 0.045 to 0.45 g-mol/L. The data obtained are plotted in Figure 7. It is observed that the rate of absorption increased linearly with reactant concentration. According to eq 2, this observation indicates the reaction to be second order with
[ 6:
Figure 8. Plot of log [B] vs. log @/[A])*.
respect to ammonium sulfite. Alternatively, as already noted, the reaction is first order with respect to oxygen. Thus, with the value of n = 1 in eq 2 it reduces it to
or
or
Thus a plot of log [R/[A]]2 vs. log [B] may be used to determine the order with respect to the reactant B. Figure 8 shows such a plot. The slope of the straight line of Figure 8 is found to be equal to 2. It confirms that the reaction is second order with respect to ammonium sulfite. It has been reported (Danckwerts, 1970) for the system sodium sulfite and oxygen that the pH of aqueous solution influences the rate of absorption. The pH of the aqueous solutions of ammonium sulfite used in this study was found to vary from 7.9 to 8.1. The variation was negligibly small and the rates of absorption are unlikely to be seriously affected. However, a few runs were carried out after adjusting the pH of solutions to different levels between 7.0 and 8.0. The rate of absorption of oxygen was found to be unaffected.
Physicochemical Data The values of the solubility and diffusivity of oxygen in aqueous solutions of ammonium sulfite have to be computed for determining the reaction rate constants.
Ind. Eng. Chem. Fundam., Vol. 19, No. 1, 1980 39
Table I. Reaction Rate Constants for the Reaction between Oxygen and Ammonium Sulfitea reaction rate constant, h , , (L/g-mol)' s - '
temp, "C
10 500
20 30 40 46
27 000 49 500 8 1 500
CoSO, catalyst concentration = 4.70 x Energy of activation ( E ) = 14.5 kcal/g-mol.
g-mol/L.
The solubility of oxygen in water has been reported by Morrison and Billet (1952). Its solubility in the reactant solutions was estimated by using the expression [AI log - = K J [Awl where [A] = solubility of oxygen in aqueous ammonium sulfite solutions; [A,] = solubility of oxygen in water; K, = i, + i- + i ; i = contribution due to various species, L/g-ion; and = ionic strength of solutions, g-ion/L. van Krevelen and Hoftizer (1948) have given the values of i for various ions and gases. The values of diffusivity of oxygen in water have been reported by Himmelblau (1964). The values of diffusivity of oxygen in various reactant solutions were estimated by the expression
f
DA - = constant PT where DA = diffusivity of oxygen in solution, cm2/s; p = viscosity of solution, cP; and T = temperature, K. Physical Mass Transfer Coefficient. The true values of the physical mass transfer coefficient are required to check the various conditions given by expression 3. The values of the physical mass transfer coefficient for the S02-water system a t different speeds of agitation have been reported by Gehlawat (1969) for the same stirred cell. They have been corrected for diffusivity and viscosity effects by the following expression.
For a typical run for the ammonium sulfite concentration of 0.414 g-mol/L the specific rate of absorption was R = 3.03 X g-mol/s cm2. The solubility of oxygen [A] = 9.4 X g-mol/cm3 and the physical mass transfer coefficient kL = 3.12 X cm/s. Thus D
which satisfied the condition given by expression 3. Further, the value of [B]/Z[A] is 213, indicating that the condition given by expression 4 was also satisfied. Hence the reaction is found to conform to fast pseudo-nth-order regime with values of m = 2 and n = 1. Reaction Rate Constant For the present system, eq 2 reduces to R = [A][DA~~[B]~]~'~ (10) from which
3c
31
33
32 1 T
~
1
34 O3 K)'
3L
~
Figure 9. Arrhenius plot for the reaction between oxygen and ammonium sulfite.
The values of the third-order reaction rate constant k3 calculated by using eq 11are reported in Table I. Figure 9 shows the Arrhenius plot of 1/T vs. log k3. The apparent energy of activation is found to be 14.5 kcal/g-mol.
Acknowledgment One of us (K.N.) wishes to thank the Government of Kerala and Quality Improvement Programme for an award of a Scholarship which enabled this work to be carried out.
Nomenclature [A] = solubility of the solute gas (oxygen) in solution, g-mol/ cm3 a = effective interfacial area in stirred cell, cm2 [B] = concentration of the reactant (ammonium sulfite), gmol/cm3 DA = liquid phase diffusivity of the solute gas, cm2/s 1 = ionic strength of electrolyte solution, g-ion/L i = contribution due to various species, L/g-ion k , = third-order reaction rate constant, (cm3 g mol s-l k,,, = reaction rate constant, (~m~/g-mol)"'~-;s-l IZL = liquid-phase mass transfer coefficient, cm/s m = order of reaction with respect to ammonium sulfite n = order of reaction with respect to oxygen R = specific rate of absorption, g-mol/cm2 s T = temperature of solution, K 2 = number of moles of reactant, B, reacting with one mole of the solute gas, A p = viscosity of solution, CP
Literature Cited Brian, P. L. T. AIChE J . 1964, 10, 5. Danckwerts, P. V. "Gas Liquid Reactions", McGraw-Hill: New York, 1970; pp 254-255. Gahlawat, J. K.; Sharma, M. M. Chem. Eng. Sci. 1968, 23, 1173. Gehlawat, J . K. P h D Thesis, Bombay University, 1969. Grigorayan, G. 0.Arm. Khem. Zh. 1968, 21, 711. Himmelblau, D. M. Chem. Rev. 1964, 64, 527. Hori, S.,Nippon Gakujutsu Kyokai Hokoku 1937, 13570. Jhaveri, A. S . ; Sharma, M. M. Chem. Eng. Sci. 1967, 22, 1. Matsuura. R.; Harada, J.; Akehata, T.; Shirai, J. J . Chem. Eng. Jpn. 1969, 2, 199. Mishra, G. C.; Srivastava, R. D. Chem. Eng. Sci. 1975, 30, 1387. Mishra, G. C.;Srivastava, R. D. J . Appl. Chem. Biotechnol. 1978, 26, 401. Morrison, T. J.; Billet, F. J . Chem. Soc. 1952, 3819. Van Krevelen. D. W.; Hoftizer, P. J. Chem. Ind. 21st Congr. Int. Chem. Ind. 1948. Vogel, A. I. "A. Textbook of Quantitative Inorganic Analysis", Longmans Green and Co. Ltd.: London, 1951; p 370. Vorlander. D.; Lainau, A. J. Pr. Chem 1929, 123, 351. Young, S. L. J . Am. Chem. SOC.1902, 24, 297.
Received for review January 29, 1979 Accepted August 17, 1979
