and useful discussions with J. F. Davidson are acknowledged. Nomenclature
D = column diameter, m G = superficial gas mass velocity, kg/m2 sec g = gravitional acceleration, m/sec2 1 = length of tube section, m L = liquid volumetric flow rate, m3/sec A p / l = gas pressure gradient, N/m3 t = film thickness, m u = liquid velocity, m/sec UC,= superficial gas velocity, m/sec a = liquid fraction Ti = interfacial shear stress, N/m2
Literature Cited
Cetinbudaklar, A. G., Jameson, G. J.. Chem. Eng. Sci.. 24, 1969 (1969). Davidson, J. F., University of Cambridge, private communication, 1972. Davidson, J. F.. Shearer, C. J.. J. Fluid Mech., 22, 321 (1965). Hewitt, G. F., "Analysis of Annular Two Phase Flow Applications of the Dukler Analysis to Vertical Upward Flow in a Tube," United Kingdom Atomic Energy Authority, A.E.R.E.-R3680. 1961, Hutton, E. E. T., Ph.D. Thesis, University of Queensland, 1974. Hutton, E. E. T.. Leung, L. S., Brooks, P. C., Nicklin, D. J., Chem. Eng. Sci., 1974,29, 493 (1974). Kafarov, V. V.. "International Symposium on Distillation." pp 153-158, Institution of Chemical Engineers, 1960. Koch, C. T., Ph.D. Thesis, Department of Chemical Engineering, University of Queensland, Australia. 1971. Lockhart, R. W., Martinelli, R. C., Chem. Eng. Progr., 45, 39 (1949). Nicklin, D. J., Koch, C. T., "A Model of Annular Flow," "Co-current Gas Liquid Flow," E. Rhodes and D. S. Scott, Ed., p 239, Plenum Press, NewYork, N.Y., 1969. Wallis, G. 6.. "One Dimensional Two-Phase Flow," pp 330-345, McGraw-Hill, New York, N.Y.. 1969. Wallis, G. E., "Flooding Velocities for Air and Water in Vertical Tubes," United Kingdom Atomic Energy Authority, A.E.E.W., R-123, 1961.
Anderson, G. H., Mantzouranis, B. G., Chem. Eng. Sci., 12, 109. 233 (1960). Calvert, D., Williams, B.,A.I.Ch.E. J., 1, 78 (1955).
Received for review March 28, 1974 Accepted November 4, 1974
Sulfur Dioxide Reactions with Ammonia in Humid Air Edwin M. Hartley, Jr., and Michael J. Matteson* School o f Chemical Engineering, Georgia lnstitute of Technology,Atlanta, Georgia 30332
The reaction of gaseous SO2 and NH3 in humid air at 23°C to form solid reaction products was studied experimentally in a flow-type reactor. With excess water vapor and oxygen, pure ammonium sulfate was formed in an initial concentration range of 4 to 60 mmol m-3. At equimolar ratios of NH3 and Son, ammonium sulfamate (3%) was also obtained. At water vapor concentrations approaching those of NH3 and SO2, the principal products were NH3.S02 and (NH3)2-S02 adducts with minor amounts of "$303, (NH4)2S207, NH4N3, and N3H7S04. At lower concentrations of 0 2 the reaction product was primarily (NH3)2-S02 with secondary products of N3H7S04 and NH3S03. The reaction rate was dependent on the amount of water vapor present but independent of the oxygen concentration. Rate constants were in the range 1-6 X l o 5 I. mol-' sec-'.
Introduction The reactions of gaseous NH3 and SO2 have received little attention in textbooks, although they were first studied by Dobereiner (1826). A property of this reaction which has concerned many investigators is the diversity of reaction products, dependent on the relative concentrations of the two species as well as the presence of oxygen and water vapor, and the temperature. Various researchers have found either N H 3 4 0 2 or (NH3)2-S02 adducts result as primary products (Schumann, 1900; Ephraim and Piotrowiski, 1911; Badar-ud-Din and Aslam, 1953; McLaren, et al., 1974) with a host of secondary products such as imides, polythionates, sulfates, thiosulfates; in the presence of 0 2 and H2O vapor, ammonium sulfate and sulfite are obtained. These products are usually formed in the condensed phase after an extremely rapid nucleation period. Ammonia and SO2 gases, upon reaction, condense out of the gas phase in an approximate ratio of 1:l NH3 to SO2 in the presence of excess S02, and in an approximate ratio of 2 : l NH3 to SO2 in the presence of excess "3. It is not certain whether the solid products are ionic salts or polymers. The reaction between NH3 and SO2 gases has had some application industrially mainly in the areas of ammonium
sulfate production and for recovering or removing SO2 from flue gas streams. In a process developed by two French companies (Mascorello, et al., 1969) flue gases are treated with gaseous ammonia and subsequently washed to remove 93 to 97% of the sulfur compounds in the form of ammonium sulfite, bisulfite, and sulfate. The wash liquors are treated to recover and recycle the ammonia and to recover the S02. An American process (Cann, 1971) treats SO2 with ammonia to form either ammonium sulfite or bisulfite which is separated and treated with either zinc oxide or an aqueous alkaline earth metal to liberate the NH3 for recycle and form an insoluble metal sulfite. The industrial concern in the production of ammonium sulfate, which is used mainly as a fertilizer, is the avoidance of sulfite, bisulfite, and sulfamate. Sulfite and bisulfite require additional costly operations devoted to the oxidation to sulfate. Ammonium sulfamate is to be avoided because of its herbicidal properties. The object of this work was to develop basic kinetic data for the formation of ammonium sulfate using stackgas concentrations (100-1000 ppm) of SO2 and to characterize the conditions under which other sulfur products are obtained. A reaction scheme has been developed and Ind. Eng. Chern., Fundarn., Vol. 14, No. 1, 1975
67
rate constants have been evaluated for conditions at 296"K,excess HzO and 0 2 . The effect of varying HzO and 0 2 on the reaction product was studied as well as the range of aerodynamic diameters of the particulate product.
68
Ind. Eng. Chem., Fundam., Vol. 14, No. 1, 1975
~F
o
G~ L
~A
S E S TEE~
O-RINGS
' I
Experimental Details An experimental arrangement was needed in which the quantity of solid reaction product and the concentration of the reactants could be measured a t various times during a reaction in order to obtain kinetic rate data. Preliminary experiments indicated that the reaction is extremely rapid. In one early test wherein about 4000 ppm each of SO2 and NH3 gases in moist air were introduced in a mixing tee, the tee almost instantaneously plugged with white crystalline solid. Another test at 500 ppm in moist air indicated the reaction had proceeded to over 50% completion in less than 2 sec. Because of the speed of the reaction and the low partial pressures of the limiting reactants, a constant-volume batch reactor was judged impractical. The method selected was a steady state flow reactor shown in Figure 1. The gases were introduced to the reactor through two concentric nozzles. Through one of the nozzles flowed humid air and SOz, and humid air-NH3 flowed through the other. The solid reaction product which formed in the reactor was either deposited on the surfaces of the reactor or caught by a membrane filter at the end of the reactor. Before deciding to use this reactor scheme, a test was made to determine if the reaction was surface dependent. Duplicate tests were made in which the only difference was the ratio of surface area to the volume of the reactor. This was done by packing the reactor with glass wool. No significant increase of reaction product was obtained with the packed reactor. With plug flow assumed, the residence time for any reaction was simply the reactor volume divided by the volumetric flow rate. Turbulence a t the inner nozzle exit was assumed sufficient to produce adequate mixing. The presence of solid deposit on the walls of the glass flow tube just behind the nozzle exit and a uniform deposit on the entire surface of the flow tube support this assumption. By varying the length of the inner concentric tube, or the total flow rate, various residence times were obtained for a series of tests at a fixed set of concentrations. Residence times of 0.02 to 1.00 sec were found appropriate. Total flow rates varied from 2 to 3 l./min. The quantity of reaction product formed during a given test was determined by weighing the reactor (less bottom assembly) before and after the test. Identification of product was by X-ray diffraction. All tests were carried a t 23.0 f 1°C and 750 h 5 Torr (1mmol m- = 24.61 ppm). Duration of tests varied from 12 min for high concentrations and long residence times to 60 min for low concentrations and short residence times. Care was taken to avoid excessive product build-up on the filter, which could increase pressure by plugging. A 47-mm membrane type filter of 1.2-ym pore size offered the optimum flowthrough characteristics, while still retaining maximum product. To test the effectiveness of the 1.2-pm pore size, duplicate experiments were carried out with 0.45-pm filters. The smaller pore size yielded a 4.0% increase in retained product weight. Tests to determine reproducibility resulted in from 1.2% to 7.1% variation in yield based on the lowest weight. The complete apparatus is shown in Figure 2. Compressed air was filtered and all, or part, of the stream dried to a dew point of -70°C in a series silica gel-ace-
I
SILICONE sRUBBER T
I SILICONE RUBBER 7
GLASS TUBING
r
PLASTIC
CAP SCREWS?
47mm OIA
MEMBRANE FILTER
ACRYLIC PLATE
BOTTOM ASSEMBLY MILLIPORE CORP. PLASTIC FILTER HOLOER ASSEMBLY
Figure 1 . Reactor cell. R-1
R. - 7 -
4
I
U
Y
8
&
8
PRESSURE R E G U L A T O R
? PRESSURE I N D I C A T O R 0 MEMBRANE F I L T E R
1
Q +@
U
1. COMPRESSED A I R
2. D R Y I N G TUBE, SILICA GEL 3, H U M I D I F I E R
ROTAMETER
4. N I T R O G E N BOTTLE
VALVE
5. A M M O N I A BOTTLE
NEEDLE VALVE
7. REACTOR
MANOMETER
8. O R A I N
Figure 2. Experimental arrangement.
tone/Dry Ice cold trap. Part or all of the air could be humidified to saturation by sparging through distilled water. The desired HzO vapor concentration could be obtained with the appropriate blend of dry and saturated air. Sulfur dioxide concentrations were set prior to each test by diverting part of the gas stream through a Beckman Model 215A IR analyzer. The ammonia stream flowmeter was calibrated by weighing the uptake of NH3 from a measured gas volume flowing through concentrated HzSO4. Results The first set of conditions tested was a stoichiometric excess of O2 and water vapor and NH3/S02 ranging from
-
-
N
N
0
r
I
N
c
0
I
I
-
If
35
1
a-
zo
~
'
15
O
/[ H 0 ] = 1 6 2 m M o l e - m - 3
2
000
005
010
015
020
025
030
035
040
045
055
050
060
065
V
I
1
I
I
I
1
070
075
080
085
090
095
I 100
TIME, 1. SECS
Figure 3. Determination of second-order reaction rate constant for the initial relative reactant conditions: (a) [NH3]o = 2 [SO+; (b) [NH3]o # 1,2[SO2]0; (c) [NH3]o = [SOzlo; and three levels of water vapor concentration. Legend: [HzO] = 668-682 mmol m-3; series A,O;B,~;C,~,D,~;E,~;F,~;H~O=3l.lmmolm-3;seriesG,~;H~O=16.2mmolm-~;seriesH,~;I,O;J,~.
Table I . NH3-S02 Reactant and Product Analysisa-d Series
Initial reactant concn, mmol m-3
Product concn, mmol mm3 Residence time, sec
SO2 A B C
D" E F b
F-IC
3.98 6.05 9.95 27.0 10.1 20.6 20.6
NH,
HZO
0 2
27.0 27.0 27.0 27.0 36.7 47.3 47.3
668 682 682 682 682 668 668
8530 8530 8530 8530 8530 8530 31
0.029
0.057
0.119
0.190
0.286
0.388
1.02 2.08 3.40 8.49
2.65 4.03 4.98 9.38 6.20 10.5 14.3
3.46 5.40 6.41 12.9 7.10 15.1 19.2
3.84 6.29 8.12 13.9 9.32 16.6 22.1
...
...
6.45 9.76 13.9 10.6 18.3 27.1
...
9 .o 11.0
... 10.3
... 0 19.6
...
Residence time, sec 0.100
0.212
0.338
0.510
31.1 8530 13.2 14.6 17.4 17.4 16.2 8530 3.60 5.30 6.90 8.78 16.2 8530 6.65 11.6 13.5 17.0 J 16.2 8530 7.10 14.0 20.4 20.3 a D: 97% ( N H ~ I z S O3% ~ ; NH4S03NH2. F: 100% (xH4)z(SO4). F-1: 85% (NHs)z.SOz; 10% N3H7S04; (NH3)z.SOz; 20% ",.SO,; 7% NH3SO3; 5% NH4N3.
Gd
H I
20.9 20.9 20.9 20.9
40.4 20.7 40.4 60.1
1 to 6.78 mole ratio. Water vapor, 682 mmol m-3 and oxygen, 8530 mmol m-3 ( 0 2 content of air) were in large enough excess that their concentrations could be considered constant. The kinetics, therefore, were simplified to the concentration dependency of SO2 and "3. A sample of solid reaction product for the condition NH3/S02 = 2.3 was determined by X-ray diffraction analysis to be 100% ammonium sulfate. A sample produced under the condition NH3/S02 = 1 was found to contain 3% ammonium sulfamate, the remainder being ammonium sulfate. This is to be compared with the work of Vian, e t al., (1959); in describing their process for making ammonium sulfate they comment that the sulfamate begins to form as SO2 becomes in excess. What we experienced was that the sulfamate begins to appear a t ratios of NHs/S02 of 1to 1. (See Table I for reactant and product concentrations.) The apparent ease with which ammonium sulfate was produced was unexpected in light of the experience of 0thers as reported in the literature, where sulfites were almost always encountered. Sulfites were not detected in any of the various samples of this work. One reason for this may be that in the case of previous reports, concen-
0.691
0.957
*..
...
10.0 9.80 18.1 18.3 20.3 5% NH3S03. d G : 68%
...
trations and temperatures were much higher than those used here. In the case of flue gas treatment, the oxygen concentrations were usually to 1hof those used here. In series G through J, ammonia was in the range of 20-60 mmol m-3, and ( S 0 ~ ) at o 20.9 mmol m-3; air was the carrier gas. The water vapor content was reduced to 8Wo and 150% of the stoichiometric requirement for ammonium sulfate production. The NH3/S02 ratios were 1, 2, and 3. Analysis revealed 7% sulfamic acid, NH3S03; 5% ammonium azide, NH4N3; 20% amorphous material; the balance was a crystalline substance which is suspected to be ammonium amido sulfite, (NH3)2602. The amorphous material may be NH3mS02 (amidosulfurous acid adduct). The products reported in Table I, tests G-J, were calculated using an average molecular weight of 93 as determined from the above mix. Series L featured an NH3/S02 ratio of 2, but with only a trace (0.12-0.20 mmol m-3) of water vapor in air. The X-ray diffraction analysis of this reaction product indicated ammonium sulfate; ammonium pyrosulfate, (NH4)~Sz07;sulfamic acid; and amidosulfate hydrazine, N3H7S04. The presence of (NH3)2402 was also suspectInd. Eng. Chem., Fundam., Vol. 14, No. 1, 1975
69
Table 11. NH3-SO2 Per Cent Consumption Residence time. sec Series
0.029
0.057
0.119
0.190
% NH, used
25.6 7.48 34.4 15.4 34.2 25.2 31.4 62.8
% SO, removed % NH, used % SO2 removed % NH, used % SO, removed % NH, used
43.7 38.1 53.4 46.5
66.6 19.6 66.6 29.9 50.1 37.0 34.7 69.4 61.4 28.9 51 .O 44.4 69.4 60.5
86.9 25.6 89.3 40 .O 64.4 47.5 47.8 95.6 70.3 38.7 73.3 63.8 93.2 81.2
96.5 28.4 > 100 46.6 81.6 60.2 51.5 > 100 92.3 50.8 80.6 70.2 > 100 93.4
0 -100
0.212
60 .O 54.9 16.4 29.2 30.2 27.7 32.3 19.8
66.4 60.7 24.1 43 .o 52.7 48.2 63.6 39.1
% SOz removed % NH, used o/c SO2 removed % NH, used o/c SO, removed % NH, used o/G SO, removed
A B
C D E F
F-1
G
% SO2 removed % NH, used
H
4°C
SOz removed % NH, used % SO2 removed
I
% NH, used % SO2 removed % NH, used
J
... ...
ed. The weight of the reaction product, however, was inconsistent in three identical tests; a variation of 300% was obtained. Another test in the presence of trace H2O was Results indiconducted with SO2 in large excess of "3. cated mostly N3H7S04 and some amorphous material, suspected to be NH3.SO2. Series F-1 was an attempt to determine the oxygen concentration dependence of the reaction. An ammonia/sulfur dioxide ratio of 2.3 was injected in the presence of excess water vapor but with 1.5 times the stoichiometric oxygen requirement for ammonium sulfate. The product was determined to be 10% amidosulfate hydrazine, 5% sulfamic acid, and the balance assumed to be ("3)2*S02.
Discussion Several different reaction schemes were considered when interpreting the results of Table I. An expression for first-order dependence on both ammonia and sulfur dioxide (irreversible second-order reaction overall) appears to fit the experimental data fairly well. -
70
@a% ! t
= K[SO2][NH3]
Ind. Eng. Chern., Fundarn., Vol. 14, No. 1, 1975
Residence time, sec 0.338 0.510 79.1 72.4 31.4 56 .O 61.4 56.1 92.7 57.0
79.1 72.4 39.9 71.3 77.2 70.7 92.3 56.7
0.286
0.388
... ...
... ... ..
> 100 47.8 98.1 72.3 51.5 > 100 > 100 57.8 88.8 77.4 > 100 > 100 0.691
*
...
> 100 76.3
... ... ... ...
95.1 82.9
... ...
0.957
... ...
..
45.4 81.2 82.3 75.3 92.3 56.7
44.6 79.5 83.2 76.1
... ... ...
us. time as shown in Figure 3. Rate constants for the various series were found by fitting the data for those series using linear regression techniques. These constants are: series A, 7.04 X 105; B, 8.09 X 105; C, 6.85 X 105; D, 7.04 X 105; E, 5.10 X 105; F, 4.40 X lo5 and F-1, 9.80 X 105 1. mol-' sec-l. A line representing the series A through F-1 is shown in Figure 3. This line has a value corresponding to a constant of 6.1 X lo5 1. mol-I sec-I. Series G is represented by the next lower line corresponding to a water vapor concentration of 31.1 mmol m-3. The rate constant here is 3.1 X 105 1. mol-1 sec-1. Series H, I, and J, with a water vapor concentration of 16.2 mmol m-3 exhibit rate constants of 1.20 X 105, 1.64 X 105, and 2.08 x 105 1. mol-1 sec-1, respectively. These series are grouped around a line drawn a t a constant of 1.6 X lo5. Regarding the scatter in the above rate constants, it should be noted that some of the tests yielded more solid product than was possible from the quantity of limiting reactant. The series with the highest error, series F-1, yielded a product concentration of 27.1 mmol m-3 at 0.286 sec reaction time, with a limiting reactant concentration of 20.6 mmol m-3. This is a +31.5% error based on the SO2 concentration. The moles of product was calculated as 85% (NH3)2.S02, 10% N3H7S04, and 5% NH3S03 with a composite molecular weight of 102.8. This composition was arrived at by standard powder X-ray diffraction techniques and the error in the estimated component concentration is *2.0%. The ring structure corresponding to what we assume is (NH3)2.S02 does not fit any known diffraction patterns and the assumption is based on past experience noted in the literature. Another means of estimating the reaction rate constant for series F-1 is to
assume that the moles of product corresponding to 0.286 sec reaction time is equivalent to the number of moles of limiting reactant. This yields a product molecular weight of 135.2. Based on this molecular weight, the reaction rate constant for F-1 is 4.12 X 105 1. mol-1 sec-I. Whichever method is chosen, it is apparent that a reduction in oxygen concentration by a factor of over 200 has relatively little influence on the rate of product formation. Series B yielded a product concentration higher than the limiting reactant by 6.63% and series F was low by 5.0%. So other than series F-1 the concentration of solid product formed fell within an accuracy of 7.0%. Series G through J reactions, with H2O limited to a range close to the stoichiometric requirement for ammonium sulfate production, results in a complete absence of (NH&S04. Also in series F-1, where oxygen concentration was near stoichiometric, no ("&SO4 was found. Therefore we suspect that the solid that initially precipitates out of the gas stream may be a precursor, which is the result of the reaction NH,(g) + SOzk)
--t
with the competing reactions NH, 'S02(g) + NH3(g) xNH, * SO:! ( g )
3"(
+
' SO2(g)
3"
(NH& 'SOZ(S) *
SO~),(S)
(2 1
(3) (4 )
Further reaction with water vapor and oxygen may take place after the solids have been collected on surfaces (",),SO,(s) "4SO,"2(s)
+ Y!02(g)
-
+
+ H,O(g)
NH,SO,NHz(s) ("4),SO,(s)
(5)
amorphous product in both cases. The low-temperature reaction product, however, when exposed to the atmosphere, was transformed into ammonium sulfate, while the higher temperature product was converted into a mixture which included elemental sulfur and a slight amount of ammonium sulfate. We were unable to confirm the presence of elemental sulfur in any of our tests; however, we always worked with at least trace amounts of 0 2 and H2O. Friend (1974) experimented with trace quantities of and 0 2 in air of varying proportions and HzO, S02, "3, with various conditions of radiation with ultraviolet light. He reports no reaction in the dark or with 2500-4000-i% wavelength uv. He suggests that the addition compounds of NH3 and SO2 are not precursors to the formation of ammonium sulfate. We found that, within the concentration range of gases in our tests, there was no significant difference in reaction kinetics or products when carried out in the absence or presence of light. Several questions remain to be answered regarding the application of this reaction to flue gas scrubbing. We have conindicated the percentage of SO2 removal and 3" sumption for the various reaction series in Table 11. From the point of view of air pollution control, if NH3 were injected in a flue gas stream it would be undesirable to release any unreacted fraction to the atmosphere. Therefore from Table 11, complete consumption of NH3 might be best achieved when injection is on a 1:l NH3/SO2 basis. On the other hand, if one is concerned about eliminating ammonium sulfamate from the reaction product, then a 2:l NH3/S02 injection is more desirable. Further tests must be made at 100-200°C to determine if the same products are obtained at stack gas temperatures.
(6)
The number of moles of solid collected appears to be independent of the oxygen concentration, which would agree with the above scheme. The apparent dependence of the number of moles of solid formed on the H20 concentration suggests that the formation of NH3.SO2 and/or (NH3)2.S02 may be catalyzed by H2O. The first appearance of condensation nuclei in the form of amorphous material seems to be a common characteristic in nucleation phenomena. Matteson, et al. (1972), and Boscoe, et al. (1973), report on the behavior of sodium chloride aerosols condensed from the vapor. Amorphous spherical particles were obtained which were of variable and lower density than the bulk crystal. Upon exposure to trace amounts of water vapor the spheres quickly converted to NaCl crystals. In the case of NH3.SO2, the condensation material may be in some polymeric form. The presence of water vapor is not only needed to drive the reaction further but may act as a catalyst in condensing the product. A test was made with an aerosol spectrometer developed by Preining (1974) to determine the aerodynamic diameter of particles generated in a type L reaction (trace H2O). The reaction yielded particles of diameters in the range from 1.2 and 2.0 pm with a mean of 1.5 pm. The results of McLaren, et al. (1974), indicate the importance of water vapor in the overall reaction process. They found no significant change in the heat of reaction of NH3 and SO2 in the presence and absence of oxygen ( 30.3 us. -29.9 kcal mol-I) when no water vapor was present. However, when water vapor was added, the heat of reaction was -34.4 kcal mol-I for no 0 2 and -45.0 kcal mol-1 with 0 2 . Yencha, et a1 (19741, studied the gas-phase reaction of anhydrous, ammonia and anhydrous SO2 in the presence of nitrogen gas at -50 and +22"C. They reported a semi-
Summary The reaction of SO2 and NH3 in humid air at 23°C to form solid reaction products was studied experimentally. A flow type reactor was devised to study the gas-phase reaction. A variety of products was formed depending on the concentration of the reactants. With a large excess of H2O vapor in air ( e . g . , 50% relative humidity) and SO2 and NH3 in the initial concentration range of 4 to 60 mmol m-3, and in the molar ratios of >1:1::NH3:S02, the product is crystalline ammonium sulfate. At equimolar concentrations, a few per cent of ammonium sulfamate is also formed. The reaction appears to be first order with and is irreversible. The respect to both SO2 and "3, reaction rate is dependent on the amount of water vapor present but is independent of the oxygen concentration. Rate constants were in the range 1-6 x 105 1. mol-' sec-I. A reaction rate model is suggested which describes the data within the estimated 7% accuracy of the experimental results. At lower concentrations of HzO (trace to 31 mmol m-3) the principal products are NH3S02 and ("&SO2 adducts with minor amounts of NH3S03, (NH&S207, NH4N3, and N3H7S04. Product identification of solid reaction products was by X-ray diffraction. At a lower concentration of 0 2 (16 mmol m-3) the reaction product was primarily (NH3)2+302 with secondary products of N3H7S04 and "$303. The aerodynamic diameter of particles produced from NH3 and SO2 gases in air containing a trace amount of water vapor ranges from 1.2 to 2 pm with a mass median diameter of 1.5 pm. Literature Cited Badar-ud-Din, Aslam, M.. Pak. J. Sci. Res., 5. 6 (1953). Boscoe. G. F.. Matteson, M . J., Preining, O.,Staub-Reinhalt. Luft. 33, 163 (1973). Cann. E. D., U.S. Patent 3,579,296 (1971). Dbbereiner. M., Schw. J., 47, 119 (1826). Ephraim, F.,Piotrowski, H., Ber. Deut. Chem. Ges., 44, 379 (1911)
Ind. Eng. Chern., Fundarn., Vol. 14, No. 1, 1975
71
Friend, J. P., Leifer, R., Trichon, M.. J. Atrnos. Sci., 30, 465 (1973). McLaren, E., Yencha, A. J., Kushnir, J. M., Mohnen, V. A., Tellus, 26, 291 (1974). Mascorello, J., Auclair, J.. Hamelin. R.. Pglecier, C.. Proc. Arner. Power Conf., 31, 439 (1969). Matteson, M. J., Fox, J. J., Preining, O., Nature Phys. Sci., 238, 61
Schumann, H., 2.Anorg. Chem., 23,43 (1900). Vian, O., Iriarte, F., Melcheso, S.,U.S. Patent2,912,304 (1959). Yencha, A. J., Kushnir. J. M.. McLaren, E., Mohnen, V. A,, Chessin, H., Tellus, in press.
110791 \‘“.L,.
Received for review May 20,1974 Accepted November 4,1974
Preining, O.,Boscoe. G. F., Matteson, M. J., J. Aerosol Sci., 5, 71 (1974).
CORRESPONDENCE
Use of Infinite-Dilution Activity Coefficients for Predicting Azeotrope Formation at Constant Temperature and Partial Miscibility in Binary Liquid Mixtures
Sir: Brandani (1974) has proposed using infinite-dilution activity coefficients to predict partial miscibility in binary liquid mixtures. For a binary mixture which is described by the van Laar equation, Brandani states that a miscibility gap will exist if
where A = In T i m , B = In Y 2 m and Q = A/B. The symbol [Q] represents “the integer part of Q” and A and B are defined so that Q 2 1. Inequality (1) was apparently derived from thermodynamic stability theory. However, the result is unnecessarily slack and a precisely rigorous form is available. Rigorously, for A and B such that
A
>
1
-[2(1 2Q
- Q
+
Q2)3/2
-
(2
- 3 8 - 38’ +
2@)] (2)
the van Laar equation predicts a miscibility gap. If the inequality in (2) is replaced with the equality sign, the value of A calculated corresponds to critical solubility conditions. The consolute composition may be cal-
culated from
Equations 2 and 3 follow from critical solubility conditions appled to the van Laar equation as presented by Treybal (1963). They have an additional virtue in that they apply for any positive Q (not only for Q > 1). If A is less than the limiting value implied by eq 2 the van Laar equation will predict no miscibility gap. Equation 1cannot be used with this assurance. Limiting values of A calculated from the inequality of Brandani (1974) and from eq 2 are presented in Table I for comparison. Brandani calculates that for Q = 5.581 (phenol, water), there will be a miscibility gap for A > 3.538. In fact, the van Laar equation predicts a miscibility gap forA > 3.080. I should like to point out also the way in which Brandani has dealt with the data of Brian (1965). The five systems involved are indicated by an asterisk in Table I. Brian in the first place calculated A and B for these five systems beginning with mutual solubility data. Nothing a t all is proved by comparing the resulting values with ei-
Table I. Prediction of Partial Miscibility
Acetonitrile Ethanol Aniline 2-BUtanol 1- Butanol
Phenol Propylenoxide Ethanol Methyl ethyl ketone 1-Propanol Nitromethane Ethanol 72
Benzene Benzene Water* Water* Water* Water* Water* n- Hexane u- Hexane Water Carbon tetrachloride Isooctane
Ind. Eng. Chern., Fundarn., Vol. 14, No. 1, 1975
1.163 2.361 4.223 3.807 3.795 3.691 2.557 3.045 1.301 2.642
1,059 1.581 3.022 4.112 4.487 5.581 1.430 1.305 1.114 2.152
2.361 3.314
1.138 1.393
2.060 2.719 3.245 3.406 3.538 2.509 2.346 2.120 2.772
2.057 2.420 2. a44 2.979 3.011 3.080 2.336 2.255 2.106 2.648
2.146 2.459
2.127 2.313
3.011
