T.K. WIEWIOROWSKI AND B. L. SLATEN
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Molten Sulfur Chemistry. IV.
The Oxidation of Liquid Sulfur
by T. K. Wiewiorowski and B. L. Slaten Freeport Sulphur Company, Belle Chasse, Louisiana
(Received March 9, 1967)
The solubility of oxygen in molten sulfur was determined in the temperature range between 125 and 150". Dissolved oxygen reacts with the sulfur to form sulfur dioxide. The kinetic aspects of this oxidation process were investigated. At 140.5" the first-order rate constant is 6.8 X min-'. The energy of activation is 28,800 cal.
Introduction The solubility and chemical behavior of gases dissolved in molten sulfur has been the subject of several recent investigation^.^-^ In this paper we wish to report the results of a study on the cheniistry of oxygen dissolved in molten sulfur. The reaction between oxygen and sulfur has been previously studied by Norrish and Ridea14 and by S a y ~ e .These ~ ~ ~ workers limited their investigations to temperatures exceeding 235". From the mechanistic point of view, the primary conclusion of these workers is that the reaction takes place predominantly a t the surface of liquid sulfur. However, an examination of the experimental approach employed in these studies suggests that this conclusion does not necessarily have to be applicable to the lower temperature range (125lt5Oo) covered in this study. Consequently, it was of interest to establish whether the reaction between liquid sulfur and oxygen in this temperature range takes place in the liquid or gas phase, or at the gasliquid interface. Also, the kinetic behavior of the system was investigated and the solubility of oxygen in molten sulfur.was determined. Experimental Section
A . Preliminary Experiments. Before a detailed kinetic study of sulfur oxidation could be undertaken, it was necessary to establish whether the reaction occurs in the gaseous phase between sulfur vapor and oxygen, in the liquid phase between dissolved oxygen and sulfur, or at the molten sulfur surface. A series of tests was carried out for this purpose. In test no. 1, a reaction vessel containing molten sulfur was placed in a constant-temperature bath held a t 151.5" as shown in Figure 1A. The vessel was equipped T h e Journal of Physical Chemietry
with a fritted tube through which air was fed a t 31.6 ml/min into the molten sulfur. The effluent from the vessel was passed to the gas chromatograph for SO2 determination. For details concerning the chromatographic analysis, see section C. The test was designed to measure the extent of sulfur dioxide generation as a function of the amount of sulfur and of the height of the sulfur column in the reaction vessel. The results are presented in Table I. In test no. 2, the same reaction vessel was employed, but in this case it was filled with 6 X 6 mm Raschig rings which were wetted with about 200 g of pure sulfur. This experimental arrangement provided a large available surface area. The temperature and air flow were the same as in test no. 1. The concentration of sulfur dioxide generated, shown in Table I, was not enhanced as a result of the large surface area available for sulfur-air contact. The results of the first two tests suggested that the reaction occurs in the liquid phase between dissolved oxygen and molten sulfur. To verify this conclusion, test no. 3 was performed in which an experimental arrangement shown in Figure 1B was employed. Here three reaction vessels differing in diameter (and thus capacity) but not in height were filled with molten sulfur and placed in a constant-temperature bath. It was theorized that if the reaction takes place in the liquid phase, the amount of sulfur dioxide generated (1) T. K. Wiewiorowski and F. J. Touro, J. Phys. Chem., 70, 234 (1966). (2) F. J. Touro and T. K. Wiewiorowski, ibid., 70, 3531 (1966). (3) F. J. Touro and T. K. Wiewiorowski, ibid., 70, 3534 (1966). (4) R. G. W. Norrish and E. K. Rideal, J. Chem. Soc., 3202 (1923). (5) L. A. Sayce, ibid., 1767 (1935). (6) L. A. Sayce, ibid., 744 (1937).
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HERYOMETER CHROMATOGRAPH
A HEATING MANTLE
TO CHROMATOGRAPH CONSTANT TEMPERATURE BATH
B
HEATING MANTLE Y
TO GAS CHROMATOGRAPH
LlOUlO SULFUR LEVEL
C A t ITATO R
HEATING TAPE FRITTED GAS INLET
Figure 1. Experimental arrangement: A, for tests 1 and 2;
B, for test 3; C, for tests 4-6.
should depend on the amount of sulfur in the reaction vessel. The results of this test, presented in Table 11, confirmed this line of reasoning. The three preliminary tests demonstrated that lowtemperature sulfur oxidation is a liquid phase reaction and that contributions from possible sulfur dioxide generation in the vapor phase or at the sulfur surface are negligible. This finding constitutes the basis for
Table I
Teat no.
1
2
Amount of sulfur, B
300 500 700 900 200
Height of sulfur
column, om
11.4 18.1 24.8
31.8 Suspended on Raschig rings
SO1 concn
in gas effluent,
%
0.015 0.029 0.044 0.056 0.010
Table 11: Sulfur Dioxide Concentration in Test No. 3 (Temperature, 151'; Flow Rate, 31.6 ml/min) Amount of sulfur, g
SO, concn in gas effluent,
162 750 3500
0,009 0.048 0.147
%
the experimental and theoretical approach employed in this study of the oxidation kinetics of molten sulfur. The sulfur dioxide concentrations shown in Table I1 are the concentrations established when the rate at which sulfur dioxide is removed from the system is equal to the rate at which it is formed. This steadystate condition can be mathematically formulated by equating the rate of SO2 removal from the system, Cso2R, with the rate of SO2 formation in the system, 2krC0,~m. CSO,R = 2k,C0~~rn
(1)
where Cso2 is the sulfur dioxide concentration effluent stream; R is the air rate; kr is the oxidation rate constant; COaSis the concentration of oxygen dissolved in liquid sulfur; m is the amount of sulfur; and 2 is the value of the conversion factor reflecting the ratio of the molecular weight of SO2to that of 02. From the experimental point of veiw, the values of CSO~, R, and m are easily available by direct measurement. Consequently, the product of krCo: can be readily calculated from eq 1. Theoretically, however, it is of interest to determine the absolute values of k, and of CoaS. It should be mentioned at this point that in test no. 3 the concentrations of oxygen dissolved in liquid sulfur were not identical in all three reaction vessels, and consequently the experimental data shown in Table I1 do not indicate a direct quantitative linear relationship between C S Oand ~ m. B. Experimental Approach to the Determination of Oxygen Solubility in Molten Sulfur. The determination of oxygen solubility in molten sulfur poses unusual experimental problems. First, since a reaction between dissolved oxygen and liquid sulfur takes place, it is virtually impossible to obtain liquid sulfur saturated with dissolved oxygen. Secondly, the solubility of oxygen in liquid sulfur is very low, which further complicates its experimental determination. The problem was attacked through a series of experiments (tests no. 4-6) in which oxygen and sulfur dioxide concentrations in the effluent gas from a reaction vessel were measured as a function of time at three different temperatures. Volume 71 I h'umber 0 August 1067
T. K. WIEWIOROWSKI AND B. L. SLATEN
3016
1E Imin)
Figure 2. Oxygen concentration us. time in tests 4A (circles) and 4B (solid points).
into the sulfur through a fine frit for a period of 1 hr. It was experimentally established that this procedure resulted in nearly saturating the sulfur with oxygen a t 1 atm of air overpressure or 0.21 atm of partial oxygen pressure. The air flow was then discontinued and nitrogen a t 38.2 cc/min was admitted through the same fine frit t o scrub the oxygen out of the system. The effluent gas was passed to a gas chromatograph for oxygen determination. Test no. 4B differs from the preceding test only in the manner in which the dissolved oxygen was scrubbed out of the system, namely in this case nitrogen was admitted at 26.1 cc/min through a coarse frit. The change in oxygen concentration in the effluent as a function of time in tests 4A and B is plotted in Figure 2. The significance of frit porosity will be considered in the Discussion. In test 4C, the sulfur dioxide generation was followed vs. time, while air was introduced at a slow rate into molten sulfur initially free of oxygen and sulfur dioxide. As shown in Figure 3, the sulfur dioxide concentration in the effluent increases continuously, asymptotically approaching a steady-state concentration. Tests 5A, B, C, and 6A, B, C, were identical with tests 4A, B, C, except for sulfur temperature. The test 5 series was conducted a t 140.5', while in test 6 a temperature of 150.5" was maintained. Experimental data obtained in these tests are presented and interpreted in the Discussion of Results. C. Gas Chromatographic Analysis. The effluent gases from the sulfur dioxide generation tests were analyzed by gas chromatography using a Model 720 F & hf instrument. The following experimental conditions were employed: column for SO*, 1 ft X 0.25 in. aluminum column packed with 80-100 mesh Davidson Grade 08 silica gel; for 0 2 , 2.5 ft X 0.25 in. aluminum column packed with 40-60 mesh Rlolecular Sieve 5A; column temperature, 130' for S02, 25" for 02;detector temperature, 135" ; carrier flow (helium), 40 ml/min ; sampling, manually operated valve with 5-ml sample loop.
Discussion of Results (min)
Figure 3. Sulfur dioxide Concentration a8 a function of time in test 4C.
I n test 4A, an agitated reaction vessel was filled with 34.1 kg of pure sulfur, as illustrated in Figure 1C. The sulfur was kept a t 125.5" by means of a thermoswitch-heating tape arrangement. After stripping the sulfur with nitrogen to remove traces of volatile contaminants, a vigorous stream of air was introduced The Journal of Physical Chemistry
Consider the results obtained in test 4A in which the concentration of oxygen in an effluent stream from molten sulfur, previously nearly saturated with oxygen a t 1 atm of air overpressure, was measured as a function of time. As is evident from Figure 2, the logarithm of the oxygen concentration exhibits a linear decrease with time in accordance with a first-order kinetic equation
OXIDATION OF LIQUIDSULFUR
3017
where CO: is the oxygen concentration in effluent gas, 1 is the time, and K is the observed total rate constant. Since the oxygen concentration in the effluent gas, CO:, is linearly related to the concentration of oxygen dissolved in sulfur, the following relationship should also hold S
-~ dCo2 - KCo2S dt
where -dCo?(S)/dt is the rate of oxygen removal from sulfur due to st]ripping and -dCo:(r)/dt is the rate of oxygen removal from sulfur due to reaction leading to SO2 formation. Since the oxygen removal due to stripping can be safely assumed to exhibit first-order kinetic behavior, and since the combined process was experimentally observed to obey first-order kinetics, it follows that the oxidation reaction itself must also be first order, that is
where k, is the rate constant governing the oxygen stripping process, and k, is the reaction rate constant for the reaction O2 sulfu_r SO2. Substitution of eq 5 and 6 into eq 4 leads to the relationship S
dt
+ kr)Co,S
(7)
A comparison of eq 3 and 7 indicates that the observed total rate constant, K , is a sum of k, and k,
K
=
k,
+ kr
cO:
= COg~O2)e-list
(9)
where Cog(02) is the initial oxygen concentration in the effluent gas. The solubility of oxygen in liquid sulfur, S, can be obtained by integration
(3)
where Cor is the concentration of oxygen dissolved in molten sulfur. Equation 3 merely states that the rate of decrease in dissolved oxygen concentration is proportional to this concentration. Two factors contribute to the observed rate, namely the actual removal of oxygen due to the nitrogen stripping process and the consumption of oxygen in the process of sulfur dioxide formation. It can, therefore, be stated that
-dCoz - (k,
This hypothetical oxygen concentration can be expressed as a function of time
(8)
Let us examine how these equations can be utilized in calculating oxygen solubilities in liquid sulfur and reaction rate constants. Consider the hypothetical concentration of oxygen in the effluent gas in test 4A, assuming that no reaction occurs, only stripping.
The factor, F, in eq 10 serves to convert the concentration units (% by volume) in which Colg is expressed to concentration units (% by weight) used for Co?
F =
ill X R X 273" VM X m X T
where M is the molecular weight of oxygen in grams, R is the stripping rate, ml/min, VM is the molecular volume, 22,400 nil, T is the absolute temperature a t which R is measured, and m is the amount of liquid sulfur in grams. Upon integration and substitution of eq 11 into eq 10, one obtains
or
Equations 8 and 12B can be utilized to treat experimental data obtained in tests 4A and 4B. It will be recalled that the method of oxygen stripping in these tests was different. In test 4A, nitrogen was bubbled into the sulfur through a finer frit and at a faster rate than in test 4B. As a result, the stripping rate, k,, was higher in test 4A than in test 4B, as evidenced by Figure 2. The oxygen solubility, however, is identical in both cases, and therefore S=
M X R X 273" X Cog(02)(K - k r ) v M X m X T M X R' X 273" X Co'(on)' (13N (K' - k r ) V M X m X T
Consequently
R X Cog(op)- R' X Cog(02)' K - k, K' - kr
(13B)
where R, CO'~O~), and K refer to run 4A, and R', COg(o2)' and K' refer to run 4B. This relationship allows one to calculate the reaction rate constant, k,, directly Volume 71,Number 9 Auguat 1967
T. K. WIEWIOROWSKI AND B. L. SLATEN
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Table 111: Experimental Results Obtained in Tests No. 4-6A and B 4.4
R, ccjmin
38.2 2.96 0.0157
CO~(OZ), % by volume K, min-1
4B
5A
5B
6A
6B
26.1 0.388 0.00292
55.5 4.71 0.0434
27.5 0.870 0.0100
84.5 8.46 0.0879
39.7 2.57 0.0241
from experimental data condensed in Table 111. Using tests 4A and 4B as an example, one obtains 38.2 X 2.96 0.0157 - k r
kr
- 26.1 X
0.388 0.00292 - k r
-1.9
= 0.0016 min-*
Once the reaction rate, k r , is established, the stripping rate, k,, and oxygen solubility can be easily calculated. Using the data obtained a t 125.5' (test 4A) as an example, we have
k,
=
K - k,
4.8
=
-2.0
-
-2.1
.
-2.2.
-2.3. -2.4.
-
-2.5
-2.6 *
0.0157
- 0.0016 = 0.0141 min-1
(14)
and
-
-21
X R X 273" X Cog(ot) = 0.00030% (15) k, X VM X m X T
The reaction rates and oxygen solubilities a t higher temperatures were calculated in R similar fashion, and the results are presented in Table IV. As expected, the reaction rate constant is strongly temperature dependent. The logarithm of the reaction rate vs. the reciprocal of absolute temperature is plotted in Figure 4. From the slope of this plot, an activation energy of 28,800 cal is obtained for the sulfur oxidation reaction. Presumably, this experimental activation energy is related to the dissociation energy of a terminal sulfur-sulfur bond in a sulfur chain molecule upon attack by an oxygen molecule. This activation energy is somewhat smaller than the dissociation energy of a sulfur-sulfur bond in a polysulfide system, in which oxygen does not participate.' The pronounced temperature effect on the reaction rate helps to explain the results reported by earlier Table IV: Reaction Rate Constant and Oxygen Solubility as a Function of Temperature Temp, o c
125.5 140.5 150.5
Reaction rate constant, kr, min-1
Oxygen &olubility, %
0.0016
0.00030 0.00027 O.OOO36
0.0068
0.0135
The J o u r d of Physical Chemistry
-
'
-2.8
s = M-
-
2.35
2.40
2.41 250
Y
Figure 4. Plot of log k, vs. 1 / T .
worker^,^-^ who concluded that a t temperatures between 235 and 280' the reaction proceeds at the surface of liquid sulfur. Extrapolation of our data indicates that in this temperature range the half-life of the reaction between dissolved oxygen and the solvent is in the order of seconds. Under those circumstances the oxygen reacts very shortly after it enters into the liquid phase, primarily in the surface layer of the liquid sulfur, but not necessarily a t the liquid sulfur-air interface. I n the investigated temperature range, the oxygen solubility is on the order of 0.0003% at 0.21 atm of partial oxygen overpressure and its apparently erratic temperature dependence may be due to experimental errors. The magnitude of the experimental error cannot be accurately determined on the basis of the data available, but is believed to be about 5 X 10-s70. It will be recalled that the concentration of oxygen dissolved in sulfur enters into eq 1 from which the concentration of sulfur dioxide in the effluent gas stream can be calculated. If oxygen solubility values are used, one can calculate that for an air flow rate of 37.5 (7) I. Kende, T. L. Pickering, and A. V. Tobolsky, J . Am. Chem. Soc., 8 7 , 5582 (1966).
OXIDATION OF IJQUID SULFUR
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ml/min and 34,500 g of sulfur in the reaction vessel the maximum sulfur dioxide concentration in the gas effluent at 258°F is
cso2=
2kCo;rn
R
- 8.84 X lo-'
g of so2 ml ~
Let us consider now how this maximum theoretical concentration compares with experimental data obtained in test 4C. In this test, sulfur dioxide generation was followed as a function of time. As is evident from Figure 3, the SO2 concentration asymptotically approached an equilibrium concentration of 0.197% SO2, or 5.68 X 1W6g of S02/ml. This observed value is somewhat smaller than the maximum value calculated for the same air flow rate and sulfur temperature, indicating that the concentration of oxygen reached in test 4C was at about 64% of oxygen solubility. Table V provides a comparison of values of sulfur dioxide concentration [Cso,(max)1, calculated for a hypothetical equilibrium condition assuming an oxygen concentration equal to oxygen solubility, and the values of SO2concentration actually observed in tests 4C, 5C, and 6C [Cso,(exptl)].
where dCoZs is the change in total concentration of oxygen in sulfur, dCo?(in) is the change in concentration of oxygen due to O2 introduced into sulfur, and dCo?(r) is the change in concentration of oxygen due to sulfur oxidation. Each of the two terms on the right side of the equation can be expressed separately
where A is the rate constant of oxygen introduction. As time approaches infinity, dCoZSgoes to zero. Consequently, eq 17 and 18 can be combined to yield
The solution of a general time-dependent function for oxygen concentrations calls for substitution of eq 17 and 18 into eq 16 and integration
Table V : Comparison of Experimental and Maximum Theoretical Sulfur Dioxide Concentration R, Test
ml/min
4C 5C 6C
37.5 34.9 40.0
Caoz(max), dml
8.84 x 3.64 X 8.42 X
Equation 21 implies that at time zero, CO? = 0 and as 1 -t , eq 19 becomes effective. A similar approach can be utilized in predicting the shape of the SO2 us. time curve depicted in Figure 3. The change in sulfur dioxide concentration can be expressed in terms of the equation Q)
-Cao2(exptl)-g/ml
%
5.68 X 2.40 X 5.78 X
0.197 0.84 2.02
The observation that the oxygen concentration in liquid sulfur is normally below the solubility limit brings up an interesting question concerning the time dependence of oxygen concentration in sulfur in an experiment such as test 4C. The initial oxygen concentration is, of course, equal to zero. As air is introduced into the system, the oxygen concentrations can be expressed in terms of the following differential equation
This equation has the same.form as eq 16 and a similar mathematical treatment can be applied to provide an interpretation of the shape of the curve shown in Figure 3. The experimental techniques employed in this investigation provide a new approach to the simultaneous investigation of the solubility and reactivity of gases in liquids and may be applicable to other systems in which chemical reactions complicate the determination of gas solubility in liquids by conventional methods.
Volume 7 1 . Number 9 August 1967
