Chemistry of Sulfur Dioxide Reduction THERMODYNAMICS ROBERT LEPSOE Trail, British Columbia
HE determination of the economics and efficiency of
by Lewis and Randall (6). The free energy for S(rhombic) = SAp(L) is thus obtained by adding together AF", S(rhombic) = SX and AF', SX = SAP'. Figure 1 and the following table show the values for various temperatures:
T
sulfur dioxide reduction to elemental sulfur is essentially a matter of physico-chemical knowledge of the reactions involved. In this respect the thermodynamics of the reactions is of as much importance as the kinetics, since it furnishes the fundamental information regarding the maximum conversions attainable under any prevailing conditions. The equilibrium gas compositions, as calculated in the following from thermodynamic data, do not in every case pretend to be exact figures. I n some cases, particularly in connection with carbon oxysulfide, carbon disulfide, and the various forms of sulfur vapor, where the accurately known data refer only to a specific temperature range, the use of the standard free energy equation may introduce considerable error in the final results. Nevertheless, the calculations give information which otherwise would be almost unobtainable and thus present a valuable guide. Most of the fundamental data have been taken from Lewis and Randall (4). More recent publications, such as International Critical Tables, republish the same data. A few values (specific heat and free energy of sulfur dioxide, specific heats of carbon monoxide and dioxide) have been revised since these calculations were made, but the differences are not sufficient to warrant recalculation.
Temp., C. 25 110.4 120 150 180 300 350 445 527
AFO
S(rhombic) -+ SA
AFO
AF4 S(rhombio)
-+ SAP
SXdL)
94 2.5
-0.8
-1
-3
-2.5
-55 -85 -280 -440 -580 -800
-5
- 10
-46 -71 -Q2 -120
-+
93 0 -4 -60 -Q5 -325 -511 -672 -Q20
Gaseous Sulfur The vapor pressure of liquid sulfur as taken from the International Critical Tables is shown in Table I and Figure 2. The gas phase in equilibrium with liquid sulfur contains and SS. At low temperatures the the molecular species Sz, So, vapor consists mainly of s6 and SS. With increasing temperature SSdissociates to s6, and Se to SZ. Preuner and Schupp (9) determined the partial pressure of the individual sulfur species and found ps, = 0.482 and 0.093, pa6 = 0.592 and 0.074, and paz = 0.0416 and 0.0017 a t 450' and 350' C., respectively. By slight interpolation we have for the boiling point (444.6' C . ) p s , = 0.416, pas = 0.546, and pal = 0.038 atmosphere. When these species are a t equilibrium we can write:
Solid Sulfur The following equation is valid between 0' and 100' C. but is also used to advantage in a formal manner for high temperatures : S rhombic): C = 4.12 0.00472' S[monoclinic)= 3.62 0.0072T for S(rhombicj = S(monoc1inic) A F o = 120 0 . 5 T h T - 0.00125T' - 2.827'
++
4
S
K1
+
'/s
S6
=
sz;
Kz
Liquid Sulfur This form consists of a mixture of SA and
8s and s6: C, (SA)
S(rhombic) AC, AHm
whence AF'
= 5.4
Sp
or probably
As a n average from several of Preuner and Schupp's isotherms, Lewis and Randall calculated the following figures which will be accepted for this paper:
+
0.0052' SA (L) 1.28 f 0.0003T = 467 and AHo = -35 = =
=
-35
-
1.28T In T
8 S(rhombic) = SS; AFO = 20,000 6 S(rhombic) = Sg; AFO = 22,600 2 S(rhombic) = S2; AFO = 30,580
- 0.000157'2 + 7.77T
for Sz at 25'
e.:
AH = 29,690 AF' = 18,280 for SIat 444.6' C.: AF" = 3,320
Rhombic sulfur melts to form pure SX at 112.8' C. The natural melting point for rhombic sulfur is 110.4' C. and for monoclinic sulfur 114.6' C. I n both cases the liquid contains a mixture of SA and SP in equilibrium with each other or SAp. The relation has been calculated by a special method
- 33.62'
+- 35.9T 1.743" In T + 0.0042T2 - 52.4T
Since nothing is known about AC, in the first two equations, these values have been entirely neglected; hence the full validity of the free energy equations for SSand SS outside 92
JANUARY, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
93
sulfur figured as Sz. In order to avoid plotting a wide range of numbers, the plot is made for log Ps, vs. t. I n the first example log Ps,= -0.4815, and the corresponding Semperature in Figure 2 is 325" C. which is therefore the dew point or the point where condensation of sulfur starts. In the
the temperature range 450" to 350" C. cannot be guaranteed. However, the above equations give more than approximate figures; and as they are extremely useful, they have been used to a great extent. Thus, by them the partial pressures of SS,Se,and Szare calculated in equilibrium with liquid sulfur (Table I and Figure 2).
Condensation of Sulfur Vapor On account of the variable composition of gaseous sulfur, the total sulfur vapor pressure is in no sense a criterion comparable with, for example, the vapor pressure of water or zinc. If in a gas mixture of zinc and carbon monoxide we know the partial pressure of zinc, the dew point can immediately be found by consulting the zinc vapor pressure curve. It is not quite as simple with sulfur, but the problem can be solved by the following method: Suppose we have a gas mixture comprising one mole of carbon dioxide and one mole of sulfur present as Ss,Se, and Szin unknown proportions. If the total sulfur is figured as Sz,we have a mixture of one mole of carbon dioxide and half a mole of SZor 0.5 mole S1 in proportion to 1.0 mole carbon dioxide. Similarly, if the gas mixture contains 0.95 mole nitrogen, 0.05 mole carbon dioxide, and 0.05 mole sulfur as SS, Sg, and SZ, figuring the total sulfur as Szwe have 0.025 mole Szper 1.0 mole carbon dioxide plus nitrogen. If the vapor pressures of Sa.and S6in Table I are multiplied by 4 and 3, respectively, and then added to the vapor pressure of Sz,we can draw a new curve representing the total
*
'I'
FIGURE 2.
-140
-00 -110 4lO
-IW
-90
-20
-IO m
5
w ~ m 7 Temperature OK.
w
B
o
350
410
4%
VAPORPRESSURE OF MOLTEN AXD SOLID SULFUR
So far, the vapor pressure of the various forms of gaseous sulfur have been obtained in equilibrium with the molten and solid sulfur phase. We now go a step farther and calculate the individual vapor pressures above the dew point curve-i. e., the field of unsaturated or superheated sulfur vapor. The isotherms for 350", 450", 500", 550", 625", 700°, and 800" C. were calculated for the following cases, which substantially cover the field of practical interest:
-9
o
250 Temperature ?c,
Composition of Gaseous Sulfur above the Boiling Point
-40
y
2W
1.50
second example log Ps,= - 1.6126; hence, the dew point for this gas mixture is 215" C. If we also want to know how much of the sulfur remains uncondensed a t the melting point (114.5"C.), this can be done as follows. At this temperature the log Ps,is -3.8097; hence Ps,= 0.000155. I n the first example there remains uncondensed (0.000155/0.5) X 100 = 0.031 per cent and in the second example (0.000155/0.025) x 100 = 0.62 per cent. The capital letter is used for the vapor pressure of total sulfur figured as Szin order to distinguish it from the real vapor pressure of Sz,ps,. I n the above examples the first represents the condition when 100 per cent sulfur dioxide gas is reduced by solid carbon to elemental sulfur. The second represents a 5 per cent sulfur dioxide gas *
-W
100
IC0
0 o
FIGURE1. FREE ENERGYCURVESFOR SX(1)S(1) AND FOR ~ ( R H O M B I-+ C) Shp(1)
TABLE I. VAPORPRESSURE OF LIQUIDAND SOLID SULFUR Temp.,
c.
---Total PSZ
S as SLog Psx
Total Vapor Pressure
-Partial
Pressure-
7
SS
96
SI
Total
0.455 0.416 0.241 0.0928 0.0397 0.011 0.0023 0.0325 0.0435 0.0599 0.0629
0,592 0.546 0.246 0.074 0.023 0.0047 0.0369 0.045 0,055 0.051 0.071
0.0415 0,038 0.0095 0.0017 0.0338 0.0443 0.0527 o 0780 0.0832 0.094 0.01332
0.037 0,000 -0.3036 -0.775 -1.201 -1.785 -2.523 -3.523 -4.432 -5.000 -6.55
Log Pressure ss sa
91
Atm.
450 444 .65 400 350 300 250 200 150 114 .5 100 50 4
....
......
1.712 0.595 0.228
0.063 1.13 X 10-1 1.15 X 10-8 1.55 X lo-' 4.2 x 10-5 1.2 x 10-1
Boiling point.
0: 233 -0.226 -0.642 -1.202 -1.947 -2.939 -3.81 -4.39 -5.92
1.09 1.00 0.497 0.168 0.063 0.016 0.003 0.033 0.044 0.041 0.063
-0,342 -0.381 -0.618 -1,033 -1.401 -1.959 -2.640 -3.602 -4.45 -5.004 -6.53
-0.2277 -0.263 -0.609 -1,131 -1.631 -2.328 -3.161 -4.301 -5.30 -6.00 -8.00
-1.382 -1.42 -2.022 -2.77 -3.42 -4.37 -5.56 -7.10 -8.50 -9.4 -13.50
INDUSTRIAL AND ENGINEERING CHEMISTRY
94
++
VOL. 30, NO. 1
++
1. Reaction CSz SO, = COS 3s 2. Reaction 2H2S SO, = 2H2 3s with 100 per cent SO1 and HzS gas 3. Gas mixtures resulting from reduction of SO2gas with carbon at various concentrations of SO, 4. One hundred per cent sulfur vapor above the boiling point
The first task is to determine the value of KI and K2 for these temperatures by means of Equations 1 to 3. The results are tabulated as case 3 in the following section.
By selecting values for z and y (by trial and error) to satisfy Kz and K1K2, the partial pressures are found. (In order t o avoid some of the tedious work of selecting exact values, those have been accepted which approximate the conditions.) The values so determined are tabulated in the following section and plotted in Figures 3 and 4.
Vapor Pressures of Sulfur above the Boiling Point
+
CASE 1. The gas mixture is the result of CSz SOz = COz 3s. Total sulfur is figured as S S ; Ps, = 0.600, log P = -0.225, and dew point = 375" C.:
+
Temp., C. 445 500 550
/Sz/ 0 0268
0 0860 0 190
/ss/
/Sa/
0 194 0 200 0 160
0.107 0.085 0 053
/ s g 3 of 2 6 9 0 21 0
+
CASE2. The gas mixture is the result of 2H2S SOz = 2Hz0 3s. Total sulfur is figured as SS; PsP= 0.430, log P = -0.366, and dew point = 360" C.:
+
FIGURE3.
GASEOIXSULFURAT TEMPERATURES ABOVE CONDENSATION POINT
THE
The individual vapor pressures were calculated by a method illustrated in the following example: A sulfur-carbon dioxide gas mixture is condensing a t 350" C. From Table I total sulfur figured as S2 = 0.595 (= approximately 0.60); the remainder, P C O = ~ 0.405. This is the initial gas mixture from which the equilibrium is approached: KS =
and KIK2 /S2/
=
+ 4/&/ + 3/&/
/SZ/ for -
'/s
/S6/'/3
/SZ/ for
'/4
/SS/'/4
Se
= SS
SS = SZ
T e m p , C. 450 500 560
S?)
/s6/
0.114 0.131 0.094
/s2/,
% of
Total 3.8 12.0 30.0
/Sa/
0.0515 0,025 0.026
+
+
CASE3 . The gas mixture is the result of C SOs = COz S (with 100 per cent SOz gas). Total sulfur is figured as Sz; Ps, = 0.33, log P = -0.481, and dew point = 325" C.: Temp., C. 350 445 500 550 600 700
/Sz/ 0.00157 0.0202 0.065 0.143 0.204 0.296 0 327 0.3195
SO0
= PSZ(total sulfur figured as
/SZ/
0,023 0.078 0.160
750
/So/
0.056 0.082 0.083 0.062 0.0425 0.0102 0.0016 0.0035
/Sd> % of Total 0.0615 0.5 0.0328 5.0 0.024 16.0 0.015 37.0 0.0085 58.0 0,0005 90.5 ,... 99.0 . . .. 97.0
/sa/
Kn
KI 0.76 1.015 1.085 1.14 1.35 1.57 1.77 1.68
KlKz
0.0041 0.047 0.155 0.389 0.47
1.38 3.16 2.29
0.00312 0.0478 0.168 0.444 0.635 2.17 5.60 3.85
+
CASE4. The gas mixture is the result of C SO2 = COz'+ S a t such a concentration of SOZ that the dew pointlis 275' C. Total sulfur is figured as Sz; Ps,= 0.107 and log P = -0.971: Temp., O
c.
350 450 500 550 600
/Sa/
0.00105 0.0134 0.0390 0.0765 0.096
/so/ 0.0168 0.0234 0.0167 0.0091 0.0036
/Sa/
0.0128 0.0063 0.0031 0.0013
....
/s+(Iz of 1.0 23.0 38.0 70.0 85.0
CASE5. The gas mixture is the result of 5 per cent SOn + C. Total sulfur is figured as Sz;Ps, = 0.0244, log P = -1.613, and dew point = 215" C.:
gas
L o g P . 2 (Total FIGURE 4.
sulphur flawed
Temp.,
c.
i~ $2)
GASEOUS SULFURAT TEMPERATURES ABOVE THE CONDENSATION POINT
A fraction 2 of the initial Sz reacts to form 0.602/3 (or 0.22) of Sa, and a fraction y reacts to form 0.60y/4 (or 0.15~) of Sa, and the gas volume is reduced to 1 - (0.42 0.45~). The individual partial pressures a t equilibrium are thus:
+
350 445 500 550
= 1
-
= 1
-
+ +
0.0007 0.0080 0.0170 0,0220
/sS/
0,0049 0.0049 0.0015 0.0002
/Sa/
0.0025 0.0008 0.0001
....
/ S a / . % of
Total 2.8 30.0 78.0 98.3
CASE6. When thereis 100 per cent sulfur vapor above the boiling point (444.6"C.), and Ps2 = 1.00: Temp., O
0.22 (0.42: 0 . 4 5 ~ ) 0.15~ (0.42 0 . 4 5 ~ )
/sz/
c.
/sz/
/sa/ % of Total 1.1 4.2
11.0 56.0 81.0 92.0
JANUARY, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
Log K and K were calculated from the free energy equation for the temperature range 350" to 1200" C. of the reaction 2~~ + soz= 2 c 0 2 + 1/>s2:
Monoatomic Sulfur It has already been shown that, by increasing the temperature, Sa is first depleted, then S6, and a t temperatures above 700" C. the vapor consists practically entirely of Sz. At still higher temperatures S2starts to dissociate into S, monoatomic sulfur. According to Lewis and Randall (6) and International Critical Tables, the free energy equation for the reaction S2 = 25 is :
Temp., ' C.
Initial Pa?
Dissociation.
1.0 0.33
0.024
=
2
x
10-1
%
/SZ/
/S/
0.7 1.2 4.6
0.986 0.326 0,023
0.014 0.085 0,002
1 2 0 0 ~c., K = 3 . 2 Dissociation.
%
/S2/
2.8 5.0 18.0
0.946 0.308 0,0197
x
10-
/S/
200 2290 136 X los 174 X lo4
Temp., C . Log K 600 7.60 500 9.29 350 12.88
K 398 X 106 195 X 759 X 10
Exact thermodynamic data are not yet available but there is sufficient material on hand with which to make fair approximations. For the reaction CO ~/zSZ = 2 . 4 x 10-2 (g) = COS (g), Lewis and Randall (8) write:
+
1400O C., K Dissociation,
0.054 0.032 0.0114
K
Carbon Oxysulfide
A few values were calculated by means of this equation: iooo0 c.,K
Log K 2.30 3.36 5.13 6.24
1200 1000 800 700
- 3.57' In T + 0.0005Tz + 4.6T
AF" = 46,700
95
%
/Sa/
7.7 13.5 50.5
0,012
+
AF" = -22,500 21.0T 4920 or log K = -- 4.6 T
/S/
0.857 0.272
0.143 0.085 0,011
By going a step farther: The dissociation of S2 does not become appreciable except a t temperatures above 1200" C. and in a high state of dilution.
AF"(C0S) = AF"(reaction)
It has been calculated for
Free Energies of Sulfur and Carbon For carbon monoxide : AF" CO = -26,600 - 2.15T In T
+ +
that AF"?lr and AFOT
+ 0.00215T2 -
0.0000002T3 - 8 2T
AF0298
AF02sg = -32,510 AFDa7s = -38,500
For carbon dioxide: So COz = -94,110 0.607' In T
+
- 0.00065TZ+
0.00000011T3 - 3.74T
+ 0.0071T - 0.00000186T2
K = 500 PBz= 0.0095 (constant) /CO/ /COS/ = 1 - 0.0095 = 0.9905 /cos/ - 0.9905 - /CO/ 500 = /CO//SZ/l/2 - O.O98/CO/ /co/ = 0.0198 /COS/ = 0.9707
+
+
For the reaction (g) 0 2 = SO2 (g), Lewis and Randall give the free energy equation: AF"
=
-83,260
+ 2.752' In T - 0.0028T2 + 0.00000031T3 + 0.9T
By adding to this the free energy equation for 2 s (rhombic) = S2 (g) we obtain for 2 s (rhombic) 0, = SO2 (g):
+
A F o = -67,970
+ 3.622' In T AF"2ss
+
+
+
AFOzss = -94,260
For sulfur dioxide: C, = 7.0
S(rhombic) C 1/202 = COS ( 9 ) -48,000 = -33,810 - 1.28T In T 0.00425T2 - 13.42' = -39,600 and AH298 = -33,800
=
The significance of the reaction CO '/zS~ = COS is illustrated by a few examples. At temperatures above 1000" C. very little carbon oxysulfide is found whereas a t 400" C. almost complete conversion to carbon oxysulfide has taken place. If carbon monoxide is bubbled through molten sulfur a t 400' C. so that equilibrium is obtained, we can calculate the gas composition as follows:
-42,300
AF0,18
+ AF"(C0) + A F o ( l / ~ S ~ )
- 0.0007T2 + 0.00000031T3 -
25.3T
-69,400
+
The reaction 2CO SO2 = 2C02 '/zSZ was carefully studied by Ferguson (1). Equilibrium constants were determined for 1000" and 1200" C., and from these, constants were calculated up t o 1500" C. His data were of considerable value in the present work. With a knowledge of the free energies involved , the equilibrium conditions of the reaction can be calculated over a wide range of temperatures :
At temperatures above the existence of the liquid sulfur phase, the calculation takes the following form: I n the initial gas mixture /CO/ = u and /S2/ = b. The fraction of carbon monoxide converted is X, giving X u of carbon oxysulfide and leaving a(1 X) of carbon monoxide and b - '/*Xu of SI, all divided by 1 - 0.5Xu, since the gas volume has contracted by one-half of every unit of carbon monoxide converted. The results at different temperatures are shown in Table 11. The initial gas mixture is assumed to contain /CO/ = 0.67 and /Sz/= 0.33. These equilibria were calculated on the assumption that no other reactions take place. Actually, as will be shown, two
++ ++ + +
-
+ +
AF" = 15,290 0.87Tln T 0.0021Tz - 26.2T AF" = -188,220 1.20T In T - 0.0013T2 0.000CO022T3 - 7.482' -172,930 2.07T In T 0.00082'2 0.000000227'3 - 33.682' 2c 0 2 = 2CO; AFO = 53,200 4.305" In T - 0.0043T2 0.000000407's 16.40T - 119,730 6.372' In T - 0 .0035TZ 0 .ooOOO062Ta - 17.287' AFo = S(rhombic) 0 2 = SOZ; 67,970 - 3.62T In T 0.0007T2 - 0.00000031T3 25.307' Reaction : AF" = - 51,760 2.75T In T - 0.0028T2 0.00000031T3 8.022' A F " 11 300 L o g K == L - 1.375 log T 0.0OO6T - 0.00000007T2 - 1.77 2.3RT
S(rhombic) 2c 202
= l/zS2 ( g ) ; = 2c02;
+
+
+
+
/co2/=/sz/l'z= /CO/~/SO*/
+
+ + +
+ +
+ + +
96
INDUSTRIAL AND ENGINEERING CHEMISTRY
TABLE11. RESULTSFOR Temp.. ' C. Log K 1200 -1.40 1000 -0.80
K
THE
/GO/ 0.664 0.605 0.504 0.370 0.190 0.096 0.020
EQUILIBRIUM REACTION CO +1/2S1 = COS /COS/ 0.0134 0.0527 0.248 0.450
/Sn/ 0.310 0.305 0.248
30 C8S .030 98.0 2.0 ::: :;E 3!:g ' .. 45.0
/Ss/
/S/
.... .. ...
VOL. 30, NO. 1
hence
log K T =
- 790 T + 0.33
log K633 = -1.15
and
Lewis and Lacey found -1.79. Their figure may be too low, or Stock and Pohland's figure 700 0.46 0.178 ... 55.0 may be too high. If both investigations were 600 1.04 0.720 0.088 21.0 79.0 500 1 .76 0.866 0.028 o:oo4 ' : :: 10.0 90.0 right, the heat of formation of carbon disulfide 350 3.28 0.980 0.0004 0.001 . .. 2.0 98.0 would be equal to 34,000 instead of 28,600 which is the figure given in International Critical Tables. From the above figures the free energy of formation of carbon disulfide from C and S(rhombic) can be exmore reactions take place simultaneously with this one and to some extent disturb the equilibria. pressed by AF" = 28,600 - 36.2T. Furthermore for the reaction C Sz (g) = CSz (g), it is asCarbon Disulfide sumed that AH is the same a t 873" as a t 298' K. (- 1090) : The literature contains only a few thermodynamic data and hence log K T = 0.284 these are unreliable. The heat of formation of carbon disulfide is (according to International Critical Tables) : and Kaa = 3.6 BOO
0.0
0.04
0.16
1.00 2.90 11.0 58.0 1905
+
+
C
+ 2S(rhombic) = CSZ(g);
AH2o1 = 28,600
This value probably changes very little with the temperature. The dissociation constants determined by Koref (2) for the reaction CS2(g) = C S2 (g) are inconsistent. The heat of dissociation calculated from these varies between -4000 and -12,500 calories. The most reliable information is obtained from the investigations of the reaction 2COS = CSz CO,by Lewis and Lacey (3) and by Stock and co-workers ( 1 1 ) . This reaction is obviously the result of:
+
+
There is evidence that a compound CS exists. According to Lewis and Lacey's figures (S),the amount that could exist in the present equilibrium would be practically nil.
Complete Carbon Monoxide Plus Sulfur Dioxide Reduction Equilibrium We have now to consider the following reactions which all take place simultaneously: 2co
(4)
C
+ S2
/se/
/COS/
/GO/ 0.150
/Sa/
/Ss/
0.058
0.007
s2
/CQi/ 0.201
/Csa/ 0,201
By testing these values in the respective equilibrium equations, we find: K I ll(11) K2 = g(12.6) Ka = 3 . 6 The figures in parentheses are the true constants, which show fair agreement. For the reaction 2COS = COz CSZa t 873" K. we thus find :
+
and
log K = -0.569
It will be assumed that the heat of reaction at 873 " K. is the same as a t 298" K.-vie., 3600:
1/2s2;
/C02/~/Sz/l K 1 = /COP/S02/
/cos/
co + 1/2s2 = cos;
~'
(7) (*)
K 2 = /CO//SZ/l/2
+
cos
/C&/ CSz; Ka = -
Stock et al. found that at 873O.K. carbon oxysulfide had dissociated 16 per cent to carbon monoxide and S2 and 43 per cent to carbon dioxide and carbon disulfide. This may be expressed as follows: By the first dissociation, 1 mole carbon oxysulfide forms 0.84 mole carbon oxysulfide, 0.16 carbon monoxide, and 0.08 SZ(as total sulfur which a t 873 " K. is actually present as 0.06 SZand 0.00'7 S6). As a result of the second dissociation 0.215 mole carbon dioxide and 0.215 carbon disulfide are formed, and 0.41 mole carbon oxysulfide remains undissociated. Bringing the volume to unity, the gas mixture at equilibrium is thus composed of: 0.385
+ so2 = 2c02 +
Ka =
= 1/2COZ '/2CSz; = '/as6 = '/Ss
/co2//cs2/ /cos/, (10)
I n a gas mixture originally composed of carbon monoxide and sulfur dioxide in proportion 2 : l (or excess sulfur dioxide) the amount of carbon disulfide will be negligible. At 600" C. it will amount to only 1.3 X Reaction 9 will therefore be omitted from the calculation. The calculation of the equilibrium may be based on any initial gas mixture of carbon monoxide and sulfur dioxide or carbon dioxide and SZbecause it does not matter in the calculation from which side of the equation the equilibrium is approached. The gas mixture which will be considered consists of carbon dioxide and Szin the proportions 1:0.5; i. e. the partial pressures are /COz/ = 0.677 and /SZ/= 0.323. The reason for selecting this gas mixture is because it closely approaches the gas mixture obtained when 100 per cent sulfur dioxide gas is passed through incandescent carbon in a furnace with subsequent catalysis of the gases until equilibrium is established. For instance: l/,SOZ
1/2SOz
= + + CCO =
+ CO (incandescent carbon reduction) + COZ (subsequent gas reduction)
l/&
1/82
The net result is:
so2 + c
=
/'ZSZ
+ COZ
The method of calculation is as follows: I n the initial gas mixture /GO,/ = a; /Sz/ = b. The fractions X of a and X / 4 of b react to form X a of carbon monoxide and '/ZXa of sulfur dioxide, and the volume increases to 1 Xa/4. Furthermore, Y parts of carbon monoxide react with Y/2 parts of S2 to form carbon oxysulfide, and the volume is reduced by the Y/2 parts of carbon monoxide which has reacted. The gas composition at equilibrium is thus composed of:
+
JANUARY, 1938
INDUSTRIAL AND ENGINEERING CHEMISTRY
/CO/ = X a ( 1 - Y ) /C02/ = a(1 - X ) /COS/ = X Y a
/SO21 = 1/&a
/&/
- 1/Xa - i / z Y a
= b
+
All are divided by the total gas volume which is 1 X u / 4 X Y u / 2 . Corrections are also made for changes in the composition of gaseous sulfur, At temperatures down to 800" C. the initial gas mixture is 0.677 carbon dioxide and 0.323 SZ; correction is made afterwards for monoatomic sulfur. At temperatures below 800" C . the initial gas mixture is the same as calculated under case 3 of the section on "Vapor Pressures of Sulfur above the Boiling Point:" Temp., C. 700 600 500 350
/Sd 0.296 0.204
/ss/
/SO/
0.0102 0.0425 0.083 0.056
0.065
0,00167
/COP/ 0.6933 0.745 0.828 0.881
0,0005 0.0085 0.024 0.0615
X and Y are determined by trial and error. As a guide for the determination of Y , the conversions calculated in Table I1 were used; and for X , those found by calculating the equilibrium : 2c02 1/2SZ = 2 c o so2
+
+
The values thus calculated do not always give the true equilibrium constants; such an acoomplishment would involve too much tedious work. The apparent and true constants are both given so that the accuracy of the calculations can be judged. Usually the difference is very small and actually the effect will hardly be noticeable. The result of these calculations is shown in Table 111. The constants in brackets are the true constants. K1 refers to: 2co so2 = 2c02 1/*SZ and K 2 to: co '/2SZ = cos
+ +
FOR TABLE 111. RESULTS
Temp.,
c.
1200 1000 800 700 600 500 350
THE
210 (2001 2200 (2290) 1.28 X 106 (I 35 X 1.80 X 106 (1.74X 4.10 X 107 (3 98 X 1.85 X l o 9 (1.95 X .5 7 X 1 O l z (7.59.X
105)
106) 107) 101)
JOl?
0.039 0.18 0.9 2.3 10.8 57 2 X 10s
(0.04) (0.18) (1 0 )
(2.9) (11.0) (58) ( 2 X lo?
+
1/2s2
Reaction 7 has already been dealt with; reaction 11 is the so-called producer gas reaction. The free energy of the latter is calculated by the Lewis and Randall equations (7) : log K =
8930 - 2.451 log T
+ 0.0011T - 0.0000001T2 - 2.76
and the values of the constant are as follows: Temp., 'C. 1200 1000 800 700
Log K
Temp C." Log K 1.10 $00 do0 2.49 350 5.30
K
-3.07 -2.13 -0.80 0 05
8.5 X 10-4 7.4 X 1.6 X 10-1 1 12
K 12.6 309 200.000
The following method has been used for calculating the equilibrium. (Reaction 2C02 ' / p Sz = 2CO SO2is of no
+
+
+ SO2 = C02 + 1/2Sz and CO + 1/~S2= COS
Y
/cog/
/co/
0.18 0.09 0.03 0.016 0.010 0.0042 0.0005
0.02 0.08 0.33 0.55 0.80 0.935 0.988
0.527 0.607
0.114 0.055 0.0136 0.005 0.0013 0.0002 0.055
% COz
0.656
0.681 0.738 0.825 0.881
/cos/ 0.0023 0.0055 0,0067 0,006 0.0062 0,0033 0.0004
/so2/
/S/
0.058 0.030 0.0102 0.005 0.0037 0,0017 0.0002
0.028 0.006
.. ... . .. ... . .. ,
/s2/
0.271 0.297 0.314 0.292 0.202 0,064
0.0016
/SK/ . .. ... ...
0.01 0.042 0.082 0.056
/Sa/
...
... 01004 0.008 0,024 0.062
significance with continuous reduction. /SOZ/ is practically nil) : The initial gas mixture comprises carbon dioxide and Sz, the partial pressure or concentration of which is, respectively, a and b:
76.2 87.0 96.6 97.8 98.5 99.4 99.94
SULFURCONVERSION
% CO 16.2 7.9 2 0 0 7 0.2 0 02 < o 01
% ' COS
% SO2
0.33 0.80 1.00 0.80 0.80 0.40 0.04
8.27 4.30 1.40 0.70 0.50 0.20 0.02
%S
Conversion 90.5 94.5 97.5 98.5 98.8 99.4
In a similar way we may also calculate the gas composition if either sulfur dioxide or carbon monoxide is in excess. For approximation we may assume that for small changes / C o t / and /S2/ remain constant and therefore: /CO/
= 2c02
PERCENTAGE GAS COMPOSITION AT TOTAL EQUILIBRIUM
Tpp., C. 1200 1000 800 700 600 500 350
follows:
x
Since i t is convenient to have the above gas composition expressed in per cent, such figures, exclusive of elemental sulfur, are shown in Table IV. This table also contains the per cent conversion to elemental sulfur. The per cent gas composition is plotted in Figure 5 . TABLE IV.
I n the presence of carbon, the reduction of sulfur dioxide by carbonmonoxide takes place continuously; i. e., the carbon dioxide formed by the reaction of carbon monoxide and sulfur dioxide is again reduced to carbon monoxide. At any temperature the carbon monoxide in equilibrium with carbon is more than required for the complete sulfur dioxide reduction; hence, reduction of sulfur dioxide by solid carbon will theoretically take place a t any temperature, but the result actually obtained will depend on reaction rates. There is no critical range nor are there any invariant systems. The continuous sulfur dioxide reduction is expressed as
CO-EQUILIBRIUM 2CO
Kz
KI
If, for example, /SOJ is'increased three times,- /CO/ and /COS/ are decreased by 1/3 = 1.73 times; if /CO/ and/or /COS/ are increased three times, /SO2/ is decreased nine times. Continuous Reduction
+
Carbon disulfide is present in quantities estimated to the over the temperature range order of 2 X and 3 X 1000" to 350" C.
97
= constant
1
and /COS/ = constant /CO/
If a fraction X of carbon dioxide reacts to form carbon oxysulfide, a fraction Y forms carbon monoxide, and a fraction 2 of S2 forms carbon disulfide, we have:
+ + +
/COS/ = 2 X a / ( 1 Y a ) /CO/ = 2Ya/(1 Ya) /CSZ/ = Z b / ( l Ya)
/sz/
b
- X a - Zb
+ Ya
= -___1
INDUSTRIAL AND ENGINEERING CHEMISTRY
98
VOL. 30, NO. 1
TABLEV.
GAS COMPOSITION IN CONTINUOUS REDUCTION
Kz
Ka
X
Y
O.IS(O.18) 1 . 0 (1.0) 2.9 (2.9) 12.711) 57 /58) 2200 (2000)
2.6C2.7) 3.1(3.0) 3 . 0 (3.2) 3.4(3.6) 3 . 5 (3.9) L O (4.6)
0.04 0.4 0.2 0.3 0.3 0.3
0.955 0.70 0.40 0.14 0.03 0.0015
Temp., C. 1000 800 700 600 500 350
KO 6.6X10-*(7.4XlO-a) 0.165 (0.16) 1.1 (1.12) 12.6 (12.6) 304 (309) 2 1 X 106 (2 X l o 5 )
These equations are solved by trial and error by selecting such values of X , Y , and Z as will satisfy the three equations. In order to avoid much tedious work, such values as approach the true values have been accepted. The true and the apparent constants are shown in Table V; the true values are in parentheses. The initial gas mixture has a = 0.67 and b = 0.33 (total sulfur figured as SS). Table VI and Figure 6 give the percentage gas composition.
0.67 0.53 0.45 0.30 0.35 0.02
/CO/
/Cod
0.78 0.64 0.425 0.172 0,039 0.002
0.004 0.068 0.204 0.342
/COS/
/CSd
/Sd
0.13 0.122 0.120 0.100 0.095 0.006
0.053 0.040 0.041 0,017 0.006 0.001
0.033 0.128 0.210 0.369 0.310 0.134
0,490
0.757
/Ss/
% ' Con
%COS
"/o CSz
Conversion
0.4 7.2 21.3 34.8 49.3 84 2
82.4 66.8 44.4 17.5 3.9 0.2
3.5 13.3 21.8 37.5 37.2 14.9
13.7 12 7 12.5 10 2 9.6 0.7
26.5 17.7 15.4 5,7 3.0 82 5
THE
SOz-H2S-HzO-H&
Temp., C. Log KI 1100 900 700 500 300 113
3.53 4.51 5.85 7.82 11.10
...
KI 3.4 x 3.2 X 7 1X 6.6 X 1.3 X
103 10' 10: 10
10"
......
Log Kz Kz 7.4 0.87 1.47 29.5 2.28 191 103 3.49 3 . 1 105 5.60 4.0
x x
...,.
Sulfur and Hydrogen The free energies for: Hz + S(rhombic) = H2S + 1.81T In T + 0.00375T2 -
AF" = -3910
- 24.552'
The following figures regarding this reaction are taken from Lewis and Randall, as given by Preuner and Schupp (10) :
SYSTEM
Log Ks
Ka
-1.77 -1.57 -1.29 -0.84 0.00 1.30
1.16 X 10-2 2.69 X 10-2 5.13 X 10-2 1 45 x 10-1 1.0 20.0
So far we have calculated the reduction equilibrium on the basis of an initial gas containing /C02/ = 0.67 and / S J = 0.33, which is the type of gas resulting from the reduction of 100 per cent sulfur dioxide with carbon. In the two reactions considered there is a decrease in volume in the one and an increase in the other. Thus if both took place a t the same rate, no volume change would be involved, co cos so2 = 2c02 sz K = -Ki = /COZ/~/SZ/ K2 /co//coS//so2/
+
...
0:045
high as in the case of 100 per cent gas, the effect on the sulfur conversion is hardly noticeable-viz., 98.9 against 99.4 per cent.
Temp., 500 750 830 945 1065
Log K
C.
+
K
3.490 2.025 1.710 1.305 0.946
3090 106 51 20 8.8
If we assume /SZ/to be constant apd equaI to 0.1, the relation of /&/ to /HB/ is as follows: /HlS/
Temp.,
/Hz/
C.
300 500 750
+
.,.
....
0,0005
0.055
%S
% CO
CONSTANTS FOR TABLEVII. EQUILIBRIUM
...
, ,
0.000000037T3
C. 1000 800 700 600 500 360
...
....
and for TABLEVI. PERCENTAGE GAS COMPOSITION IN CONTINUOUS REDUCTION Temp.,
/Sa/
...
Temp.,
C.
830 945 1065
120,000 1,000 33
/HIS/ /&/ 16 6
3
REDUCTION OF SULFUR DIOXIDE BY HYDROGEN. The products of reduction are controlled by three reactions:
+ 2Hz = 2Hz0 (9) + '/zS, + = HzS
SO2 H2
'/2S2
2H2O (g)
+
3/2&
=
ZHnS
+ SOZ
(12) (13) (14)
and the reduction would be independent of the venting pressure; but in addition there is the dissociation of SSand S g to Sz which takes place when the gas is expanded. I n case of the reduction of a dilute gas-say, 5 per cent sulfur dioxide-it is of some interest to ascertain the extent the equilibrium has changed. The calculation is the same as before except that /SZ/ = 0.0244; /COz/ = 0.0488. The temperature is 500' C. By selecting X = 0.007 and Y = 0.9, we find :
/co/ = 3 . 4 x 10-5 /COz/ = 0.0485 /cos/ = 3.1 x 10-4 /SOI/ /Sz/
= 1.7 X 0.0193
The percentage composition is 99 per cent carbon dioxide, 0.07 per cent carbon monoxide, 0.6 per cent carbon oxysuEde, 0.35 per cent sulfur dioxide. Although carbon monoxide, carbon oxysulfide, and sulfur dioxide are almost twice as
TEMPERATURE %,
FIQVRE 5. EQVILIBRIA 2CO
CO
+ SO2 = 2C02 + '/,SZ
+ ' / A= COS for gas mixtures which initially contained /Sz/ = 0.523 and /COY/ 0.677 or 1360 grams sulfur per cubic meter of residual gas.
-
99
INDUSTRIAL AND ENGINEERING CHEMISTRY
JANUARY, 1938
\
-4
%CO/
-
/H20/ = 0.8(1 X ) = 0 . 2 - 0.2x - 0 . 4 X Y /S2/
+
all divided by 1 0.2X - 0.4XY. X and Y have to be found by trial and error. As a guide for Y , Preuner and Schupp's data given in the section on "Sulfur and Hydrogen" are used:
E/= K / S 2 / W = approximate constant /Ha/
FIGURE 6. CONTINUOUS REDUCTION = CS? +++ co2 + sz = 2cos coz = 2co Initial gas mixture: /Sz/ = 0.33
Equilibria: C
S2
c c
/COS/ = 0.67
The equilibrium constants are calculated by means of the free energies as given by Lewis and Randall (4): 6900
Log K I = T AFo
=
+
+ 0.435 log T
- 0.0013T2 0.00000023T3 - 1 . 5 (reaction 12)
-19,200 f 0.942' h 7'
+ 0.00165T2 -
0.00000037Ts
hperature ' C
FIQURE7. EQUILIBRIUM GAS COMPOSITION FOR REDUCTION OF SULFUR DIOXIDEWITH HYDROGEN
+ 1.65T
TABLEVIII. CO-EQUILIBRIUM' 2H2
+ SO2 = 2H20 +
'/2S2 AND
Hz
+
'/2S2
= Ha&
Temp.,
c. KI Ka 7.6 (7.4) 3.5 X 10' (3.4 X 108) 1100 32 (30) 900 3.7 X lo' (3.2X lo') 165 (191) 700 7.2 X 105 (7.1 X 105) 500 Ka = 0.160 (0.145) .... 400 Ka = 0.34 (0.302) .... 350 Ka = 0.53 (0.49) .... 300 Ka = 1.0 (1.0) .... a Monoatomic sulfur at llOOo C. has been ignored
- AF" Log K2 = _ _ 4.58T
47
X
Y
0.14 0.73 0.14 0.92 0.982 0.14 0.13 0.10 ... 0.05 ... 0.025 ... in this calculation.
...
- 0.00036T + 0.0782' - 0.36 (reaction 13)
0.47 log T
From the free energy equations we find: Log K3 =
-AF"
=
- - 1.38 log T
' ; w
+ 0.0006T + 0.79 (reaction 14)
0.077T2
Values calculated from the equations for these three reactions are shown in Table VII; incidentally
/H2/ 0.030 0.009
0.002
... ...
t . .
...
/Sod
/El&/ 0.082 0.105 0.113 0.116 0.90 0.033 0.024
0.057 0.057 0.057 0.058 0.045 0.017 0.012
0.910
0.910
/Sa/
/sS/
0.131 0,123 0,120 0.040 0.013 0.0013 Constant
... ..
... ...
o:oie
01605
0.026
0,009
0.029
0.022
,.
...
,
X is selected according to the single equilibrium (Equation 12), the figures of which are not included here. The results are shown in Table VI11 together with the apparent constants and true constants in parentheses. Figure 1 and Table IX give the percentage gas composition. TABLEIx. PERCENTAGE Temp., C.
% SO?
3.4 1.1 0.2
6.6
... ...
COMPOSITION AT EQUILIBRIUM
GAS
% Hz
...
According to the above figures, the amount of hydrogen below 750" C. is insignificant. For temperatures above 750" C. reactions 12 and 13 are used for calculations, but below 750" C. it is sufficient to consider reaction 14 alone. The same method as was used for the sulfur-carbon calculations will be followed and will be based on an initial mixture consisting of 2 moles water plus 0.5 mole Sz. Or if the venting pressure is 1 atmosphere: /H20/ = 0.8; /S2/ = 0.2. At equilibrium the gas is composed of /Sod = 0 . 4 X /Ha/ = O.SX(1 - Y ) /H,S/ = 0 . 8 X Y
/sa/
/HzO/ 0.700 0,716 0.710 0.770 0.817
% HzS
% Hz0
9.4
80.6 80.6 80.5 81.45 86.90 94 69 96 25
11.8 12.8
6.5 6.5 6 15 4.70 1.77 1 25
12.3 9.4 3.54 2.50
Conversion %S
65 62
60
59 67 87.5 01
For temperatures 500" C. and below, the equilibrium is computed from reaction 14 alone as follows: aX parts of water react with 0.75aX parts of sulfur to form aX parts of hydrogen sulfide and 0.5aX parts of sulfur dioxide: 0.5aX 0,25x
/sod
= 1 -
/Has/
=
1 - 0.25x
/H@/ 1
/w
b = 1
-
- 0.25X - 0.75aX - 0.25ax
INDUSTRIAL AND ENGINEERING CHEMISTRY
100
The sulfur concentration and thus the /H20/in the initial gas mixture is as follows : Temp., O C. 500
/sS/
/Sf/ 0.06
/ss/
0.035
0.009
/Ha01 0.896
The dew point of the gas mixture is 300" C. The value of /SZ/ a t this temperature is 3.8 X 10 -4. The reduction equilibrium SO2 HZis less complete by far than the corresponding equilibrium SO2 CO. In the temperature range 400" to 600" C. where the reaction rate is presumably rapid, the theoretical conversion is only 60 per cent. As the temperature approaches the condensation point, the conversion increases rapidly to 90 per cent, owing to the association of S2 to S g and SS, and from then on slowly as the sulfur condenses and its vapor phase disappears from the system. Conversion is practically 100 per cent a t the freezing point (114" C.). The reaction 2H20 3 / 8=~ 2H2S SO2 involves a decrease in volume; hence, slightly better conversion is obtained with dilute than with 100 per cent gas. Obviously, the above method of calculation can be used for 3/2S~,starting from the reaction 2H2S SO2 = 2HtO hydrogen sulfide and sulfur dioxide, an old process for producing sulfur.
+
+
+
+
VOL. 30, NO. 1
Reduction of Sulfur Dioxide with Methane The free energy equation for methane is taken from Lewis and Randall (7): 2SOz
+ CHd = Cog + Sz + 2HzO
This equation is probably in error by several per cent. Without going deeply into the matter of reduction of sulfur dioxide by methane, the data calculated merely serve to give a general idea of the reaction. Log K
5700 4- A. F5o8 ~= T + 4.83 log T - 0.0016T +
0.0000002Ta - 6 . 2
At 800" C. and at 1 atmosphere pressure the methane and sulfur dioxide concentrations are 0.005 and 0.01 per cent, At lower temperatures the reaction is still more complete: Temp..
Log K
C.
K
+
+
Effect of Water Vapor in Carbon MonoxideSulfur Dioxide Reduction System For small amounts of water vapor present in the sulfur dioxide-carbon monoxide equilibrium, we can write :
The secondary reactions are the same as with the hydrogen reduction-i. e., the action of water vapor on gaseous sulfur to form sulfur dioxide and hydrogen sulfide, except that these reactions take place only to half the extent as with hydrogen alone. In addition, the side react,ions to carbon oxysulfide and carbon disulfide especially if methane is used in excess, will have to be considered.
Literature Cited It will be assumed that the hydrogen sulfide-sulfur dioxide equilibrium is established a t 500" C. The initial gas mixture consists of /H20/ = a
$k&/ == b
c
in addition to carbon dioxide, monoxide, and oxysulfide which do not enter this equilibrium. At the new equilibrium we have :
/sod /"to/
=c
/&S/ /S2/
+ '/lax
a(l - X) = ax = b - 0.75aX
=
(1) Ferguson, J . Am. Chem. Soc., 40, 1626-44 (1918). (2) Koref, 2. anorg. Chem., 66, 73 (1910). (3) Lewis and Lacey, J. Am. Chem. SOC.,37, 1976-83 (1915). (4) Lewis and Randall, "Thermodynamics," New York, McGrawHill Book Co., 1923. (5) Ibid., p. 535,Table 1. (6) Ibid., p. 539. (7) Ibid., p. 573. (8) Ibid., p. 582. (9) Preuner and Schupp, 2. physik. Chem., 68, 129 (1909). (10) Ibid., 68,157 (1909). (11) Stock and co-workers, Ber., 52B, 672. 681 (1919); 57B, 719 (1924). RECEIVED February 25, 1937.
EXAMPLE 1. The conditions are: a = 0.01 (i. e., 1 per cent water vapor in initial gas mixture, since 1.5 per cent water in the coke used for reduction produces ap roximately 1 per cent water in the gas) 6 = 0.064 (Table &I) c = 0.01 (i. e., 1 per cent SO2 in initial gas)
By selecting X = 0.3 we find a t equilibrium: = 0.0155 /HzS/ e 0.003 /HzO/ = 0.007
/SOz/
/Sz/
5
0.064
The loss of sulfur conversion incurred by 1 per cent water vapor is 0.6 per cent. Approximately 25 to 30 per cent of small amounts of water vapor present is converted to hydrogen sulfide with a loss of 1 per cent conversion for every 1 per cent water vapor present. It may also be stated that, if the final gas contains 1 per cent sulfur dioxide, for every 1 per cent water vapor present there is 0.5 per cent hydrogen sulfide; and if 2 per cent sulfur dioxide, 0.3 per cent hydrogen sulfide for every 1 per cent water present. The effect of moisture in the sulfur dioxidecarbon reduction process is thus quite objectionable if present in appreciable amounts.
Courteey, School of Mineral Industries GaZlery, The Pennslrluania State College
ANTHRACITE COLLIERY DISMANTLED
