Mechanism, Kinetics, and Equilibrium of Thermal Decomposition of Ammonium Sulfate Raisaku Kiyoura and Kohei Urano Tokyo Insitute of Technology, 0-okayama, Meguro-ku, Tokyo. Japan
The thermal decomposition mechanism of ammonium sulfate, the reaction rate and equilibrium of the deammoniation from ammonium sulfate, a n d the reaction rate of the dehydration of ammonium bisulfate were investigated b y DTA, TGA, a n d x-ray diffraction. Ammonium sulfate on heating decomposed into triatnmonium hydrogen sulfate or ammonium bisulfate, which subsequently decomposed into ammonium pyrosulfate or sulfamic acid, and finally into several gases. The activation energies for the deammoniation a n d dehydration were calculated, a n d the enthalpy change of the deammoniation was evaluated. The results of this work should be helpful in many industrial processes dealing with ammonium sulfate or its thermal decomposition products a t elevated temperatures.
THE
thermal decomposition of ammonium sulfate has been studied since the early part of the 20th century. Dixon (1944) investigated the residue of heating in an atmosphere of wet room air. Duval et al. (1959) and Erdey et al. (1964) studied the thermal stabilities of the reagents by TGA. Rafal'skii and Ostrovskaya (1964) proposed a theory for the decomposition mechanism from kinetic studies. However, many problems, such as the decomposition equilibrium or the boiling point of ammonium bisulfate, are not yet solved. Many industrial processes dealing with ammonium sulfate or its thermal decomposition products a t elevated temperatures have been proposed. John (1962) and Datin (1965) proposed production of fertilizers from rock phosphate with ammonium sulfate or bisulfate. McCullough (1960), Montgomery (1962), Haeter and Reichau (1963), and Bonfield and Bohn (1966) proposed recovery of ammonia and sulfur oxides by the thermal decomposition of ammonium sulfate. Kiyoura (1966a,b) developed a process for the production of ammonium sulfate from hot flue gases by recovery of sulfur dioxide. The present work gives the mechanism, kinetics, and equilibrium of the thermal decomposition of ammonium sulfate to enhance understanding and its application in industry. Experimental
Mechanism. DTA and TGA curves were plotted by apparatus assembled in the laboratory with automatic temperature programmers and recorders. X-ray powder diffractions were carried out with CuK, radiation and a nickel filter a t room temperature. The released gases were analyzed qualitatively by gas chromatography and
chemical analysis. The amounts of NH,' in solutions of the heated residues were analyzed by colorimetry, and the amounts of H - and Sod2- were evaluated by titration. Kinetics and Equilibrium. Studies on the thermal decomposition mechanism concluded that the deammoniation reaction occurred first, producing ammonium bisulfate, which decomposed mainly into ammonium pyrosulfate by dehydration, and further into gases. With sufficient water vapor in the system, the weight decrease on heating could be attributed only to the release of ammonia. Therefore, the deammoniation rate may be obtained from the rate of weight decrease. Likewise, the rate of ammonium bisulfate dehydration may be obtained by heating in dry air when other decompositions are negligible. It is also necessary to select sample quantities and temperatures such that the diffusion of the released gases does not control the rates of decomposition. I n this case, the real chemical reaction rates corresponding t o the maximum decomposition rates a t the given temperatures can be measured. About 250 mg. of ammonium sulfate was used in the temperature range from 140" to 240" C. for measurement of the deammoniation reaction rates, About 50 mg. of ammonium bisulfate was used in the range of 160" to 200°C. for measurement of the dehydration reaction rates. The rates of weight decrease were observed with a thermobalance a t constant temperatures. The total equilibrium of the thermal decomposition of ammonium sulfate cannot be measured by conventional methods, because it releases too many kinds of gases. The authors devised a method, where only the deammoniation equilibrium was determined with the thermobalance (Figure 1). A quartz container was preferred to platinum, Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 4, 1970 489
the given atmosphere. At this temperature, the equilibrium pressures of ammonia will be equal to its concentration in the given atmosphere. The gas flow rates had no effect from 25 to 100 ml. per minute. Accuracy of the temperature measurements was within f 2 " C., and weight measurements were within + O . l mg. Results and Discussion
Mechanism. The DTA curve for ammonium sulfate (Figure 2 ) shows two endothermic peaks, indicating that decomposition occurs in at least two steps. The TGA curves (Figure 3) at the lower heating rate show an inflection point corresponding to a loss of 1 mole of ammonia from 1 mole of ammonium sulfate. The release of ammonia was observed by gas chromatography, and found to occur above 100°C. The reaction expressed by Equation 1 was inferred.
I
I
Figure 1. Diagram of thermobalance A. Gos storage G. Thermocouple 8. Pump H. Transformer C. Water bath D. Differential coil E. Furnace F. Sample container
I.
Temperature programmer
1. Displacement meter
K.
Recorder
as the latter promoted decomposition, catalytically. Ammonium sulfate was heated in an atmosphere of nitrogen, ammonia, and water vapor. Water vapor repressed dehydration and subsequent decomposition. The heating temperature was elevated step by step a t intervals of about 2 hours. The authors determined the highest temperature at which no weight decrease was observed in
100
Temperatm 'C. 200 300
However, the x-ray patterns of the heated residue of ammonium sulfate (Figure 4) show no ammonium bisulfate at 160°C., but confirm the presence of triammonium hydrogen sulfate, (NH4)sH(SO4j2. The x-ray patterns of a mixture of 1 gram-mole of ammonium sulfate and 1 gram-mole of bisulfate ground in a mortar showed that triammonium hydrogen sulfate was easily formed on grinding. This double salt released ammonia on heating a t 180" C. and changed to ammonium bisulfate. However, when heated a t 160°C. for 4 days, it showed no weight decrease. Figure 2 shows the DTA curve of this salt.
400
(NHhSQ
Temperature "C. Figure 2. DTA curves of ammonium sulfate, bisulfate, and the double salt heated a t 4°C. per minute in dry air
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Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 4, 1970
Figure 3. TGA curves of ammonium sulfate
20
30
and decomposition. Qualitative analysis of the released gases showed the presence of water, ammonia, sulfur dioxide, sulfur trioxide, sulfuric acid, hydrogen, and nitrogen. The TGA curves (Figure 5 ) show no inflections even a t the lower heating rate of 0.25'C. per minute, but show that the weight decrease ceased a t a point of 8 % decrease in weight, when it was heated a t 200'C. for 12 hours. The decomposition was repressed by water vapor, confirming that dehydration is the first step in the decomposition of ammonium bisulfate. The reaction expressed by Equation 3 was inferred.
40
D i f f r a c t i o n Angle 28' Figure 4. X-ray diffraction pattern of ammonium sulfate heated at 160"C.for 2 weeks in dry air
I t is concluded that ammonium sulfate releases ammonia above 100°C. as in Equation 1, but from 100" to about 170" C., the ammonium bisulfate produced forms triammonium hydrogen sulfate directly with the ammonium sulfate. Thus the deammoniation reaction above 170" C. can be written as in Equation 1, but the reaction up to 170°C. may be expressed by Equation 2 .
2(NH,)?S04 2 (NHI)3H(S0,)2 + NH,
T
(2)
The DTA curve of ammonium bisulfate (Figure 2) shows two endothermic peaks corresponding to the melting point
However, sulfamic acid (NH2S03H) formed a brown melt around its melting point (205"C.) and decomposed to many gases, such as hydrogen, ammonia, and sulfur dioxide. The DTA curve of the mixture of sulfamic acid and ammonium bisulfate (Figure 6) shows a large exothermic peak. The x-ray pattern of the heated sample of this mixture (Figure 7) shows the presence of ammonium pyrosulfate, confirming that sulfamic acid easily reacted with ammonium bisulfate to form ammonium pyrosulfate as in Equation 4.
NHZSO3H
+ NH,HSO,
+
(NH4)ZSzO;
(4)
The x-ray patterns of the heated residues of ammonium bisulfate did not show any sulfamic acid, but confirmed the presence of ammonium pyrosulfate. However, the presence of small amounts of sulfamic acid in the heated residue was ascertained, because the heated sample was
1CO Temperature 'C.
90.
.0 _
A. 4'C. per min. in dry air 80 . B. 0.25'C. per rnin. in dry air C.4'CC. per min. i n dryair kept at 200'C.for 72 hrs. 7o D. 4'C. per min. in 25 per cent HP
100
200
300
4co
w
2 60 a,
%
$ 50:
8 +
5~40 ~
%
30 -
1I ,
Figure 5 . TGA curves of ammonium bisulfate
Figure 6. DTA curves of sulfamic acid heated at 4°C.per minute in dry air Ind. Eng. Chem. Process Des. Develop., Vol. 9,No. 4, 1970 491
According to these studies on the mechanism, the decomposition temperature of ammonium sulfate is lower than previously stated. The boiling point of ammonium bisulfate in Lange's handbook (1961) is unreliable, because ammonium bisulfate decomposes before boiling. Erdey's decomposition mechanism, expressed by Equations 1 and 6, is rather simple and inadequate for the thermal decomposition of ammonium sulfate.
20
30 40 Diffraction Angle 2 0 "
Kinetics and Equilibrium. The decomposition reaction rate is in proportion to the amount of undecomposed ratio of sample. I t can be expressed by Equation 7,
Figure 7. X-ray diffraction pattern of mixture of sulfamic acid and ammonium bisulfate heated a t 210°C. for 2 minutes in dry air
brown and more acidic than the mixture of ammonium bisulfate and pyrosulfate. A slight increase of N H 4 + in its solution was observed on heating, and many gases such as hydrogen were released below the decomposition temperature of ammonium pyrosulfate. I t can be concluded that ammonium bisulfate releases water above 150°C. as in Equation 3, but most of the sulfamic acid produced changes to ammonium pyrosulfate by reaction with ammonium bisulfate. The melt of ammonium bisulfate becomes stable solid again, and the dehydration reaction is written as in Equation 5.
dX
-=
dt
h(100 -
X) :.ln(100 - X)= -ht
(7)
where X = decomposed ratio in percentage, t = heating time in hours, k = reaction rate constant in hrf'. The deammoniation reaction of ammonium sulfate is expressed by Equation 2 (up to 170°C.) and Equation 1 (above 170°C.). Therefore, the decomposed ratio X can be written as in Equations 8 and 8' for the deammoniation. For the dehydration of ammonium bisulfate expressed by Equation 5, it can be written as in Equation 9.
X=
W" MI
w t -~wo x 100 = 1553 wo-wt* 2M2 wo ' , '
up t o 170°C. (8) The reversibility of the reactions expressed by Equations 1, 2, 3, and 5 was ascertained by TGA, x-ray measurements, and chemical analyses. Erdey et al. (1964) reported that ammonium pyrosulfate released sulfur trioxide and changed to ammonium sulfate above 250" C. However, ammonium sulfate decomposes quickly into ammonium bisulfate, and changes further a t this temperature. Ito and Uchida (1952) reported the presence of a double salt of sulfamic acid and ammonium sulfate. The DTA curve of this salt prepared from the solution (Figure 6) shows that this salt is not stable above 150"C., and may be irrelevant to the decomposition of ammonium sulfate. Further studies on the complex decomposition of sulfamic acid have to be carried out. The mechanism of the thermal decomposition of ammonium sulfate is illustrated by Figure 8.
Figure 8. Thermal decomposition mechanism of ammonium sulfate
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Ind. Eng. Chem. Process Des. Develop., Vol. 9, No. 4, 1970
-
w,-wt -~ . w o x 100 = MI
Me
'
777
wo - wt. wo '
above 170°C. ( 8 ' )
. Wo X = W,I - wt -~ M.3
'
x 100 = 1279
2M4
wo - wt W"
(9)
where W o and W , = weight of salt after 0 and t hours, and M1, M z , MB,and M , = molecular weight of ammonia, ammonium sulfate, water, and ammonium bisulfate, respectively. From the rate of weight decrease measured with a thermobalance a t constant temperatures, the reaction rates were calculated by Equations 7, 8, 8', and 9. Figures 9 and 10 show the logarithmic undecomposed percentage (100 - X) as functions of the heating time, t. These are projected as straight lines a t least in early stages, when the other reactions were negligible. Figure 11 shows the relations between temperatures and the reaction rate constants calculated from the gradients of Figures 9 and 10, and expressed by Equations 10 and 11. The activation energies calculated by Equations 10 and 11 are, respectively, 16 and 13 kcal. per mole for deammoniation and dehydration.
log hl = -3.46 x 103/T+ 5.03
(10)
log hz = -2.83 x 103/T+ 5.53
(11)
where h l and k l = rate constants of deammoniation and dehydration in hr.-', and T = heating temperature in K.
100
200
250
90
80
c.
150
-1
\
0 : De-ammoniation
70 .-0
"
%eo
2 io-'
01
10-I
In CI
c ru
cIn -'
c 0
0
2
0
4
6 8 Time days
1 0 1 2 1 4
Figure 9. Reaction rate of deammoniation of ammonium sulfate
10'
100 90
'
80
1 0-3
2.2 2.3 Temperature 103/"K.
1.9 2.0
2.4
2.1
Figure 11. Arrhenius plots of deammoniation of ammonium sulfate and dehydration o f ammonium bisulfate
.-0
T 70 CL
'C. 200
4v
' 0
150
\
1
1
2 Time hrs.
3
4
I
b \
Figure 10. Reaction rate of dehydration of ammonium bisulfate
Figure 12 shows the relation between the equilibrium pressures and temperatures for deammoniation of ammonium sulfate, as expressed by Equation 12. The enthalpy change of 34 kcal. per mole is evaluated by Equation 12.
log K , = -7.34 x 103/T+ 11.52
i b
(12)
where K , = equilibrium pressure of ammonia in atmospheres. By this equilibrium relation, the theoretical yield of Kiyoura's process for the synthesis of ammonium sulfate from hot flue gases can be evaluated. Flue gases will contain sufficient water vapor, so that dehydrated materials will not be produced. Ammonium sulfate, bisulfate, or the double salt of these two will be produced. Other experiments have shown that the synthesis reaction rate is very rapid. Therefore, ammonium sulfate will be produced until the concentration of ammonia equals its equilibrium pressure at the temperature of the final state
1.8
1.9
2.0
2.1
2.2
2.3
24
Temperature 10YK. Figure 12. Equilibrium ammonium sulfate
pressure
of
deammoniation
Ind. Eng. Chem. Process Des. Develop., Vol. 9,No. 4, 1970
of
493
of the synthesis process. An insufficiency of ammonia will produce ammonium bisulfate or triammonium hydrogen sulfate-for example, the theoretical yield of ammonium sulfate can be calculated when 0 . 2 7 of the sulfur dioxide in flue gas is completely oxidized to sulfur trioxide, and 0.4% of the ammonia is added to the system at 200°C. The equilibrium pressure of ammonia a t 200°C. calculated from Equation 12 is atm., which is equal to 0.014.Therefore, 0.39% of the ammonia will react, leaving behind 0.01”C a t 200°C. Thus 0.19% of the sulfur dioxide will change to ammonium sulfate, and the residual 0.OlLCwill change to ammonium bisulfate. Miller’s (1955) process for pickling iron with ammonium bisulfate, Holowaty’s (1959) process for recovering ammonia from coke oven gas, and the many industrial processes mentioned above can be investigated in detail by utilizing Equations 10, 11, 12, and Figure 8.
Acknowledgment
The authors express sincere thanks to H. Kuronuma and G. Uwanishi of the laboratory for their useful suggestions.
Literature Cited
Bonfield, J. H., Bohn, F. L., U. S.Patent 3,282,646 (1966). Datin, R. C., U.S. Patent 3,172,751 (1965). Dixon, P., Nature 154, 706 (1944). Duval, C., Wadier, C., Servigne, Y., Anal. Chim. Acta 20, 263 (1959). Erdey, L., Gal, S., Liptay, G., Talanta (London) 11, 913 (1964). Haeter, L., Reichau, U., Ger. Patent 1,151,492 (1963); C A 59, 8386h (1963). Holowaty, M. O., U. S. Patent 2,899,277 (1959). Ito, S., Uchida, S., J . Chem. SOC.Japan. Pure Chem. Sec. 73,348 (1952). John, C. M., U. S. Patent 3,047,369 (1962). Kiyoura, R., Chem. Erg. News 44 (26), 23; (27), 36 (1966a). Kiyoura, R., J . A i r Pollution Control Assoc. 16, 488 (1966b). Lange, N. A., Ed., “Handbook of Chemistry,” 10th ed., p. 219, McGraw-Hill, New York, 1961. McCullough, R . F., U. S. Patent 2,927,001 (1960). Miller, C. O., U. S. Patent 2,700,004 (1955). Montgomery, J. C., U. S. Patent 3,047,369 (1962). Rafal’skii, N. G., Ostrovskaya, L. E., Geterogennye Reaktsii i Reakts. Sposobnost 1964, 95 (1964); C A 64, 15057h (1966).
RECEIVED for review December 18, 1968 ACCEPTED April 25, 1970
Model Predictive Time-Opti mal Control of Second-Order Processes D. A. Mellichamp Department o f Chemical and Nuclear Engineering, University of California, Santa Barbara, Calif. 931 06
Set point changes for second-order processes are implemented using a hybrid computer and a fast-time model of the controlled process to search out the time-optimal trajectory.
Process outputs are used as initial conditions to monitor the process transition in continuous, closed loop fashion. Model scan rates up to 100 per second (with convergence to the optimal solution in milliseconds) furnish a continuous updating of predicted switch times for the controlled process and make possible the multiplexing of a single hybrid controller to a large number of controlled processes. The controller has excellent characteristics for set point changes and also as a regulator with both analog simulated processes and an experimental two-tank liquid level system.
C o n t r o l methods that use predictive techniques are applied in many critical aerospace and military situations. The ability to predict and program system changes in advance is a well-recognized practice in the supervision of space probes and satellite orbit changes, and control of high performance aircraft and submarines. Most predictive techniques rely on a rather sophisticated mathematical model of the controlled system; a computer is used to scan a large number of possible control schemes, from which the most useful is selected. Alternatively, a large 494
Ind. Eng. Chern. Process Des. Develop., Vol. 9, No. 4,1970
body of mathematical theory has been developed which can be used with a linear system model to generate a control procedure that will be optimal in some sense. Procedures differ, depending on the immediacy of the situation: The rocket burn time for a deep space probe obviously can be computed months in advance; a similar calculation for satellite rendezvous may have to be made as approach occurs. I n either case, although minor corrections will have to be made during the transition to take into account discrepancies between the actual system and
