Mar., 1955
THESYSTEM SODIUM SULFATE-SODIUM MOLYBDATE-WATER
Fig. 2), a constant gradient of 2000"/cm. is recorded over the entire curve up to the drop-off point, B. This leads to a rate of evaporation lower than the burning rate by a factor of 38. It is clear, therefore, that the available data do not support a phase-change mechaiiism involving simple vaporization of the fuel. The calculations pertinent to this point are based on the equations H I = H,r kdT Hz = dx where H I is the rate of heat absorption necessary for vaporization, cal./cm.Z see., H2 is the rate of heat conduction to the surface, cal./cm.2 sec., H , is the volumetric heat of vaporization of the liquid, cal./cm.*; r is the burning rate, em./ see.; k is the he2t conductivity of the gas, taken to be 5 X 10-6 cal./cm. C. see., and dT/dx is the otemperature gradient in the gas just outside the surface, C./cm., assumed to be equal to the temperature gradient in the liquid at the surface. I n the case EGDN, H , = 124 cal./cm.aB6r = 0.031 sec., so that H I= 3.8 cal./cm.2 see., whereas Hz = 0.1 cal./ em.$ sec.
It is recognized t,hat, if a very steep temperature gradient did exist a t the surface, the thermocouple used here would be too large to record it accurately. In a purely thermal model the temperature would be expected to rise to a surface temperature of about 500" over a distance of 10 microns,' whereas our thermocouples are approximately 25 microns in thickness. However, since the thermocouple indicates an average temperature across its diamethe record should give evidence of such large changes in some manner. In actual fact, the rec(5) T . E. Jordan, "Vapor Pressure of Organic Compounds," Interscience Publishers, Inc., New York, N. Y., 1954. (6) R. H. Olds and G . B. Shook, U. S. Naval Ordnance Test Station Technical Memorandum 917, 1952. (7) N. P . Bailey, Mech. En&, 65, 797 (1931).
257
ords in the neighborhood of the surface are smooth, free from discontinuities, and low in slope. Therefore this difficulty would not appear to be present. 2. A second phase-change mechanism involves a chemical reaction, the usual postulate being invoked that the nitrate ester forms gaseous products by a unimolecular decomposition. However, the surface temperature necessary for this reaction to take place a t the observed rate is on the order of 500°6~s~9~10 so that this mechanism also is incompatible with the experimental observations. 3. A third mechanism, also chemical in nature, involves the attack on the nitrate ester by a second species. Such a mechanism is in accord with the temperature data, provided a material can be found which will react with the nitrate ester a t the required speed a t room temperature. Clearly, one is looking here for highly reactive free radicals. It is postulated that such reagents are generated in appreciable concentration in the flame and that they diffuse back to the liquid surface to initiate reaction. This type of chemical mechanism, therefore, requires that a diffusion mechanism of flame propagation be operative. Unfortunately, no unanimity exists in the literature as to the relative importance of thermal and diffusion processes in flames. The present data tend to underscore the latter. It is hoped that studies now in progress -will help to clarify this point further. Acknowledgment.-The authors wish to thank Dr. Lyman G. Bonner and Dr. Frank H. Westheimer for their continued interest and many helpful discussions. This study was sponsored by the U. S. Navy under Contract NOrd 10431. (8) R. E. Wilfong, 6 . S. Penner and F. Daniels, THISJOURNAL, 64, 863 (1950). (9) 0. K. Rice and R. Ginell. ibid.. 64, 885 (1050). (10) R. G. Parr and B. Crawford, Jr., ibid., 64, 929 (1950).
L.
THE SYSTEM SODIUM SULFATE-SODIUM MOLYBDATE-WATER BY WILLIAME. CADBURY, JR. Contribulion from the Chemistry Department of Haverford College, Haverford, Pa. Received September 87, 1064
Solubility relationships in the system sodium sulfate-sodium molybdate-water a t various temperatures are reported.
At temperatures where it exists as a stable phase, the decahydrate of each of these salts takes up the other in solid solution, but the amount of sodium sulfate taken up by sodium molybdate decahydrate is very small. Boundary conditions for some of the three-phase equilibria in the system have been determined, as have the locations of two quadruple points.
The work reported in this paper is similar, in methods and in significance, to previously reported studies of the systems sodium sulfate-sodium chromate-water' and sodium chromate-sodium molybdate-water.2 Ricci and Link@ have studied the systemsodium sulfate-sodium molybdate-water a t 25'. Experimental The salts used were C.P.grade sodium sulfate and sodium molybdate which had been recrystallized once as decahy(1) W. E. Cadbury, Jr., W. B. Meldrum and FV. W. Lucasse, J . Am. C h r n . SOC.,68, 2262 (1941). (2) W. E. Cadbury, Jr., i b i d , , 67, 262 (1945). (3) J. E.Ricci and W. F. Linke, ibid.. 13. 3607 (1951).
drate. TOdetermine solubility, the pure salt, a batch of mixed crystals prepared by crystallization as d e ~ a h y d r a t e , ~ or a mixture of salts of about the desired commsition, was placed in a test-tube, 150 mm. x 25 mm. Unless solution was formed by transition, the desired amount of water was added. The tube was placed in a thermostat. After a few hours, with occasional stirring, equilibrium was reached, as indicated by agreement in analysis when the period of stirring was varied and whether the approach was from undersaturation or supersaturation. Liquid free from solid phase, and moist solids, were obtained by fihation through paper on a small buchner funnel. Data for the condition of equilibrium resulting when liquid and a second solid'phase were formed by transition of (4) Ref. 1, P. 2263; ref. 2, p. 262.
258
WILLIAM E. CADBURY, JR.
decahydrate were obtained as follows: a sample of decahydrate solid solution of suitable composition was warmed until partial transition had occurred; the tube containing the mixture was placed in the thermostat, set at approximately the desired temperature, and when the temperature of the mixture was constant, a liquid sample was filtered off and analyzed. For analysis, the samples, whether liquid or moist solid, were transferred to weighed weighing bottles. Percenbage water was determined from the loss in weight after the sample had been heated for several hours to about 150'. In samples where sodium sulfate was in excess, sodium molybdate was determined directly, and vice versa; the other salt was determined by difference. As a check on the analytical method, both salts were determined directly in a few cases. Sodium molybdate was determined by the indirect Volhard method, as in ref. 3. Sodium sulfate was determined as follows. The sample, dissolved in about 100 ml. of water, was heated to boiling and a slight excess of silver nitrate solution was added to remove molybdate as insoluble silver molybdate. This precipitate was filtered off, and a slight excess of hydrochloric acid solution was.added to remove excess silver. After the precipitate of silver chloride was filtered off, sulfate was determined in the usual way by precipitation as barium sulfate.
Results In Table I are given representative data on solubility measurements a t the various temperatures. The solid phases are indicated as follows: A, NazMo04; Az, NazMo04.2Hz0; Am, NazMo04.10 HzO; B, NazSOr; Blo,Na2SO4.10Hz0; SA,decahydrateholid solution containing very little Bm; SB, decahydrate solid solution containing appreciable Aio. The relations covered are indicated in the polythermal diagram, Fig. 1. For clarity, the figure is distorted somewhat; correct quantitative values can be inferred from the tables and from later figures. Dotted segments of the boundary curves indicate the general direction of some equilibrium conditions possible in this system which were not investigated in this study.
VOl. 59
PQ, SBan3 Az; along a&, SAand Az; along QR, SA and SB;along pP, A2 and B. TABLE I SOLUBILITY DATA:SYSTEMN ~ & ~ O ~ - N ~ ~ M O O K - H & Temp.,
OC.
0
8.5
12.1
20.0
28.0
Satd. soh. Nait304, NaaMoOd,,
%
Each of the polythermal boundary curves, on which the direction of decreasing temperature is indicated by arrows, represents equilibrium among liquid solution and two solid phases. These solid phases are as follows: along bP, SB and B; along
Moist solid NazS04, NatMoO4,
%
Solid phase
%
4.46 3.32 2.23 1.16 1.08 0.81 0.56 0
0 7.00 13.86 29.10 31.24 31.52 31.12 30.60
...
...
38.48 36.62 33.55 8.40 1.02 0.72
1.11 3.02 8.34 38.40 48.80 54.15
7.74 5.74 3.40 2.45 1.90 1.51 0.81 0
0 7.75 20.66 31.37 36.91 36.95 37.67 37.29
37.89 30.71 30.10 6.10 1.83 0.89
9.65 8.85 6.32 4.00 3.02 2.87 2.93 0.49 0
0 2.40 12.68 23.29 34.03 36.57 36.52 38.60 39.08
...
...
40.40 36.76 39.90 31.46 31.47 0.76 0.13
trace 3.21 2.50 11.36 12.54 73.54 70.32
15.96 13.82 10.97 7.03 6.42 6.22 2.99 1.96 0
0 5.04 14.22 28.49 34.10 34.36 37.28 37.56 39.30
40.20 37.15 34.75 27.09 2.74 1.58 1.44
0.66 3.48 8.11 22.82 61.07 56.78 52.18
25.54 20.80 17.22 15.78 12.42 11.84 10.06 7.07 1.78 0
0 10.11 17.87 22.97 28.09 29.06 31.56 33.69 38.17 39 * 74
...
...
Bio
41.48 36.71 62.30 90.33 89.09 58.63 2.73 0.78
1.26 5.80 2.97 3.45 4.53 25.36 64.52 64.09
SB SB
... ...
Bio SB SB SB SB, SA
...
Aio
*..
Bia
1.68 7.73 11.98 41.82 47.56 49.32
SA
SA
SB SB SB SB,
I
SA
SA
SA Aio
Bio SB SB SB SB SB
Az Az A2
Bio
...
...
...
SB SB SB
SB,A2 Az Az A2
Az
...
SB,€3
B B B, Az AS A2
Az
+
Points a and b represent transition points, Aio cal. -P A2 L, and Bla cal. -t B L, respectively. The curves a& and bP are transition curves, along which a new solid and solution, L, are formed by adding heat t o a decahydrat,e solid solution: SA + cal. --t Az L and SB cal. B L, respectively. The curve PQ represents equilibrium among cal.; i.e., solution, SB,and Az: L --t SB A2 SBand A2 separate out when the saturated solution is cooled. The points P and Qarequadruplepoints, invariant points at constant pressure in a three-component
+
Fig. 1.-Polythermal solubility diagram for the system Na2SOd-Na2M004-H~0 (not to scale).
%
+
+
+
+
+
+
+
--+
Mar., 1955
THESYSTEM SODIUM SULFATE~ODIUM MOLYBDATE-WATER
system. They are transition points a t which the reactions on cooling are: at P: L B -+ SB A2 cd., and at Q: L A2 -+ SA SB cal. Isothermal solubility data were obtained at five temperatures: 0, 8.5, 12.1, 20.0 and 28.0'. In their study of this system at 25' Ricci and Linke3 observed that sodium sulfate decahydrate dissolves some sodium molybdate decahydrate in solid solution, but that sodium molybdate dihydrate does not dissolve detectable amounts of sodium sulfate. The data reported here lead to the same conclusion at these temperatures, as well as to the conclusion that sodium molybdate decahydrate dissolves a small amount of sodium sulfate decahydrate at temperatures at which the molybdate decahydrate is stable. There is no evidence that anhydrous sodium sulfate dissolves any sodium molybdate. Figure 2 shows the data for 0", plotted to scale on rectangular coordinates. The line EF on this and subsequent figures represents calculated compositions of decahydrate solid solutions of sodium molybdate and sodium sulfate. The tie lines, located after analysis of solutions and corresponding slightly moist solids, show that the solid phases in equilibrium along the two branches of the curve are respectively sodium sulfate decahydrate (BIo)containing some sodium molybdate in solid solution, and sodium molybdate decahydrate (Alo) containing very little sodium sulfate in solid solution. These are the phases designated above as SB and
+
+
++ + +
259
SA,respectively, indicated on the polythermal diagram (Fig. l) by the solid portions of the line joining Alo and Bla. The break in the curve in Fig. 2 gives the location of the 0" point on QR of Fig. 1. Figure 3 shows the data for 12.1". The tie lines in this figure show that the solid phases are decahydrate solid solution, SB, as before, and sodium molybdate dihydrate, Az. The break in this curve gives the location of the 12.1' point on PQ of Fig. 1. 50 I
I
0
20
Fig. 3.-System
I
I
I
I
40 60 80 NazMoO4, %. NazS04-NaaMoO*-HzO at 12.1
90
'.
Isotherms at 8.5 and 20.0" are omitted, since they are similar in all except quantitative aspects to those at 0" and 12.1", respectively. Figure 4 is a plot of the data obtained at 28.0'. Three different solid phases can exist at this temperature, as indicated by the three branches of the
50
40
30
?&
d 20
0
Fig. 4.-Systern
10
0
20 40 NazMo04, %. Fig. 2.-System NazSOa-iYazMo04-Hz0 a t 0'.
0
20
60
40 60 80 NazMoOl, %. NazS04-NazMo04-Hz0at 28'.
curve. Two of these solids are SBand Az, the same as those which can exist at 12 and 20"; the third, represented by the middle branch of the curve, is anhydrous sodium sulfate. The break, J, in the 28" isotherm corresponds to a point on b P of Fig. 1, and the second break, K, on the same isotherm gives a point on Pp. Other points along the curve bP were located, as described above, by analyzing the solutions formed
WILLIAM E. CADBURY, JR.
260
a t measured temperatures by partial transition of decahydrate solid solutions, Sg, of various compositions. Attempts to locate the curve a& by an analogous method, by warming solid solutions SA,gave results which were not satisfactorily reproducible. Since this curve is so short, however, it was located with sufficient precision by determining its extremities only, points a and Q. Data for curves bP and a&, Fig. 1, are given in Table 11. TABLE I1 CONCENTRATIONS ALONG TRANSITION CURVES Along curve bP NazM004,
%
NazSO4,
OC.
%
Solid phases
32.4 31.1 29.0 27.0 24.8
0 8.9 18.5 25.2 30.3
33.1 26.2 19.0 14.2 11.0
Bio, B SEI B B SBj B SB,Bl Az
10.3 9.8
Along curve a& 39.0 0 37.3 2.2
4
Aio, A2
SB, Az, SB
The curve QR is the locus of points representing breaks in the appropriate isothermal solubility curves, such as those at 0 and 8.5", where SB and SA can exist in equilibrium with solution. The curve PQ is the locus of points representing breaks in the isothermal curves where SB, A2 and solution can coexist, as a t 12.1 and 20". The quadruple point, P, was located as follows: A mixture of B and Blottogether with solution of approximately the right composition, and another mixture of B and A2, with the appropriate liquid, were prepared. These mixtures were placed in two test-tubes in a thermostat at 28", and after equilibrium was reached, a sample of liquid was removed and analyzed. This was repeated a t temperatures of 25.8 and 24". The data obtained are given in Table 111. As the temperature goes down, the yosodium sulfate in the first mixture decreases and the % sodium
Vol. 59
TABLE I11 DATAFOR LOCATION OF POINT P. FIG.1 Mixture L-B-Blo
4.
NazSO4,
%
NazMo04, %
28.0 25.8 24.0
15.7 12.5 9.6
23.0 27.2 30.9
Mixture L-B-Aa NazSOr, NaaMoO4, % %
10.1 10.8 11.0
31.5 30.5 30.3
molybdate increases; in the second mixture, the reverse is true. The ratio of sodium sulfate to sodium molybdate was plotted against temperature for each mixture; the temperature where the two curves cross-24.8"-is the desired point, the temperature at which a liquid phme of definite composition can exist in equilibrium with three solid phases. The composition of the liquid a t this point, determined by analysis of a solution in equilibrium with the three solids at this temperature, is given in line 5 of Table 11. The quadruple point, Q, was located by mixing the three solids, Alo, Blo,and Az, with a little water at 9.5'. (On standing, the solids Alo and Blowere doubtless converted t o solid solutions, SAand SB; whether diffusion is sufficiently rapid to result in internal equilibrium in the solid is immaterial, since equilibrium between the solution and the surface of the solid is established rapidly.) After this mixture had stood for some time, with occasional stirring, in a thermostat adjusted to the temperature of the mixture, the temperature became constant at 9.82", and a sample of the solution was removed for analysis. As a further check, the rest of the liquid was returned to a tube in the thermostat, set a t 9.8", containing a mixture of the three solids. This mixture was stirred from time to time; after temporary slight changes, the temperature became constant at 9.81". Analysis of samples of the liquid gave results not significantly different from those obtained before. The composition, which is that of point Q, is given in the last line of Table 11. The author wishes to express his thanks to the Chemistry Department of the University of Colorado for making available t o him their facilities while much of this study was being made.
