January 1948
INDUSTRIAL A N D ENGINEERING CHEMISTRY
down t o a value of 2.0. However, a bed of such finely divided material would offer great resistance to flow of liquid; increasing the particle size would permit better flow rates but decrease the reaction rate. The Germans evidently encountered a similar problem, since there are statements (I) that they found the best catalyst to be large porous particles prepared by sintering finely ground base-exchange resin, lightly coated with a thermosetting phenolic. The authors have no data to support any explanation of the failure of the bimolecular equation t o hold over the first 4 hours of the reaction. There appears to be some inhibiting process or induction period involved when the base-exchange resin is present. This is borne out by the fact that the 4-hour acid values for the runs with coarse catalyst (F and G) are actually higher than that for the run with no catalyst (A), although the 8- and 12hour values are lower. It was thought that this might be due to adsorbed water on the surface of the catalyst. However, a check of several runs in which either added water or bone-dry catalyst was employed (Figure 3) did not bear this out. This matter is of considerable practical importance for continuous column operation. If it is due to an integfal part of the reaction mechanism, the 2 hours' contact time mentioned above would need to be considerably increased to obtain a product with an acid number of 2 or lower. The phenol-formaldehyde-ulfonic acid resins are similar to Zeo-Karb H (6) in maintaining catalytic activity over a series of
99
runs. The one exception t o this is the sharp drop between m u 1 1 8B and C, the first and second runs with the fine catalyst. This drop could be due either to the elution of a small amount of adsorbed strong acid or to the loss of a very finely divided fraction during the a t r a t i o n of the catalyst from run B. Data for the uncatalyzed run (A) are a t variance with Sussman's findings of no "indication of esterification" for the same system under similar conditions (6). The close conformity of the rate found for this run with those for the catalyzed runs (Figure 4) leads to the belief that tlie authors' results are correct, ACKNOWLEDGMENT
The samples of base-exchange reain were prepared by B. Coe and G. Bodamer. The authors are indebted t o R. J. Myers, W. S. Niederhauser, and L..P. Hammett for advice and criticism. LITERATURE CITED
(1) Diericks, FIAT Report PB866, O5ce of Technical Services, Dept. of Commerce, Washington, 1947.
(2) Leyer and Othmer, IND. ENQ.CBEM.,37,968(1945). (3) Myers, F. J., FIAT Report PB42,802,Office of Technical Services, Dept. of Commerce, Washington, 1947. (4) Myers, Eastes, and Myers, IND. ENQ.CEEM.,38,697-706 (1941). (5) Sussman, Ibid., 38,1228 (1946). (6) Sussman, private communication. (7) Thomas and Davies, Nature, 159,372(1947). RECBIVED February 11, 1947.
Thermochemistry of Sodium Carbonate and Its Solutions KENNETH A. KOBE1 AND THOMAS M. SHEEHY2 University of Washington, Seattle, Wash. T h e solubility and thermochemical data for sodium carbonate, its hydrates, and its concentrated solutions have been reviewed and collated. New data are: Specijic heat of saturated solution 20-32' C. is 64.0 calories per gram NaCz03.10H20dissolving during heating; mean specitic heat from 33' to boiling point is 0.851 calorie per ' per gram of solution? heat of melting for Na2C02.10H~0 is 21,400 calories per gram mole.
c.
I
N 1944 the production of sodium carbonate, 4,693,000 tons,
was exceeded only by sulfuric acid as a manufactured chemicat utilized for chemical purposes. The physical and chemical properties of such an industrial compound are of the utmost importance. It is the purpose of this paper to review and collate the thermochemical properties of sodium carbonate, its hydrates and its concentrated solutions. New data are given on the specific heat of the saturated solution and heat of transition. SOLUBILITY
The solubility data, solid phases, transition temperatures, and vapor pressures of saturated solutions are of fundamental importance. The solubility data given in the International Critical Tables (II) were derived mainly from three sources (8, 84, 40). During the elapsed time several investigators have given new data from the cryohydric t o the critical temperature. 1
9
Present address, University of Texas, Austin, Tex. Present address, Standard Oil Company (California). EL Segund6 Calif.
Caspari (4, Hill and Bacon (IO), and Kobe and Leipper (92) investigated ranges from the cryohydric t o the boiling point. Seyer and Todd (36)investigated the range 17' t o 173' C., and Ervin, Giorgi, and McCarthy (9) made determinations a t 100' to 150' C. The high temperature range was investigated from 50' t o 348' by Waldeck, Lynn, and Hill (B), and from 150' t o 350' by Schroeder, Beck, and Gabriel (34). These newer data have been plobted on a large scale and compared with the data from which the I.C.T. (International Critical Tables) curve was drawn. The best curve was drawn through the points, giving due weight t o the reliability the data were believed t o have. From this curve were taken solubility values a t regular temperature intervals. These are given in Table I. Below 50' the data of the more recent workers (6,10,@) correspond to those of the earlier workers (8, 84, 90); the data of Wells and McAdam (40) from 28' t o 44" are highly accurate. Above 50" the data of Caspari (6) are definitely high, whereas those of Kobe and Leipper (82)are lower than I.C.T. values but not so low as those of Waldeck, Lynn, and Hill (38),whose data are about 1.5% lower. These latter workers used glass below 100' and a steel bomb up t o 348", and report their solubility values accurate t o 0.1% from 50' t o 150', 0.2% from 150" t o 250°, and 0.3% above 250" C. Schroeder, Beck, and Gabriel (34) checked the data of Waldeck, Lynn, and Hill a t four temperatures from 150' t o 350' and obtained satisfactory agreement except at 350°, at whieh temperature the latter workers reported a zero solubility which is refuted by the former. Waldeck, Lynn, and Hill also report determinations a t 112.5' 'and 113.0°
INDUSTRIAL AND ENGINEERING CHEMISTRY
100
TABLE I. SOLUBILITY OF SODIUM CARBONATE IN WATER Temp.0, 0
c.
-2.1 0 5 10 15 20 25
90
22.0ou 3?.96mU 30m 35.37u 40 60 60
70 75 80 90 100 104.8
1 1 1
l + p 0
0
0 0 0 0 0 0 0 0 0 0 0 0 0
150 E60 180 200 2.20
240
280 260
ZBO 300
850
Om
78
10m
P5m 20m 25m
30n 32.00U 34 35.3713
U
l0+7 1 7ffl
1 1 1 1
140
0
lo+?
1
109 110 113 120 130
Om 10m 15m 20m
Water pf
Hydration 10 10 10 10 10 10 10 10
'7Ba 78 7' ! l O t j 7 78 7-1
G. NazCOa/ 100 G. NazCOa, HIO % 6.10 7.00 8.90 12.1 16.4 22.2 29.4 39.2 45.4 49.9 50.7
46.3 45.6 45.4 45.2 44.9 44.7 44.6
5.75 6.54 8.2 10.8 14 1 18.1 22.7 28.2 31.2 33.3 33.6 33.1 32.8 32.2 31.6 31.3 31.2 31.1 31 .O 30.9 30.8
4.20 4.20 4.20 4.03 3.86 3.71 3.57 3.44 3.16 2.89 2.56 2.16 1 . 95 1.75 1.32 0.88 0.19
44.5 44.5 44.5 42.7 40.9 39.3 37.8 36.5 33.5 30.6 27.1 22.9 20.7 18.6 14.0 9.3 2.0
30.8 30.8 30.8 29.9 29.0 28.2 27.4 26.7 25.1 23.4 21.3 18.6 17.1 15.7 12.3 8.5 2.0
1.92 2.48 2.79 3.17 3.59 4.08 4.28 4.51 4.67
20.4 26.3 29.6 33.6 38.0 43.2 48.4 47.8 49.5
16.9 20.8 22.8 25.2 27.6 30.2 31.2 32.3 33.1
3.01 3.57 3.92 4.32
4 4 3 47.5
31.9 24.2 27.4 37.8 41.6 29.4 45.8 7a 31.4 transition temperature; m = metastable equilibrium. 7a 7a
-
G. Moles/ 1000 G. Hz0 0.575 0.66 0.84 1 . 14 1.55 2.09 2.77 3.70 4.28 4.71 4.78 4.67 4.60 4.48 4.37 4.30 4.28 4.26 4.24 4.22 4.21
7a
Vapor Pressure, Mm. Ha.
....
.... .... ....
12.3 16.9 21.4 26.8 29.0 29.5
....
34.0 43.6 74.1 121.5 192.7 239,8 296.2 442.4 631.7 760.0 (atm. 1.15 1.19
.....
1.65 2.25 3.02 4.01 5.27 8.67 13.7 21.0 30.9 37.0 44.2 61.7 83.8 I66
.... .... ,...
.... .,..
....
. . I .
....
,...
.... ...* .... ....
Vol. 40, No. I
divergence has been reported in the transition temperature of monohydrate to anydrous salt. Waldeck, Lynn, and Hill (38) reported 112.5' * 1" C. based on the abrupt change in slope of the solubility curve a t this temperature. Janecke (14) reported 107"by a dilatometric method a t approximately 450 atmospheres pressure. An inspection of his pressure-time curve shows that 107' represents a minimum value. Keene and Julien (16) reported approximately 109'. Keene (16) stated that by a phase rule method the transition point was determined to he 108.8" * 0.2' C. A value of 109" is selected to indicate that some uncertainty may exist until further work has been done. HEATS O F FORMATION, SOLUTION, AND DILUTION
The critical compilation of thermochemical data on heats o f formation, solution, and dilution by Bichomky and Rossini (4) give values sclf-consistent with other thermochemical data in their book. Therefore, their values are taken as the best available and aregiven in Table 111. Kelley and Anderson (20) give Q, for sodium carbonate at 25" C. as 271,020 calories per gram mole. Perreu (SO) has determined the heat of solution of sodium carbonate decahvdrate in solutions of increasing concentration a t 11-12' C. aiid extrapolated the data to give A H = - 13,540 calories per gram mole as the heat of solution in a saturated solution. This valut. was checked by measuring heats of dilution a t the same teniperature. At 20" this value was determined as AH = - 13,960 calories per gram mole. Williamson (41) has derived a method for the calculation of heats of solution from solubility and vapor pressure data, from which he calculates a value of 13,500 ca1oric.s per gram mole of decahydrate. Swallow and Alty (36) determined the heats of solution of anhydrous sodium carbonate and dilution a t 30' for solutions up to 25% sodium carbonate. Watson and Kowalke (39) have given a method of calculating the differential heats of solution of sodium carbonate at various cow centrations and temperatures. From their dissolution charts may be obtained the temperature reached in the adiabatir formation of a sodium carbonate solution.
TABLE 11. TRANSITIONS I N SYSTGV SODIUM CARBONATE-WATER which give identical results and which represent a point of abruptly changing slope of the solubility curve. This was interpreted by them to be the transition point of the monohydrate to the anhydrous form; however, other work makes this conclusion extremely doubtful. This point remains unexplained but is given full weight because of the check determinations. The values of Seyer and Todd (36)are definitely low. Solubilities of the alpha form of heptahydrate and beta form below 25' were determined in 1851 by Loewel (84) and are of doubtful accuracy, as they have never been checked. The existence of a trihydrate as asserted by Bain ( 8 ) is extremely doubtful. I t is believed that the solubility data of Table I for decahydrate, heptahydrate from 30" t o 35.5", and monohydrate are accurate within 0.4%. The vapor pressure of the saturated solution also is given in Table I. The figures are those of I.C.T. (11 ) up to IOO", which are checked by the data of Rode (33)from 15" to 40" C. Above the boiling point the data of Waldeck, Lynn, and Hill (38)and of Keevil (f7)were used to prepare a log p us. 1 / T plot from which the vapor pressure was read at the temperatures shown. The sgreement between the two sets of data is excellent. Using the vapor pressure curve the heat of vaporization of water a t the normal boiling point of the solution is calculated as 10,400 calories per gram mole water evaporated. The transition temperatures are given in Table 11. The temperatures determined by Wells and McAdam (40) with an accuracy of 0.02" C. remain the most reliable despite various determinations by other workers (10, 26,27, 32). Considerable
Phases
Temp.,
C.
References
TABLE 111. HEATSOF FORMATION, SOLUTION, A N D DILCTIOK OF SODIUM CARBONATE AT 18" C. Formula NazCOa
G. Cal./G. Qj = - AMoleb H,
State"
269,890
..._.
27.5 460 -
CL
6400 ,3200 1600 800
275.370 273,360 275,360 275,400 2 75,520 275,770
400
200 100 R0
276,lRO
i
5 _.
NazCOa, Hz0 NazCOa.7HzO NazCOa. lOH2O HzO
20 18 15 C
c C
1
-
276.830 277.590 277,830 277,940 278,130 341,640 764.860 975,380 68,370
a c = crystalline state: 1 = liquid state; 0: infinite dilution of t h r solution numbers refers to the gram moles water in which 1 gram mole sodium
carbonate is dissolved. b Heats of dilution are calculated by subtracting the Qf value in the final s t a t e from t h a t in the initial state. Heats of solution are calculated by subtracting from Q j of the solution the Q j of the crystal minus the Qf of the water with the crystal.
INDUSTRIAL AND ENGINEERING CHEMISTRY
January 1948
101
SPECfFIC HEATS
The specific heat of anhydrous sodium carbonate has been determined by Anderson ( I ) from 55" to 300" K. The extrapolated curve gives a value of 26.38 calories per gram mole per " C. for the heat capacity at 25' C. The value of Matsui and Kitazato (28) a t 25" is too high, as is the value of Regnault (SI), while that of Kopp (23) is too low. The specific heat of sodium carbonate decahydrate between 2.6" and 19.2' C. was determined by D'Ans and Tollert ( 7 ) t o be 127.4 calories per gram mole. The specific heat of sodium carbonate solutions is given by I.C.T. ( 1 3 ) a t 20" from the data of Marignag between 21' to 52' (26) and of Thomsen at 18" (37). Swallow and Alty (36) determined the specific heat of solutions a t various concentrations up t o 25% a t 17.6", 30.0°, 76.6', and 98.0" C. with an estimated accuracy of 0.5%. For the specific heat curve at 30" the following equation was derived:
830
0.9986
- 0,01123X + 0.000223X2
where Sa0= specific heat at 30" X = concentration of solutions in per cent sodium carbonate As no data are available for a solution saturated with sodium carbonate at all temperatures, such data have been determined by the authors. The apparatus used was similar to that of Kobe and Anderson (21) and consists of a 200-cc. wide-mouth Dewar flask as the calorimeter. Through the rubber stopper in the mouth of the flask pass a calibrated thermometer graduated in tenths of a degree, a glass dril) stirring rod driven by a motor stirrer, and the leads to the heating element. The heating element consists of 1 meter of No. 28 constantan wire threaded through a fine glass tube wound into a spiral about 2 inches long and 1.25 inches wide. A molybdcnum lead wire about 4 inches long is silver-soldered to each end of the constantan resistance wire and the glass tubing sealed around the molybdenum lead wire. The glass coil is then evacuated through a side tube and sealed off; thus any corrosion or gathering of moisture within the coil is prevented and a constant resistance is obtained. The ends of the molybdenum lead wire pass through the stopper and are connected in the electrical circuit. The Dewar flask is placed within an iron container and surrounded with a 3-inch layer of cotton to decrease radiation losses. The water equivalent of the calorimeter is determined by passing I ampere through the heating element and raising the temperature of 150 grams of water from 25" to 95" C. At each 10' interval the current is shut off and the rate of cooling determined. The room temperature is maintained constant. A saturated solution of sodium carbonate is prepared a t 36', and its density and concentrat,ion are determined. Approxi-
>
080
< I
$
OB5
$
OB4
IA
2.
t
g
083
0
$ I
OB2 30
40
50
00
70
TEMPERATURE
80
-
90
100
'C.
Figure 1. Heat Capacity of Saturated Sodium Carbonate Solution
TABLEIV. HEATCAPACITY OF SATURATED SODIUM CARBONATE SOLUTIONS FROM 36" TO 95" C. Temp. Range,
c.
36-45 45-55 55-65 65-75 75-85 85-95
Run 3
Heat Capacity, Cal./Gram/O C. Run 4 Run 5
0.853 0.857 0.851 0.865 0.851
...
0.855 0:857 0,862
o:s39
0.855 0.854 0.854 0.853 0.852 0.843
AV.
0.854 0.856 0,857 0,880 0.852 0.841
TABLE: V. HEATCAPACITY OF SATURATED SODIUM CARBONATE SOLUTJONS FROM 20" TO 32" C.
Run
Temp. Range, O C.
16 18 19 20
20-26
3 4
26-32
Heat Capacity Cal./e. NazCOd. IOHzO CSl./O c./g. dissolving satd. during soln.. av. heating
3.93 3.77 3.87 3.79 Av. 3.84
9.72 9.72 Av. 9.72
65.7 61.1
63.4 62.3 63.4 83.4 64.5 64.0
mately 150 ml. of solution are weighed into the calorimeter, and 1 gram of sodium carbonate monohydrate is added. After stirring for several minutes to bring the solution to equilibrium, the current is turned on and the temperature brought back t o approximately 36". The solution then is heated t o approximately 45", and the cooling rate determined. This procedure is repeated a t 10" intervals up t o 95'. From the corrected temperature rise and current input, the calories used are computed. In the calculation of the specific heat of the solution a correction must be made for the sodium Carbonate monohydrate that precipitates out during the heating, decreasing both the sodium carbonate and water in the solution. By a graphical integration over 10" intervals the average weight of solution in the interval is determined. The total heat input is corrected for the water equivalent of the calorimeter and the heat content of the average amount of suspended sodium carbonate monohydrate present during each temperature interval. The net heat input thus found divided by the corrected temperature rise gives the average hcat capacity over that temperature interval. The results are given in Table I V and shown in Figure 1. A graphical integration of the curve of Figure 1 from the transition temperature (33") to the boiling temperature (104.8') gives 0.851 calorie per degree per gram of solution graphically averaged over this same temperature range. Extrapolation of the data of Swallow and Alty (36) at 76.6" to a saturated solution gives about 0.85 calorie per gram per " C., whereas Figure I shows 0.855. The heat capacity of the saturated solution includes the heat of crystallization of the sodium carbonate monohydrate from the solution. The heat capacity of a saturated sodium carbonate solution was determined over the range 20" to 32" C. by maintaining a saturated solution of sodium carbonate in contact with sodium carbonate decahydrate as the temperature was raised. To a solution saturatcd a t 19" are added sufficient decahydrate crystals to saturate the solution at 28". The heat input necessary to raise the temperature of this mixture is measured and corrected for the graphically determined average weight of decahydrate crystals undissolved over this range. The average weight of solution is determined graphically and the heat capacity calculated for this average weight of solution. A similar determination was made over the range 26" t o 32". The results are shown in Table V. The heat capacity of the saturated solution from 20" t o 32' rises rapidly because of the rapidly increasing solubility over this
I N D U S T R I A L A N D E N G I N E E R IN G C H E M I S.T R Y
102
TABLEVI. HEATOF TRANSITION OF SODIUM CARBONATE DECAHYDRATE TO MONOHYDRATE A T 32.96' C. R u n No. 7 9 11 12 13 14
Heat of Transition, Cal./G. Mole 20,900 21,700 22,100 21,400 21,400 21,000 Av. 21,400 =k 300
Medium Nitrobenzene Nitrobenzene h-itrobenzene h7trobenzene Carbon tetrachloride Carbon tetrachloride
range. A more useful value than the heat capacity of the average weight of saturated solution is the heat capacity of the solution in terms of sodium carbonate decahydrate that must be dissolved to maintain a saturated solution. This value remains approximately constant a t 64.0 calories per gram Na2C03.10H20 dissolving during heating, or 18,100 calories per gram mole Na2CO8.lOH2O dissolving. HEATS OF DECOMPOSITION
The heats of decomposition of the various hydrates and sodium carbonate itself were determined from vapor pressure determinations. The pressure of sodium carbonate monohydrate was determined by Caven and Sand (6),who obtained the equation l o g P = 10.825
From this the heat ofreaction for the equation
+ H,O(g)
Na2CO8.€I20(s)-+-Na2C03(s)
gives 13,800 calories per gram mole as the heat of drying of sodium carbonate monohydrate. The vapor pressure of sodium carbonate decahydrate was determined by Baxter and Cooper (5),who obtained the equation
+
3634.51 46,45 +
From this the heat of reaction for the equation
+ 3H,O(g)
NalCO3.1OH2O(s)--+ Xa2CO3.7HzO(s)
gives 29,400 calories per gram mole as the heat of drying sodium carbonate decahydrate t o the heptahydrate. Combining the result for decahydrate to heptahydrate and monohydrate to anhydrous, and assuming that the heat required for the six middle molecules is an average of two end values, the heat of reaction for the equation h'a~C01.1OH~O(s) -+- Na2COa(s)
about 40" and then rises rapidly. By plotting temperature against time the intersection of the two lines gives the end of the transition. Correction is made for the heat necessary to bring the crystals from room temperature and the liquid to the melting temperature of 32.96", and the liquid, saturated solution, and monohydrate to the temperature a t the end of the experiment, The results are given in Table VI. The data on heats of fusion and heats of dissociation of sodium carbonate have been discussed by Kelley (18, 19), who points out the unreliability of the present data. Sodium carbona€e melts a t 854" C., and 7000 calories per gram mole may be taken as an approximate value of the heat of fusion (18). The heat of dissociation, calculated to 18" C., is given as 76,900 calories per gram mole but is a very uncertain value (19). SUMMARY
1. Data in the literature for the solubility and thermochemistry of sodium carbonate, its hydrates, and its concentrated solutions have been reviewed and collated. 2. The heat capacity of a saturated sodium carbonate solution in contact with a solid phase has been determined over the range 20' to 95" C. 3. The heat of transition or melting of sodium carbonate decahydrate to monohydrate has been determined as 21,400 * 300 calories per gram mole. LITERATURE CITED
- 3000.0 T
where P = vapor pressure, mm. Hg T = OK.
log P = 11.8071
Vol. 40, No. 1
+ 10HzO(g)
gives 114,000 caloriesyer gram mole as the heat of drying of sodium Carbonate decahydrate to the anhydrous state. The heat of transition of sodium carbonate decahydrate to monohydrate, or the heat of melting when the decahydrate melts incongruently to form monohydrate and saturated solution has been determined in this work. The equation is:
+
KaiCO3.1OH~O(s)-+ Na2C03.H20(s) 9H20 (satd. soln.) The heat of transition or melting was determined by introducing sodium carbonate decahydrate into the calorimeter containing nitrobenzene (21) or carbon tetrachloride as a heat transfer medium from the resistance spiral to the crystals of solid. The liquid is heated to about 31.6", the decahydratc added, and heatnpplied. The temperature rises s l o ~ l yuntil the melting is complete at
(1) Anderson, J . Am. Chem. SOC., 55. 3621-3 (1933). (2) Bain, Zbid., 49, 2734-8 (1927), (3) Baxter and Cooper, Zbid., 46, '923-33 (1924). (4) Bichowsky and Rossini, "Thermochemistry of Chemical Substances," pp. 114, 377, New York, Reinhold Pub. Corp., 1936. (5) Caspari, J. Chem. SOC.,125, 2381-7 (1924). (6) Caven and Sand, Zbid., 99, 1364 (1911). (7) D'Ans and Tollert, 2. Elektrochem., 43, 87-91 (1937). (8) Epple, Dissertation, Heidelburg (1899). (9) Ervin, Giorgi, - and McCarthy, J . Am. Chem. Soc., 66, 384-7 (1944). Hill and Bacon, Zbid., 49, 2487-95 (1927). International Critical Tables, 3, 372 (1928). I b i d , 4, 237 (1928). I b i d , 5, 124 (1929). Janecke, 2. physik. Chem., 90, 269 (1915). Keene, private communication (July 29, 1946). Keene and Julien, U. S. Patent 2,133,455 (Oct. 18, 1938). Keevil. J . Am. Chem. Soc., 64, 849-50 (1942). Kel1ey:U. S. Bur. Mines, Bull. 371, 68 (1934). Kelley, Zbid., 393, 108 (1936). Kelley and Anderson, Zbid., 384, 36 (1935). Kobe and Anderson, J . P h y s . Chem., 40, 429-33 (1936). Kobe and Leipper, IND.ENG.CHEM, 3 2 , 198-203 (1940). Kopp, Trans. Royal SOC.(London), 155,71 (1865). Loevel, Ann. chim. phys., 33, 334-90 (1851). Marignag, Ibid., [5] 8, 410 (1876). iMatsui and Kambara, J . Soc. Chem. I n d . (Japan), 35, suppl. binding 308-13 (1932). Matsui, Kambara, and Yoshino, Zbid., 35, suppl. binding 313-6 (1932). Matsui and Kitazato, Zbid., 40, suppl. binding, 246-8 (1937). Mondain-Monvall, Compt. rend., 174, 1014 (1922); 175, 162 (1922). Perreu, Ibid.,189, 167-9, 285-7 (1929). Regnault, Ann. chim. phys., [3] 1, 168 (1841). Richards and Fiske, J . Am. Chem. SOC.,36, 486-90 (1914). Rode, Ann. inst. anal. phys-chim. (U.S.S.R.), 6, 97-134 (1933). Schroeder, Berk, and Gabriel, J . Am. Chem. Soc., 58, 843-9 (1936). Seyer and Todd, Trans. R a y . Sac. Can.. [3] 23, 67-70 (1929). Swallow and Alty, J . Chem. SOC.,1931, 3062-79. Thomsen, A n n . Phvsik., 142, 337 (1871). Waldeok, Lynn, and Hill, J . Am. Chem. SOC.,54, 928-36 (1932), 56, 43-7 (1934). Watson and Kowalke, IND. ENG.CHEM.,22, 370-6 (1930). Wells and McAdam, J . Am. Chem. SOC.,29, 721-7 (1907). \T.'illiarnson, Trans. Faraday Soc., 40, 421-36 (1944). R E C E I V ESeptember D 30, 1946.
