THE HEAT CAPACITY OF SATURATED SODIUM SULFATE SOLUTION KENNETH A. KOBE
AND
CLARENCE H. ANDERSON
Department of Chemical Engineering, University of Washington, Seattle, Washington Received October 17, 1095
The heat capacity of saturated sodium sulfate solution is of importance in the problem of recovery of the anhydrous salt from its aqueous solution. No data are reported in the literature for the saturated solution. In fact, data for heat capacities of practically all saturated solutionsrin contact with the salt are not in the literature. APPARATUS
Heating element. A piece of Pyrex tubing, inside diameter 3 mm., is drawn out to give a thin-walled center section 1 meter long and 1 mm. in diameter. A 20-gauge copper wire is soldered to one end of a piece of 28gauge constantan wire 1 meter long. The constantan wire is threaded through the tubing and the end soldered to another 20-gauge copper lead wire. The fine glass tubing is wound into a spiral approximately 35 mm. in diameter and with 3 mm. between the turns. The ends of the heavy tubing containing the copper leads are brought up a t right angles t o the plane of the spiral. The copper leads are connected to the lower ends of binding posts in a suitable cork stopper. Calorimeter arrangement. A 200-cc. wide-mouth Dewar flask is used. In the cork containing the heating element are a 100°C. calibrated thermometer graduated in tenths and a glass drill stirring rod driven by a motor stirrer. The heating element is placed in a circuit with suitable variable resistances, calibrated ammeter, and voltmeter across the heating element to check constantly the resistance of the heating element. Water equivalent. A constant current of 1 ampere is passed through the heating element immersed in 100 g. of water in the calorimeter. The range of temperature is 25" to 95°C. At each 10OC. interval the current is shut off and the rate of cooling determined. The room temperature is maintained constant. HEAT CAPACITY, 32.4"C. TO 102.8"C. Above the transition temperature of sodium sulfate decahydrate (32.4OC.) the solubility curve is inverted. A saturated solution of the
429 TH& JOURNAL OF PEYSICAL CHEMISTRY, VOL. 40, NO. 4
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KENNETH A. KOBE AND CLARENCE H. ANDERSON
salt is prepared at 34.5OC. and 100 ml. of it is pipetted into the calorimeter. One gram of excess anhydrous salt is added t o insure crystallization of salt from the solution as the temperature rises. Data are taken over the range 35" t o 95"C., with cooling curves at 10OC. intervals, as in the determination of the water equivalent. One additional correction must be made in the TABLE 1 Heat capacitg of saturated sodium sulfate solution TEMPERATURE
-
___-
13
RUN
14
-I
GRADUATED
15
VALUE,
c
AVER.'=E
CALCULATE[ VALUE, BY EQUATION 1
c,
"C.
32.5 35-45 45-55 55-65 65-75 75-85 85-95 100 102.8
ERROR
per cent
0 793 0.789 0.785 0.779 0 775 0.763
0.793 0.790 0.787 0.780 0.775 0.768
0.795 0.790 0.785 0.778 0.774 0.767
0.7946 0.7934 0.7902 0,7854 0,7799 0.7742 0.7672 0.7563 0.7528
0.794 0.790 0.786 0.779 0 775 0.7675
rCh#Wt?ATGWC
-
0,7959 0,7933 0.7893 0.7846 0,7793 0,7734 0.7668 0.7596 0.7575
+0.16 -0.01 -0.11 -0.10 -0.08 -0.10 -0 05 i-0 44 +O .62
*C.
FIG.1. Heat capacity of saturated sodium sulfate solution
calculations t o account for the heat content of the anhydrous sodium sulfate precipitated from the solution as the temperature rises. The average amount of this salt (+1 g.) is determined by a graphical integration of the solubility curve. The heat content is then calculated for each temperature interval, using the heat capacity from the International Critical Tables ( 5 ) .
HEAT CAPACITY OF SATURATED SODIUM SULFATE SOLUTION
431
The data are tabulated in table 1. From the average of values for the heat capacity a graduated value is determined by the method of Eggers (3). This method also gives zi means of extrapolation which is used to give the heat capacity curve over the ranges 32.4" to 40°C. and 90" to 102.8OC. The graduated curve for heat cstpacity is shown in figure 1. This curve may be expressed by equation I, where t = "C.
C = 0.803 - 1.14 X 10-4t - 3.2 X 10-Bt2
(11
The agreement between the values calculated by equation 1 and the graduated values is shown in table 1. The mean heat capacity over the range 32.4" to 102.8"C. determined by graphical integration is 0.7796 cal. per gram. This value is very close to the 0.781 cal. per gram reported by Pagliani (8), who determined the heat capacity of 1 mole of sodium sulfate in 18 moles of water over the range 24" to 100°C. This system has an excess of the decahydrate up to 31"C., is unsaturated between 31" and 74"C., and has an excess of the anhydrous salt above 74°C. MEAN HEAT CAPACITY,
20°C.
TO
32.4"C.
Below 32.4"C. the saturated solution is in equilibrium with the decahydrate, for which the solubility curve rises steeply. Fifty milliliters of a solution saturated at 20°C. are pipetted into the calorimeter. Calculation shows 91.5 g. of sodium sulfate decahydrate will dissolve in this to give a solution saturated at 32.4"C. The decahydrate is added to the solution in four portions over equal parts of the temperature range. Room temperature is raised a t the same rate as the temperature of the calorimeter to eliminate radiation and emergent stem correction. Corrections must be made for thk excess decahydrate crystals present in the solution. Data are not available for the heat capacity of sodium sulfate decahydrate; Kopp's rule (4) may be used over this small range without great error. The mean heat capacity may be calculated per gram of initial solution or per gram of average solution. The average weight of solution is found by graphical integration of the solubility curve over the range 20" to 32.4"C. The average weight must be corrected for the amount of unhydrated sodium sulfate in the decahydrate, as the hydrate readily effloresces. From the data the mean heat capacities calculated are: 5.51 calories per gram of solution (average) and 7.92 calories per gram of solution (initial). HEAT OF TRANBITION
Two values for the heat of transition are found in the literature. Cohen (2) found 16,509 cal. per gram-mole, and Leenhardt and Boutaric (7) found 18,400 cal. per gram-mole. The method used by both workers
432
KENNETH A. KOBE AND CLARENCE H. ANDERSON
started with the salt in solution and measured the heat of crystallization, which may be lower than the heat of transition as all of the heat of the crystal may not be given up immediately. The method used in this work was to measure directly the heat of transition. Sodium sulfate decahydrate crystals are introduced into either nitrobenzene or toluene as the heat transfer liquid. The liquid is heated to 32.4"C., the decahydrate crystals added, and heat applied. As heat is applied, the temperature rises s l o d y until the transition is complete, 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 t o bring the crystals from room temperature t o the transition temperature. The heat capacity data for nitrobenzene as given in International Critical Tables (6) do not agree nith those of Parks and Todd (9), whose data are used. The results are given in table 2. TABLE 2
Heat of
transition of
K:anSOa,10H20
RUN
H E A T OF T R A N S I T I O N I N CAL. PER GRAM-MOLE
9 12 13 14 15 16 17
18,800 18,900 18,900 18,600 18,600 18,400 18,700
MEDIUM
Xitrobenzene Nitrobenzene Xitrobenzene Toluene Toluene Toluene Toluene
1
18,700
Average
I
. I
The heat of transition may also be calculated from the vapor pressure data for the decahydrate crystals and the saturated solution by using the Clausius-Clapeyron equation. The value found by this calculation is 19,000 cal. per gram-mole. Data, calculations, and corrections applied are too detailed t o be given here, but may be found in the original report of the n-ork (1). SUMM.4RT
1. The heat capacity of saturated sodium sulfate solution from 32.4"
to 102.8"C. niay be represented by the equation C = 0.803
- 1.14 X
- 3.2 X
10-V
The mean heat capacity over this range is 0.780 cal. per gram. 2 . The mean heat capacity of saturated sodium sulfate solution from 20" to 32.4"C. is: 5.51 cal. per gram of solution (average) and 7.92 cal. per gram of solution (initial).
HEAT CAPACITY OF SATURATED SODIUM SULFATE SOLUTION
433
3. The heat of transition of sodium sulfate decahydrate is 18,700 cal. per gram-mole. REFERENCES (1) ANDERSON: Thesis, University of Washington, 1935. (2) COHEN:2. physik. Chem. 14, 53 (1894). (3) EGGERS:Trans. Am. Inst. Chem. Engrs. 27,334-74 (1931). (4) HOUGENAND WATSON:Industrial Chemical Calculations, p. 211. John Wiley and Sons, New York (1931). (5) International Critical Tables, Vol. VII, p. 100. McGraw-Hill Book Co., New York (1930). (6) International Critical Tables, Vol. V, p. 110. McGraw-Hill Book Co., New York (1929). (7) LEENHARDT AND BOUTARIC: Bull. SOC.chim. 13,651-7 (1913). (8) PAGLIANI: Atti Torino 17, 97 (1881-2) ; Landolt-Bornstein, Physikalisch-Chemische Tabellen, Vol. 2, p. 1262 (1923). (9) PARKS AND TODD:J. Chem. Physics 2,440-1 (1934).
