THE LATENT HEAT OF FUSION AND IDEAL SOLUBILITY OF NAPHTHALENE‘ H. LEE WARD Chemical Laboratorv of Washington University, S t . Louis, !Missouri Received October I$, 1933
In some previous work from this laboratory (8) it has been shown that the solubility of naphthalene in chlorobenzene exceeds the ideal solubility as calculated from the generally accepted value of the latent heat of fusion of the naphthalene by means of the Schroder (6) equation. This result is not to be expected on account of the relatively non-polar character of both substances. &!!oreover, a determination of the heat of fusion by Bogojawlenski (2) gave a value considerably lower than that accepted, and one which would give a n ideal solubility more nearly in accord with that obtained in chlorobenzene. With the above exception, the earlier determinations as summarized by Mathews (4) give a latent heat of fusion per mole of 4560 calories. This is the value accepted by the International Critical Tables. Later determinations by Andrews, Lynn, and Johnston (1) and Spaght, Thomas, and Parks (7) give 4540 and 4585 calories, respectively. The former value is probably more reliable, but the authors do not claim an accuracy of more than f 1per cent. I n view of the uncertainty it was deemed best to make a more accurate determination of the latent heat of fusion of naphthalene and especially to measure the heat capacities of the solid and liquid in order to determine the variation of the heat of fusion with the temperature and thus to fix the exact form of the ideal solubility curve. EXPERIMENTAL
Materials Naphthalene (L‘Baker’sAnalyzed”) was recrystallized three times from methanol and further purified by fractional freezing twice. Neither method alone gave a pure product, but the combination gave a material that on freezing shrank in volume by about 20 per cent and formed an almost perfectly transparent solid which clung closely to the walls of the tube leaving a clean core in the center. The same freezing phenomena had been previously observed in the case of very pure benzene prepared by the 1 This work was made possible by assistance from a grant made by the Rockefeller Foundation t o Washington University for research in science. 761
762
H. LEE WARD
method of Richards and Shipley ( 5 ) . The maximum amount of impurity which may be present in such materials is that which can form a saturated solid solution with the substance which freezes in the above manner, and perhaps a very slight amount which might be held in the interstices in the secondary or mosaic structure (10). The melting point of the purified naphthalene was not less than 80.25"C. A sample from Kahlbaum and designated "for calorimetric purposes" showed the same melting point and was employed in a few determinations. The naphthalene was sealed up in soft glass tubes of about 9-mm. outside diameter and a wall thickness of about 0.5 mm. The total length of the tubes was about 18 cm. and the weight of naphthalene about 7 g.
The calorimeter The container was a wide mouth Dewar flask of 1-liter capacity. This carried a closely fitting copper cover which extended on the outside about 3+ inches below the top of the calorimeter. The cover carried a small high speed turbine type of stirrer which revolved in a tube. There were also two holes with sliding covers for the admission of the sample and the thermometer, and a third very small hole for adjusting the level of the calorimetric liquid. The thermometer was of the platinum resistance type with a sensitive portion 10 cm. long and 1cm:wide enclosed in a metal tube. It had been calibrated by the Bureau of Standards. A Mueller bridge was used to measure the resistance. Readings were made to 0.0001 ohm corresponding to about 0.001"C. The calorimeter was clamped in the center of a 6-gallon earthenware jar filled with water until 2 inches of the calorimeter cover was immersed. The temperature of the water was regulated to =t0.001"C. during the progress of the later calorimetric runs. To attain this constancy it was necessary to regulate the heating current and to stir violently with a large turbine type of stirrer. In some of the early determinations the regulation was to f 0.01"C. The calorimetric liquid was kerosene and the supply was kept constant by filling every day to a level exactly 3 cm. below the top of the cover. This adjustment was made by adding kerosene until the liquid rose in a small capillary tube a t a calorimeter temperature of 22°C. The calorimeter was stirred at a constant rate of 1200 revolutions per minute by a small electric motor with a speed regulating device. The constancy of stirring during a run was tested by means of an A. c. neon light, applying the stroboscopic method to determine the rate of revolution of the pulley on the cover of the calorimeter. In a few of the earlier determinations the stirring rate was 1600 revolutions per minute and in others 1000 per minute.
HEAT OF FUSION AND SOLUBILITY OF NAPHTHALENE
763
T h e high temperature bath This bath was made by winding a 1-inch round copper rod one loot long with nichrome ribbon, &inchwide, No. 30 B & S, 0.43 ohm per foot. Thin asbestos sheet was placed between the ribbon and the rod, and the outside wound with several layers of sheet asbestos. The rod was bored from each end with a one-half inch hole and the upper end closed with a copper plug. Three and a half inches above the bottom of the furnace there was a small hole, through which a glass rod projected to hold the specimen in place. The temperature of the hot bath was determined by a single junction thermocouple constructed of No. 26 constantan and No. 28 copper wire. The hot junction was placed in a small hole bored parallel to the axis of the furnace and 4 inches deep. The electromotive force of the couple was measured by a Leeds and Northrup Type K potentiometer. The couple was calibrated in the same position in the furnace in which it was employed in the measurements. The standard instrument used for the comparison was a platinum resistance thermometer enclosed in glass, the sensitive portion being about 2 inches long. This portion was placed as nearly as possible in the position occupied by the specimen. Uniformity in this section was tested by raising and lowering the thermometer; the variation a t 160°C. amounted to about 0.2"C. with a corresponding lower variation a t the lower temperatures. It is estimated that the average temperature of the specimen under conditions of thermal equilibrium was known to less than O.l"C., except possibly a t temperatures above 130°C. In order to attain this accuracy it was necessary to heat with the current from storage batteries and to allow a t least three hours from the start of the heating for the system to come to equilibrium. Even when changing the bath temperature but a few degrees, a 2-hour period was necessary for the temperature to become constant. It is probable that the greatest source of inaccuracy in the measurements was failure to attain equilibrium in the hot bath.
Calorimetric procedurp Before a run the temperature of the hot bath was read a t intervals of five to ten minutes. When the temperature remained practically constant over such an interval, readings were made of the temperatures of the hot bath and the calorimeter on alternate minutes for a 10-minute rating period befxe the specimen was dropped into the calorimeter. After this, readings of the calorimetric temperatures were made during twenty minutes, for the first 2 minutes a t half minute intervals and later every minute. The time intervals were observed on a stopclock which was started a t the beginning of the run. The times between runs were in most cases sufficient to insure that the temperature of the calorimeter was not far from that of
764
H. LEE WARD
the bath a t the start of the procedure. It was seldom that more than three runs could be made in a single day. The temperature rise At was calculated from the formula, At = + r, where e3is the temperature a t the end of the 10-minute calorimetric period and O 2 that a t the beginning of this period. The extrapolation correction, 7, was calculated by means of the modification of the Regnault-Pfaundler formula due to White (9).
The calorimeter equitralent Three materials were used as a basis for the measurement of this quantity. The first was a sample of parting silver of 99.95 per cent purity cast in a graphite mold. The sample meighed 53.5 g. The second was a bar of annealed electrolytic copper weighing 84 g., and the third 5.55 g. of water sealed in the same glass as mas used to contain the naphthalene specimen. The heat capacities for the copper and silver were obtained from the International Critical Tables. When the determinations were made the same day, the calorimetric equivalent showed the same value for the different samples. For example, the temperature rise was 2.471 X "C. per calorie for the silver sample, while the corresponding figures for copper and water were 2.473 and 2.473. Other determinations showed essentially the same agreement. There was, however, a considerable change in the calorimeter equivalent with the time. The highest value over a period of four months was 2.498 and the lowest 2.452. The maximum deviation from the mean of 2.475 was 0.9 per cent and the average 0.3 per cent. Certain causes of such deviations are slight variations in the amount of calorimetric liquid and the mending of the basket for holding the calorimetric specimen, but the most important was a change caused by two periods of abnormally cold weather. The equivalent rose rather rapidly during these periods and subsequently declined over a period of about a week. This change was probably due to the loss of moisture from the calorimeter, due to extremely low relative humidity. No change in the calorimetric equivalent was found when the temperature of the hot bath was changed. The above changes in the calorimeter equivalent made necessary the determination of its value on practically every day upon which a run was made, especially in the case of the liquid naphthalene. The metal, usually copper, was heated to nearly the same temperature as that employed for the naphthalene or glass samples. THE EXPERIMENTAL RESULTS
All the observations on naphthalene were reduced to a common calorimeter equivalent of 2.470 X 10-3 "C. per calorie and to a basic temperature of 22°C. Correction was then made for the glass which enclosed the specimen from a large scale curve drawn for that substance. The experimental
765
HEAT OF FUSION AND SOLUBILITY O F NAPHTHALENE
results were then plotted on a large scale, curves were drawn, and their equations calculated. The experimental results appear in tables 1 and 2. TABLE 1 Molal heaf content f o r solid naphthalene reckoned from a basic temperature of 82°C. ,TEMPERATURE
HS (OBSERVED)
A
H,
TEMPERATURE
A
(OBPERVED)
degrees C.
36.67 48.79 59.61 65.48 66.41 68.33 69.28 72.58
d o r i e s per mole
.
588 1096 1563 1874 1881 1988 2033 2192
degrees C.
:alwies per m o l e
74.21 76.35 76.51 76.69 77.08 77I37 79.59 79,90
0 +6 - 12 +26 - 10 13 +4 +4*
+
2291 2375 2412 2351 2399 2412 2552 2750
+24* +2 +32t -38 - 10 -11 $18 +200
* Kahlbaum’s naphthalene (for calorimetric purposes). t Bath stirring irregular. TABLE 2 Molal heat content of liquid naphthalene reckoned f r o m a basic temperature of 33°C. TEMPERATURE
degrees C.
70.03 74.16 75,53 76,24 76.51 79.75 79.79 80.43 81.09 81,77 84,OO 86.91 87.68 89.46 95.29
Hi (OBSERVED)
A
,alories per mole
6550 6755 6825 6863 6863 7050 7025 7058 7147 7145 7195 7370 7460 7520 7840
degrees C
-7
+42* +6 -591 +7 +41
Hi
TEMPERATURE
(OBSERVED)
:alories per molt
108 54
1
I
[
j
A
136 50 137 86 143 74 150 25 160 41
8062 8030 8230 8480 8540 8865 9460 9640 10150 10190 10510 10920 11515 11560 12210
+3
-67: -20 -42 - 12 - 13 $17 - 12 +43* +2 -19 +14
~
+z ,
-34
-48
* Kahlbaum’s naphthalene (for calorimetric purposes).
t
Irregularity in calorimetric equivalent.
3 Bath temperature not constant.
All observations made after a certain date are included except two or three for which a very definite reason for rejection could be assigned. The determinations on liquid naphthalene below 80°C. were made by first heating
766
H. LEE WARD
the specimen above 90°C. for a considerable time and then cooling in the furnace until temperature equilibrium was reached. The sample of naphthalene from Kahlbaum did not supercool to any extent, but on fractional freezing behaved as regards supercooling in the same manner as did the highly purified material employed in most of the calorimetric determinations. The values under the heading A in the tables indicate the deviations of the experimental results from the empirical curves employed to express the variation in the molal heat content with the temperature. The equations employed are H , = -781 33.17 t 0.1068t2 calories per mole for the 42.45 0.0546t2 calories per mole for the liquid, solid, and HI = 3309 both values being calculated from a basic temperature of 22°C. ,The symbol t denotes the centigrade temperature.
+
+
+
+
The latent heat of fusion of naphthalene When the equation for the heat content value for the solid is subtracted from that for the liquid, a n expression is obtained for the value of the molal heat of fusion of naphthalene at various temperatures, at and below the melting point. The equation obtained is A H j = 4090 + 9.235 0.0522t2. This indicates a value of the latent heat of fusion at 80°C. of 4495 calories per mole. The value at 70°C. is 4480 calories and a t 50°C. this has fallen to 4420 calories. The results show a smaller variation of the latent heat of fusion with the temperature than is the case for most organic substances. In the list studied by Andrews, Lynn, and Johnston (1) only quinone and the aminobenzoic acids had smaller differences in the heat capacities of the solid and liquid substances a t the melting point. In the latter substances the results were unsatisfactory owing to decomposition,
The ideal solubility of naphthalene Lewis (3) defines an ideal solution as one that obeys Raoult’s law at all temperatures and pressures, and shows that the formation of such a solution will take place from its component liquids without any heat of mixing or change in volume. This means for the ideal solution of a solid in a liquid that the heat of mixing shall be the heat of fusion of the solid at the temperature a t which the solution is made. On this basis the ideal solubility may be calculated by means of a modification of the Schroder (6) equation which takes into account the variation in the latent heat of fusion with the temperature. The equation expressing this variation as given above is transformed into absolute temperatures giving A H f = -2375 + 38.10T - 0.0528T2. This expression is not, of course, valid at temperatures much below 0°C. The above value is substituted in the equation d In AT dT - E -
AH,
RT2
767
HEAT OF FUSION AND SOLUBILITY OF NAPHTHALENE
and integration gives T, T
-19.17 In -
+ 0.02657(Tm- T )
where T , is the absolute melting point of the naphthalene. In table 3 appear the values of the ideal solubility, expressed in mole fraction of naphthalene, as calculated by means of the above expression. The second column gives the results obtained when 353.4' was used as the absolute melting point of the naphthalene This figure is probably within 0.05' of the melting point of perfectly pure naphthalene. Since in the investigation of the solubility of naphthalene (8) a material of an absolute melting point TABLE 3 The ideal solubility of nu ithalene
TEMPERATURE
MOLE FRACTION OF NAPHTHALENE
Tm
=
353.4
MOLE FRACTION OB NAPHTHALENE
Tm
=
353.15
MOLE FR.4CTION OF NAPHTHALENE SATCRATED SOLUTION I N CHLOROBENZENE
MOLE FRACTION OF NAPHTHALENE A H CONSTANT AT 4695 CALORIES P E R MOLE
0.830 0.716 0.682 0.555 0.540 0.473 0.444 0.352 0.349 0.292 0.277 0.215 0.208 0.185
0.829 0.717 0.680 0.551 0.540 0.470 0.441 0.348 0.342 0.285 0.269 0.205 0.198 0.174
degrees C
70 62.6 60.0
50.0 49.0 42.8 40.0 30.0 29.4 22.1 20.0 10.0
8.8 4.2 0.0
0,819 0.714 0,678 0,551 0.540 0.471 0.442 0.351 0.346 0.290 0.275 0.213 0.207 0.183 0.163
0.828 0,716 0.681 0.553 0.541 0,473 0.444 0.352 0.347 0.291 0.277 0.214 0.207 0.183 0.163
of 353.15' was employed, the ideal solubility was recalculated on that basis and the results appear in the third column. The experimental and interpolated values for the mole fraction of naphthalene when forming a saturated solution in chlorobenzene a t various temperatures are shown in the fourth column. The values at the rounded temperatures are the interpolated values, while the others are the experimentally observed points from which the rounded values were obtained by graphic interpolation. These values are taken directly from the previous publication (8). In the last column of the table appear the values for the ideal solubility as calculated by the original form of the Schroder equation, using 4495 calories as the molal heat of fusion of naphthalene.
768
H. LEE WARD
DISCUSSION
The value of the latent heat of fusion of naphthalene obtained in this investigation is about 1 per cent lower than the value found by Andrews, Lynn, and Johnston (1). A large part of the discrepancy can be accounted for by the fact that those investigators used the straight extrapolation method for obtaining the calorimetric temperature rise, while in this investigation a more exact modification of the Regnault-Pfaundler formula has been employed. I n the determination of the calorimetric equivalent, under the conditions employed in this work, the two methods give almost identical results, but with the naphthalene the simple extrapolation gave considerably higher values for the reason that the heat was developed quite slowly at the beginning of the calorimetric period even though the time at which the fall of temperature became regular differed but little from the corresponding time for the copper sample. In one measurement for the liquid naphthalene a t about 80°C. and the corresponding determination of the calorimeter equivalent, the extrapolation method gave a heat content per mole 45 calories higher than that obtained by the more exact method. For the solid naphthalene the heat exchange with the calorimeter was more rapid than for the copper sample a t the same temperature. In this instance, therefore, the method of calculation would account for the difference between the results of Andrews, Lynn, and Johnston and those reported in this paper. The measurement of the heat content of the supercooled liquid naphthalene is not important for the measurement of the variation of the latent heat of fusion with the temperature, since this variation is small and the degree of supercooling attained was not very great, but it does give a much greater certainty in obtaining the latent heat of fusion a t the melting points, since the interpolation errors in the heat content curve for the liquid are considerably less than the extrapolation errors. The extrapolation errors in the heat content curve for the solid should be small numerically, since the extrapolation is carried over a short distance and the heat content is small. It is believed that a value for the latent heat of fusion of naphthalene of 4495 calories is accurate to within =t 15 calories. It might be argued that a very long extrapolation of the heat content curve for the liquid is necessary to obtain the latent heat of fusion at the lower temperatures; this criticism is doubtless justified, but it is to be noted that the ideal solubility as calculated from an invariant heat of fusion does not differ appreciably from that taking into account such variation until a temperature a t least thirty degrees below the melting point is reached. Even at the lower temperatures the discrepancies are not great and the correction introduced by employing the more exact formula is in the right direction and of the right order of magnitude to bring the ideal solubility
HEAT OF FUSION AND SOLUBILITY OF NAPHTHALENE
769
into close agreement with the observed solubility of naphthalene in chlorobenzene. SUMMARY
1. Very pure naphthalene having a melting point of 80.25-80.3°C. has been prepared and some interesting phenomena on its freezing have been noted. 2. The latent heat of fusion of this material has been found to be 4495 calories per mole. 3. A reason has been suggested to account for the fact that this value is somewhat lower than the usually accepted value. 4. The ideal solubility of naphthalene has been calculated by a method which talres into account the variation in the latent heat of fusion with the temperature. The results show excellent agreement with previously published data on the solubility of naphthalene in chlorobenzene. REFERENCES (1) ANDREW,LYNN,AKD JOHNSTON: J. Am. Chem. SOC.48, 1274 (1926). (2) EOGOJAWLENSKI: Chem. Zentr. [5] 9,II,945 (1905). Thermodynamics, p. 222. McGraw-Hill Eook Company, (3) L E W IA~N D RANDALL: New York (1923). See also HILDEBRAND: Solubility, chap. VI. The Chemical Catalog Co., New York (1924). (4) MATHEWS:J. Am. Chem. SOC.39, 1125 (1917). (5) RICHARDS AND SHIPLEY:J. Am. Chem. Soc. 36,1825 (1914). (6) SCHRODER: Z. physik. Chem. 11, 449 (1893). (7) SPAGHT,THOMAS, AND PARKS: J. Phys. Chem. 36, 882 (1932). (8) WARD:J. Phys. Chem. 30, 1316 (1926). (9) WHITE: Chem. Met. Eng. 9, 451 (1911). See also A. C. S. Monograph, The Modern Calorimeter, p. 41. The Chemical Catalog Co., New York (1928). (10) ZWICKY:Phys. Rev. 40, 63 (1932).
