April, 1942
HEATOF FUSION AND HEATCAPACITY
839
OF WHITE PHOSPHORUS
[CONTRIBUTION FROM THE CHEMICAL LABORATORY OF THE UNIVERSITY OF CALIFORNIA]
The Heat of Fusion and the Heat Capacities of Solid and Liquid White Phosphorus' BY FRANKE. YOUNGAND JOEL H. HILDEBRAND The motive for this investigation has been the method of Hildebrand and B ~ e h r e r . ~Care was fact that liquid white phosphorus has an extra- taken to protect the phosphorus sample from the ordinarily large molecular field strength or "in- light during the heat capacity measurements. ternal pressure'' and therefore its solutions in orApparatus.-We used the method of mixtures. dinary non-polar solvents show unusually large The phosphorus, sealed in a Pyrex tube, was deviations from ideal behavior.'" Phosphorus is brought to a constant temperature in a solid particularly interesting from our standpoint be- cylindrical copper block 8.5 cm. in diameter and cause it is so readily supercooled that the heat 30 cm. high. The temperature of this block was capacities for liquid and solid can be obtained determined by a copper-constantan thermocouple through the same temperature range. Unfortu- that had been carefully calibrated. The copper nately, however, the difference in free energy be- block was insulated from the heating coil by sevtween the solid and the supercooled liquid, from eral layers of asbestos. Manual control of the which the ideal solubility is calculated, has been heating current was sufficient in view of the high subject to considerable uncertainty in view of the capacityof the furnace andconsequent slowchanges variation between the values reported by different in its temperature. The heater was covered with observers. severalmorelayersof asbestosand, finally, byacover The heat capacity of the solid in the region of of monel metal. A cylindrical radiation shield of room temperature has been given as 24.1 calories sheet metal about 10 cm. away gave further inper mole by Desains1222.3 by Personla 23.4 by sulation. The cylinder was supported on a movable arm so that it could be moved over the caloRegnault1422.02 between 1' and 17" by E ~ a l d . ~ For the liquid we have only 24.1 by Desains2 and rimeter immediately before dropping the tube, The heat of fusion is given as thus minimizing the radiation from the furnace 25.2 by P e r ~ o n . ~ 670 cal. per mole by Desains,2 624 by P e r ~ o n , ~to the calorimeter. The calorimeter was a silvered, wide-mouthed 592 by Pettersoq6 608 by Bridgman,' calculated from changes in volume on fusion a t various pres- pint vacuum flask whose inner surface was prosures, and 615, calculated by Kelley8 from the tected from breakage on dropping the tube of phosphorus by a screen of monel metal. The devapor pressure curves for the two phases. One reason for the poor agreement between pre- tails of the construction and manipulation are vious investigations lies in the fact that the heat available elsewhere and hence are not repeated of fusion is rather small so that the heat capacity here.1° The temperature measurements were of the container is large compared to that of the made on a Mueller bridge reading to 0.0001 ohm. phosphorus. Temperature measurements must The calorimeter temperatures were either 0" or be made to an accuracy greater than is feasible approximately 25 O . The lower temperature was with mercury thermometers. The procedure necessary because of the difficulty of freezing followed by Person was such as to allow appreci- liquid phosphorus a t 25'. The heat given up to able heat loss while transferring the sample from the calorimeter a t 25" per gram of glass from initial temperatures ranging from 40 up to 104' was the furnace to the calorimeter. Preparation of Sample.-The phosphorus used given with a maximum deviation of 0.2% by the in these determinations was prepared by the equation (1) Condensed from the thesis for the Ph. D. degree by the junior author. (la) Hildebrand, "Solubility," Reinhold Pub. Corp., New York, N. Y.,1936,cf. pp. 147, 161. (2) Desains, A n n . chim. phys., [3]PI, 432 (1848). (3) Person, rbid., 21, 295 (1847). (4) Regnault, Pogg. Alrn., 89, 496 (1853). (5) Ewald, A n n . Physik, [4]44, 1213 (1914). (6) Petterson, J . p r a k f . Chem., 24, 129 (1881). (7) Bridgman, P h y s . Reu., [2; 8, 153 (1914). (8) Kelley, Bull. U.S. Bur. Mines, 383, 80 (1935).
Ht
- H26
= 0.1853(t
10-4(t
- 25") + 2.019 X
- 25')1
-7.080 X lO-'(t
- 25')s
(1)
The corresponding heat given to the calorimeter a t 0' from initial temperatures between 25 and 36 O was reproduced accurately by (9) J. H.Hildebrand and T. F. Buehrer, THIS JOURNAL, 42, 2213 (1920). (10) M. A. Mosesman and Kenneth S. Pitzer, ibid., 63, 2348 (1941).
FRANK E. YOUNGAND
840
Nt - H,, = 0.1742 + 1.987 X 10-.4P ( 2 ) The heat capacity of solid phosphorus was determined by six runs in which the initial temperatures ranged from 25 to 43' and the final temperature was 0'. Table I gives the results of these runs, corrected for the heat capacity of the glass in the capsule, together with the values calculated by the equation Eft - Ho = 21.4At + I X W X lO-'t' (3'1
JOISL
lo-"'
Calculated
544.8 697.0 780.2 872.8 944.7
545.6 696.8 779.4 873.7 944.7 9%. 8
The values for liquid phosphorus, supercooled to 2 5 O , are given in Table 11. The measured values were calculated by the equation I-/t - €€tb
24.19(t - 2 5 9 -5.954X 1@-"(t- 2 3 0 ) Y -7,991 x 10-sjt - 25
0)"
(4)
TABLE I1 LIQUIDPHOSPHOKUS 1,
Ht
"C.
Measured
48.8T 50.50 73,53 74.32 74.54 97.14
- Hal, (cal./mole)
Calculated
673.7 611.6 1158 1176 1182 1711
573.8 611.6 1159 1177 1182 1711
1.309 X 10-la ( 5 )
TABLE IV LIQUID TO SOLID PHOSPHORUS Ht
- HI
Ht
measured cal./rnol;
oc. 25.00 44.2 50.50 57.09 59.02 59.92 60.04 73.53 74.32 74.54 97.14 I,
Measured
-
giving excellent agreement. All heats are given per mole of phosphorus.
Ht - Ha. (cal./mole)
oc. 25.00 31.79 35.47 39.69 42.79 44.2
Vol. 64
column of Table IV compared to results calculated from the equation EIt - NO = ,506 + 24.48t - 1.761 X
TABLE I SOLIDPHOSPHORUS 1,
H. HILDEBRAND
1115.5 1727 1883 1935 1953 1954 2275 2293 2298 2827
- HQ,
calculated, cal./rnole
Diff.,
1115 1578 1728 1882 1933 1954 1953 2275 2294 2300 2827
0.04 .00 .05 .05 - .1 .05 - .05 .00 .04 .09 * 00
%
+ -
+ +
The melting point was taken as 44.2'.* H44,1 - Ho was calculated from Eq. (3) for solid phosphorus and subtracted from H44.2- HO for liquid to solid phosphorus calculated from Eq. (5) giving the heat of fusion as 601 e 2 cal./mole. The equations for the heat capacity of solid phosphorus derived from Eq. (3) are C,
=
c,
= 0 1731
21 46
or
+ 2.872 X 10-2t (per mole)
16)
+ 2 316 X 10-4t (per Gam)
(7)
and for liquid phosphorus from equation (5)
Table I11 gives the four values of I& - HO C, = 24 47 - 0 521 X l O W 3 t - 3.927 X 10-6ta (per mole) (8) determined in the ice calorimeter in one column or and in the next column the values of H , - H26 calculated from Eq. (4). The average of the c, = 0 1974 - 7.678 X 10-Y - 3 167 X 10-7t2 (per gram) (9) differences of the values in the third column from The equations for the solid are valid in the range those in the second is 11lr5.5 cal./mole. from 0" to the melting point while the equations TABLE 111 for the liquid should hold from 25 to 100'. PHOSPHORUS (LIQVIDTO SOLID)
-
Ht
- HZ
t , OC.
Hi Hn measured, cal./mole
(supercooled), calculated cal./mole
57.09 59.02 59.92 60.04
1883 1935 1953 1954
'770 816 837 840
Difi.
1113 1119 1116 1114 Average 1115.5
- H a ) make up The heat of fusion and the 1115.5 cal. found in this way. Addition of 1 115.5 to each of the (W, - HZ5)values given i n Table I1 gives the results shown in the second
Summary The molal heat capacity of solid white phosphorus, P4, in the range 0-44.2' is given by C, = 21.46
+ 2.872 X
10-*t
That of liquid phosphorus in the range 25-97' is C, = 2447 - 9 521 X 10-3t - 3.927 X 10W5t2
The heat of fusion is 801 cal./mole a t the melting point, 44.2'. BERKELEY, CALIFOKSIA
RECEIVED JANUARY 26, 194%
