March, 1961
HEAT
O F SOLUTION OF
the Bi and the pressure of the Bi13were both varied. Peaks corresponding to Bi13+, Bi12+,BiIf and Bi+ were observed. The relative intensities of these peaks for &I3only were: weak, medium, strong, medium, respectively; and for BiIa passed over hot Bi they were: weak, medium, very strong and strong. The BiI+ and Bi+ peaks increased relative to the Bi13+ as the temperature of the Bi in the cell was increased. There were no peaks at masses greater than 600 so that no polymers of BiI were observed, although the mass spectrometer was capable of detecting masses as great as 1000. Thus the experiment confimed the presence of BiI in the vapor, and its increase as the Bi temperature was increased. It was felt that the polymer of BiI was not observed in this experiment because the vapor did not come to equilibrium with the Bi metal; therefore, the pressure of BiI was much lower than the equilibrium pressure, and that of the polymer was so much lower as not to be observable. It was estimated that the Bi13 in this experiment was in contact with the Bi for only one hundredth the time of contact found necessary in the transpiration experiments, so that presumably the equi-
ORTHOPHOSPHORIC ACID
523
librium concentration of BiI and BiJn did not have enough contact time to be formed. A comparison of the three Bi-halide systems studied shows some regularities. The equilibrium constants for the formation of the monohalide (cf. reaction 1) tend to increase slightly in going from C1 to Br and from Br to I (;.e., a t 600': Kci = 0.011; K B = ~ 0.014; KI = 0,019). This increase is due to a progressively more favorable enthalpy change for the reaction which just barely overrides the progressively less fayorable entropy change. In the iodide system there was evidence for a polymer of the monohalide a t pressures of BiI3 above about 3 mm. In the chloride and bromide systems no evidence for polymers was observed; however, those systems vere investigated a t lower BiX3 pressures. It may well be that a t higher pressures measurable amounts of polymers may be formed. Acknowledgments.-The author is indebted to Mr. William E. Robbins, who performed the Milne, transpiration experiments, to Dr. Thomas -4. who did the mass spectrometer experiment, and to Dr. Francis J. Keneshea, Jr. for fruitful discussions.
HEAT OF SOLUTION OF ORTHOPHOSPHORIC ACID BY EDWARD P. EGAN,JR.,AND BASILB. LUFF Diwision of Chemical Development, Tennessee Valley Authority, Wilson Dam, Alabama Recezved Octobei 6 , 1960
From measurements of the heat, of solution of orthophosphoric acid over the range 0 to 89.13% H3P04, tables were derived relating the relative apparent molal heat content ( 6 ~and ) the partial molal heat contents (12, to concentration a t intervals of 5y0H,PO,. The molal heat of formation from the elements at 25" was calculated as a function of moles of water in solution.
zl)
The heat of solution of phosphoric acid in water was summarized by the National Bureau of Standards' from scattered values appearing before 1915. Another summary tabulatioq2 which drew upon unpublished work by TVA, had among its shortcomings a gap between 35 and 45% H2P04. This paper describes a redetermination of the heat of solution over the range 0 to 89.13% H3P04. Measurements a t higher concentrations would have heen complicated by the presence of non-ortho forms of acid,3 with their heats of hydrolysis. Materials and Apparatus.-Reagent grade phosphoric acid was recrystallized twice as the hemihydrate. Stock solutions were prepared from the drained, unwashed crystals. A solution calorimeter from earlier work4,6 was modified in :t few details. The capsule-type platinum resistance thermometer was exposed directly to the solution. The head of the thermometer was sealed into a small glass support tube with Apiezon W wax. The thermometer was suspended in the glass draft tube of the stirrer with the tip of the capsule a few millimeters above the impeller. A 100-ohm heater was wound directly on the outside of the draft tube. (1) National Bureau of Standards Circular 500, U. S. Govt. Printing Office, Washington, D. C., 1952. (2) T. D. Farr, Tennessee Valley Authority, C h e n . E n g . Rept., N o . 8 ( 1950).
(3) E. P. Egan, Jr., and Z . T. Wakefield, J . Phys. Chem., 61, 1500 (1957). (4) E. P. Egan, Jr., B. B. Luff and Z. T. Wakefield, ibid., 62, 1091 ( 1958). ( 5 ) E. P. Egan, Jr.. Z . T. Wakefield and K . Id,Elmora. .I. Am. Chem. Sac, 78, 1811 (1866),
Assembly and disassembly of the calorimeter were facilitated by attaching the head to the body by means of six small parallel-jawed spring clamps of a type used in sheet metal assembly. The clamps were completely covered by the water-bath and were without observable effect on the heat leak. The initial bulk charge of liquid for each measurement (850 ml.) was weighed. Each incremental addition to the bulk liquid in the calorimeter was suspended inside the stirrer shaft in a thinwalled glass bulb which was crushed against the bottom of the Dewar to start the solution period. The calorimeter system was calibrated electrically immediately before and after each measurement. One defined calorie was taken as 4.1840 abs. j . Temperatures were recorded to four decimal places, as small differences were important. The conditions of measurement ensured a temperature rise of at least 0.15' for every observation. The temperature at the end of each measurement was 25 5 0.05", and no temperature corrections were necessary. As the water-bath around the calorimeter was held a t 26 f 0.02", heat leaks were always in the same direction.
Heats of Solution.-The concentration range 0 to 83.6 molal (89.13Oj,) &Po4 was covered in five series of measurements: Series 1 : H2@plus successive increments of 75.14yo H3P04;final concentration, 49.4y0 &Pod; Series 2 : same; Series 3: H,O plus successive increments of 43.86% H3P04; final concentration, 17.0% H3P04; Series 4 : 44.58y0 plus successive increments of 89.13y0 HaPod; final concentration, 75y0 H3P04; Series 5: 89.13% H31'04 plus successive increments of HzO; final concentration, 727, &Po4. Incremental
EDWARD P. EGAX,JR.,AKD BASILB. LUFF
524
Yo]. G5
yield values of 4 ~ .From a similar plot between 0.5 and 1.6 molal, a value of - 1497 cal. per mole H3P04 4000 was obtained for the heat of solution a t infinite dilution of 49.86% H3P04. Values of 41,calculated 'II from the series 3 measurements with 49.86% 0 U agreed with those calculated from series 1 and 2 2 3000 b with 75.14% H3P04. W In series 4, the integral heats of solution resulting -1 0 from sohtion of 89.13y0 H3PO4in an initial solution E of 44.58% H3P04 were too far from the axis a t m = 5a 2000 0 for a satisfactory extrapolation against ml/'. The intercept was calculated to be -4250 cal. per mole H3P04 by successive approximations in the region where series 1 and 2 overlapped series 4. In'$eries 5, calculation of the heats of solution per mole of H3P04 for 89.13% H3P04 was straightforward. Two of the final solutions overlapped series 4. The measured heats of dilution were com" bined with values of t $ ~as calculated a t the con0 20 40 60 00 centrations in the region of overlap between series 4 H 3 P 0 4 , W T ',e. Fig. 1.--Relative apparent molal heat content of phosphoric and 5 to obtain +L between 70 and 89% HaP04. Calculated values of C#L in calories per mole acid solutions. H3P04 at the observed final concentrations are dilution of 90% H3P04 with water to a concentra- shown in Fig. 1 and Table 11. The abscissas in tion approaching infinite dilution would have been Fig. 1 are expressed in weight per tent. instead of more straigh tfonvard, but the construction of the molality to avoid compression of the data at low calorimeter limited each addition to 35 ml. Dilu- molalities. The data summarized by NBS' agree tion of 850 nil. of phosphoric acid solution with 35- reasonably well with the present measurements up ml. portions of water soon would have run into to 20% H3P04; above 20%, the earlier data are undesirably small increments of concentration and somewhat scattered. The earlier TVA data2above 45% H3P04 are roughly parallel to the present data of heat. and about 120 tal. per mole higher. The observed heat effects on a molal basis are The heats of formation of H3P04a t the lowest shown in Table I. (For internal consistency, more significant figures were used in calculation than are concentrations cited by KBS1 were plotted against shown in Table I.) The average deviation of the ml/'and extrapolated to yield -309,440 cal. per mole as the heat of formation at infinite dilumeasured heats of solution was 0.3%. Rlanipulative details in adjusting the end solution tion. This value was combined with the smoothed to relate heat of formation to concentrafrom a measurement to a weighed fixed volume of values of 41, 850 ml. for the next measurement entailed loss of 1 tion in handbook-type Table 111. to 2% of the solution. Linear corrections were TABLE I made in sample weights and in heat effects to put OBSERVED HEATSOF SOLUTION OF &PO4 SOLUTIONS initial ,and filial solutions for each run on the same WZI(HIPO~TZIH~O) m(HoPOd.ntHzO) = V L ~ ( H S P O ~ , ~ ~ H ~ O ) basis. na Q, cal. nl mr mr When small portions of 75.14 or 49.86% H B P O ~ ml Series 1, 75.14% HaPOl stock soln. (n2 = 1.80) were djluted with various amounts of water, the observed heat dfects became increasingly exothermic 0 (46.998) 0.2787 0.2787 170.426 761.56 with decrease in the final concentration. When 0.2720 170.426 .5724 81.915 758.15 .3005 plotted against final concentration, the heat of .5568 81.915 .9426 49.125 929.03 .3858 solution approached the axis at m = 0 almost .3028 1.2121 37.304 701.13 .9094 49.125 asymptotically. Unpublished calculations a t TVA .2908 1.4700 30.281 648.47 1.1792 37.304 suggest that the degree of dissociation of H3P04goes 1 ,4299 30.281 .3100 1.7400 25.206 664.92 through a minimum a t about 1.2 molal, then rises .2938 1.9449 21.741 605.96 1.6910 25.206 sharply to 1.0 a t the axis where m = 0. A parallel 1.9310 21.741 .2992 2.2302 19.065 593.41 behavior of the heats of solution in dilute solution .2829 2.4512 17.073 538.36 2.1684 19.065 indicates that the measured heats of solution in 2.3885 17.073 .2976 2.6861 15.381 543.89 dilute solutions included heats of ionization. 2.6102 15.381 .3534 2.9636 13.761 615.13 The integral heats of solution in calories per mole 2.8647 13.761 .3049 3.1696 12.610 504.95 H3P04 at the observed final concentrations are 3.0806 12.610 ,2597 3.3403 11.770 409.99 shorn in Table 11. ,3266 3.5799 10.860 499.46 3.2533 11.770 When the integral heats of solution of 75.14% 3.4681 10.860 .2478 3.7160 10.256 364.33 .3131 3.9470 H3P04a t final concentrations between 0.2 and 1.3 3.6340 10.256 9.585 435.07 molal were plotted against m'Iy, the resultant .3498 4.1814 3.8315 9.585 8.934 461.58 straight line indicated a value of -2913 cal. per 4.0432 8.934 .2839 4.3271 8.466 355.51 4.2149 8.466 mole H3P04for the heat of solution a t infinite dilu7.990 387.17 .3236 4.5385 4.3696 7.990 7.607 327.65 tion of 75.14'%H3P04. This value was subtracted .2883 4.6580 from values of A H at each final concentration t o 4.5640 7.607 .3149 4.8789 7.232 340 37
I
L
I
i
I
I
i'
I
A
+
HEATO F SOLUTION O F ORTHOPHOSPHORIC ACID
March, 1961 rnl
TlI
mz
ma
4.7308 4.9228 5.0802 5.2428 5.3836 5.5260
7.232 6.853 6.547 6.256 6.015 5.794
.3548 .3170 .3324 ,3003 .2977 .3421
5.0855 5.2398 5.4126 5.5432 5.6814 5.8681
nr
6.853 6.547 6.256 6.015 5.794 5.561
Q, cal.
362.65 306.79 303.22 259.59 245.19 266.24
Series 2, 75.147, HaPO4stock soln. (n2 = 1.800) 0 46.980 0.1948 0.1949 242.833 538.49 0.1917 242.833 .3490 .5408 87.243 889.86 .5235 87.243 .1779 .io14 65.573 436.29 65.573 ,3599 1.0497 43.711 853.77 .6899 1.0155 43.711 .3423 1.3577 33.147 775.17 1.3153 33.147 .3293 1.6447 26.870 716.20 1.5940 26.870 .3330 1.9270 22.537 693.90 1.8686 22.537 .3226 2.1912 19.485 641.47 2.1260 19.485 ,3530 2.4790 16.967 671.33 2.3993 16.967 ,3459 2.7452 15.055 627.55 2.6573 15.055 .SO60 2.9634 13.686 528.03 2.8781 13.686 ,2808 3.1589 12.630 465.02 3.0768 12.630 .3260 3.4028 11.592 514.41 3.2989 11.592 ,3049 3.6038 10.764 459.20 3.5016 10.764 ,3129 3.8146 10.028 446.97 3.7037 10.028 .2947 3.9984 9.422 401.80 3.8878 9.42’2 .3678 4.2556 8.763 474.74 4.1105 8.763 ,3466 4.4571 8.221 421.93 4.3115 8.221 .3819 4.6934 7.699 439.45 4.5256 7.699 .3732 4.8989 7.249 401 96 4.7283 7.249 .3592 5.0874 6.865 364.06 4.9192 6.865 .3759 5.2951 6.505 356.98 5.1060 6.505 .3550 5.4610 6.199 317.58 5.2811 6.199 ,3633 5.6444 5.916 306.41 5.4521 5.916 .3466 5.7987 5.670 276.17 0 (46.971) ,0083 0.0083 5633.8 29.45 0 (46.979) ,0093 .0093 5042.5 31.48 0 (46.965) .0105 .0105 4478.9 35.55 (47.001) .0128 0 .0128 3668.0 41.70 0 (46.990) ,0145 .0145 3247.0 48.54 0 .0140 (46.994) .0149 3164.3 49.22 0 ( 27.00‘3) .0218 .0218 2153.2 69.85 0 (47.002) ,0349 .0349 1347.4 108.09 0 (46.984) .0427 .0427 1101.6 127.55 0 (47.009) .0640 ,0640 736.0 190.71 (46.990) .0737 0 .0737 639.6 215.63 (47.028) 0 .0904 .0904 522.2 257.82 0 (46.971) .12‘30 ,1290 365.8 368.27
Scrics 3, 49.86y0 &POa stock soln. (47.031) 0.1831 0.1831 ,1981 263.047 .3751 ,1873 127.03’3 .5502 85.644 .7221 .1890 64.658 .1854 .8849 52.256 . IS09 1.0384 44.105 ,1940 1.2010 37.866 ,2009 1.3629 33.090 .1894 1.5066 29,618 ,1816 1.6410
0 0.1771 ,3629 .5330 .6995 .S575 1.0070 1.1619 1.3172 1.4594
(nn= 5.470)
26‘3.047 127.039 85.644 64.658 52.256 44.105 37.866 33.090 29.618 26.946
252.20 229.57 2002.44 194.20 180.76 167.03 171.37 167.88 149.79 138.00
Series 4, 89.13% HsPOi stock soh. (ne = 0.663) 4,9700 6.761 0.4742 5,4442 6.230 976.02 5.2614 6.230 .41357 5.7271 5,777 915.11 5,5376 5,777 ,4638 6.0014 5.382 853.92 5.8047 5.382 .4619 6.2666 5.034 805.35 6.0625 5,034 .4740 6.5365 4.717 782.23 6.3176 4.717 .4372 6.7548 4.455 678.59 6 5430 4.455 ,4713 7.0143 4.200 695.45
6.7775 7.0158 7.2438 7.4438 7.6502 7.8278 8.0189 8.1989 8.3965 8.5728 8.7295 8.8669 9.0187 9.1537 9.3126 9.4508 9.4876 9.6957 9.8216 9.9369 10.0559
4.200 3.960 3.752 3.568 3.393 3.254 3.101 2.971 2.838 2.713 2.611 2.521 2.435 2.350 2.266 2.185 2.118 2.053 1.990 1.928 1.871
.4936 .4732 .4577 .4791 .4106 .4888 .4530 .5016 .4703 ,4491 .4219 .4296 .4545 .4821 .4961 .4316 .4482 ,4611 .4816 .4654 .4015
525
7.2711 7.4890 7.7015 7.9229 8.0608 8.3166 8.4719 8.7005 8.8768 9.0219 9.1514 9.2965 9.4732 9.6358 9.8087 9.8824 9.9358 10.1568 10.3032 10.4023 10.4574
3.960 3.752 3.568 3.393 3.254 3.101 2.971 2.838 2.713 2.611 2.521 2.435 2.350 2.266 2.185 2.118 2.053 1.990 1.928 1.871 1.825
686.99 618.93 566.76 558.22 453.94 512.13 445.44 466.00 410.6‘3 369.05 328.31 317.36 316.2-1 314.39 804.15 250.40 245.73 238.22 233.04 211.33 173.76
+
~ I ( H ~ P O ~ . ~ ~nzH20 H ~ O=) ~ ~ ( H I P O ~ ~ H Z O ) 13.2810 12.9221 12.5948 12.2280 11.9247 11.5815 11.2086 10 .8277 10.4902 10.1673 9.8638
Series 5, 0.663 .762 ,879 .993 1.103 1.224 1.370 1.528 1.671 1.817 1.970
dilution of 89.13y0 H8POI 1.3050 13.2810 0.762 2038.38 1.5105 12.9221 .879 2200.66 .993 1934.59 1.4451 12.5948 1.3368 12.2280 1.103 1655.98 1.4463 11.9247 1.224 1674.98 1.6910 11.5815 1.370 1794.70 1.7677 11.2086 1.528 1710.00 1.5545 10.8277 1.671 1375.51 1.817 1244.86 1.5267 10.4902 1.5641 10.1673 1.970 1172.55 2.125 1055.80 1.5249 9.8638
Partial Molal Heat Contents.-Values of qiL from Table 11 were fitted to polynomials in molality and weight fraction over various ranges of concentration and with various functions of the variables. The equations giving the best fit were 369.50mlh 180.46 185.45~2 22.08mz 22.33m3 4.03m4 @L = 292.06 923.79~ 3 3 7 4 . 8 7 ~ ~ 2478.92~’ 3473.99w4 @L =
@L =
-
+
+
-
+
+
+ +
m = 0 to 1.5
(1)
m = 1.5 to 2.5
(2)
VL =
2 . 5 to 85.0
(3)
where m = molality and w = n-eight fraction of H3P04. The mean probable error in equations I and 3 is 2.5 cal. per mole HJ’O-in equation 2, 0.2 cal. per mole. A deviation of 2.5 cal. per mole is well within the error of observation, but smooth slopes a t the point of overlap of two equations require first diff erencw with deviations of 0.1 cal. per mole or less. The slopes at the points of overlap thus show slight breaks that seem unavoidable without resort. t o a more elaborate method of representation. Relative partial molal heat contents a t molalities up to 2.6 were calculated by conventional meth0ds.j Above 2.5 molal, the slope b h l b m was converted analytically to the slope in terms of weight fraction, (5) 5. Glaastone, “Thermodynan~icsfor Chemkts,” 1). Van trand Go., Inc., New York, N. Y., 1947.
Sos-
526
EDWARD P. EGAN,JR.,AND BASILB. LUFF
Vol. 65
TABLEI11 TABLE I1 OF PHOSPHORIC ACID SOLUTIONS, HEAT01% SOLUTIOW AND RELATIVE APPAREST MOLALHEAT HEATSOF FORMATION KCAL.PER hfOLE HaPo4 AT 298.16'K. CONTEXT A T O'BSERVED FIXAL CONCESTRATION, CAL. PER - AHfo -AHP nHaO nH,O MOLEHap04 hIolality -.AH .$L Molality -AH 309.16 100 $1. +305.68 1 309.25 200 Series 1, 75.14% &Po4 2 306.64 309.28 307.21 300 3 0 2931 0 5.1110 2007 924 309.30 400 307.59 4 0.3257 108 5.4122 1971 960 2733 309.32 500 307.84 5 0.6776 2623 1925 1006 308 5.7908 309.34 700 308.04 6 1.120!1 396 6.2131 1874 2535 1057 309.35 1000 308.29 8 1.4880 2480 451 6.5567 1833 1098 309.38 2000 308.46 10 1143 2431 500 1.8330 6.9469 1788 309.39 3000 308.57 12 2,202i 1748 2380 551 1183 7.2969 309.40 4000 308.69 15 1226 1705 2333 598 2.5531 7.6750 309.40 5000 308.81 20 1271 2.9114 1657 2286 615 8.0993 309,41 7000 308.88 25 1316 3.2511. 2242 689 1615 8.4776 309.41 10,000 308.94 30 1572 2196 735 1359 3.6088 8.8726 309.42 20,000 309.00 40 1397 4.0330 2141 789 9.2287 1534 309.43 50,000 309. 05 50 1434 4.4016 1497 2095 83G 9.5806 309.43 100,000 309.12 75 1455 21056 876 1476 4.7160 9.9818 m 309.44 Series 2, 75.14OGHJ'Ol d+~/bw. Table IV, in concentration increments of 2042 0 2'331 0 4.7882 889 5%, was derived from the results. 0,2252 1996 935 168 5.1568 2'763 1949 982 306 5.5350 .6362 21525 TABLE IV 1025 1906 2,581 349 5.8913 .846B RELATIVEPARTIAL MOLAL HEAT CONTESTS O F ?&PO4 1078 2510 1853 1.2698 421 6.3342 SOLUTIONS, GAL. PER MOLEH3P04 1127 2448 483 1804 1,6746 6.7514 Hspo4, -Lz - LI #I. wt. % 1180 1751 2394 537 7.2096 2.0658 0 0 1232 2340 1699 2.4628 591 7.6686 @ 0 406 1 313 1280 1651 2288 643 8.0858 271 2.8486 5 590 4.020 1330 3.2715 1601 698 8.5327 346 2233 10 754 8.288 1375 3.686ti 2:LSO 751 8.9538 1556 498 15 931 15 35 1422 1509 2l34 797 4.0555 9.3823 598 20 1152 27 15 1464 2091 840 9.7894 1467 709 4.3949 25 1392 43 92 834 30 Series 3, 49.86% &PO4 1651 66 91 075 35 0 1497 0 1.2589 1084 413 1929 100.2 4u 1144 1378 119 1.4663 1051 446 0.2116 138 5 1308 2229 45 1262 235 1.6779 1020 477 .4374 2549 192.0 1505 50 1201 '796 1.8745 991 506 ,6486 2889 261.3 1727 53 11 55 342 2.OG03 965 532 .8589 3247 350 6 1976 GO 1.0626 11.18 379 3619 464.9 2258 65 Series 4, 89.13% &POI 3998 609 9 70 2576 m4374 792.7 2937 13 4250 0 19.5570 1944 2306 0 4733 1021 80 3345 2884 1366 20.3856 1887 2363 8.9080 5059 1305 8.5 3807 2416 2809 1441 21.1841 1834 9.6060 5328 1653 90 4328 2734 1516 21.9403 1785 10.3115 2465 11.0240 2661 1589 22.7155 1737 2513 The measurements were not extrapolated to 100 2588 1662 23.5391 1687 11.7648 2563 % H3P04. The heat of formation of H3P04(aq)is 2521 1729 24.4179 1635 12.4578 2615 taken as -309,440 cal. per mole, the heat of forma13.2135 24-51 I799 25.3257 1583 2667 tion of H 3 P 0 4 ( ~as ) 1-306,200 cal. per mole. If the 14.0147 22b70 1871 26.1219 lSd0 2711 heat of fusion is taken as 3100 cal. per mole,3 then 14.7929 2311 1939 26,9590 1495 2755 the iiicrenient H81'04(1 -aq) should lie 6340 cal. 2247 2003 27.8157 1450 15.5539 2800 per mole H3P04. The equation for +L a t high 16.3593 2182 2068 28.7123 1405 2845 molalities extrapolates sinoothly to 5585 cal. at 2127 2123 29.5822 1362 17.0584 2888 It is not clear whether the curve for 1007, I-TJ'O,. 2C64 2186 30.3356 1327 2923 17.8959 +L should turn up sharply above 9076 HSP04 to an 2006 2244 18.6811 intercept of 6340 or whether the value for the heat Series 5, diln. 89.13% H3POa of formation of H3P04(aq)or that for HsPOQ(C) is in 0 4240 error by about 800 cal., which is within the accuracy 40.520 908 83.671 3332 1061 72,878 3179 154 4086 36.337 with which they are known. 321 3916 63.181 3052 33.216 1188 The present results affect the values reported in 55.881 2933 an article4 on the heat capacity of phosphoric acid 4i8 1307 3762 30.555 1422 solutions. Revisions of Tables V through VI11 in 2818 ;3@27 28.170 613 50.3-40 201 that article will 1)e subniitted for publication. -44.445 1539 i53 3487 25.599
