2740
M. N. PAPADOPOULOS AND W. F.
[ COSTRIBUTION FROM
THE
GIAUQUE
vO1. 77
Low TEMPERATURE LABORATORY OF THE DEPARTMEXT OF CHEMISTRY A N D CHEMICAL ENGINEERING, UNIVERSITY O F CALIFORNIA, BERKELEY]
Cadmium Sulfate and its Hydrates. Heat Capacities and Heats of Hydration. Application of the Third Law of Thermodynamics1 BY M. N. PAPADOPOULOS AND W. F. GIAUQUE RECEIVED DECEMBER 27, 1954 The heat capacities of CdSOd, CdSOI.HS0 and CdS04,8/3HzO have been measured from 15 to 315OK. The entropies are 29.41, 36.82 and 54.89 cal. deg. -l mole-', respectively, a t 298.16'K. Tables of thermodynamic properties have been prepared for each of these substanccs. Their molal heats of solution in 400 moles of water are - 10,977, -6095 and -2899 cal. was calculated mole-', respectively, a t 298.16"K. For the r:acti?n .CdS04.H20 5/3Hz0(g) = CdSOa+3/3Hz0, AH2g8.16 from the above entropy values and available dissocration pressures over a range of temperature. This value, -20,738 cal. mole-', obtained from the third law of thermodynamics is in excellent agreement with the calorimetric result -20,729. A similar calculation for the reaction CdSOa HBO(g) = CdSOd,H20utilizing a single available value of the dissociation pressure gives AH2~8.16= - 15,451 cal. mole-'. This agrees with the calorimetric value, - 15,401"within the limit of error of the dissociation pressure. I t is concluded that cadmium sulfate and its two hydrates approach zero entropy a t limiting low temperatures.
+
+
The research reported in this paper is one of a series in this Laboratory on a variety of hydrated substances. The purpose is to find if possible disorder, particularly of the type due to hydrogen bonding, remains a t limiting low temperatures. In the present case the compound CdS0443/3HzO is also of special interest because it is a product of the reaction in the Weston standard cell. The thermodynamics of this cell will be considered in another paper. The reactions to be considered are
sealed to the flat elids of the sample tube with a w r y sniall amount of paraffin wax, and the plunger, for breaking the seals, was designed so that it would penetrate the top and push the sample through the bottom. The lower gold seal assembly was broken off intact from the wax rim by this process, which facilitated rapid solution of the sample. However, this had an unexpected result, which was not understood until a run was simulated with an unsilvered Dewar vessel t o enable visual observation. I t had becii shown in preliminary experiments t h a t the rate of heat illtroduction due to stirring was a constant. After the samplcs were dissolved the rate of heat introduction due to stirring changed in some samples. Visual observation showed that the loose piece of gold foil sometimes became attached to the stirrer and changed the rate of heat introduction. The da'a CdSOa,HzO(s) 5/3HzO(g) = CdSOa,8/3HzO(s) (1) enabled correction for this effect but we recommend that no gold foil should be allowed to come loose and thus change and stirring characteristics. CdSOa(s) HzO(g) = CdSOa,HzO(s) (2) The average equilibrium times were 4, 8 , 12 and 30 AH = A F TAS minutes for KCl, CdSOd.8/3H20, CdSOI,H20 and CdSO,, although observations were continued over In each case AF, the free energy change, may be respectively, considerably longer periods. calculated from available dissociation pressures of All instruments involving accuracy of the heat of solution the hydrate systems. The entropy values obtained measurements were checked against standards calibrated by means of the third law of thermodynamics and a t the rational Bureau of Standards. The temperature of the calorimeter was kept below the the present heat capacity measurements can be thermostated bath temperature a t all times to avoid posused to calculate A S and thus A H , for each reac- sible distillation of water t o the surroundings. The temperature of the thermostat was obtained by tion. These results may then be compared with calorimetric determinations of A H to be given be- means of a Bureau of Standards thermometer graduated a t 0.02" intervals. A Beckmann thermometer showed t h a t low. the thermostat stayed constant within 0.002' for the heat capacity and heat of solution runs for each samplc. The Apparatus .-The low temperature heat capacities were measured by means of a calorimeter described by Kemp temperature difference between t h e thermostat and the and Giauque,2 except t h a t Gold Calorimeter IV was re- calorimeter was measured by means of a single copperplaced by a copper calorimeter with a gold resistance ther- constantan thermocouple. A copper resistance thermomemometer-heater. This was similar t o t h e copper calorime- ter heater was used in the calorimeter for the high precision needed. ter described by Giauque and A r ~ h i b a l d . ~ The solution experiments were arranged to give the same Laboratory Standard Copper Constantan Thermocouple No. 105, which was used, was compared with several fixed final concentration and essentially the same water level in points. It was found t o be 0.01' high a t both t h e triple the calorimeter in all cases. The amount of water was depoint (13.94'K.) and t h e boiling point (20.36"K.) of hydro- termined by weight. When it was necessary to cool the calorimeter, this was gen. I t was correct a t the triple point (63.1.5'K.) of nitrodone by means of cold nitrogen as described in detail by gen and read 0.01" high a t the boiling point (77.34'K.) of Kunzler and G i a ~ q u e . ~ nitrogen. Several heat capacity measurements were made beforc One defined calorie was taken as 4.1840 absolute joules and after solution in order to obtain the electrical equivalent and 0°C. = 273.16"K. The heat of solution measurements were made in a calor- of the heat of solution and to enable correction over a 1.5'' imeter recently described by Kunzler and Giauque,* for the interval t o 2.5'. This was a straightforward procedure esheats of dilution of sulfuric acid, except t h a t the solid samples cept t h a t the plunger used to break the seals was above thc This I\ ere introduced as described by Giauque and A r ~ h i b a l d . ~liquid before solution and was left in it afterwards. Water-proof plastic adhesive tape was used t o fasten t h e correction was only about 0.5 cal. mole-' in the final value Pyrex sample tube, which was approx. 7 cm. long and 2 cm. of the heat of solution a t 25'. Preparation and Analysis of Samples.-Pure c:idiniuni in diam., t o a Pyrex rod. Gold foil, 0.025 mm. thick, was metal (J. T . Baker Analyzed, total impurities 0.008c/,) was (1) This research was supported in part by thc Office of S a v a I Reoxidized with excess "03. Excess HzSO4 was then addccl, search, United States N a v y , and the United States Atomic Energy dropwise, and the crystals and liquid were heated to and Commission. held in the temperature range 130-150" for 36 hr. The ( 2 ) J . D. Kemp and W. F. Giauque, THISJ O U R N A L , 69, 79 (1937). mixture was then placed in an oven and the temperature ( 3 ) W. I?. Giauque and R. C. Archibald, i b i d . , 6 9 , 561 (193i). was raised sloivly to 300' and finally to 500", and kept a t ( 1 ) J. E . Kunzler and W. F. Giauque. ibid., 74, 3472 (1952). that temperature for several days. The anhydrous, rhom-
+
+
+
CADMIUM SULFATE AND ITS HYDRATES
May 20, 1955
bic, CdSO, crystals were white, lustrous, well-formed and averaged 0.2 mm. in size. As a check on the above procedure five samples were given a similar treatment on an analytical scale. The Cd/CdSO4 ratios were found to be 0.53924, 0.53924, 0.53914, 0.53917, 3.53929, compared to the theoretical value 0.53921. To ensure that all excess HzS04 was removed by heating, a pH meter was used in a 0.1 molal solution of the CdSO,. The value 5.12 obtained corresponds to that given by Latimer5 for the pure salt. CdSO4.8/3H20was prepared by dissolving some of the anhydrous salt t o form a nearly saturated solution. This was thermostated a t 35 + 0.1' and water was pumped off for 12 days. Crystals which started a t the surface level were shaken to the bottom so that they were kept covered by the solution. After pumping \vas stopped they were allowed to stand a t 35' for two weeks. The preparation was drained on a Buchiier funnel. The material was polycrystalline, opalescent, white and ranged in size from 0.5 t o 5 mm. The crystals were cracked t o an average size of 0.5 mm. and were cooled in liquid nitrogen in the hope of fracturing any crystal that had a solution inclusion. Final drying was accomplished by means of a stream of dry oxygen, which happened to be conveniently available. Analysis for water content was effected by heating t o a constant weight a t 500". Preliminary heating was carried out slowly until most of the water was removed slowly a t relatively low temperatures. The material used for the heat capacity and solution experiments contained 99.69 mole % CdSOa,8/3H~0and 0.31 mole % CdS04,HZO as calculated from the hydrate-anhydrous ratio equivalent t o CdSOa .2.6615H20. One of the difficulties in working with hydrated crystals is the prevalence of solution inclusion, "brine holes." The presence of solution inclusion is made evident by eutectic melting superimposed on heat capacity measurements below
TABLE I HEATCAPACITY OF ANHYDROUS CdS04 Cal. deg.-l mole-', O'C. = 273.16'K., mol. wt. CdSO, = 208.470, 1.,5657 moles in calorimeter. Tave.,
CP
OK.
Series 15.22 17.07 19.06 21.97 25.49 28.52 31.13 34.27 38.19 42.70 47.36 52.12 56.73 56.28 61.52 66.84 72.32 78.59 84.58 90 49 96.84 103.08 109 35 115.93 122.64 129.72 130 61 143.35
1
0.595 0.785 1.056 1.466 1.947 2.464 2.903 3.451 4.148 4.955 5.730 6.520 7,212 7.172 7.956 8.708 9.454 10 23 10.88 11.50 12.13 12 70 13.27 13.82 14.36 14 93 15 45 15.92
Tave.,
CP
O K .
150.03 156.72 163.49 170.54 177.73 184.79 192.07 199.44
16.39 16.83 17.27 17.72 18.14 18.56 18.97 19.34
Series 2 181.56 187.92 194.65 201 64 208 85 215.95 222.84 229.19 243.91 250,85 257.49 264.54 272.17 279.68 286.48 293.26 300.01 306.71 312.81
18.37 18.76 19.12 19.52 19.93 20.22 20.63 20.97 21.63 21.92 22.19 22.48 22.78 23.02 23.34 23.58 23.86 24.16 24.29
( 5 ) W. M . Latimer, "The Oxidation States of the Elements a n d their Potentials in Aqueous Solutions," 2nd E d . , Prentice-Hall, New York, N. Y.,1952, p . 172.
2741
0'. This is a very sensitive test. Heat capacity measurements over the range 250 t o 280'K. showed no evidence of brine holes in CdS04.8/3HzO, nor were any found in the monohydrate. The a form of CdS04.H20 is stable in contact with saturated solution over the range 45 t o 75'. The preparation was similar to that of CdS0,4/3Ha0 except that the solution was thermostated at 68" during evaporaGon. The crystals were filtered and broken to a n average size of 0.2 mm. in a box thermostated a t 65'. Final drying was carried out a t 68" in a thermostated flask by means of a pump. Analysis for water by heating t o 500' gave the hydrate/ anhydrous ratio equivalent to CdS04.1.0011HzO corresponding to 99.934 mole yo CdSO4,HsO and 0.066 mole 70 CdSOa.8/3HzO. The heat of solution measurements on the hydrates utilized the same samples as those used for the low temperature heat capacities. A new batch of well-formed anhydrous CdS04 crystals, averaging 0.2 mm. in size was prepared for the heat of solution experiments. The pH test gave 5.2 for a 0.1 A l solution.
Low Temperature Heat Capacity Measurements.-The heat capacity observations are given in Tables I , I1 and 111. Smoothed values of the thermodynamic properties are given in interpolation Tables IV, V and VI. The heat capacities of the two hydrates were each corrected for the small amount of the other one present. A smooth curve through the data should be accurate to 3% a t 15"K., 1% a t 20'K. and 0.1% above 35'K. TABLE I1 HEATCAPACITY OF CdS04 .I ,0011H20 Cal. deg.-l mole-', mol. wt. CdSOa,H20 = 226.486, 0.00078 0°C. = 273.16'K. (1.11279 moles CdSOd.H20 mole CdSO4,8/3HzOj in calorimeter.
+
Tave.,
CP
OK.
Series 1 253.07 29.20 259.99 29.66 267.57 30.16 274.26 30.61 Series 2 14.88 17.02 18.58 20.04 21.71 23.47 25.72 28.62 32.04 36.04 40.69 46.14 52.00 57.75 64.43 71.20 78.02 85.09 92.16 98.72 105.03 111.69 118.71 126.16 134.01 141.97 150.01
0,632 0.895 1,138 1.369 1.669 2,044 2.375 2.988 3.761 4.510 5.458 6.527 7.516 8.692 9,845 10.98 12.05 13.07 14.04 14.90 15.70 16.52 17.34 18.18 19.02 19.85 20.64
Tave.,
CP
OK.
158.08 166,20 174.52 182.79 190.78 199.34 208.79 216.98 225.61 234.01 242.50 251.15 259.99 268.85 277.66 287.05
21.43 22.20 22.94 23.67 24.37 25.13 25.88 26.62 27.20 27.75 28.45 29.04 29.68 30.25 30.81 31.41
Series 3 305.25 317.40 329.16 314.92 322.74
32.50 33.36 34.14 33.25 33.72
Series 4 118.75 126.02 128.67 231.82 240.08 286.69 296.44 306.40 316.75
17.33 18.15 18.44 27.64 28.26 31.40 32.04 32.67 33.36
M. N. PAPADOPOULOS AND W.
2742
TABLE I11 HEAT CAPACITY O F CdS0+,2.6615H20 Cat. deg.-' mole-', mol. wt. CdSO4.8/3€1?0 = 256.513, 0°C. = 273.16"K. (1.09059 moles CdSOc4/3H20 0.00339 mole CdSOa.H?O) in calorimeter.
+
Teve.,
Tave.,
CP
OK.
Series 1 256.21 261.92 268.10 274.28
45.73 46.43 47.17 47.92
Series 2 15.50 17.41 18.92 20.57 22.25 23.84 25.95 28.68 31.56 34.71 38.36 42.31 46.40 50.94 55.75 60.05 64.31 69.23 74.70 80.42 86.25 91.74 96.97
0.867 1.213 1,544 1 898 2.266 2.672 3.198 3.940 4,764 5.688 6.766 7.961 9.165 10.50 11.87 13.05 14.20 15.50 16.87 18.17 10.43 20.57 21.65
OK.
102.21 107.43 112.81 118.31 123.87 129.54 135.23 140.94 146.68 152,62 158.00 164.92 171.50 178.43 185.21 191 .66 19s. 14 204, 67 211.23 218.10 225.20 232.44 239.83 247.27 254.86 262.26 269.58 277.07 284.55 291.97 299.39
CP
22.73 23.66 24.66 25.67 26.64 27 63 28.57 29.53 30.43 31 .35 32.32 33.25 34.26 35.30 36.26 37.23 38.07 38.97 39. e9 41.16 41.80 42,57 43.77 44.60 45.68 46.53 47.44 45.37 49.23 50.16 51.17
TABLE IV THERMODYNAMIC PROPERTIES OF CdS04, CAL. MOLE-1 (H"- I @ / T,
OK.
15 20 25 30 35 40 45 50 55 60 70 80 90 100 110 120 130 140 150 160
170 180 190 200
CPO
0.570 1.180 1.899 2.712 3.581 4.474 5.344 6.173 6.969 7.724 9.149 10. 384 11.451 12.420 13.316 14.151 14 937 1 5 679 16 351 17 049 17.687 18.297 18.880 19.438
SO 0.190 0,433 0,771 1.188 1.671 2.207 2.785 3.391 4.017 4.656 5.956 7,260 8.530 9,804 11.031 12.227 13,301 13,526 15,632 16.710 17.761 18.787 19,791 20,774
T
0 , 1.u
0.321 0,563 0.853 1.180
1.530 1.911 2.296 2.685 3 . 071 3 , 842 ,1,Lj%i
5.290 5.955 1;. 585 7.182 7
I ,
"
149
x.200
8.800 9.300 9,775 10,230 10.669 11.094
14'.
210 220 230 240 250 260 270 280 290 298 16 300 310 320
- II;)/T 0.047 .112 .208 .335 ,491 . 671 874 1.095 1 .:En 1 ,582 2.114 2.673 3,256 3.819 -1.446 5.035 5.642 6,236 ti. 82fj
7.410 7.980 8.557 9.122 9,680
21 21 22 22 23 23 23 23 24 24
134 879 306 717 115
500 800 87.5 240 596
21 736 22.678 23 GO0 24 503 25 388 26 254 27 103 27 935 28 752 29 408 29 554 30 342 3 1 116
11.504
11.902 12.2sfi
1 2 ,M9 13 (120 13 369 13, 706 11,034 14.353 11.G05 1 4 . Mi3 14 965 ,
,
15.2C!)
0,638 1.370 2.2G9 3,266 4.297 5,318 0.314 c '>-i . r li
0,216 0.491 0.R90 1.391 1.072. 2 , fil2 3 ,206
0 . 150
4.0il8
55
S , 206
4.711
2 . 721 3 176
60 70 80 90 100 110 120 130 130
9.099 10.779 12.328 13.745 15.065 16.307 17.482 18.597 19.658 20.672 21. 644 22.597 23,470 24.346 25.183 25.991 26.771 27.525 28,254 28,902 29.651 30.324 30.984 31.631 32 157 32 275 32 910 33 511
5,490
l(i0
-(PO
19 972 20 482 20 909
Vol. 77
15 20 23 30 35 40 45 50
im DEC..'
GIAUQUE
170 1h0 1no 20(3 210 220
230 240 250 260 270 280 290 295 1 , ; 300 3 I 1) 320
7.010 $3. 500
1O.iNj
11,012 13. I07 14.577 16.021 17.43fi 18.87 20.190 21.528 22.842 24.131 25.400 26.6-1s 27. si5 29. os2 30.269 31,438 33 588 33.720 3-4,8:35
35,933 Xi XI5 37 014 38 081 30 133
0.372 0,659 1 ,000 1.405 1,830 2 273 ,
3.025 3 527 5 ,409 0.258 7,073 7 . s57 5.B11 '3.336 10 0:H 10.700 11.300
11.990 12,601 13,19-1 13.771 13.331 14.881 15,415
15.934 16,441 10.936 17.420 17.892 18.354 18 724
18 807 19 253 19 087
10.23'' 10,776 11 , 3 1 4 I 1 8.4-1 11' 3(iS 12.555 13 397 13.001 14, :390 14 803 ,
,
,
1-1. X ! i l
15.377 l5.86ii
0 ,O M ,119 ,231
382
mi
,752
1 ,023 1 284 1 Sfi5 1 862 2,389 3,l.jt 3.837 4,539 5.250 5 . 966 (i.6X5 7,402 8.118 8.830 9.535
10.241 1o,o:37 11.G29 13. 3 14 1 2 ,094 13 067 14.335 14.997 15.06" l f j ,300
16.9-13 17,579 15 0 ~ ~ 1 1s 207 18 8d) 10 446
The heat capacity ~~ie;~sureiiieiit~ wcre continuous in the sense that each one started where thc previous one ended, thus there were 110 uninvestigated intervals. The values of CL,,/l' d l ' for CdSOl, CdSOr H 2 0 and CclSO4~S/;3H2Owere fouiicl to bc 2Q.41, 36.S2 and 54.b0 eal. deg.-' mole-', incluclirlg extrapolated amounts of 0.10,0.22 and 0.26 cal. deg.-' mole-', respectively, below 15°K The heat capaci-
CAD~IILJ~\.I SULFATE AND ITS HYERATES
May 20, 1955
TABLE VI1 HEATOF SOLUTIOS DATA AH in cal. mole-' at 25"
TABLE VI THERMODYNAMIC PROPERTIES OF CdSOa.8/3Hs0, CAL. DEG.-' MOLE-' T , 'IC.
15 20 25 30 35 40 45 50 55 60 70 80 90
100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 298.16 300 310 320
CPO
SO
0,776 1.770 2.958 4.302 5.754 7.254 8.755 10.221 11.662 13.048 15.710 18.OS0 20.258 22,292 24.209 26,027 27.756 29,420 31.025 32.581 34.094 35.568 37,005 38.411 39.789 41.137 42.458 43.758 45.031 46.282 47.520 48.750 49.975 50.972 51.197 52.417 53.637
0.259 0.612 1.132 1,789 2.564 3.431 4.373 5.372 6.416 7.490 9.704 11.964 14,220 16,458
18.670 20.852 23.002 25.117 27.199 29.249 31.269 33.258 35.218 37.150 39.055 40.936 42.794 44.630 46,443 48.235 50.005 51.754 53.485 54.886 55.201 56.899 58,582
- ( P- H ; ) / T 0.194 0.065 0.459 ,153 0.839 ,293 1.305 ,484 1.838 ,726 2.422 1.009 3.045 1.328 3.690 1.682 4.353 2.063 5.019 2.471 6.358 3.346 7.681 4,283 8.959 5.261 10,189 6,269 11.375 7.295 12.517 8.335 13.621 9,381 10.429 14.6% 11.477 15.722 12.523 16.726 17.702 13.567 18.652 14.606 15.639 19.579 20.484 16.666 21.367 17.688 22.234 18,702 23.086 19.708 23.922 20.708 21.702 24.741 25.546 22.689 26.337 23,668 27.115 24.639 27,881 25.604 28.500 26.386 28.639 26.562 29.390 27.509 30.134 28.448 T
ties between 0 and 15°K. wereestimated by plotting C p / T 2 v s T. . The curves approached linearity below 15°K. since the Cp's were nearing the T 3 limiting law. The Heat of Hydration of Cadmium Sulfate.The AHfor the process CdS04.xH20
+ yH2O = (CdSOa.[x + y]H*O)s o h .
was obtained for each of the three samples. The data relating to the solution of the several substances are given in Table VII. Several measurements on KCI are included as a check. The C.P. KCl used in the experiments was dried by heating a t about 130" for 36 hours. The average result for the reaction KCI
+ 200H20
= s o h AH2s0 = 4188 f 4 cat. mole-'
may be compared with a value 4192 f 3 cal. mole-' obtained by Cohen and Kooy.'j The value of C. and K. has been corrected to the defined calorie. The results in Table VI1 have been corrected for the small amount of CdS04.8/3 HzO in the CdSO4. HzO and for the presence of monohydrate in the CdS04*28/3H20. (6) E. Cohen and J. Kooy, 2. p h r s i k . Chem., AlS9, 331 (1928).
2743
KCI,
KCI.200HzO
moles
AH
0.20727 ,20721 ,30723
4194 4184 4186 __ 4188 f 4
Av
.
CdSOc2.6615€120, moles
CdS04, moles
0 103532
102421 ,106332 Av.
CdS04.400HtO AH
-10,978 -10,979 - 10,973 -10,977 f 2
CdSOd~400F'~O CdSOd.1 001 1- CdSPd.400F20 H?O, 4Hcor t o Alfcor to CdSC)4.8/3I-lzO moles CdSOa.H?U
0.102919 ,104919 .lo4881
-2901 -2S99 -2898 -2899 A 1
Av.
0.10499 ,104701 ,104967 .lo4964 Av.
- 6098 -6084 - 6096 -6100 -6095 f 5
The difference in total heat capacities before and after solution permitted a rough evaluation of for CdS04 a t the concentration CdS04.400H20. The values obtained from CdS04, CdS04.HzO and CdS044/3Hz0 were, respectively, - 51.2, - 51.2 and -52.7; average -52 cal. deg.-' mole-'. Cohen, Helderman and Moesveld' measured the heat of solution of CdS04.28/3 H20 in 400 moles of water a t 18'. This may be corrected to 25' by means of the temperature coefficient from the present work. Their value is -2918 A 6 cal. mole-' compared to the present value -22899. They also measured the heat of solution of CdS04 which was obtained by heating the hydrate a t 200". Their value, corrected to 25", is - 11220 cal. mole-' compared to the present value -10977. The difference may possibly be attributed to the presence of some microscopic material in their sample due to the method of dehydration.
cp,
+
CdSO*.H20(S) 5/3H20(1) = CdSOa,8/3HzO(s) (3) AHu0 = -6095 2899 = -3196 cat. mole-' CdSOa(s) H20(1) = CdSOa,H10 (4) AHzj0 = -10,977 6095 = -4882 cal. mole-'
+ + +
For the heat of vaporization of water a t 25" Osborne, Stimson and Ginnings8 give A H = 10514 cal. mole-'. Keyesggives an equation for the gas imperfection of water which leads to HzO(g)sat. = H~O(g)ideal, AH = 6 cal. mole-'. Combining the above two results the ideal heat of vaporization, H0(g)- II(1) = 10520 cal. mole-'. Combining the ideal heat of vaporization with equations 3 and 4
+ 5/3HzO(g) = CdS01.8/3H20(~) ( 1 ) = -20,729 cat. mote-' CdSOl(s) + HzO(g) = CdSOa.H20(s) (2)
CdSOa,HzO(s)
AH02sa.16
AHozsn.is =
- 15,402 cal. mole-'
The entropy values obtained by means of tl-e third law of thermodynamics may be tested by combining them with free energy data, to calculate the heats of hydration a t 25", and comparing these results with the calorimetrically measured values. (7) E. Cohen, W. D. Helderman and A. L. T h . Moesveld. i b i d . , 96, 259 (1921). (8) N. S . Osborne, H. F. Stimson, D. C. Ginnings, Null. But. Standards J . Research, 23. 235 (1939). (9) F G. Keyes, J . Chcm. Phys., 16, 602 (1947).
E. W. HORNUNC AND W. F. GIAUQUE
2T44
VOl. 77
the vapor pressure and gas imperfection equations of Keyesg to give HzO(l), SO298.16 = 16.71. CdSOa,8/3Hz0, SZ,,.IC, = 54.89 cal. tieg.-' mole l h e free energy of reaction 1 may be calculated from data of Carpenter and Jette,lo and Ishikawa and Murool;a.'l Carpenter and Jette measured the dissociation pressure over CdS04.HzO(s) CdS0.$.S/3H20(s). Ishikawa and Murooka measured the pressure of water vapor over saturated solutions of cadmium sulfate hydrates. -kt :i1(;.76'K., CdSO4.S/3H20underpoes a transition to a-CdS04.1120,thus we may use I . and M . ' s value a t the transition temperature. The free energy of formation of CdSO1,S/3H20 from liquid water and CdSO$.H2Ois given by the expression AFo = 5 / 3 R T In P ~ ~ 2 0 ( a t i n . ) . The heat capacity and entropy of water were based on spectroscopic data.'? I-I?O(g),SO~YS 16 = 43.106. This was combined with the heat of vaporization of Osborne, Stiinson and Ginningsg and
CdSO4.Hp0, s 2 9 8 . 1 6 = 36.82 c d . deg.-' mole-' CdSOd, S298.~6= 29.41 cal. deg.-' mole-'
The results are summarized in Table VIII. The lack of trend in the values of A 1 1 2 9 8 . 1 6 in Table VI11 supports the accuracy of the third law values although the individual values deviate appreciably from the average due to the limitations of the dissociation pressure data. However, the agreement of the calorimetric and third law values of the heat of reaction within 0 cal. mole-' shows a consistency in terms of entropy of 0.03 cal. deg.-' mole-' For the reaction
+
CdSOi(s) H?O(g) = CdSOi.H20 AFO = RT In Pn,o(atni.)
these is only one observation due to Ishikawa and
Murooka13 who give TABLE \-I11 PFI,O= 0.62 mm. a t 25'. AH0 = AFO TASO HEAI. O F T H E R E A C T I O X cdSo~.Hno(S) 5/3Hzo(g) = CtlSOl.R/3H20(s) FROM THE THIRDLaw OF THERMO- A H z s ~ . i s= -4210 298.16 (36.82 - 29.41 - 45.11) DYNAMICS = - 1 3 5 1 cat. mole-'. Units are cat. mole-'
+
298.13 2ClS.Il3 303.33 308 33 313 28 313 11 316 76
~~~
C. a n d J. C and J . C. and J . C and J C. and J . C . and J I. and M .
-3719 -3i08 -3411 -3144
0 0 -31 -62
0
0 38 79
-20748 -20738 -20727 -20736 -20740 -20740 -20738
115 -91 116 -9.5 -180U0 -118 144 A v from third law = -20738 Is-thermal cals,rimetric measurement = -20729
-2871 -28.52 -2671
. .. .
-17027 -17028 -17323 -1760Q -17891 -17890
+
.
( I O ) C. D . Carlrenter a n d E . R Jette, Tiirs J O W R K A L , 45, 578 (1923). (11) I' Ishikawa and H . Xfurooka, Bull. I n s t . P h y s . C h e m . Res. ( y ' ( > k Y < J )9, , 781 (1933). (12) "Selected Values of Chemical Thermodynamic Properties," Series I11 National Bureau of Standards, June 30, 1948.
!C )STRIBUTION
FROM THE L O W
+
This is in satisfactory agreement with the more reliable calorimetric value, - 15,402 cal. ~nole-', especially considering that each 0.01 mm. error in P H ~ Orepresents 10 cal. mole-'. The two third law agreements presented above indicate that CdSO4, CdS04,HzO and CdSOd.S/XH 2 0all approach zero entropy a t limiting low temperatures. We thank E. M'. Hornung, IT.P. Cox and R. H. Sherman for assistance with the low temperature measurements. (13) F. Ishikawa and H . hlurooka, Sci. Refits. Tokoku I m p . U s i n . . 2 8 , 138 (1933).
BERKELEY, CALIFORNIA
TEMPERATURE LABORATORY, DEPARTMENT OF
CHEMISTRY AND C H E M I C A L UNIVERSITY O F C A L I F O R S I A , BERKELEY]
ENGINEERING.
The Vapor Pressure of Water Over Aqueous Sulfuric Acid at 2501 BY E. W. HORNUNG AND Tir. F. GIAUQUE RECEIVED JANUARY 17, 1955 Dircct observations of the vapor pressure of water over HzS0.t.4H20, H2SOa.3H20and H2S04,2Hs0have been made over a range of temperatures above 25'. These results with available partial molal heat content and heat capacity data have been used t o calculate accurate values of the partial pressure of mater at 25'. These results confirm the accuracy of the direct pressure observations of Shankman and Gordon, and of Stokes, and reinforce the earlier conclusion of Stokes that the cells €12, H2SOa, PbS04, P b 0 2 , Pt and Hz, H2S04,HgzS04,Hg have not given accurate activities of water or of sulfuric acid in the more concentrated range.
In connection with our series of investigations on the thermodynamics of the sulfuric acid-water system, from 15 to 300"K., accurate d?ta on the free energy of dilution at 25' are essential. I n much of the range below 20 molal H2S04 the most effective nlethods aprear to be either the direct measureinent of the vapor pressure of water over the s o h [ I ) This work was supported in part b y the Office of Naval Research, United States N a v y , and by the United States Atomic Energy Cornmission.
tions, or measurements with some cell involving SUIfuric acid, e.g. HgzSOi
+ Hz = H~S04(~rn) + 2Hg
Both types of measurement have been made bv several observers. Results calculated froln Cell measurements by means of the Duhem equation fail to agree with the direct measurements within the expected limits Of error' Our problem was to extend the data to a somewhat higher concentra-
