hug. 20, 1'35'3
TENPER~~T HEAT U R EC A P A C I T Y
LOW
The dibasic salt similarly was shown to decompose to potassium uranate on heating in accordance with the equation K2COS --+
KJCO,
+
1/>02
(2)
The formation of potassium pyrouranate and potassium uranate as thermal decomposition products was substantiated by X-ray diffraction patterns and chemical analyses. Conclusions The chemical reactions of the compound prepared by either the precipitation of uranium from uranyl nitrate solutions with hydrogen peroxide or the reaction of uranium trioxide with aqueous hydrogen peroxide can be suitably explained by the existence of a peroxyuranic acid structure. Of the two previously proposed acid structures (H4U06 or HzUO6.Hz0),infrared spectral data, by establishing the presence of a hydrate water group, indicate that hydrated peroxyuranic acid (HzU05. H20) most truly represents the chemical nature of the compound. The uranium-oxygen-peroxyoxygen acid system shows a similarity to the known inorganic oxygenperoxyoxygen acid systems. This similarity is [COSTRIBUTION FROM
THE
.IND
ENTROPY O F TK~LLOUS CIILORIDE
416'3
based on the preparation of the oxygen acid and the peroxyoxygen acid from the acid anhydride by the addition of water and peroxide, respectively. A comparison of the sulfur and uranium acid systems suitably illustrates this similarity.
sod
A4cidanhydride UO3 Primary oxygen acid H~UOI H~SOS Peroxyoxygen acid H2UOj H~SOI.HJOHydrated oxygen acid II2UOa.H>O H2S05,HzO Hydrated peroxyoxygen acid H2COj.H~O H&O? P5ro (oxygen) acid H2U20i
The preceding data and discussion were primarily intended to establish the structure of hydrated uranium peroxide through reaction with strong bases. In light of the previously established amphoteric character of other hexavalent uranium oxide hydrates, peroxyuranic acid would be expected to react, as a base, with strong acids. Acknowledgment.-\Ye wish t o express our appreciation to F. H. Ford for obtaining and interpreting the X-ray diffraction patterns, to B. Gessiness and his staff for the analytical results, and to P. S. Gentile, L. H. Talley and D. A. Stock for their help in obtaining the above data. CIXCISSATI,OHIO
Low TEMPERATURE LABORATORY, DEPARTMENTS OF CHEMISTRY A N D CHEMICAL ENGINEERING UNIVERSITY O F CALIFORNIA, BERKELEY]
The Low Temperature Heat Capacity and Entropy of Thallous Chloride1 BY I. R. BARTKYAND W. F. GIAUQUE RECEIVEDFEBRUARY 19, 1959 The heat capacity of thallous chloride has been measured from 15 to 310°K. The entropy at 298 15'K was found to be 26.59 cal. deg.-' mole-'. T h e heat capacity, entropy, (P- Hoo)/Tand ( H O- Ho0)/Tfunctions for TlCl are tabulated from 15 t o 300°K. The entropy change calculated from the third law of thermodynamics for the cellreaction T1 AgCl = TlCl Ag was found to be in good agreement with the cell temperature coefficients of Gerke provided the entropy change for the step Tl(s) = Tl(amalg) is calculated from A S = (-lHLalorlmotrlo FE)/T rather than from dE/dT. It is evidently difficult to obtain reliable cell temperature coefficients involving a metal electrode even when it is as soft as thallium, Third XgCl = TlCl -Ig, AH0 = law results have been used to calculate these heats of reaction a t 298.15"K.: Tljcryst.) -18,430 cal. mole-'; T1 l/1C12 = TlC1, AHu = -48,800 cal. mole-'.
+
+
+
+
+
Gerkea studied a number of cells in order to test the validity of the third law of thermodynamics by comparing the entropy changes as calculated from the temperature coefficients of the cell voltages with those calculated from the available low temperature heat capacity data by means of the third law. He found a discrepancy of 2.0 cal. deg.-l mole-' in the cell T1
+ .igC1 = TlCl + -Ig
(1)
The heat capacity data available at that early date often were inaccurate since the techniques of low temperature calorimetry were in the first stages of their development. Thus Gerke considered that the discrepancy had its origin in the heat capacity data and particularly in that on thallous chloride. The present work provides accurate heat capacity data for thallous chloride. Calorimetry and Material.-The low temperature heat capacity was measured in 311 apparatus similar to that described by Giauque and Egan . 3 T h e particular caloritn(1) This work was supported in part by t h e National Science Foundation. T h e U. S. Government may reproduce this article. (2) R . H . Gerke. THIS JOURNAL, 4 4 , 108.1 (1922). (:i) W. IT. Giauclue and C. J . Bgan, J. C h e i n . Phys.. 5 , 4.5 (I'JH7).
+
eter was described by Kemp and Giauque4 and its most recent modification by Papadopoulos and Giauque.6 Briefly, the present calorimeter was of copper and the temperature was measured by a gold resistance thermometer-heater, for high precision, and Laboratory Standard Copper-Constantan Thermocouple hTo. 105 for simultaneous reference before and after every heat input. The thermocouple was compared with the triple (13.94'K.) and boiling points (20.36' K . ) of hydrogen and the triple (63.15OK.) and boiling points (77.34'K.) of nitrogen, during tlie course of the present work. O D was taken as 273.15"K. and 1 defined calorie was taken equal t o 4.1840 absolute joules. The thallous chloride was supplied 99.9+'r, pure by the Chemical Commerce Co. It was received in tlie form of a rather voluminous precipitated powder. This material was heated to the melting point (about 430°), in a Pyrex beaker so t h a t a large reduction in volume occurred. This eliminated the possibility t h a t particles with microscopic properties could remain in the sample used for the heat capacity measurements as could be the case with a fine powder. The well-crystallized solid was broken easily with a mortar and pestle and the crystals were passed through an 8 mesh i n - l screen so that they would pack well within the calorimeter. The use of this material, rather than the powder, a t least doubled the amount of material which could be placed in the calorimeter and a1m improved the heat con(4) J. D. Kemp and W . F.C.iauque. THISJ O U R N A L , 59, 70 (lW37). (3) hl. N. Papadripoulos and W. F. Giauque. ibid., 7 7 , 27-10 (1955).
I.
4 170
rc. UARTKY
AND
ductivity coiisiderably; 569.550 g. of TlCl was taken for the measurements. Helium was used within t h e calorimeter t o facilitate heat conduction.
The Heat Capacity Measurements and Derived Thermodynamic Properties.-The actual observations are given in Table I. The measurements were continuous in the sense that each one began where the previous one stopped so that there were no unobserved regions. The approximate temperature rises may be estimated from the average temperatures given in the table. TABLE I CIILURIUE, CAL. L)li:c. --' MOLE-l 569.550 g. in the calorimeter; 0" C. = 273.15"K.; molecular weight = 239.847. ' k E H E A T CAPACITY OF T H A L L O U S
T, "6.
CD
T ,OK.
CD
2',
OK.
c,,
81.09 10.20 216.03 12.06 Series 1 223.87 12.08 86.58 10.35 13.55 2.035 232.10 12.06 92.78 10.54 14.39 2.248 239.66 12.10 99.09 10.72 15.91 2.609 10.87 247.10 12.10 18.02 3.096 105.01 254.83 12.11 110.60 11.02 21.07 3.731 262.53 12.14 116.33 11.09 24.51 4.437 11.20 270.52 12.18 27.30 4.948 122.28 11.30 277.08 12.20 30.48 5.478 128.74 285.32 12.13 135.66 11.42 33.00 6.068 11.49 292.73 12.19 37.86 6.596 142.49 300.31 12.17 149.80 11,55 41.97 7.105 11.63 Series 2 45.62 7.594 158.17 164.32 11.66 167.36 11.69 49.53 8.042 11,:s 172.54 11.72 54.26 8.543 175.78 180.48 11.79 183.80 11.93" 59.11 8.984 188.16 11.84 191.88 11.78" 64.04 9.345 195.73 11.89 200.22 11.91" i0.04 9.686 203.08 11.93 208.27 12.02 i5.79 9.977 a Results given no weight because of heat transfer duc to water vapor in iiisulating vacuum space.
The several measurements of series 2 were niadc to replace several measurements of series 1 near 200°K. which were of lesser accuracy due to water vapor which accidentally had entered the insulating vacuum space. The thermodynamic properties of thallous chloride are given in Table 11. A Debye extrapolation of 0.81G cal. deg.-' mole-l was made below 13°K. A salt with the mass ratios of T1 and C1 should deviate somewhat from a Debye function a t very low temperatures; however, the entropy effect due to such a deviation should be very small in the present case. Comparison of the Entropy Differences from Cell Data with those Obtained from the Third Law of Thermodynamics.-Gerke2 studied the cells
Vol.
W. E'. GIAUQUIC
s1
TABLE i1 FUSCTIONS FOR SOLID 'rwLLLOUS CIILORIDE, CAL.D E G . - ~MOLE-^ PO - HaO IIO -'I00 -~ - _-
'hBRMODYNAhlIC
1',
CPO
OK.
15 20 25 30 35 40 45 5(1 60
2.394 3.524 4.527 5.432 6.209 6.892 7.522 8.092 9.050 9.685 10.13 10.47 10.75 10.98 11.16 11.31 11.46 11.56 11.64 11.i1 11.78 11.85 11.91 11.06 12.00 12.03 12.0; 12.10 12.12 12.13 12.14 12.16 12.16 12.17 12.18
TO 81)
9U
100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 25;o 200 27 0 22.15 280 290 298.15 300
SO
T
?'
(1.097) 1.945 2.810 3.747 4.645 5.510 6.368 7.190
(0.314) 0.614 0.069 1.357 1.763 2.178 2.596 3,015 3,843
(0.783) 1.331 1.871 2.390 2,882 3.341 3.77% 4.175 4.912 3.553 6,099 6,567 6,971 7.326 7 .ti38 7.914 8.162 8.386 8.586 8.768 8.933 9 . 083 0.221 9,354
8.'"I ai)
10.202 11.526 12.740 13.858 14.894 15.857 16.756 17.599 18.391 19.142 19.850 20.521 21.160 21.769 23.352 22.909 23.443 23. 956 24,449 24.924 25.381 25.521 25.823 26.249 26.586 26 662
4,649
5.427 6.173 6.8X7
7.568 8.219 5.842 0.437 10.008 10.556 11.082 11.588 12.075 12.545 12.998 13.436 13.859 14,269 14. 667 13.052 15 426 15,541 15,790 16.143 16.423 16.487
9.473 !).681 9 . (j87 9.78" '3.87% 9 . 955
9.980 10. 033
10. 106 10. 163 10.175
tropies a t 2908.15"K. were utilized Alg,6S
S(TlC1)
=
-1.09
10.21 cal. dep.-' niolc-I AgCl,7 S = 22.97 T1,8 S = 15.35 S(T1) S(.lgCl) - S(Ag)
=
+
+
=
27.02
which may be compared with the value 26.59 cal. deg.-' mole-l observed in this research. The accuracy of the various heat capacity determinations is such that the discrepancy of (cellthird law) 0.43 cal. deg.-hole-l is almost certainly due to the difficulty in measuring cell temperature coefficients. Gerke's research was concerned with cell temTl(2-phasc amalg.) + AgCl = TIC1 Ag (2) perature coefficients, and it was reasonable that he and should try to determine the entropy changes in Tl(cryst.) = Tl(2-phase amalg.) ( 31 the cells concerned entirely by rneaiis of the obThe values of dE/dT were (a), -0.0000794 and ( 3 ) , served temperature coefficients of e.m.f. How+0.000032 volts deg.-'. The combined value, ever, he proposed and calculated an alternative for the most difficult step, namely, cell 3, involving -0,0000474 gives A S = -1.09 cal. deg.-l mole-' the solid thallium metal although he did not utifor reaction 1 lize the result. Especially when the free energy Tl(s) + 4gC1 = TIC1 Ag (1)
+
+
This result may be taken to apply to temperatures near 298°K. since there should be a trivial temperature coefficient of AS, These values of en-
( G ) P. F. Meads, W.R. Forsythe and W. F. Giauque, TFISJ O U R 63, 1002 (10-11). (7) E. D. Eastman and R . 1'.Rlilner, J . C ' l t c v ~ ,lJlzJj5., 1 , 111 fl!J:4:{). ( 8 ) J F,(>, Hicks, J r . , TIIISJ O U R N A L , 60, 1000 (lL(Y8).
NAL,
Low TEMPERATURE HEATCAPACITY AND ENTROPY OF THALLOUS CHLORIDE
Aug. 20, 1959
and heat of a reaction are small, the most reliable way to obtain the entropy change is to calculate A S = ( A H - AF)/T. Richards and Danielsg measured the heat of solution of thallium in mercury over a range of composition. They also measured the e.m.f. of cells in which the only process was the transfer of thallium from the pure metal to certain amalgam concentrations. The e.m.f. of the reaction (4)
Tl(s) = Tl(2-phase amalgam)
with various conditions of the solid thallium has been measured by several observers whose data are given in Table 111. Where necessary small corrections have been applied to adjust the data to 25". TABLE 111 CELL Tl(s) = TI(2-PHASE AMALGAM) T = 298.'K., A S in cal. deg.-' mole-'
DATA
FOR
Observer Richards and Daniels9 Jones a n d Schurnblo Richards and Smythll Richards and S m y t h Gerke2 Gerke
Condition of T! Stick 1 Solid casting Electrolytic crystals Stick Crystals
E ,v . 0.0026 ,0028 .a021 ,0027 ,0027 ,0024
10s dE/dT
1.8 4
AS 0.41
.9
(Decreased to lower values) 2.0 .46 3.2 .74
The data in Table 111 indicate that an e.m.f. of 0.0024 volt is unlikely to be in error by as much as half a millivolt which is only 0.04 cal. deg.-', mole-' in A S = (AH - AF)/T, whereas the temperature coefficient data are uncertain to about half a unit. There is no simple way of utilizing thermal data to calculate A S = (AH - A F ) / T for the reaction in Table I11 because the process is rather involved as TI
+
B
A
Tl.AHg(1) = -Tl.BHg(s) A - B
(5)
where A and B represent the moles of Hg per mole of T1 in the liquid and solid phases, respectively. There are insufficient data to enable the calculation of the partial molal entropies of the T1 and Hg in the solid amalgam. Thus the data in Table I11 are useful only in displaying the variation which we assume to be due to microscopic surface effects on the solid electrode. Gerke avoided the thermodynamic complexities of the 2-phase amalgam by considering the two steps Tl(s) = Tl(N2 = 0.336)
(6)
where N 2 refers to the mole fraction of T1; t = 30"; E = 0.01246 v.; A F = -2289 cal. mole-'; = +720 cal. mole-' from which A S = 3.34 cal. deg.-l mole-', and the calculated value of dE/dT = 0.000145 v. deg.-l and Tl(N2 = 0.336) = Tl(2-phase amalgam)
(7)
t = 30°, dE/dT = -0.000126 v. deg.-'. Adding reactions 6 and 7, the resultant dE/dT = +0.000019 (9) T. W. Richards a n d F. Daniels, THIS J O U R N A L , 41, 1732 (1919). (10) G. Jones and W. C. Schumb, Proc. Ameu. Acad. Arls Sci., 66, 217 (1919). (11) T. W. Richards a n d C. P. Smyth, THISJOURNAL, 44, 524 (1922).
4171
v. deg.-', as compared to the directly observed value +0.000032 found by Gerke for reaction 3. Combining the results for reactions 2, 6 and 7 the calculated dE/dT for reaction 1 is -0.0000604 v. deg.-l and A S = -1.39 cal. deg.-l mole-l, S(TIC1) = -1.39 S(T1) S(AgC1) -S(Ag) = 26.72. Considering the various possible errors in the several data used in the calculation, the above value is in very satisfactory agreement with the result 26.59 cal. deg.-l mole-' obtained by direct measurement in this research. Gerke comments on the fact that the stick of thallium used for his measurements produced crystals during the measurements, that the e.m.f. dropped slightly and the dE/dT increased as might be expected of a more stable metal. One of us (W.F.G.) recalls seeing the very pronounced crystal growth of the thallium during Gerke's experiment and a t that time i t seemed justifiable to accept the temperature coefficient results after this occurrence. However, in view of the above results i t seems necessary to conclude that crystallization probably still in process, was complicating the temperature coefficient measurements. The temperature coefficient, 0.000020 v. deg.-', obtained by Gerke for reaction 3, in the first measurements before the recrystallization started is essentially correct, and this is in accord with the fact that microcrystals such as might be expected on a surface should have a higher free energy but only a very small increase in entropy. This is due to the fact that most of the microcrystalline energy and free energy exist a t the absolute zero. These properties have only modest temperature coefficients and only a small associated entropy change. The heat of reaction for Tl(cryst.) AgCl = TIC1 Ag may be calculated from the cell e.m.f. and the entropy change. For such a purpose we consider that A S from the third law of thermodynamics will ordinarily be the more reliable. Utilizing data from Gerke's2 several cells and converting to absolute volts
+
+
+
+
Tl(cryst.)
+ AgCl = TlCl + Ag
A P l j o = -FE
= -23062 X 0.7795 = -17977 cal. mole-' A H O d = A F o -I- 298.15( -1.52) = -18430 cal. mole-' Tl(cryst.) f 1/2C12 = TlCl AFo$ = -23062 X 1.9161 = -44209 cal. mole-'
and utilizing the entropy of Clz = 53.290 cal. deg.-l mole-l;12 AH02d = A P -I- 298.15(--15.40) = -48800 cal. mole-' Gerke comments on the difficulty in measuring the temperature coefficient of the chlorine electrode and this is borne out by a comparison of his value -15.12 compared to the third law result -15.40 given above for the formation of TlCl from the elements. In obtaining the value - 15.12 we have utilized the calorimetric correction for the electrode Tl(cryst.) = TI(N2 = 0.336) discussed above. However, the agreement is close enough to indicate that the e.m.f. of the cell T1+1/2C12 = TIC1 should be quite accurate. BERKELEY, CALIFORNIA (12) R . H. Sherman and W. F. Giauque, ibid., 76, 2007 (1953).
