Heat capacity of α-sodium uranate (α-Na2UO4) from 5 to 350 K. Standard Gibbs energy of formation at 298.15 K

J. Chem. Thermodynamics 1974,6, 751-156

Heat capacity of a-sodium from 5 to 350 K. Standard formation at 298.15 K”

uranate (a=Na,UOJ Gibbs energy of

DARRELL W. OSBORNE, HOWARD E. FLOTOW, RICHARD P. DALLINGER, and HENRY R. HOEKSTRA Chemistry Division, Argonne National Argonne, Illinois 60439, U.S.A.

Laboratory,

(Received 6 November 1973) The molar heat capacity of a-NaaUO1 was determined by adiabatic calorimetry from 5 to 350 K. No unusual thermally-related phenomena were observed. The following thermodynamic results were calculated: heat capacity at constant pressure: Ci(298.15 K) = (146.67 f 0.29) J K-l mol-I; standardentropy: S”(298.15 K) = (166.02 i 0.33) J K-l mol-I; enthalpy increment: (H”(298.15 K) - H”(O)} = (26227 f 52) J mol-‘; standard Gibbs energy divided by temperature tG”(298.15 K) - H”(0)]/298.15 K = -(78.05 f 0.16) J K-l mol-I. The enthalpy of formation of a-NaaUOI reported by O’Hare and Hoekstra and the entropies of a-NazIJO,, Na, U, and 0 were used to calculate the standard Gibbs energy of formation AGF(a-NaaUO,, c, 298.15 K) = -(1745.8 f 3.6) kJ mol-I.

1. Mroduction The use of liquid sodium as the primary coolant for the Liquid Metal Fast Breeder Reactor has occasioned an interest in the thermodynamic properties of stable compounds formed by the reaction of sodium with the reactor fuel (a mixed U-f- Pu oxide) and also with some of the fission product elements. In a recent series of articles,(‘-4’ some thermodynamic properties of Na,UO, were presented in detail. A similar investigation of a-Na,U04 is in progress. The enthalpy of formation at 298.15 K has been published ;(5) we present here the heat capacity from 5 to 350 K, and another group at Argonne National Laboratory plans to determine the enthalpy from about 500 K to 1200 K.

2. Experimental SAMPLE

The a-Na,UO, was prepared by the reaction of Na,CO, with u-U03 +0.78H,O in a gold crucible at 1023 Kin air. (6)Chemical analyses gave (13.27 + 0.13) mass per cent Na (theoretical, 13.21 mass per cent) and (68.21 kO.07) mass per cent U (theoretical, 68.40 mass per cent). The X-ray powder diffraction pattern of this material was indistinguishable from one obtained on an earlier sample prepared by Hoekstra.(@ Just prior to LIWork performed under auspicesof the US, Atomic Energy Commission,

752

D. W. OSBORNE,

H. E. FLOTOW,

R. P. DALLINGER,

AND H. R. HOEKSTRA

loading the sample into the calorimeter, the a-Na,UO, was heated in a quartz tube to 1023 K in air for 4 h in order to remove any traces of water without otherwise affecting the sample composition. After the sample had cooled to 473 K, it was transferred to a dry (10 p.p.m. HzO) helium-filled glove box where the sample was loaded into the calorimeter. CALORIMETER

The cylindrical calorimeter was made of OFHC grade copper, was gold-plated on the exterior, and had a central re-entrant well to contain a bifilarly-wound Evanohm heater and an encapsulated platinum resistance thermometer. The internal volume of the calorimeter was 33.99 cm3 and its mass was 47.135 g. The sample was loaded into the calorimeter in the helium-filled glove box, and the calorimeter put into a vacuumtight stainless-steel can (‘I which could be attached to a vacuum line and permitted the final tightening of a gold-gasket seal.(‘) The pressure of helium (used to promote heat exchange between the sample and the calorimeter) was reduced from 1 atm to 40.0 Torr at 298.35 K, and then the calorimeter was sealed.7 TECHNIQUES The essential features of the adiabatic-calorimetric technique and a description of the calorimetric equipment used for the measurements reported here have been given in recent publications. (‘9 *) We judge that our platinum-resistance-thermometer temperature scale agrees with the thermodynamic scale to within 0.1 K from 3 to 14 K, to within 0.03 K from 14 to 90 K, and to within 0.05 K between 90 and 373 K. Temperature differences, however, are determined reliably to 0.01 K at 4.2 K, to 0.0008 K at 14 K, to 0.0001 K from 25 K to 58 K, and to 0.001 K above 58 K. Our standards of electrical potential difference, resistance, and mass were calibrated against standards calibrated at the U.S. National Bureau of Standards. The Wang electronic timer was checked against signals from station WWV. Two series of measurements were made over the temperature range 5 to 350 K, one on the empty calorimeter and a second one on the calorimeter and 51.275 g of sample. The heat capacity of the sample was then determined by the difference between the two series after making small corrections for variant amounts of helium, Apiezon T grease, copper, and gold, associated with the empty and with the loaded calorimeter. A small correction for the finite temperature increment, equal to - (d2CP/dT2)(AT)2/24, was applied to each heat-capacity determination. The heat capacity of the sample was 50 per cent of the total near 10 K, increased to a maximum of 60 per cent near 50 K, and then decreased gradually to 48 per cent at 350 K.

3. Heat capacity results The experimental heat capacities are presented in order of ascending average temperatures (T) in table 1. The temperature rise AT for each value below 20 K is approximately 2 K, for values between 20 K and 100 K, AT x 0.1(T), and for values above 100 K, AT = 10 K. The estimated uncertainty of individual values of C; in table 1 is t atm = 101.325 kPa; Torr = (101.325/760) kPa.

HEAT CAPACITY TABLE

(T) K

5.99 6.02 a.33 a.34 10.43 10.50 12.48 12.69 14.47 14.84 16.41 16.91 18.34 la.93 20.31 21.06 22.37 23.13 24.57 25.30 26.99 27.82 29.69 30.85 32.67 34.18 35.96

G J Kvlmol-’ O.loo5 0.1025 0.2866 0.2905 0.6263 0.6385 1.141 1.203 1.784 1.914 2.536 2.746 3.394 3.685 4.365 4.751 5.445 5.858 6.662 7.085 8.100 8.611 9.819 10.59 11.83 12.89 14.18

753

OF a-NaJJO,

1. Molar heat capacity Cg of a-Na2UOl(c) at constant pressure M(a-Na&O,) = 348.006 g mol-’


G


K

J K-l mol-’

??-

J K-l mole1

C,d


39.63 41.01 43.65 45.02 47.33 49.52 52.09 54.48 57.30 59.89 63.02 65.92 69.29 72.63 76.23 80.06 83.89 87.06 88.30 92.24 96.07 97.49 97.61 101.47 105.59 107.49 115.33

16.98 la.08 20.27 21.43 23.43 25.39 27.72 29.93 32.59 35.02 38.00 40.73 43.91 47.00 50.27 53.69 57.08 59.82 60.87 64.11 67.12 68.18 68.26 71.19 74.26 75.60 al.22

117.55 124.63 127.59 133.85 137.57 143.32 147.47 153.03 157.34 162.78 167.21 172.47 177.06 182.16 186.93 191.92 196.85 201.85 206.85 211.79 216.89 221.90 226.94 232.06 236.91 241.45

82.72 87.36 89.23 93.05 95.17 98.38 loo.55 103.35 105.45 108.07 109.98 112.23 114.17 116.26 118.08 119.96 121.60 123.40 124.99 126.52 128.01 129.47 130.94 132.23 133.59 134.82

246.86 251.49 256.84 261.47 266.81 271.41 272.92 276.76 281.31 282.92 291.18 292.94 301.09 302.92 311.02 312.86 317.88 320.94 321.34 327.83 330.89 331.31 338.24 339.80 346.66 346.82

c,” J Kelmolbl 136.09 137.19 138.46 139.48 140.52 141.55 141.80 142.62 143.50 143.89 145.49 145.79 147.12 147.49 148.89 149.05 149.96 150.31 150.41 151.34 151.75 151.91 152.87 153.04 153.80 154.16

5 per cent near 6 K, 1 per cent near 14 K, and 0.2 per cent above 25 K. No correction was applied either for sample deviation from stoichiometric a-Na,UO, nor for sample impurities; however, we judge that these effects would not cause errors in excess of the uncertainties given above. No anomalous behavior was observed, and a plot of C,” against (T) exhibited the usual sigmoid shape. 4. Derived thermodynamic

results

The second column from the left in table 2 gives Ci of ol-NazIlO (crystal) at selected temperatures from 5 to 350 K. These values were derived from the data in table 1 as follows. The values below (T) = 40 K were fitted to a polynomial in T by means of a computer program employing weighted least squares, and similarly the values above (T) = 20 K were fitted to a second polynomial in T. The standard deviations from these polynomials were 0.25 per cent and 0.06 per cent, respectively. The values of the functions in table 2 at 5 K were obtained by an extrapolation of C; to T = 0. It was apparent from a plot of CJT against T2 below 20 K that the

754

D. W. OSBORNE, TABLE

T ii

R. P. DALLINGER,

15

ii 100 110 120 130 140 150 160 170 180 190 E 220 230 240 250 260 270 280 290 300 310 320 330 340 350 273.15 298.15

was tending

AND H. R. HOEKSTRA

2. Thermodynamic functions of a-Na&JO,(c) M = 348.006 g mol-1

C, J K-l

20 25 30 35 40 45 50 60 70

curve

H. E. FLOTOW,

mol-1

0.0577 0.5421 1.979 4.203 6.916 10.02 13.48 17.28 21.42 25.82 35.13 44.57 53.68 62.21 70.13 77.49 84.34 90.68 96.52 101.87 106.76 111.24 115.37 119.18 122.70 125.97 128.99 131.78 134.38 136.81 139.10 141.26 143.30 145.21 146.99 148.65 150.22 151.68 153.07 154.42 141.92 146.67 f 0.29

toward

W”) J K-l

H”(T) - H”(O)

mol-1

line

-WV’9 - fWN/~

J mol-1

(0.0192) 0.1646 0.624 1.483 2.706 4.234 6.033 8.077 10.349 12.831 18.354 24.480 31.03 37.85 44.82 51.86 58.90 65.90 72.84 79.68 86.41 93.02 99.50 105.84 112.05 118.11 124.04 129.84 135.50 141.04 146.45 151.74 156.91 161.98 166.93 171.78 176.52 181.17 185.71 190.17 153.38 166.02 f 0.33

a straight

to 350 K

J K-l

(0.0721) 1.249 7.159 22.35 50.00 92.15 150.7 227.5 324.1 442.1 746.4 1145 1637 2217 2879 3617 4427 5303 6239 7231 8275 9365 10499 11671 12881 14125 15400 16704 18035 19391 20770 22172 23595 25038 26499 27977 29471 30981 32505 34042 22618 26227 zk 52

below

10 K which

mol-’

(0.0048) 0.0396 0.147 0.365 0.706 1.162 1.727 2.390 3.146 3.989 5.913 a.122 10.57 13.22 16.03 18.97 22.00 25.11 28.27 31.47 34.70 37.93 41.18 44.41 47.64 50.85 54.04 57.21 60.36 63.48 66.56 69.62 72.65 75.64 78.60 81.53 84.42 87.28 90.11 92.91 70.58 78.05 f 0.16

would

pass through

C,IT = 0 when T = 0. Accordingly, it was assumed the heat capacity below 5 K followed the relation: C, = aT3 ; the functions in parentheses at 5 K were calculated from this equation. The value of C!; at 5 K was calculated from the polynomial that represented the data below 40 K. The polynomial fits were also used in a computer

HEAT CAPACITY

755

OF u-Na&O*

program to calculate the standard entropy S”(T), the standard enthalpy increment and the standard Gibbs energy divided by temperature {G”(T) {H”(~Hf”Ko}, - H”(O))/T. The standard entropies at 298.15 K of sodium,(‘) uranium,(“) and oxygen(“) were combined with the standard entropy of a-Na,UO, given in table 2 to calculate the standard entropy of formation of cr-Na,UO,. The result is AS,“(a-Na,UO,,

c, 298.15 K) = -(397.15+

The standard enthalpy at 298.15 K of cr-Na,UO, Hoekstra(‘) to be AH,“(a-Na,UO,,

1.02) J K-’

has been reported by O’Hare and

c, 298.15 K) = -(445.56f0.85) = -(1864.22+3.56)

kcal,, mol-’ kJ mol-‘,

where cal th = 4.184 J. The standard Gibbs energy of formation calculated to be : AG,“(c+Na,UO,,

mol-‘.

c, 298.15 K) = -(1745.8+3.6)

at 298.15 K is then

kJ mol-‘.

5. Discussion The only other known experimental

heat capacities ofcl-NazUO, are those of Faustova, Ippolitova, and Spitsyn (I’) from 662 to 1189 K. Their value of C; at 662 K is equal to our value at 298 K and is about 20 per cent lower than the value obtained by a reasonable extrapolation of our results to 662 K. The method used by Faustova et ai. was to measure the rate of temperature rise of a small sample (1 to 3 g) plus the calorimeter, of a standard sample (aluminium oxide) plus the calorimeter, and of the empty calorimeter, all with a constant heat flow. This method is much less accurate than the adiabatic method. We believe that the comparison of the two sets of results indicates serious error in the results of Faustova et al. (12) Further investigation of the thermal properties of a-Na,UO, above 350 K will be needed to establish reasonably accurate tables of the thermodynamic properties of a-Na,UO, at higher temperatures. The authors acknowledge the careful chemical analysis of the cc-Na2U04 sample by K. Jensen. REFERENCES 1. O’Hare, P. A. G.; Shinn, W. A.; Mrazek, F. C.; Martin, A. E. J. Chem. Thermodynamics 1972, 4, 401.

2. 3. 4. 5. 6. 7. 8.

Osborne, D. W.; Flotow, H. E. J. Chem. Thermodynamics 1972,4, 411. Fredrickson, D. R.; Chasanov, M. G. J. Chem. Thermodynamics 1972,4,419. Battles, J. E.; Shinn, W. A.; Blackburn, P. E. J. Chem. l%ermodynamics 1972,4, 425. O’Hare, P. A. G.; Hoekstra, H. R. J. Chem. Thermodynamics 1973, 5, 769. Hoekstra, H. R. J. Znorg. Nucl. Chem. 1%5,27, 802. Flotow, H. E.; Klocek, E. E. Rev. Scient. Instrum. 1968, 39, 1578. Osborne, D. W.; Schreiner, F.; Flotow, H. E.; Maim, J. G. J. Gem. Phys. 1972,57,3401. Also see this paper for additional references on techniques and temperature scale. 9. JANAF Thermochemical Tables. The Dow Chemical Co. : Midland Michigan. June 30, 1962.

756 D. W. OSBORNE, H. E. FLOTOW, R. P. DALLINGER,

AND H. R. HOEKSTRA

10. Flotow, H. E.; L&r, H. R. J. Phys. Gem. 1960, 64, 904. 11. JANAF l%ermochemical Tables. The Dow ChemicalCo.: Midland, Michigan. September30, 1965.

12. Faustova,D. G.; Ippolitova, E. A.; Spitsyn,V. I. Issledovaniya v Oblasti Khimii Urana, Spitsyn, V. I.; editor. Izdatel’stvoMoskovskogoUniversiteta,l%l, 149.(U.S. Atomic EnergyCommission,ANL-Trans-33,p. 173.Englishtranslationavailablefrom the Clearinghouse for FederalScientificandTechnicalInformation,NationalBureauof Standards, U.S.Department of Commerce, Springfield,Virginia, U.S.A.).