NOTES
Mass UCI.,,
Moss U.
B.
rng.
Energy equiv.. cal./dea.
AT, ‘IC.
Energy Viring fr~llll energy, T’CZ. cal./n. cnl.
lhv.
Sample I 78.52 76.27 75..55 75.29 76.34 80 15 76 03 75 4 5
1.5131 1.6617 1 ,6669 1.7288 1.4756 1 . 8498 1.4774 1.7381
2393 6 2394 3 2394.2 2894.2 2394.2 2394.3 2394.3
1.1090 1.2178 1.2295 1.26.44 1.0377 1.2006 1.1062 1.2781
2394.3
1.3 1.3 1.1 1.1
1.1 1.2 0.9 1.4 AV.
1693.6 1708.9 1718.1 1703.7 1707.8 16‘33.3
16.4 1.1 8.1 6.3 2.2 16.7
1733.2 1722.3
22.2
1710.0
2 X standard dev.
12.3 10.7 g.6
Sample 11 122.12 113.32 108.10 117.48
1,5592 1.5080 1.5542 1 3714
2394.8 2394.6 2394.6 2304.5
1.1754 1.1313 1.1618 1.0356
1.7 1.7 1 8
1.8 AV. 2 X standard dev.
1729.0 1719.7 1721.1 1711.0 1720.2
8.8 0.5 0.9 9.2 4.9 7.4
Sample I 1 with UO2 0.7360 ,8354 .82095 .8405
17.2995 16.2635 15.1206 1 7 ,1308
61 10 57 36
56.68 52.18
1.3 0.9 1.1863 0 . 9 1.2873 1.0 A\.. 2 X standard dev.
2391.6 2391.6 2391.6 2391.7
1.2118 1.2305
1700.4 1697.2 1700.0 1703.0 1700.4
0.0 3.2 0.4 3.5 1.8 2.7
The calculated valucs of the heats of formation for the three series of runs were: for sample I, A H f = - 1!1.7 f 2.0; for sample 11, -18.6 1.95; and for sample I1 burned with UO,, -21.1 f 1.4 kcal./molc. The uncertainties at1ached to these values include the uncertainties in the caloriiiietric nie~surenientsand i l l thc energy equivalent of thc calorimeter, both expressed as twice the standard deviation, combined with the uiicertainties in the ainounts of impurities and the uncertainties in the heats of formation of the corresponding oxides. Bccausc sample I1 was of higher purity than sample I, and because tlic combustions with KO? were 100yo complete and the oxide formcd was more probably U30s than in the combustion without UOZ, the 1.4 kcal./mole is taken for the vnluc AHf = -21.1 heat of formation of UC1.90. This value is the same, within the uncertaint ics iiivolvcd, as the value obtained for (lie heat of formation of CC.13 I+:stimated values in the literature arc those of S.B.S. Circular 500,l5 - 42 kcnl.,’mole; Kubaschewski and FJvans,16 8 kcal./mole; -38.8 kcal./niolc; Krikorian,!’ -27 - 30 kcal./mole. and Rand and Kuba~chen-ski,~ Acknowledgments-The authors acknowledge the valuablc assistance of C. G. Hoffman, metallographic analysis; and G. C. Heasley, G. B. Eelson, and Helen D. Cowan, chemical analysis.
*
*
*
Appendix The difficulty of preparing stoichiometric UlO8 is well known. For much the same reasons, the determination of the formula of a uranium oxide is difficult unless the uranium content is accurately known. The following experiment shows that within an uncertainty of a few units in the third dccininl place, the oxidation (15) “Selected Values of Chemical Thermodynamic Propertiep,” N.B.S. Circular 500, 1952, p. 362. (16) 0. Kubaschewski a n d E. I,. Evans, “Metallurgical Thermochemistrv,” 2nd Eli., Peraninon l’rew. I,on(lon, 1958, p. 278. (17) 0. H. Krikoiinn, “Hiah Temperature Studies. Part 11. Thermodynamic Properties of the Carbides,” University of Cnlifornin Radirtion Laboratory Report, UCRL-2888, April, 1956.
1731
of UO, in oxygen under such conditions that it ignites, followcd by cooling in oxygen, leads to u308. piccv of uranium nictal sheet (90.9870 U, 0 01% C:, 0.01yo othcr metals) weigliiiig 7.3747 g. \vas oxidized slo~vlyin oxygen as the tcnipcrature was iaised to 1000° aiid then lowered to givc :ti1 oxide weighing 8.7C01 g. arid having the formula IJ02.689. ‘l’his was then reduced a t 1000° with CO to give an oxide weighing 8.3607 g. and btlr-ing the formula C;02.00~.Finally, this was tlurned in oxygen so that it ignited and glowed, and then cooled in oxygen, giving an oxide weighing 8.GIGl g. and having the formula L 0 2 . 6 6 9 . In a similar experiment, the combustion product from a calorimetric experiment on a 1;C1.9-UOz mixture weighing about 17 g. was heatcd in oxygen a t 750’ with no resultant change in weight. It was then reduced with CO and reoxidized with oxygen. The final weight was 2 mg. less than the starting weight. Therefore, i t was concluded that the combustion product was very or U308. close to U02.66i
THE HEAT OF FORML4TIO?r’OF SCllNDIUiLI OXIDE’ BY ELMERJ. HUBER,JR.,GEORGE C. FITZGIBBON, EARL L. HEAD,ASD CHARLES E. HOLLEY, JR. Unrnerstty of Calt/ornta, Loa Alamos Sczenttfic Laboratory, Lo8 Alamoa, Mew Mezreo Received March 11, 1065
The heats of formation of the oxides of the metals of groups IA and IIA increase with decreasing atomic number. This tendency also appears in group IIIA for Laz03and Y203. The heat of formation of ScZO3is of considerable interest because, if its heat of formation should be larger than that of Y&, it would be the oxide with the highest heat of formation per oxygen atom. The authors reported a preliminary value for the heat of formation of SczOa as AHzeg0 = -456.23 0.55 kcal./ m o k 2 This value was based on experiments in which scandium metal was burned on impurc scandium oxide disks, and the scandium oxide combustion product did not have the right lattice size. These experiments have now been supplemented by combustion on purified scandium oxide disks, and experiment,s have been done on the heat of solution of scandium metal and scandium oxide.
*
Experimental Scandium Metal.-Scandium oxide obtained from the 1,ahol atoire des Terres Itares, Paris, France, wm purified by the thiocyanate method of Fischer and Bock.$ Metal was prepared from this purified oxide by the Ames Laboratory, A.E.C., through the courtesy of Dr. F. N.Spedding. It was found by analysis to contain the following per cent impurities: C, 0.062; H, 0.0085; 0, 0.0375; N, 0.0075; Ta, 0.009; M g , 0.01; AI, 0.05; a n d Y , 0.05. No other metallic impurities were detected. The total impurities amount to about 0.24%. An X-ray pattern revealed hexagonal Sc only with no impurities. A metallographic examination showed unidentified i m p ities a t the grain boundaries. If it is assumed that the C, H, 0, and N are combined with scandium as the carbide, hydride, oxide, and nitride, the scandlurn is 09.51 mole 70metal (atomic weight of Yc = 44.96). Combustion of Scandium.-The method, which involves tti I
(1) Work done under the a1ispicps of the Atomio Eneigy Commission. (2) E. J. Huber, Jr.. and C. 1:. ?Idle),, Jr., “l*:xperimental Thorrnoclirmr+ trq,” Vol. 2, €1. .{ f3kinnc.r. Cd , In’ersclci c r I’ublishert, I n c , S r w York. N. Y , 1962. Chapter 5 , p 89 (3) W.Fischor nnd R. Bock, Z. arroio. allgem. Ciiem., 249, 146
(1942).
NOTES
1732
determination of the heat evolved from the combustion of a weighed sample of the metal in a bomb calorimeter a t a known initial pressure of oxygen, has been d e ~ c r i b e d . ~The same units and conventions are used here. The scandium was burned on sintered disks of SczOain oxygen a t 25 atm. pressure. The metal did not gain weight when exposed to this pressure for 1 hr. Ignition was by means of a magnesium fuse wire. Completeness of combustion was determined by dissolving the combustion products in hydrochloric acid solution, measuring the amount of gas formed, and analyzing the gas for hydrogen with a mass spectrograph. The average initial temperature for the runs was 24.9'. The results are listed in Table I. The fmt 10 runs were done on impure Scz03 d i s h which contained a few per cent of Tho2. The completeness of coinbustion varied between 99.03 and 100.00%. The last three runs were done on purified sCzo3 disks. For these three runs, the completeness of combustion was 97.4,94.0, and 93.5%, respectively. No satisfactory explanation for this difference is readily available. The scandium oxide from the first 10 runs had a lattice conwhich is high. This is believed to be due stant of about 9.948 i., to Tho2 from the impure disk dissolving in the molten Scz03from the combustion. From the last three runs the lattice constant was 9.8450 f 0.0003 A. The average value of 5056.1 i 4.6 cal./g. for the heat of combustion must be corrected for the impurities present.
Vol. 67
which is estimated at O.OGYo. The combined uncertainty is 0.12% or 5.6 cal./g., which does not include the possibility that the COZ, H20, and NO2 may react with the ScZO3. The value for tlie heat of combustion of 2 moles of Sc is 455.18 f 0.50 kcal. under bomb conditions. Heat of Solution of Scandium.-The heat of solution of scandium metal was measured in a solution of HCl which contained a small amount of NaeSiFa. The latter compound was used as a solution aid for ScsOsand was present in the Sc metal experiments so that the final solution would be the same in both cases. The solution calorimeter has been described.6 The same metal was used as for the combustion experiments. The solvent was saturated with hydrogen before the start of the experiment, and the atmosphere above the solution was hydrogen. The metal was contained in a small Pyrex glass ampoule which mas broken to start the reaction. The results of five experiment's are shown in Table 11. TABLE I1 THEHEATO F SOLUTION O F SClRDIUV METSL Solvent: 4.020 il.1HCl plus 200 mg. of KazSiFe
TABLE I THEHEATO F COMBUSTION O F Mass of So burned, g.
0.4460 ,5937 .5414 .5808 .5419 .4881 ,5096 .5649 .5223 .5113 .5150 ,5199 ,5448
Wt.
Wt. of
of Mg, Sczoi, mg. p.
6.05 6.05 8.03 6.01 6.53 5 93 6.93 7.02 6.02 5.94 6.50 6.67 6.82
24.7 16.8 17.0 16.9 16.8 16.8 17.1 16.9 16.3 16.8 15.1 17.4 18 0
Energy equiv., cal./ deg.a
2397.0 2394.8 2394.9 2394.8 2394 8 2394 8 2394.9 2394.8 2394.7 2394.8 2394.3 2395.0 2395.1
AT,
"K.
0.9602 1.2720 1.1636 1.2473 1.1631 1.0453 1.0951 1.2123 1.1195 1.0981 1.1032 1.1147 1.1687
SC-4NDIUv
Energy from Firing, So, cal. oal./g.
5 9 9.7 6.0 4.7 5.2 6.1 6.8 6.7 7.0 6.5 4.9 5.3 4 2
5067.1 5054.5 5059.5 5073.8 5059.3 5044.4 5053.0 5054.2 5051.4 5061.4 5044.9 5048.8 5056.9
Dev. from mean, oal./g.
Mass of s o dissolved,
11.0 1.6 3.4 17.7 3.2 11.7 3.1 1.9 4.7 5.3 11.2 7.3 0.8
g.
Mass of solvent, g.
Energy equis., cal./ arbitrary unit
Temp. rise, arbitrary units
Energy from So, oal./g.
0.12962 .13012 ,13048 ,13027 ,13078
383.88 385.35 386.42 385.80 387.31
15.257 15.278 15.258 15.290 15.335
28.335 28.395 28.515 28.395 28.475
3335.1 3333.9 3334.4 3333.2 3338.9 __
Av. 3335.1 Cor. for HzO evap.
Dev., oal./g.
0 1.2 0.7 1.9 3.8 1.5
15.6
Heat of soh. of Sc metal 3350.7 2 x stand. dev.
2.0
Correction for Impurities.-The calculated percentage composition of the scandium by weight is Sc metal, 99.37; ScH2, 0.19; Sc208, 0.11; ScN, 0.03; ScC2, 0.18; Tal 0.01; Mg, 0.01; AI, 0.05; Y, 0.05. The heat of combustion of Sc metal corrected for impurities is 5062.1 f 5.6 cal./g., or 0.12y0larger than the uncorrected value.5 This value would be decreased by 0.06% if the combustion products, COZ, H20, and NO2, were assumed to react with the Sc203 to form Scz(COa)a,SC(OH)~, and sC(n'o&. This is not believed to occur because of the rather unreactive nature of fired Sc2Oa. The uncertainty attached to this corrected value includes the uncertainty in the energy equivalent of the calorimeter, which is 0.04yc, the uncertainty in the calorimetric measurements, 4.6 cal./g. or 0.09%) and the uncertainty in the correction for the impurities,
The average value for the five experiments is 3350.7 2.0 cal./g. for the heat of solution of this scandium metal in this solvent. When corrected for tlie presence of impurities, this becomes 3359.2 f 5.7 cal./g , or 151.02 f 0.26 kcal./mole, where the uncertainty includes an estimated uncertainty of 0.16% in the correction for the impurities.' The Heat of Solution of Scandium Oxide.-Scandium oxide as ordinarily prepared by ignition of the oxalate to 1000-1100" is only slowly soluble in HC1 solutions, even in the presence of fluorosilicate ion. If, however, the oxide is prepared by igiiitioii at only GOO", it will dissolve rapidly enough in the presence of fluorosilicate ion to be used in the experiments. Prepared in this manner it is about 99.2% Sc203, with the impurit,ies probably being oxalate fragments plus some excess carbon.8 The heat of solution of this scandium oxide was measured in the same solvent as for the scandium metal including the saturation of the solvent n-ith hydrogen and the presence of a hydrogen atmosphere above it. An amount of SczO3 was used so that the concentration
(4) E. J. Huber, Jr., C. 0. RIatthews, a n d C . E. Holley, Jr., J . Am. Chem. Soc., 77,6493 (1956). (5) The heat of formation of SoHz is taken a5 -52 kcal./mole. T h a t of SON IS estimated a t - 7 5 koal./mole, a n d of ScCm a t -30 kcal./mole. The heat8 of combustion of RIg, Al, Y, a n d T a are taken as 5900,7400,2660, a n d 1,460 cal./g., respectively. The heate of formation of HaO(g) and NOa m e taken an -68 a n d +8 koal,/mole.
(6) G. C. Fitzgibbon, E. J. Huber, Jr., a n d C. E. Holley, Jr., "A Ne,\ Solution Calorimeter." Lo5 Alamos Boienufic Laboratory, L A Report, .n preparation. (7) H. Bommer a n d E. Hohmann, 2. anorg. allgem. Chem., 248, 3,57 (1941),give 149.0 j, 0.7 kcal./mole for the heat of solution of scendluin metal i n dilute hydroohloric arid eolntion. (8) E. L, Head and C,E, Holley, Jr,, to be publishad,
f
a
$v. 5056.1 6.4 2 X standard dev. 4.6 The specific heat of SczO3 is estimated a t 0.066 cal./g./deg.
KOTES
August, 1963 of scandium in the final solution mould be the same as in the final solution from the metal. The results of five runs are shown in Table 111. The final average value is 348.6 f 3.0 cal./g., or 48.7 f 0.4 kcal./mole. This value is not correct because of the impurities in the s c ~ o 3 ;however, the state of the impurities is not known and a correction for them is not possible. The value given should be regarded as a lower limit on the heat evolved because the impurities probably mould have a smaller heat of solution than the oxide. THEHEATOF SOLUTION OF SCANDIUM OXIDE Solvent: 4.020 M HCl plus 200 mg. of NazSiFB Energy
Mass of solvent,
equiv., cal./
g.
g.
arbitrary unit
0,19576 ,20006 .19966 .19918 ,19997
377.99 386.29 385.52 384.59 386.12
15.003 15.345 15.270 15.270 15.250
FURTHER REMARKS ON THE “RATEQUOTIENT LhFI7”’
Temp. rise, arbitrary units
Energy from
sc&, cal./g.
Deviation, cal./g.
Department of Chemistry, Gnaverszty of North Carolma, Chapel HzZZ, North Carolina
4.515 4.587 4.540 4.597 4.531
346.0 351.9 347.2 352.5 345.4
2.6 3.3 1.4 3.9 3.2 2.9 3.0
li’eceaned February 4> ID03
___
Av. 348.6 2 X stand. dev.
BY 0. K. RICE
The Heat of Formation of Sc20a.-Usiiig methods already d e ~ c r i b e d ,the ~ heat of formation of cubic ScZO3is calculated from the combustion results to be AHor2980~ = -456.16 :k 0.50 kcal./mole. From the heat of solution measurements the heat of formation of Sc903 may be calculated as
+
6HC1(4.020 M ) + 2Sc 2SCc13(0.0080 M ) 3Hz
+
AH = -302.04
3Hz
+ 1.502
--3
i. 0.52
kcal.
3H20(liq.) AH = -204.95 kca>l.
+
SH20(liq.)+ 2ScCl3(O.O08OM ) sCzo3 6HC1(4.020 M )
+
AH = 48.7
25c
f
1.602
results indicate that the discrepancy was caused by the &4lundum. This new value for the heat of formation of scandium oxide is the same as the value for yttrium oxide, -455.46 A 0.54 kcal./mole,ll within the experimental uncertainties involved. Acknowledgments.-The authors acknowledge the valuable assistance of D. Pavone, F. H. Rlliiiger, 0. R. Simi, and R. M. Douglass in the analytical work. (11) E. J. Huber, Jr., E. L. Head, and C . E. Holley, Jr., .I. Phys. Chem., 61, 497 (1957).
TABLE I11
Mass of sczo3 dissolved,
1733
sc203 AH = -458.3
* 0.4 kcal.
* 0.7 kcal,
Because the heat of solution of the Scz03 is a minimum value, this calculated heat of formation is a maximum value. The difference between the two values, 2 kcal., may be attribuled in part, a t least, to the impurity of the ScZO3used in the heat of solution experiments, and the combustion value s;hould be more nearly correct. This value of -456.16 f 0.50 kcal./mole is to be compared with AHor29p = -447.28 f 0.23 kcal./mole reported by Mah.g I n her work the combustion was carried out on AiiunduIn instead of on sCzo3. Because of this discrepancy, Mrs. Mah did some experiments on scandium metal supplied by us. She obtained 5065.0 cal./g.I0 when the combustion was carried out on a scandium oxide liner. ‘This value falls within our range of values. She obtained 4964.3 cal./g. when the combustion was carried out on an Alundum disk, checking her previously published value of 4964.2 cal./g. These (9) A. D. Mab, U. $5. Bur. Mines Report Invest. 596.5 (1962). (10; A. D. Mah, private comrnunicacion.
In a recent publication, Pritchard2 considers the effect upon the rate of dissociation of a diatomic molecule arising from a “bottleneck” with respect to quantum jumps up the vibrational ladder. He believes the possible presence of a bottleneck could vitiate the argument which this author gave,3 indicating the equality between the equilibrium constant for association of atoms and dissociation of diatomic molecules and the quotient of the rate constants (to which the author will refer as the “rate-quotient lam”), even under conditions such that equilibrium quotas were not maintained in some of the excited vibrational levels. One of the essential bases of this author’s argument was the assumption that activatioii and deactivation were rapid processes compared to reaction, which meant that the vibrational relaxation of the diatomic molecule was supposed rapid compared with the rate of reaction. The author quoted data4 which indicated that under ordinary circumstances this condition is fulfilled. Recently, Camac and Vaughan5 have investigated the dissociation of 0 2 up to 8000°, where the time for attainment of equilibrium between vibration and translation is of the same order of magnitude as the time required for dissociation. In this case, they find it impossible to analyze the data so as to determine a rate constant for dissociation, as is to be expected, but the normal situation is that relaxation is fast compared to reaction. The data for relaxation in shock waves are, however, presumably sensitive only to relaxation of some of the lower vibrational levels, and a bottleneck is something which might hinder the relaxation of the higher vibrational levels. Pritohard’s argument, therefore, requires some further consideration. Pritchard’s bottleneck arises not from any decrease in the rate of transition as the vibrational energy level increases, because the probability of such transitions is assumed to increase as the vibrational quantum number goes up. Actually, it arises from the decrease in population due to the Boltzmann factor, which, coupled with the increase in the rate of the quantum jumps, might conceivably mean Ihat a minimum transition rate (1) R7ork supported by the Natlonal Science Foundation. (2) H. 0. Pritchnrd, J . P h y s C I m . 66, 2111 (1982) ( 3 ) 0. I
