A.J. ZIELEN
5022
sites in the metal and in which the hydrogen has exceptionally low energy. Experiment showss that the solvent power of a metal for hydrogen is enhanced by cold working. This undoubtedly results from the retention of atypical sites in the deformed metal which are energetically more favorable for hydrogen than those in the ideal lattice. Clearly no metal will be entirely free of such effects. Atypical sites will exist in any disturbed region in the lattice-at grain boundaries, along dislocations, adjacent to impurities, etc. With this viewpoint in mind the following sequence of events may be postulated. As the vanadium is hydrogenated, the low-energy, atypical sites will tend to be occupied first. This will lead to a higher than “normal” heat of vaporization a t high dilutions. However, as the amount of hydrogen is increased, the atypical sites become saturated and hydrogen will begin to enter the usual lattice sites and the normal trend for the heat of vaporization sets in. Of course, when there is preferential occupancy of sites, this is a t the expense of the entropy of the system and will tend to be discouraged the higher the temperature. For this reason and also because the importance of the heat of vaporization in comparison with the entropy of vaporization diminishes as temperature increases, the maxima in the isotherms in Fig. 1 are expected to become less pronounced the higher the temperature. This expectation is borne out by experiment. These considerations are, of course, relevant to the extrapolation procedure used to evaluate the thermodynamic properties of the system. They suggest that if data for the dissolving of hydrogen in “ideal” vanadium were desired, extrapolation should be made without regard to the fall in d P 7 N ~ a t the highest dilutions. It is not exactly clear how one would make such an extrapolation but regardless of how this might be done, it appears (9) D P Smith “Hydrogen in 2Ietals I’ress Chicago 111 1948,p 21
’ Uni\ersity
of Chlcaro
Vol. 81
that the thermodynamic properties so computed would not differ greatly from those obtained in the present work, except for the most dilute solutions. Another idea has been advanced to account for deviations from Sieverts’ Law such as have been observed for the present system a t hydrogen concentrations between 2 and about 25 atomic yo. For the Pd-H and Zr-H systems the negative departures from Sieverts’ Law have been attributed to attractive interactions between neighboring hydrogen atoms and these systems have been treated on this basis by statistical mechanical methods by Lacherlo and Rees.ll If the attractive interactions are the dominant factor, one expects a clustering of solute atoms a t low temperatures. The tendency for clustering is of course reduced as the temperature increases with the result that deviations from ideality are diminished correspondingly. Concurrently the destruction of the clusters produces a decrease in the heat of vaporization. Thus if the negative deviations originate with attractive interactions, one expects a significant change in the heat of vaporization with temperature, provided that the temperature range covered is large enough to produce an appreciable change in the magnitude of the observed deviations. This condition is fulfilled in the present study and the data show that within the limit of experimental error the heat of vaporization is invariant with temperature. Furthermore, if the solute atoms interact attractively, one expects the strongest dependence of heat of vaporization on coniposition to occur in the most concentrated solutions. Actually the converse is found to be the case. The heat of vaporization begins to level off when N His increased above about 0.2.7. Thus the observed behavior does not seem to be in accordance with that expected if attractive interactions between hydrogen atoms were the predominant factor. 110) J. R . Lacher, Pvoc. R O Y .SOC.( L o n d o n ) ,8 1 6 1 , ,523 (1937). (11) .4.I-. G,Rees, Tuaizs. F a r a d a y S P C . ,SO, .‘a35 (19.54). PITTSBIIRGH. PENNSYLVAKIA
____
- - -
[CONTRIBUTIOS FROM THE CHEMISTRY n I V I S I O N O F XRCONXE XATIONAL LABORATORY]
Thermodynamics of the Sulfate Complexes of Thorium1 BY A. J. ZIELEN RECEIVED APRIL 17, 1959 By use of the cation-exchange resin technique in perchloric w i d solutions at a n ionic strength of 2.00 and 25”, thorium(1V) was observed to associate with sulfate according t o the stepwise reactions: T h + & HSOa- = ThSOlC2 H + and ThS0,12 HSOl- = Th(SO4)2 H + with the association constants K I = 166 i 8 and K I = 21.7 zt 1.5. The heats and entropy changes of the reactions were determined calorimetrically with the results: AHl and AH, equal -0.54 & 0.05 and -0.89 =k 0.08 kcal./mole, respectively and A S , and AS, equal 8.4 f 0.2 and 3.2 i 0.3 cal. deg.-’ mole-’, respectively. The heat of ionization of bisulfate ion a t an ionic strength of 2.00 and 25’ was also measured calorimetrically with the result AH equals -5.54 i 0 , l i kcal./mole.
+
+
+
Introduction The complexing of aqueous thorium by inorganic ligands has received considerable attention in recent years,2 but certain aspects have been neg(1) Based on work performed under t h e auspices of t h e U. S. Atomic Energy Commission. (2) (a) H. W. Dodgen and G. K. Rollefson. THISJ O U R N A L , 71, 2000 (1949); (b) R. A . D a y a n d R . W. Stoughton, i b i d . , 72, 5662 (1950);
+
lected. A cursory examination of the literature has failed to reveal a single determination of the heats and entropies of complexing, and in addition nearly all colnplexing constants have been determined by (c) E. L. Zebroski, H. W. Alter and F. K. Heumann, ibid., 73, 5040 (1951); (d) ‘A’ C. Waggener a n d R . W. Stoughton, J . Phys. Chem., 66, 1 (1952); ( e ) V. V. Fomin and E. P. Maiorova, Zhzrr. S e o u g . Khim., 1,
1703 (1956).
Oct. 5 , 1959
THERMODYNAMICS OF THE SULFATE COMPLEXES OF THORIUX
the benzene-thenoyltrifluoroacetone (TTA) technique. Thus i t appeared desirable to employ an independent procedure as a check on the TTA extraction method and to combine the association constants so obtained with a calorimetric determination of the heats of complexing. The determination of complexing constants by cation exchangers has been well developed by Fronaeus3 and successfully employed in a number of systems. Due to extremely strong sorption on the resin, application of the method to a tetravalent ion presented certain experimental difficulties but in turn led to simplifications in treatment of the data. The final results indicate that the cation exchange technique should be generally applicable to the complex ion chemistry of thorium.
Experimental Cation-exchange Studies.-Distribution of thorium between t h e resin and solution phases was measured at constant thorium load on the resin as a function of varying sulfuric acid concentration. Two main series of experiments were carried out-the first at an equilibrium hydrogen ion concentration of 2.000 M (perchloric and sulfuric acids) and the second at equilibrium hydrogen and sodium ion concentrations each of 1.OOO 114 (perchloric acid-sulfuric acid-sodium perchlorate). These concentrations were calculated on the basis of the make-up solutions and took into account small corrections due t o the resin swelling factor and the dissociation of bisulfate. The thorium concentration of solutions was measured radiometrically by use of tracer Th-234 (UX1) added to Th232. Experiments employing carrier free UXI yielded erratic results undoubtedly due to adsorption on glass and resin surfaces. Since only a small fraction of the initial activity remained in solution after contact with the resin, i t was necessary to run counting determinations on a large sample. This was accomplished by use of a thin wall G-M tube especially designed for direct immersion in the radioactive solution (Mark 1, Model 81, Radiation Counter Laborato.~ calibrations with standard uranyl ries, I ~ c . ) Geometry nitrate solutions indicated t h a t 6.4% of all 2.32 mev. betas from UX, (1.1 min. Pa-234 daughter of UX1) were counted for 6.7-1111. samples. In each experiment 0.1 g. of resin and 8 ml. of appropriate sulfate solution were introduced into a 10-ml. stoppered erlenmeyer flask. A 0.300-ml. aliquot of tracer thorium then was added by means of a 1 ml. Gilmont Ultramicroburet. The initial concentration of carrier thorium in the resulting solution was about M . The flask was sealed, inserted in a special rubber container and agitated in a waterbath thermostated at 25.0 =!= 0.1" for a minimum period of 48 hr. Resin and solution phases were then quickly separated by passage through a sintered glass filter, and either direct or appropriately diluted 6.7-1111. samples of the solution were assayed for thorium radiometrically. Sufficient counts were obtained on each sample for a statistical standard deviation of 1% or less. All counting rates were corrected for the calibrated coincidence loss of the G M tube and mere then normalized to the same zero time on the basis of the 24.10 day half-life of UX1.5 Calorimetry.-After a number of minor modifications a twin calorimeter originally designed by Hatcher6 for a determination of the disintegration energy of tritium was employed in this work. The calorimeter proper consists of two soft glass commercial Thermos flasks of about 218-1111, capacity. I n operation the Dewar flasks are rigidly mounted and completely immersed in a water-bath thermostated t o f 0.01'. The flasks are sealed water tight by rubber stoppers under the pressure of thumb screws. Three inlet tubes uf Monel metal are permanently mounted in each stopper and provide housing for electrical heater, difference ther_____ (3) S Fronaeus, Acta Chem. Scand., 6 , 859 (1951); 6, 1200 (1952); 7 , 21 (1953); Suensk Kern. T i d s k r . , 64, 317 (1952); 65, 19 (1953). (4) For a good description of the use of a similar G h l tube see J. Rydberg, A c f a C h e m . Scand., 4, 1503 (1950). (5) G. B. Knight and R. L. Macklin, P h y s . Rev., 74, 1540 (1948). (6) J. B. Hatcher, unpublished d a t a , this Laboratory.
5023
mocouple and the centrally located stirring shaft The difference thermocouple consists, at each end, of 24 junctions of #38 copper and #30 constantan encased in thin wall gold tubing. The thermocouple gives approximately 1000 microvolt/degree and has a resistance of 127 ohms. T h e heaters each consist of about 94 ohms of #40 double glass insulated Manganin in double layer helical bifilar winding enca5ed in thin wall gold tubing. The heaters are provided with both voltage and current leads to provide a n accurate measurement of the resistance under working conditions. Both stirring shafts are actuated by the same sprocket chain driven by a small synchronous motor. By a simple mechanical eccentric the resultant motion of the shafts is alternate rotation of 360" in opposite directions a t a rate of 135 reversals/min. Each stirring shaft proper is a stainless steel rod encased in Monel tubing with agitation provided by small platinum paddles attached near the end. Reactant solutions (generally about 5 ml.) were introduced into the calorimetric solution by smashing fragile glass bulbs waxed to the end of the stirring shaft against a small glass anvil mounted on the base of the Dewar flask. For this purpose the stirring shafts were designed to allow a small amount of independent vertical movement. In this research the calorimeter was not employed as a twin system. One Dewar flask was filled with water taken directly from the thermostated bath and merely served as a convenient reference point for the difference thermocouple. The thermocouple output was measured with a Rubicon Six-Dial Thermofree Potentiometer conjunctive with a Model 14 Liston-Becker d.c. Breaker Amplifier and Varian Associates Model G-10 Graphic Recorder combined to serve as a null point indicator. The over-all performance of the equipment readily allowed detection of potential changes of 0.01 microvolt. Since the relative heat capacity of the chargedcalorimeter is about 0.2 cal./microvolt, this would apparently place the accuracy of a heat measurement at ztO.002 cal. However, errors introduced by the variable heat effects in breaking the sample bulb place the limiting uncertainty under favorable conditions at about f.0.01 tal.' In each calorimetric run weighed amounts of component stock solutions were added to the Dewar flask and sample bulb, giving a final solution volume of 200 ml. After an equilibration period of 2 or 3 hours, heats of reaction were measured at 25.0 =!= 0.1" using electrical heating to calibrate the heat capacity of the system immediately before and after breaking the sample bulb. T o convert concentrations t o the moles/l. scale, the density of the final solution was determined by weighing aliquots taken with a calibrated pipet. All heats are reported in terms of the defined calorie (1 cal. = 4.1840 abr. joules). ;Is a final check on the apparatus the heat of ionization of water was measured by adding 0.1 AI sodium hydroxide (sample bulb) to a slight excess of hydrochloric acid. Correcting t o standard state conditions with the appropriate heats of dilution,a two runs each with an observed heat between 7 and 8 cal. gave values for AH' of 13.342 and 13.335 kcal./mole. The close check is probably somewhat fortuitous but in satisfactory agreement with the literature value of 13.360 kcal.lmole.8 Materials.-Macro level stock solutions of thorium perchlorate were prepared by repeated fumings of reagent grade thorium nitrate in excess perchloric acid. The thorium content was determined by precipitation of the hydroxide and ignition to ThOz. The amount of excess perchloric acid was measured by passing samples through a cation exchanger column (Dowex-SO, hydrogen ion form) and titrating with standard base. The UX1 for each series of experiments was obtained by treating 1.3 kg. of uranyl nitrate hexahydrate with 1.5 1. of ether. T h e aqueous phase was drawn off, carrier thorium added and extracted with 0.5 M T T X in benzeue. The benzene phase was scrubbed repeatedly with 0.1 JI perchloric acid (9 or 10 times) until spot tests with sodium ferrocyanide indicated the aqueous phase free of uranyl ion. The T T A cycle was then repeated by extracting into 2 M perchloric (7) Six runs t o measure the heat of breaking sample bulbs filled with distilled water into distilled water gave a mean and standard deviation of 0 039 Zt 0.009 cal. evolved. A discussion of the uncertainties in the heat e f f w t sinvolved is presented by W. P. Hutchinson and A. G. White, J . Sci I i t s f r . , 32, 309 (1955). ( 8 ) "Selected Values of Chemical Thermodynamic Properties." National Bureau of Standards, Circular 500 (Feb. 1952).
5024
-1.J. ZIELEN
acid, precipitating the hydroxide, dissolving the precipitate in 0.1 M perchloric acid and extracting again with benzeneTTX. After 3 final scrubs with 0.1 M perchloric acid, the tracer stock solution was obtained by extraction into 2 M perchloric acid followed by two benzene scrubs to remove traces of T T A . Observations on the activity of a sample of this tracer carried out over a 45-day period indicated the half-life to be 24.2 =I=0.1 days (least squares with standard deviation) in good agreement with the literature value.6 The over-all yield of UX1 initially in secular equilibrium with the U-238 was about 7070. The cation exchanger employed was Analytical Grade AG 50-X12 processed from Dowex-50 by Bio Rad Laboratories, 200-400 mesh, capacity 5.0 meq./g. of dried resin. For the experiments in 2 M hydrogen ion the resin was repeatedly treated with a large excess of 2.000 M perchloric acid, thoroughly washed with water and dried a t 45". A mixed sodium-hydrogen ion form of the resin was prepared for the low acid experiments by a series of pre-equilibrations with a large excess of 1,000 Msodium perchlorate plus 1.000 Mperchloric acid. The resin then was washed and dried as above. Perchloric acid stock solutions were prepared by dilution of the G. F. Smith double vacuum distilled product and titration with standard base. Stock solutions of sodium perchlorate were prepared by neutralizing primary standard grade sodium carbonate with perchloric acid; the solutions were analyzed by gently evaporating aliquots to dryness, drying the residue for several hours a t 160" and weighing as NaClod. All other reagents were of C.P. grade and were used without additional purification. Triply distilled water was used to prepare all solutions.
Results and Discussion Cation-exchange Studies.-The necessary equations and conditions for the derivation of complexing constants from exchanger data have been presented by Fronaeus3 and need not be repeated here. Only minor modifications will be applied to Fronaeus's notation. The experimental results are presented in the form of the phase distribution function # = C ~ ~ R / where C ~ I CMRis the equilibrium total concentration of metal ion in the resin phase and C, the corresponding total metal ion concentration in solution. The resin load C ~ I R is evaluated from the equation CMR = (v/m)(CM' - CMS) (1) where v equals the volume of solution added to rn grams of resin. Primes applied to any symbol indicate a concentration (or counting rate) before the addition of resin. The resin swelling factor is represented by 6 ; and a t the 83 ml./g. value of v / m used in this research, 6 values of 0.996 and 0.993 were found, respectively, for the hydrogen ion form and mixed sodium-hydrogen ion form of the resin. These quantities were determined by the increase in hydrogen ion concentration of appropriate perchloric acid solutions after contact with the dried resin. Since all thorium concentrations were assayed a t constant geometry on a fixed sample, @ is calculated from the experimental data by .$ =
(v/m)(R' - R6)/R
(2)
where R represents the counting rate of the sample. The concentration of free ligand (considered here as HS04- S04-2) and the total ligand concentration are represented as [A] and C.4. Since in all runs
i
o!
1
I
I
0.5
I .O
1.5
l a
2 .o
X.
Fig. 2.-Graphic complexing.
presentation of the heats of thorium sulfate Intercept = - A H s and slope = - AHs.
Table V. =111 u values correspond to the 05yo confidence level with the exception of that due to Kd where again a 10% uncertainty was assumed.
SUMMARY OF
TABLE V ERRORANALYSISO F THE HEATS OF
COMPLEXING c of A H s .
r of A H s ,
kcal.
kcal.
Error due to
u of Qc
0.040 & ,002 & ,006 T ,031 ,051
(0.071)
u
81 (18) of p, ( 1 1 9 0 )
r7
Of K d
u of
*
(18) Itisinterestingtonotethattheleastsquaresanalysisindicated the standard deviation of Q. t o be 0 031 cal., which corresponds exactly t o t h e uncertainty listed for the "blank" correction.
-
(&1oc/,)
( z:U2)"P
0.042
F ,014
*
,011 i: ,046 ,065
TABLE VI SUMMARY OF THERMODYNAMIC QUANTITIESAT IONIC STREXGTH 2.00 A N D 25'
R,;z;l4 lo a
b 166 21.7 ll.g
* *
AF, AH, AS, kcal. kcal. e.u. -3,03 o , 0 3 -o,51 o,05 8 , 4 i o , l.5 -1.83 .04 -0.89 .3 lo%" -1.47 .06 .17 2 3 ' 5 .G
Units = l./mole.
*
*
*
* * *
*
*
w. E. HATTON, D. L. HILDENBRSND, G. c. SINKE AND D. R. STULL
3028
A final summary of the thermodynamic quantities for the sulfate complexes of thorium and the association of bisulfate ion is presented in Table VI. The values for the second complex correspond to the more conventional stepwise form of the reaction ThS04+2
+ HSO4-
=
Th(S04)Z
+ H+
(14)
Acknowledgments.-The author is indebted to Dr. James C. Hindman for the initial suggestion of
[COSTRIBUTION FROM
THE
Vol. 81
this research and many critical discussions throughout the entire work. Dr. Darrell W. Osborne provided helpful advice on the calorimetry problems and also made available the equipment for precision electrical heating. The technical assistance of Mr. Willard G. Greenhow in programming the majority of the least squares analyses for the GEORGE electronic digital computer was invaluable. LEMONT, ILLINOIS
THERMAL LABORATORY, THED O W CHEMICAL COMPANY]
The Chemical Thermodynamic Properties of Calcium Hydroxide BY W. E. HATTON, D. L. HILDENBRAND, G. C. SINKEAND D. R. STULL RECEIVED APRIL24, 1959 The heat capacity of crystalline calcium hydroxide was measured from 19 to 330°K. and the entropy a t 298.15*K(. calculated as 19.93 =t0.10 cal. deg.-' mole-'. The heat of dissociation was calculated from dissociation pressures by third law methods. The result is in excellent agreement with calorimetric values, indicating no residual entropy a t 0°K. Selected best values for the heat and free energy of formation a t 298.15'K. are -235.71 and -214.77 =t0.10 kcal. mole-', respectively.
Introduction Although an accurate value is available for the heat of dissociation of calcium hydroxide, the entropy listed by Kelley2 is based on fragmentary data. The free energy of formation calculated from dissociation pressures indicates Kelley's value to be too low. The entropy of calcium hydroxide therefore was determined by measurement of the heat capacity from 19 to 330'K.
TABLE I
THEHEATCAPACITY OF CALCIUM HYDROXIDE, CAL.MOLE-' DEG.-I T,
O K .
CP
Series I 0.177 18.85 ,268 .352 ,505 ,671
T.
OK.
159.46 170.25 175.35 181.34 188.21 194.92 201.50 207.98 214.36
CP
13.63 14.35 14.83 15.17 15.64 16.08 16.47 16.86 17.17
T,
O K .
136.07 140.62 145.06 150.42 156.65 162.67 168.52 174.24 179.86 185.38 190.82 196.84 203.44 209.94 216.35 222.68 228.92 247.18 283.17 259.09 264.96 270. 78 276.55 282.28 287.96 294.16 300.86 307.87 315.18 322.43 329.62
CP
11.60 12.02 12.50 12.74 13.39 13.5 14.29 14.68 15.17 15.48 15.84 16.21 16.54 17.00 17.33 17.68 18.08 18.85 19.15 19.41 19.63 19.88 20.07 20.31 20.54 20.75 21.06 21.35 21.61 21.80 22.10
Calcium hydroxide was prepared by calcining hIallinckrodt Analytical Reagent calcium carbonate and treating the resulting oxide with a stoichiometric amount of water. Analysis indicated the sample to be 99.7570 calcium hydroxide with the remainder calcium carbonate and water. The purity was considered adequate for heat capacity purposes. An X-ray diffraction pattern indicated the sample to be crystalline. Heat capacity measurements were made over the range 19 t o 330°K. with an automatically operated adiabatic calorimeter that has been described previously.3,4 A sample weighing 39.010 g. corrected t o vacuum, was sealed in a nickel-plated copper calorimeter under one atmosphere pressure of helium gas a t room temperature. The filling and sealing operation were done under anhydrous, Con-free conditions so as to avoid contamination of the sample. The experimental heat capacity data are given in Table I. Temperatures and temperature differences were measured with a platinum resistance thermometer ( K O= 96 ohms) calibrated by comparison with an hT.B.S.calibrated platinum thermometer. Temperature rises were approximately 10% of the absolute temperature below 50°K. and 5 to 7% a t higher temperatures. Corrections for curvature were not applied, nor should they be necessary with intervals of this size. The heat capacities are believed t o be accurate t o within 0.2 t o 0.3y0 above 50°K. and t o within 1% a t lower temperatures. The accuracy estimates are based on the results of a series of check measurements on a heat capacity standard! as well as on the results of several inter-laboratory comparisons. Results are given in terms of the defined thermochemical calorie, equal to 4.1840 abs. joules. T h e ice point
21.27 23. 76 26.49 29.81 33.26 36.90 41.26 45.79 50.04 54.28 59,05 63.93 68.30 71.72 76.89 83.03 88.68 03.92 98.89 103.61 108.15 112.52 116.75 120.86 124.85 130.01 136.27 142.33 148.22 153.93
(1) K. Taylor and L. S . Nells, J . Research A'afl. Bur. Standards, 21, 133 (1938). (2) K. K. Kelley, U. S. Bur. Mines Bull. 477, 1950. (3) D. R.Stull, Anal. Chim. Acta, 17, 133 (1957). (4) D. L. Hildenbrand, W. R. Kramer, R. A. McDonald and D. R. Stull, THISJOURNAL, 80, 4129 (1958).
was taken as 273.15"K. and the molecular weight of calcium hydroxide as 74.096. T h e entropy, free energy and heat content functions of crystalline calcium hydroxide, obtained by graphical integration of the heat capacity data, are listed a t even tempera-
Experimental
,887 1.185 1.466 1.867 2.211 2.677 3,158 3.677 4.257 4.477 5.040 5.814 6.492 6.975 7.778 8.205 8.699 9 . 171 9.587 10.03 10.40 10.93 11.62 12.09 12.62 13.16
Series I1 22.91 0.312 .448 25.92 ,608 28.95 .862 32.02 1.029 35.24 1.310 38.77 42.84 1.577 1.944 47.54 2,378 52.61 2.952 57.84 3.623 63.33 4.263 69.12 4.856 75.18 5.590 81.01 6.322 87.22 8.440 105.78 9.108 111.30 9.630 116.59 121.69 10.13 126.62 10.67 131.41 11.11
