522
C. A. KRIER,R. S.
C R A I Q AND
W. E. WALLACE
VOl. 01
LO\V TEfiCPI3€iATUKEHEAT CAPACITIES AND RELATED PROPEIlTIES OF POTASSIUM AND Na21C1*2 BY C. A. KRIER,R. S. CRAIGAND W. E. WALLACE Contribution No. 999 from the Departrnent of Chemistry, University of Pittsburgh, Pihhurgh, Pa. Rscsivad AUQU8l84, 1068
c
C’onshnt pressure heat capacities between 12 and 320°K. are ryented for potassium and an alloy of composition NaaK.
T h e Nn?Il-IC elitseetic point was established to be -12.65 f 0.11 , and the incongruent melting point or meritectic oint for No& was cshblished to be 6.90f 0.00”. From the heat capacity data the entropies at 273.16 and 298.16”K., rehive Lo n1)soliite zero, are foiind to be, 14.77 f 0.03 and 15.38 i 0.03 e.u./g. atom for potassium, and 12.48 f 0.02 and 16.07 f 0.03 o.u./g. atom for NnzIC, respectively. A residual entropy for NazK a t absolute zero was est,irnated, assuming an ideal vn!ropy of mining, to be -0.05 e.u./g. atom; this rcsult suggests that the entropy of formation of NazK exceeds the ideal mixing entropy. No low tem erature “transition anomalies” of the type re orted for sodium, rubidium and cesium were
dctccted. Anomalous rising ofthe heat capacit of NazK about 100 degrees h o w the incongruont melting point, as found for tho p y e metals, indicates that the cause of tge excess heat capacit is not the open structure of the body-centered cubic lattice. r h e alloy deviates negatively from the Kopp-Neumann rule %elow50°K.and in II positive manner thereafter.
Introduction The present study is part of a continuing series of investigations being carried out in this Laboratory dealing with the thermodynamics of metallic elements and selected intermediate phasesa8 NalK wm selected for inclusion in the group of studies becaiiye it seems to be an excellent example of a size stabilized compound. In addition the thermal and electrical properties of sodium and potassium exhibit a number of peculiaaities, and there waa hope that a study of the thermal properties of the alloy might further our understanding of the behavior of these elements. There are at least three unuRual properties of the alkali metals. First, the consbant volume heat capacities of sodium and potassium begin t o exceed the Dulong-Petit limit a t 240 and 150”K., respectively. Second, Dauphinee, MacDonald and Preston-ThomasS have shown that sodium in the Dry Ice range exhibits a specific heat anomaly which depends upon the thermal history of the sample. Third, MacDonald6 has pointed out that potassium, riibidiurn and cesium have resifitancetemperature characteristics between 150 and 2OO01I.which are time dependent. These phenomena clearly indicate complexities with the alkali metals which are not in accord with the usual concepts of these substances as simple and well understood metals. MacDonald’s resistance measurements suggested the possibility of a heat capacity anomaly in potassium around 175°K. This possibility, the paucity of reliable heat capacity data f o r potassium, and the need for such data in connection with the study of Na2K were the factors responsible for the dccision to redetermine the heat capacity of potassium over the range covered in the present work. (1) From a thesis submittrrl by C. A. Icricr in partial fulfillment
of the requirements for the Ph.l). degree at the University of Pittsburgh, January, 1955. (2) This work waa nsaistcd by the U. 8. Atomic Energy Commiedon. (3) L. W. Coffer, R . 8.Craig, C. A . Krirr and W. E. Wallace, J . A m . Chem. Soc., 76, 241 (1954). (4) B. Chalmcrs. “Progress in Metal Physics,” Vol. I, Intrrsoience Publishers, Now York, N . Y . , 1949, Chapter 1 by 0.V. Raynor, “Progress in Theory of Alloys,” p. 34. (5) T. M. Dauphince, D . K. C. hIacDonald and II. Preston-Thomas, Proc. Roy. Soc. (London),22lA, 267 (1954). (6) D.K . C. MacDonald, Phil. Mav., 48, 479 (1952).
Experimental Aspects
A
paratus Used.-The equipment and technique were, in e!t main, the same as have been in use in this Laboratory for several years.’ The only change necessary was to adapt the sample container to accommodate reactive metals. Ordinarily the sample container is sealed in the open. This practice cannot be followed in the present instance due to atmospheric attack of the samples. Accordingly an inner container was provided which held the potassium or Na& and which was sealed off under an atmosphere d helium in a special “dr -box” arran ement.8 The inner container was a cylindricarcop er vesseflwith a monel top and bottom. It was provided wit{ a tapered hole lying along the axie of the cylinder and extending entirely through it. The trrpered in of the regular sample container fitted into the taperecf h d e . The tapered pin was lubricated with a small amount of ApieBon grease to assist in making a good thermal bond between the inner container and the sample container. Further constructional details of the inner container are given elsewhere.# After the sample had been introduced into the inner container (the sample being liquid in each case as i t was introduced), and that container sealed, all under an atmos here of purified helium, the inner container was placezin the regular sample container and sealed in the usual way. I t was of course necessary to recalibrate the sample container with the inner container in place. The recalibration consisted of 109 determinations of the heat capacity of the empty calorimeter extending from 10 to 325°K. Preparation of Materials.-The starting materials for the samples were a pound of nominally pure potasRium and a pound of sodium-potassium a110 (approximately 44% by weight potassium). Thew were d k a t e d hy the Mine Safety Appliances Company of Cnllery, Pa.1o The potassium was triple distilled under high vacuum in an all-Pyrex still and only the first 40% of the material distilling over was retained for use. The purified potassium was a sample having a volume of 250 cm.8. Portions of this were used for the determinations on pure potamium and for preparing the sample of NazK. To ascertain the extent of the impurities present, small samples of the pure metal and the alloy were converted to the rhloride and analyzed in this state spectroscopically. Metallic impurities, other than tin, a!uminum, boron and silicon were found to be present only in spectroscopic traces. It seems fairly certain that these four elements, which were present in only slightly greater amounts, were introduced in the process of converting the metals into salts. Further details of the analysis are iven elsewhere.0 T t e bulk supply of alloy had a composition of approximately 44% potassium by weight whereas the percentage of (7) R. 8. Craig, C. A . Krier, L. W. Coffer, E. A. Bates and W. E. Wallace, J . A m . Chem. Sac.. 1 6 , 238 (1954). (8) E. E. Ketchen, F. A . Trumbore, W. E. Wallace and R. 8. Craig, Rev. Sci. Inelrumenls, 20, 524 (1949). (9) C. A. Krier. Ph. D . Dissertation, University of Pittsburgh, 1955. (10) The authors acknowledge with thanks the coeperation of Dr. C. B. Jackson in obtaining the samples.
May, 1057
HEATCAPACITIES AND RELATED PROPERTIES OF K
potassium in NazK is 45.96. T o facilitate the preparation of Na&, a portion of the bulk supply was enriched with potassium to a percentage of about 47. The compositions of these two stock alloys were then determined to be 47.44 i 0.02 and 42.95 i 0.04 weight 7' potassium by converting weighed samples into the chloride. Appropriate volumes of the two stock solutions were mixed under helium to give an alloy of composition Na2K. The prepared sample was analyzed in two ways, by conversion to the chloride and with a flame photometer. The results obtained by these two independent schemes of analysis were 46.07 f 0.02 and 46.08 i 0.16 weight % potassium, respectively. The NaeK sample therefore contained a slight excess of potassium, 0.0030 3=0.0006 gram atom out of a total of 2.0027 gram atoms of sodium and potassium. The presence of excess potassium in the sample also could be demonstrated calorimetrically. The calorimetric equipnient was used to determine cooling curves in the usual way and an arrest a t -12.65 i 0.01' was observed. This temperature corresponds to the Na2K-K eutectic point.11 It was a simple matter to determine the energy associated with this arrest, which was found to be 2.44 cal. From this it was poseible to estimate the amount of excess potassium present in the sample as 0.0018 gram atom. However, this comYtation involves the heat of mixing of the supercooled iquid metals, a quantit which is very imperfectly known, so that the estimate of txe potassium excess obtained in this way may be in error b as much as 50%: If this is borne in mind, it is seen that t l e thermal and analytical methods are in substantial agreement as regards the excess of potassium in the sample. Synthesis of NazK.-The preparation of the intermediate phase NatK, which is the stable form of the system below 7O, presented some difficulties. Above 20" NazK is liquid; on cooling, sodium begins to precipitate out at 2! . NazK forms by a meritectic reaction beginning a t 7 . If this reaction is not allowed to run to completion, the system below 7" consists of NaaK plus a mixture of sodium and potassium. The magnitude of the heat effect at the eutectic temperature can be used to estimate the degree of completion of the reaction. I n the earl attempts there was a comparatively large heat effect at t l e eutectic point indicating the reaction to be far from completion. The preliminary work indicated that to effect a complete transformation i t was necessary to cool through the two-phase region (20 to 7") as rapidly as possible. Under these conditions the precipitated sodium is well dispersed and the meritectic reaction occurs at a maximum rate. If the cooling through the twophase region is slow, the sodium particles a parently increase in size to the point that completion o r t h e reaction cannot be achieved in a length of time which is experimentally feasible. I n the technique which proved to be successful the sample was cooled using liquid nitrogen. With this procedure, its temperature dro ed to the meritectic oint in less than 9 min. and to 198°K in a total of 70 min. t! was then raised to 272°K. and kept there for six hours with the adiabatic shield control, and was kept an additional 37 hours at temperatures between 265 and 275°K. Since heat is evolved as NaZK forms, i t was possible to ascertain whether the reaction was still under way by noting the temperature rise of the sample container under adiabatic conditions. At the end of 43 hours the warm-up rate had fallen t o essentially zero and the reaction seemed to have run its course. After another 24 hours a measurement was made to see how much heat was absorbed on warming through the eutectic point; from the observed heat effect the conclusion was reached that the reaction was better than 99.8% complete. The Sam le was held an additional 12 hours a t 275°K. and was tEen permitted to drift down in temperature toward the Dry Ice point. These various operations were, of course, carried out with the sample in the calorimeter.
Experimental Results Heat Capacities of Potassium.-Measurements were made using 52.8823 g., or 1.3525 g. atoms, of potassium. Six series of determinations were carried out as shown (11) 0.L. C. M . Vsn R . €1. Van Bleiawijk, Z . Band S 162 (1912).
onorg. Chem., 74,
Series
AND
Temp. range,
523
Na2K
Thermal hiatory
OK.
I 292-321 As sealed into calorimeter I1 277-325 As sealed into calorimeter 111 200-289 Cooled from 294 to 200°K. in 45 min. Cooled from 289 to 203°K. in ,26 hr. Cooled from room temp. to 134°K. in 66 hr., then from 134 to 10°K. in one hr. Mechanical failure occurred in Collins Machine BO that experiments below 100°K. could not be performed cooled from room temp. to 144°K. in 47 hr., from 144 to 10°K. in one hr.
IV 203-289 V 101-199
VI
10-230
Results of the individual measurements and smoothed heat capacities are given in Tables I and 111. Precision of the measurements is of the order of 0.1%. The average deviation of the individual determinations from a smooth curve drawn through all the points is 0.075%and only 11 of the 110 measurements deviate by more than 0.15OJo0. TABLE I H ~ A CAPACITY T VALUESOP POTASSIUM FROM INDIVIDUAL DETK~RMINATIONB C
car/
Temp., OK.
deg. g. atom
Series I 295.09 300.32 306.68 311.60 317.61
7.048 7.096 7.163 7.208 7.313
Serics I1 279.84 284.92 290.08 296.34 300.63 308.08 311.68 317.33 322.80
6.898 6.931 6.976 7.036 7.069 7.164 7.218 7.296 7.404
Scriee I11 202.17 206.63 211.31 216.20 221.34 226.44 231.60 237.10 242.54 248.00 253.48 258.92 264.37 269.82 276.37 281.02 286.62
6.466 0 477 6.601 6.622 6.644 6.562 ti. 60fi 0,620 6.662
0.081 6.717 6.747 6.775 6.820 6.864 6.894 6.963
Temp. OK.
C oaf.'/ deg. g. atom
Series IV 205.79 210.48 216.42 220.62 226.66 230.91 236.34 241.80 247.30 252.85 258.36 263.85 269.31 274.87 280.64 286.21
6.470 6.497 6.519 6.636 6.567 6.696 6.626 0.663 6.084 6.714 6.745 6.776 6.816 6.866 6.911 6.948
Series V 103.73 109.03 114.43 119.82 125.10 130.43 105.80 141.23 146.71 162.12 157.48 162.88 168.36 173.85 179.36 184.82 190.42 196.14
5.917 5.96.5 6.000 6.036 6.069 6.009
0.132 6.164 0,196 6.225 6.267 6.290 6.307 0.326 6.363 6.376 6.399 6.424
C
Temp. OK.
os!.'/
deg. g. atom
Series VI 11.12 12.62 14.64 16.99 19.61 22.16 25,03 28.10 31.36 34.76 38.29 41.98 45.82 49.80 64.14 59.06 64.32 69.67 76.32 81.26 87.32 93.62 100.06 106.36 iia.46 118.43 124.27 129.99 136.81 141.74 147.57 153.62 159,131 105.63 171.77 178.02 184.20 190.37 196.38 202.20 207.39 212.07 217.01 222.09 227.16
0.840 1.102 1.446 1.861 2.260 2.886 3.092 3.473 3.818 4.130 4.384 4.616 4.799 4.979 6.136 6.270 6.416 6.619 6.604 6.702 6.783 6.836 6.889 6.939 5.987 6,023 6.064 6.099 6.133 6.167 6.205 e.230
6.258 6.290 6.316 6 382 6.370 6.397 6.423 6.463 6.477 6.499 6.619 6.660 6.668 I
524
C. A. KRIER,R. S. CRAIGAND W. E. WALLACE
Previously measurements of the heat capacity of potassium have been made by Simon and Zeidler,lP Carpenter and Steward,'* and Douglas, et aE.14 Simon and Zeidler covered the range 15 to 275°K. but the other two studies were for higher temperatures and only a few measurements overlapped the temperature range covered in the present study. Above 60°K. the deviation of Simon and Zeidler's results from those in this study never exceeds 1%. Between 60 and 160°K. the two sets of data are in agreement to within about 0.2% but above 160OK. their data are consistently higher by about 0.8y0. Below 60°K. their data fall well below the present determinations, being 10% lower a t 15°K. The results of Carpenter and Douglas are in most cases higher than the present data, but the scatter is large, averaging about 2%. After the present study was completed, it was learned that Dauphinee, Martin and Preston-Thomas had determined the heat capacities of potassium between 30 and 320°K. Their results, which have since been published,ls are in good agreement with the results obtained in this study. Above 50°K. their data show an average deviation of 0.2y0 from the present results. The deviations are larger below 50°K. but even here the differences average only 0.4%. Heat Capacities of NazK in the Single Phase Temperature Regions.-Measurements were made using 56.832 g. or 2.0027 g. atoms of alloy.16 A total of 115 determinations in the range 12 to 321°K. were made. The original 85 measurements were made in six series of determinations. Series I (68-205°K.): after being prepared the sample was cooled from 275 to 222°K. in 13 hours, from 222 to 68°K. in two hours. Series I1 (10-78~K.) : it was necessary to transfer the calorimeter from the liquid nitrogen cryostat used in Series I to the Collins helium cryostat without warming above the meritectic point for NaaK. The sample was cooled to 86°K. and the vacuum broken with helium. The assembly then was detached from the nitrogen cryostat vacuum line, connected temporarily with a portable vacuum system, and placed in the helium (12) F.Simon and W. Zeidler, 2.physik. Chsm.,148, 383 (1926). (13) L. G.Carpenter and C . J. steward, Phil. Map., 47,202 (1939). (14) T. B. Douglas, A. F. Ball, D. C. Ginning8 and W. D. Davis, J . Am. Chem. SOC.,74,2472(1952). (16) T. M. Dauphinee, D. L. Martin and H. Preaton-Thomaa. Proc. Roy. Soc. (London), A333,214 (1955). (16) The aample mas8 wan not obtained b y direct weighing. Initially the calorimeter wan loaded with 67.4049 g. or 2.0229 g. atoms of rample. After the entire temperature range had been covered, the equipment was taken apart to introduce another sample whereupon it was found that the calorimeter had been filled too full. The sample had expanded at the highest temperatures. broken open the seal. and 8 small amount had dropped onto the adiabatic shield. Repetition of the entire work hardly aeemed a juatifinble expenditure of time oonaidering that the error in mass was amall, about l%, and oould be estimated. I t WM not clear when the pendulant drop detached itself from the odorimeter but tho possibilities were limited to two times: (1) before any data were taken, since the aample was, for purposes of hOmOgeniZ8tiOn, warmed up to 320°K. prior to any msasurementa and (2) at the time eolid NatK was converted into liquid alloy and solid sodium, that is, a t 28O0K. Continuity of heat capacity data eroluded any other times. Acoordingly, the container was reaealed with a weighed portion of NarK and thirty additional heat capacity determinations were made, distributed equally above and below 280'K. By comparing these with the original 86 determinations it W&L)possible to determine the maas of the aample involved in the original work. In thin way i t was found that the loss in mass occurred before any measurements were made, The mam wa8 determined by this procedwe to be 66.832g. with a probable error of the mean of *0.021 g.
Vol. 61
cryostat which then was set in operation. When it had cooled to about 200°K., the vacuum in the calorimeter was broken with helium, the temporary system detached, and the permanent system connected. During these operations the sample temperature was monitored, and it a t no time rose above 200°K. The sample was cooled to 148OK. in 16 hours and from there to 4°K. in 40 min. Series I11 (195 to 263°K.) : the assembly was transferred from the helium cryostat to a Dry Iceacetone cryostat after Series I1 using the auxiliary vacuum system as described above. Series IV (237-324OK.): the sample was held a t 196°K. for two weeks while results of the earlier series were calculated. Series V (301-324°K.) : %he sample was held a t room temperature for five days. Series VI (281303OK.): after Series V the temperature was dropped from 324 to about 275°K. in 20 min. and a slow heating of the sample was begun to establish the NaaK meritectic temperature. Heating was interrupted four times and the equilibrium temperature was measured. The equipment wa8 left for 9 hours during which time the temperature fell from 281 to 262OK. With resumption of work it was heated to 281°K. and the Series VI measurements begun. The results of the determinations are assembled in Table I1 and smoothed results are given in Table 111. In each case a correction has been TABLEI 11 HEATCAPACITY VALUES OF NA,K FROM INDIVIDVAL DETERMINATIONS
c
T:mg.,
Caf.'/ deg. g. atom
Series I 71.22 80.48 86.62 93.16 99.43 105.61 111.43 117.20 122.86 128.41 133.87 130.27 144.68 149.81 164.96 160.24 185.66 171.00 176.31 181.69 186.82 192.12 197.61 202.84
4.996 6.226 6.349 6.462 6.647 8.617 6.687 6.742 6.796 6.860
6.890 6.934 5.967 6.999 6.032 6.082 6.094 6.126 6.166 6.192 6.216 6.258 6.295
6.326
c Temp., OK.
C de#. J . 7 g.
atom
Series I1 12.19 16.16 16.36 17.84
20.6e 23.66 26.34 29.34 32.86 32.63 36.80 40.98 46.67 60.37 64.97 59.43 64.31 69.64 74.94
0.320
0.600 0.733 0.916 1.208 1.676 2.018
2.880 2.774 2.732 3.137 3.490 3.834 4.147 4.394 4.589 4.745 4.946 5.092
Series I11 197.88 202.63 207.66 212.69 217.70 222.90 228.11 233.34 238.60 243.89 249.21 254.49
6.309 6.350 6.382 6.424 6.488 6.643 0.687 6.636 6.698 6.763 6.825 6.884
c Temp., OK.
deg. oaf,'/g. atom
Series IV 240.21 246.6a 250.80 256.13 265.49 268.68 271.89 215.89 284.91 288.17 291.56 295.33 299.71 304.60 309.73 315.61 321.42
8.701 6.767 6.793 6.929 7.052 7.142 7.237 7.469 16.136 14.833 13.430 11.422 10.085 8.997 8.402 8.040 7.996
Seriea V 303.57 308 01 312 12 316.32 321.00
8.148 8.113 8.082 8.042 8.007
Series VI c
282.27 284.12 286.14 288.17 290.42 293.19 fi96.65 390.87
15,973 16.156 16.263 16.996 14.876 12,624 10.408 9.142
HEATCAPACITIES AND RELATED PROPERTIEB OF K AND NalK
May, 1957
made for the heat capacity of the 0.0030 g. atom of excess potassium present. TABLE I11 Shl00TIIF.D ATOMICHEAT CAPACITY OF K AND NalK Temp., "1C.
12
14 15
I6 18 20 22
24 25 28 28 30
35 40 45 50 55 60 65 70 75 80 85 90 06 100 105 110 115 120 125 130 135 140 145 150
C.,
aal./deg.
g.
atom
I
