THE JOURNAL OF
PHYSICAL CHEMISTRY Registoed in
u. 8. Patent Ofice
@ Copyright, 1966, by the American Chemical Society
VOLUME 70, NUMBER 8 AUGUST 15,1966
Heats of Dilution of Aqueous Rare Earth Chloride Solutions at
25O1
by F. H. Spedding, D. A. Csejka, and C. W. DeKock Institute for Atomic Research and Department of Che?nistry, Iowa State University, Ames, Iowa (Received December 16, 1966)
The heats of dilution of aqueous PrC13, SmCla, GdCla, TbCla, DyC13, HOC&,TmC13, and YbCla have been measured for concentrations up to about 0.25 m. Relative apparent molal heat contents, t # ~ ~have , been calculated for these solutions, and empirical equations have been obtained for the concentration dependence of I#JL The data show that all of the salts, with the possible exception of YbCla, obey the Debye-Huckel limiting law. A qualitative interpretation is given for the behavior of $JL across the rare earth series.
Introduction
Experimental Section
Since high purity kilogram quantities of the rare earths have become available,2 an extensive research program to study their chemical and physical properties has been undertaken. As part of this+program, investigations of solution properties were initiated by Spedding and co-workersa to obtain a better understanding of higher valencetype electrolytes in aqueous solutions. Previous investigation~~g had found that the ~#IL data for the lighter rare earth chloride solutions obeyed the Debye-Huckel limiting law over the entire concentration range, but that the heavier rare earth chlorides, ErCL and YbC4, seemed to depart from the m. This work was underlimiting law below 4 X taken to see if this apparent anomaly would be present for other heavy rare earth chlorides and to observe the behavior of ~#IL across the entire rare earth series. Ytterbium chloride was remeasured to determine whether the apparent anomaly previously foundag for this salt was real.
Apparatus. Construction of an adiabatically jacketed differential calorimeter, similar to that of Gucker, Pickard, and P l a n ~ k ,has ~ been described previou~ly.~gAdditional modifications were made,6
(1) This work was done a t the Ames Laboratory of the U. 5. Atomic Energy Commkion and is based on theses submitted by D. A. Csejka and C. W. DeKock in partial fulfillment for the degree of Doctor of Philosophy a t Iowa State University; Contribution No. 1835. (2) J. E. Powell in “The Rare Earths,” F. H. Spedding and A. H. Daane, Ed., John Wiley and Sons, Inc., New York, N. Y., 1961. (3) (a) F. H. Spedding, P. E. Porter, and J. M. Wright, J . A m . C h a . SOC.,74,2055,2778,2781 (1952) ; (b) F. H. Spedding and C. F. Miller, ibid., 74, 3158, 4195 (1952); (c) F. H. Spedding and I. S, Yaffe, ibid., 74, 4751 (1952); (d) F. H. Spedding and J. L. Dye, ibid., 76, 879 (1954); (e) F. H. Spedding and 9. Jaffe, ibid., 76, 882, 884 (1954); (f) F. H. Spedding and J. P. Flynn, ibid., 76, 1474, 1477 (1954); ( 9 ) F. H. Spedding, A. W. Naumann, and R. E. Eberts,
ibid., 81, 23 (1959).
(4) F. T. Gucker, Jr., H. B. Pickard, and R. W. Planck, ibid., 61, 459 (1939). (5) (a) D. A. Csejka, Ph.D. Dissertation, Iowa State University, Ames, Iowa, 1961; (b) C. W. DeKock, Ph.D. Dissertation, Iowa State University, Ames, Iowa, 1905.
2423
2424
but the essential characteristics of the calorimeter remained unchanged. Platinum disks originally used in the sample holders were replaced by 0.0005-in. Saran Wrap6 for all experimental determinations except those involving DyCl, solutions. The heats of opening of the Saran disks were smaller and more reproducible than those of the platinum disks. The breaker assembly was also changed slightly for PrC13, TbC13, and YbC13 which resulted in a negligible heat of opening for these determinations. A sensitivity of either 3.3 X or 4.5 X cal/ mm chart displacement was used. The filter circuit of the Liston-Becker breaker-type dc amplifier was modified so that static free lines could be obtained with these sensitivities. For the determinations involving PrC13, TbC13, and YbC13, the lower stirrer bearings were removed from the submarine jacket and placed in a holder mounted in a brass tube above the submarine lid. Also for these determinations the photocell relay system used to maintain adiabatic control was replaced by an electronic control built by the Ames Laboratory electronics shop. The stirring in the bath was provided by a ~ / Z O hp Cenco centrifugal stirrer. Bath control was maintained to f0.0005”. Materials. The rare earths used in this work were obtained as the oxides from the rare earth separation group of the Ames Laboratory of the U. S. Atomic Energy Commission. The rare earths were sufficiently pure that it was difficult to detect impurities in them spectrographically. The total amount of impurities of other rare earths was certainly less than 0.1%) and other total impurities, usually Ca and some Fe, were also less than 0.1%. The preparation of the stock solutions from the rare earth oxides and the analytical methods used to determine their concentrations are described elsewhere.3g All dilutions of the stock solutions were made by weight and all weights were corrected to vacuum. Conductivity water having a specific conductivity of 1.5 X mho or less was used for all dilutions. Procedure. Two sample holders were suspended in each calorimeter container. Ten milliliters of solution was measured into each sample holder with a pipet, and the samples were weighed to the nearest 0.1 mg. Enough water was weighed into each container to give a total liquid content of 900 g. The water was weighed on a 2-kg-~capacity analytical balance to i1 mg. When a sample of molality ml, containing n21 rides of salt, was diluted into water giving a solution of was When m 2 )a quantity Of heat’ the second sample of molality ml,containing n2” moles The Journal of Physical Chemistry
F. H. SPEDDING, D. A. CSEJKA,AND C. W. DEKOCK
of salt was diluted into the solution of molality m2 giving a solution of molality m3, another quantity of heat, 42, was evolved. The relation of the relative apparent niolal heat content, +L, to the heat evolved is q1 =
+
nz‘[+~(md- + ~ ( m l ) l
(1)
qB
and q2 =
(nz’
+ nZ”)+~(m3)-
+
nZ”+L(md - n2’h(mz) q B (2) The quantity q B is the heat of opening of the sample holder. The integral heats of dilution are given by the relationships
and m 3 , z=
AHi,z - AH1,3
(5) The “short chord” method of Young and his associates,’ and its niodificationa was used to analyze the data. This treatment consists of calculating Pi, the average slope of 4 L vs. m ‘Izfrom
in the very dilute concentration range. The concentration dependence of pi is derived from an equation of the form
+
where So, B, and C are constants, x1 = 1/2(m~1/’ m31/3J and 6i = (m3’/’- mz’/’). Equation 7 is then integrated to give r # d m k ) for the very dilute concentration range. Two values of 4L(ml) are then calculated from eq 3 and 4 and are averaged. I n this research, the equations
Pi
= So
+ Bxi
(8)
and
Pi
= 6925
+B x ~
(9)
(6) Saran Wrap is a thermoplastic copolymer produced by the Dow Chemical Co. (7) (a) T. F. Young and 0.G. Vogel, J. Am. Chem. Soc., 54, 3030 (1932); (b) T. F. Young and W. L. Groenier, ibid., 58, 187 (1936); (c) T.F. Young and P. Seligmann, ibid., 60, 2379 (1938). (8) (a) W. E. Wallace and A. L. Robinson, ibid., 63, 958 (1941); (b) A. L. Robinson and W. E. Wallace, ibia., 63, 1582 (1941).
HEATSOF DILUTIONOF AQUEOUS RAREEARTH CHLORIDE SOLUTIONS AT 25'
were also used to represent Pi. The value 6925 is the Debye-Huckel limiting law slope for 3-1 electrolytes as calculated by Harned and Owen.g The constants So,B, and C were determined by a least-squares analysis using the inverse square of the standard deviation of the mean of the Pi's as the weighting factors. These values are given in Table 111. The last three figures in the B coefficients are probably not significant, but were used in making the calculations. All heat dilution measurements were made at 25.00 =k 0.02". The defined thermochemical calorie, 4.1840 absolute joules, is used throughout this work.
Results Heats of Opening. A number of blank openings were made with water samples to determine the heat of opening of the sample holders. The results are given in Table I.
2425
HOC&: 6925m'" - 12,935m
(15)
TmC13: 6925m'" - 16,061m
(16)
- 15,175m
(17)
YbCI3: 6925m"'
These equations are valid for concentrations of m < 0.006. Unweighted leaat-squares analyses, using the values of 4L(ml), t$L(mz) and t$~(ma)listed in Table 11, were performed to obtain equations of 4 L as a function of m'/'valid over the entire concentration range studied. These equations fit the data over the entire concentration range with a standard deviation of 1 to 2 cal/mole. Expressions for the relative partial molal heat content of the solvent, L1,and the solute, 1 2 , can easily be obtained from these equations using
-
L1
=
mM1 -(9L 1000
- 12)
and Table I : Heats of Opening No. of
a
QB
x lo',
aa
x lo',
Disks
detns
os1
oal
Platinum Saran Saran (new breakers)
25
16.7 4.8 0.0
0.6 0.3 0.1
15 8
An IBRil 7074 computer was used to obtain the t $ ~ equations. The derived equations for +L are PrCls:
Standard deviation of the mean.
+
6945m'/* - 18,118m 31.,512ma'' - 21,862m2 (20)
SmC13: 685Om'/'
- 16,004m + 24,210m"'
Heats of Dilution. A summary of the experimental heats of dilution is given in Table 11. The values for the parameters of eq 7, 8, and 9 are listed in Table 111. All of the data were analyzed using eq 8 and 9. Since the data for YbC13 departed from a straight line for the two most dilute concentrations, it was also analyzed using eq 7. However, analysis of the YbC13 data using eq 8 showed that So for YbC13 was within experimental error of the theoretical value, 6925, and, therefore, eq 9 was used to represent the Pi data of YbC13. In all cases, the experimentally determined slope, SO, was within experimental error of 6925, and, therefore, eq 9 was used to represent the Pi data for all of the salts in this work. Equations for 41,derived from the concentration dependence of Pi are
GdC13: 7026m'/'
- 17,507m + 29,802m'/'
TbC4: 6872m'/'
- 15,042m + 20,995m"'
DyC13: 6766m'/'
- 14,374m2
(21)
- 19,897m2
(22)
- 10,611m2
(23)
- 14,641m + 21,234ma//'- 11,941m2 (24)
HOC&: 7128m'/'
- 18,831m -I34,662m'/* - 24,974m2 (25)
TmC13: 6917m'/8 - 16,663m
+
26,693m'" YbCI3: 6859m'/'
- 16,438m2
(26)
- 16,098m +
PrC13: 6925m'/'
- 16,011m
(10)
SmC13: 6925m'/'
- 15,968m
(11)
GdCI,: 6925m'I'
- 14,068m
(12)
+L
TbC13: 6925m"'
- 14,667m - 16,272m
(13)
(9) H. 8. Herned and B. B. Owen, "The Physical Chemistry of Electrolytic Solutions," 3rd ed, Reinhold Publishing Corp., New York, N. Y., 1958, p 173.
DyCl3: 6925m'l'
(14)
25,379m"* - 15,585m2 (27) Estimation of Uncertainties. The uncertainty in the values arises from two sources; the error in the
Volume 70, Number 8 August 1966
F. H. SPEDDINQ, D. A. CSEJKA, AND C . W. DEKOCK
2426
Table XI: Experimental Heats of Dilution of Rare Earth Chloride Solutions a t 25' No. of detna
n2 X 108 (nn' n2")
m
1/?
8 8 6 6 6 6 4 4 3 3
0.1373
9 9 7 7 6 6 5 5 5 5
0,1406
0.2034 0.2799 0,3552 0,5137
x
+
10'
7nk'/?
x
--pi
10%
x
108,
csl
0.1891 0.3791 0.4118 0.8235 0.7787 1.558 1.254 2.507 2.614 5.228
Praseodymium chloride 1.456 111 2.048 99 2.150 308 3.024 264 2.960 696 4.159 583 3,752 1263 5.277 1052 5.420 3156 7.624 2600
0.1966 0,3930 0.3964 0,7929 0.6623 1.325 1.287 2.573 2.577 5.155
1.486 2.089 2.110 2.967 2.727 3.836 3.802 5.346 5.382 7.569
- AHI.k,
csl/mola
Pi
@L(mk)+
@L(ml),
SPi
oal/moIe
oal/mole
587 554 747 695 894 821 1007 924 1208 1101
5600 1000 5930 300 6050 110 5500 155 4830 14
98 135 142 195 191 260 237 321 328 435
608 572 76 1 708 877 814 1040 956 1245 1139
6003 527 6124 349 5730 191 5474 89 4866 78
99 138 139 191 177 242 240 325 326 433
626 587 782 725 893 828 1069 982 1301 1190
6346 935 6529 218 5827 303 5703 134 5108 46
102 141 142 196 179 246 240 327 330 44 1
699 654 782 730 921 860 1166 1075 1284 1181
6306 729 5851 739 5364 302 5190 156 5005 126
177 162 142 195 180 247 269 361 310 412
678 889 1083 1245 1536
Samarium chloride
0,1997 0.2582 0.3601 0.5105
124 110 305 265 586 502 1343 1125 3213 2665
709 900 1055 1280 1571
Gadolinium chloride 9 9 8
8 7 7
0.1433 0.2029 0.2597
6 6 5 5
0.3561
7 7 6 6 7 7 4 4 4 4
0.1674
0.5069
0.2046 0,4088 0.4093 0.8189 0,6698 1.340 1.259 2.518 2.541 5.085
1.515 2.131 2.144 3.015 2.743 3.857 3.760 5.289 5,345 7.519
0.2790 0,5578 0.4160 0.8320 0.6929 1.387 1.659 3.320 2.303 4.606
1.770 2.488 2.161 3.039 2.789 3.923 4.317 6,074 5.088 7.155
133 124 325 279 603 516 1350 1132 3312 2749
728 922 1072 1309 1631
Dysprosium chloride
0.2045 0.2640 0.4090 0.4821
extrapolation to infinite dilution and the error in the values. If it is assumed that there is no error in the theoretical slope, 6925, then the error in the extrapolation is due only to the uncertainty in the B coeffiThe Journal of Physical Chemistry
212 187 342 299 654 570 1951 1651 2974 2497
816 925 1104 1435 1594
cients given in Table 111. The standard error of the B coefficient, calculated by the method of propagation of precision indexes,l0 was found to be of the order of 3000 and at most i5000. This gives a maximum
HEATSOF DILUTION OF AQUEOUS RAREEARTHCHLORIDE SOLUTIONS AT 25"
2427
Table I1 (continued) No. of detns
+
In ' / z
9 9 6 6 6 6 4 4 4 4
0,1325
10 10 8 8 6 6 4 4 3 3
0,1434
8 8 7 7 4 4 3 3 3 3
0,1430
12 12 7 7 6 6 4 4 3 3 a
ns X 10' (nz' nz")
0.1866 0.2591 0,3582 0,5024
0.2053 0.2908 0.4116 0.5707
0,1969 0.2518 0,3381 0,5008
0.1497 0.2082 0.2519 0,3679 0,5035
x
10'
rnk'/l
x
pi
101
x 108, cal
- AHl,k,
cal/mole
Pi ?Pi
dL(mk),
mL(mi),
cal/mole
cal/mole
0.1747 0.3493 0,3424 0.6849 0.6674 1.335 1.274 2.548 2.499 4.997
1,400 1,969 1.961 2.758 2,737 3.850 3.783 5,320 5.299 7.453
Holmium chloride 108 95 255 223 602 514 1374 1146 3257 2686
592 554 731 683 894 828 1075 985 1302 1188
6552 1001 5960 415 5910 175 5847 77 5305 104
94 131 131 181 180 247 243 332 331 444
0,2045 0.4088 0.4190 0.8382 0.8404 1.681 1.679 3.359 3.219 6.439
1,515 2.130 2.169 3.051 3,072 4.324 4,344 6.109 6,017 8.463
Thulium chloride 131 116 332 289 794 677 1929 1610 4448 3723
620 581 781 729 938 869 1146 1051 1380 1267
6424 739 5834 355 5548 143 5385 147 4607 105
101 140 143 196 198 269 270 363 358 471
0,2206 0.4412 0.3860 0.7719 0.6305 1.261 1.135 2.271 2.485 4.971
1,574 2.213 2,082 2.928 2.661 3.742 3.571 5.022 5.285 7.433
Terbium chloride 132 117 301 260 562 483 1193 1001 3263 2727
597 564 780 727 892 829 1051 966 1313 1205
5160 420 6240 340 5820 230 5840 80 5040 40
105 146 138 190 174 239 229 311 325 434
0,2228 0.4453 0.4306 0.8576 0,6300 1.260 1.343 2.685 2.509 5.017
1.581 2,224 2.198 3.087 2,659 3.740 3.884 5.462 5.310 7.467
Ytterbium chloride 140 127 339 296 551 472 1449 1205 3229 2687
628 599 786 740 875 812 1079 988 1287 1179
4780 710 5210 490 5800 95 5740 195 5010 50
106 147 145 199 173 238 246 333 323 432
686 863 1075 1318 1632
721 924 1137 1415 1738
706" 917 1067 1279 1639
740 935 1049 1323 1611
This value was not used in the least-squares analysis.
error in the extrapolation of 10 to 15 cal/mole. The ~ about 12 standard deviation in the mean for A H L ,was cal/mole for the most and about 1 cal/mole for the highest concentrations studied.
This gives a total average error of 15 to 20 cal/mole for +L over the entire concentration range. (10) A. G. Worthhg and J, Geffner, "Treatment of Experimental Data," John Wiley and Sons, Inc., New York, N. Y . , 1943.
Volume 70,Number 8 August 1966
F. H. SPEDDING, S. A. CSEJKA,AND C. W. DEKOCK
2428
Table 111: Least-Squares Coefficients for Pi Salt
SO
B
PrC13
72i6 6925 6779 6925 7178 6925 7021 6925 6198 6925 6806 6925 6672 6925 3409 6470 6925
-37,514 -32,022 -29,331 -31,937 - 32,211 -28,136 - 30,928 -29,334 - 19,558 - 32,544 - 22,629 -25,870 - 27 ,992 -32,122 125,030 - 22,550 - 30, 350
SmC13
HOC18 TmCL YbC13
C
-1,565,900
Discussion This work, combined with that of earlier investigations,3g gives the heats of dilution of 11 rare earth chloride solutions. These data are an excellent test of the Debye-Huckel theory for 3-1 electrolytes. The experimental limiting slopes, So,for these 11 rare earth chloride solutions are given in Table TV. These So values were t'aken from the analysis of the data using eq 8. The average of these values is 6600, which is only 4.7% below the theoretical value of 6925. If the value for ErC13 is omitted, the average is 6770 which is only 2.3% below 6925. Since the experimental scatter of the Pi's is large at the lowest concentrations, this agreement is an excellent confirmation of the DebyeHuckel theory for 3-1 electrolytes. The Pi's for the heavier rare earth chlorides obtained in this research do not show the apparent anomalies found for ErC13 and YbC13.3g I n particular, the data for HoC13 and TmCI3 appear normal, so it is difficult to explain the behavior found for ErC13. The Pi data found for YbCI3 in this research have approximately one-half the scatter obtained previously and do not deviate nearly as much from the limiting law at the lower concentrations. However, if the previous data are analyzed using eq 17, the agreement is within 1%. The anomaly for YbC13 is probably not due to the presence of chloride complexes of Yb, since the formation constant for the first chloride complex is near one," and, hence, very little complex would be present at the concentrations of interest. Since carbon dioxide was present in the water, the presence of carbonate complexes cannot be disregarded. However, at sufficiently low The JOUTnal of Physical Chemistry
concentrations, the presence of a complex would cause the pi's to approach, rather than depart, from the limiting value as the concentration decreased. Also, there is no other experimental evidence which would suggest that the carbonate complexes of ytterbium are more stable than those of the other rare earths. It is felt that the apparent anomaly of YbC13 is probably due to a slight hydrolysis of the Yb3+ion at the most dilute concentrations. If this is the case, then the use of the theoretical limiting slope in the analysis of the data merely subtracts out the hydrolysis effect, and enables one to compare the data of YbC13with that of the other rare earth chlorides over the entire concentration range. A plot of 61, us. rare earths at ml/' = 0.3 is shown in Figure 1. These values were obtained using eq 9 to analyze the data. This trend is present from 0.005 to 0.20 m. This same trend has been observed for apparent molal volumes at infinite dilution,12 and for the heat of formation data of some rare earth ~he1ates.I~ These data have been interpreted in terms of a change in water coordination number of the rare earth ions across the series. The extended Debye-Hiickel equation predicts that C$L (setting d In uo/dT = 0) will increase as uo, the mean distance of closest approach decreases. The trend shown in Figure 1 can be explained in terms of ao if it is
I
I190-
I
I
1180-
I
4 I
3
-
+
1150 1140
+++
1
1
1
1
I
I
-
-
A SPEDDING, NAUMANN AND EBERTS 0
THIS RESEARCH
Ill0
I loo
La Ce Pr
N d Pm Sm Eu Gd Tb Dy Ho Er Tm Yb Lu
Figure 1. The relative apparent molal heat content a t milz = 0.3 in calories per mole us. atomic number of the rare earth.
(11) D.F. Peppard, G. W. Mason, and I. Hucher, J . I m - g . Nucl. Chem., 24, 881 (1962). (12) (a) B. 0.Ayers, Ph.D. Dissertation, Iowa State University, Arnes, Iowa, 1954; (b) F. H. Spedding, M. J. Pikal, and B. 0. Ayers, J . Phys. Chem., 70, 2440 (1966). (13) (a) 3. L. Mrtckey, J. E. Powell, and F. H. Spedding, J . A m . Chem. Soc., 84, 2047 (1962); (b) I. Grenthe, Acta Chem. Scand., 17, 2487 (1963);(c) P. L. Edelin De La Praudiere and L. A. K. Staveley, J . Inorg. Nucl. Chem., 2 6 , 1713 (1964).
HEATSOF DILUTION OF AQUEOUS RAREEARTH CHLORIDE SOLUTIONS AT 25"
2429
Table IV: Observed Values of So for Aqueous Rare Earth Chloride Solutions a t 25' LaCls
PrCla
NdCla
SmCla
GdCla
TbCls
HoCla
ErCh
TmCla
YbCls
6630
7280
6630
6780
7130
7020
6310
4930
6670
6470
assumed that there are two series within the rare earths which have different water coordination numbers. It is also assumed that an equilibrium exists between these two water coordination numbers from beyond Nd to around T b or Dy, with a gradual shift in the equilibrium toward the lower coordination number as the atomic number increases. The 4 ~ 0datal2 are well understood in terms of these two postulates. The 4v0 data indicate that from La to Kd the rare earth ions have the same coordination number. Since the charge density is increasing from La to n'd, the Nd3+ ion influences the water outside the first hydration sphere more strongly than does the La3+ ion. This will give a larger hydrated radius for the Nd3+ ion with a consequent increase in ao. After Nd, a0 would decrease to around T b or Dy if a shift toward a lower hydration number occurred in this interval, since a0 depends primarily on
the number of waters in the first hydration sphere. The increase in ao from around Tb to Yb again arises from an increase in the charge density of the ions with a consequent increase in the hydrated radii. A shift of 0.6 A for ao,from say 5 to 5.6 A, would account for the between Nd and Tb. change in 41, The discrepancy noted in previous inve~tigations~g between the heats of dilution of the rare earth chlorides obtained directly and those obtained from heat of solution measurements was also noted in this work. At a concentration of 0.05 m, the relative apparent molal heat contents obtained from heat of solution measurements of PrCL and YbC13' are approximately 300 cal/ mole larger than obtained in this research. This discrepancy increases with increasing concentration. Reasons for this discrepancy have been previously discussed.Q
Volume 70,Number 8 August 1066
