HEATSOF DILUTICIN OF
Jan. 3 , 1939
forming the transition state of the hydrolytic reaction. Since the rate-determining step of this reaction is
? I! R--C--OR'
0-
+ OH- +R-A-ORr I
(5)
OH
and the transition state carries a negative charge in the same position as the ionized carboxyl groups, the identity of A F F and A F Z is not unexpected in this case.
In the case of the quaternization of PVPy by bromoacetate, a comparison of the last two columns of Table I shows that the dissociation constant of the pyridinium residues Ka is considerably more sensitive than the quaternization rate constant ks to the charge density of the polymer and the counterion atmosphere. This means that the anionic charge of the bromoacetate is, in the tran-
[CONTRIBUTION KO.591 FROM
THE
R.4RE
93
EARTHS a L T SOLUTIONS
sition state of the quaternization reaction, in a region of lower electrostatic potential than the charge of a pyridinium residue. Only if the transition state involved an attack of an un-ionized pyridine residue on the C-Br bond with simultaneous ion-pair formation of the carboxylate with a second ionized pyridine group, would variations in kp be expected to be proportional to variations in Ka. Such a simultaneous attack of two polymer groups on two distinct sites of the low molecular weight reagent, analogous to the postulated action of enzymes, may not be realizable with polymers consisting of fairly flexible chains. It seems much more probable with polymers which maintain in solution a tightly coiled helical configuration,16 so that the spacing between their functional groups is closely defined. (16) P. Doty and J. T.Yang, THISJOURNAL, 78, 408
(1956).
BROOKLYN, N. U.
INSTITUTE FOR ATOMICRESEARCH AND DEPARTMENT OF CHEMISTRY, IOWASTATE COLLEGE]
Heats of Dilution and Related Thermodynamic Properties of Aqueous Rare Earth Salt Solutions at 25" ; Integral Heats of Solution of NdC1,*6Hz01 BY F. H. SPEDDING, A. W. NAUMANN AND R. E. EBERTS RECEIVED JANUARY 2, 1958 The heats of dilution a t 25" of LaCls, NdCls, ErC13,YbCt, La(N03)3 and Y b ( N 0 & solutions have been measured for concentrations up to about 0.2 molal. Relative apparent molal heat contents of the solute, +L, have been calculated for the solutions used and empirical expressions have been derived for the concentration dependence of +I,. The integral heats of solution of NdCl3.6H20 have been measured and the relative apparent molal heat content of NdCl3 derived from these quantities. The results are compared to theoretical predictions and to previous measurements. A tentative explanation has been given for the anomalous behavior of the erbium and ytterbium salts a t very low concentrations.
Introduction Ion-exchange separation techniques have made kilogram quantities of all the rare earth elements available in high purity.2 This has made possible, and created a need for, the measurement of the properties of aqueous solutions of soluble rare earth salts. The chemical similarity of the rare earth elements, their ability to form what may be considered strong electrolytes and the regular decrease in ionic radius through the rare earth series make the lanthanide elements attractive for theoretical studies of solution phenomena. A program was undertaken in this Laboratory to determine the properties of aqueous rare earth solutions, with the general aim of obtaining a consistent set of precise data with which to check and develop theories of aqueous solution^.^ The determination of the heats of
dilution of solutions of rare earth salts of the 3-1 type was an extension of this program. Measurements of heats of dilution of 3-1 salts have been published by Nathan, Wallace and Robinson4 on lanthanum chloride and by Lange and Miederer5 on lanthanum nitrate. Both of these salts have been measured here, as a check on the data obtained in this Laboratory and to extend the data to higher concentrations. Spedding and Millersa have reported &)s for neodymium and cerium chlorides from measurements of the heats of solution of the anhydrous salts. The measurements on the heat of solution of hydrated neodymium chloride were made in an attempt to explain the discrepancy in the neodymium chloride data of Spedding and Miller and those reported here from heats of dilution.
(1) Work was performed in t h e Ames Laboratory of t h e U. S. Atomic Energy Commission. This paper is based on theses b y A. W. Naumann and R. E. Eberts, which were submitted t o Iowa State College in partial fulfiltment for degrees of Doctor of Philosophy. (2) (a) F. H. Spedding, A. F. Voigt, E. M. Gladrow and PIT. R . Sleight, THISJOURNAL, 69, 2777 (1947); (b) F. H. Spedding, J. E. Powell and E. J. Wheelwright, ibid., 76, 612, 2557 (1954). (3) (a) F. H. Spedding, P. E. Porter and J. M. Wright, ibid., 74, 2055, 2778, 2781 (1952); (b) F. H. Spedding and I. S. Yaffe, ibid., 74,4751 (1952); (c) F. H. Spedding and J. L. Dye, ibid., 7 6 , 879.(1954): (d) F. H. Spedding a n d S. Jaffe, ibid., 76, 882, 884 (1954).
Apparatus.-The apparatus was patterned after one developed by Gucker, Pickard and Planck.' Aside from several minor changes, the apparatus differed from the one
Experimental.
Heats of Dilution
(4) C. C. Nathan, W. E. Wallace and A. L. Robinson, ibid.. 65, 790 (1943). (5) E. Lange and W. Miederer, 2. Elekfmchcm., 60, 362 (1956). ( 0 ) (a) F. H. Spedding and C. F. Miller, THIS JOIJRNAI.,74, 3158 (1952); (b) 74, 4195 (1952). (7) F. T. Gucker, J r . , H. B. Pickard and R . W. Planck, ibid., 61, 459 (1939)
described by Gucker, et el., only in the manner in which the temperature difference between the calorimeter containers was measured, and in the type of sample holders employed. The details of construction have been described elsewhere.8 The temperature difference between the calorimeter containers was measured with a 60 junction copper-constantan thermel. The output of the thermel was amplified by a model 14 Liston--Becker breaker type d.c. amplifier and was recorded on a recording potentiometer. With this arrangement a sensitivity nf 1.8 X I V 4 cal. per mm. of chart displacement was realized. Each sample holder consisted of two threaded cylinders held together by a cross piece. The cylindrical tubes of the sample holders had inside diameters of two cm. and were four cm. long. The sample holders were mounted in the calorimeter by attaching the cross pieces to supporting stems extending through the lids of the calorimeter containers. Screw-on caps held platinum disks 0.0005 inch thick firmly against the ends of the tubes. The sample holders were opened by punching holes in the platinum foils. b’ith a two chambered sample holder in each container, i t was possible to obtain two “short chord” heats of dilution without dismantling the apparatus. Ten-ml. samples were measured into the sample holders with a pipet, and the samples were weighed. The tantalum containers were filled with water to give a total liquid content, water plus samples, of 900 g. for each container; the weighings were made t o the nearest drop with a 2 kg. capacity analytical balance. Materials.-The rare earths employed in this research were obtained as the oxides from the rare earth separation group of the Ames Laboratory of the U. S. Atomic Energy Commission. T h e methods of rare earth separation and purification have been described elsewhere.? T h e results of spectrographic analyses of the oxides showed the rare earths to contain less than 0.15% total impurities. The impurities consisted of traces of calcium and adjacent rare earths. The experimental measurements were carried out on solutions t h a t were prepared by diluting stock solutions. One stock solution of each salt was prepared by adding a slight excess of the oxides to C.P. Baker and Adamson hydrochloric or nitric acid. The resulting solutions were held near boiling for several hours and the excess oxides removed by filtration. The filtrates were diluted to approximately 0.25 molal, and aliquots were titrated with the appropriate acid. Typical strong acid-weak base titration curves resulted. The bulk solutions were brought to the pH of the inflection points of the titration curves, held near boiling for several hours and aliquots again taken for titration. This procedure was repeated until reproducible equivalence pH’s were obtained and the bulk solutions showed no Tyndall cones. A second neodymium chloride stock solution was prepared by treating neodymium oxide with a slight excess of redistilled hydrochloric acid. Conductivity water was added, and the solution was evaporated until crystals had formed three times. After the third heating, the solution was diluted to about one molal and titrated as described above. A second erbium chloride stock solution was prepared from hydrated erbium chloride crystals. The crystals were grown by dissolving erbium oxide in a slight excess of acid, heating the resulting solution until viscous and drying over calcium chloride in a n evacuated desiccator. I n the case of the chlorides, the stock solutions were analyzed for both rare earth content and chloride ion content; for the nitrates, only a rare earth analysis was made. T h e rare earth and chloride analyses agreed to better than one or two parts per thousand. Dilutions of the stock solutions were made by weight. T h e density data of B. 0. Ayers9 were used to calculate vacuum corrections. Conductivity water with a specific conductivity of l.,i X 10-6 mho or less was used for all dilutions.
Results. Heats of Dilution The experimental determinations were of two types. In the first type, samples containing n2’ moles of salt in nl’ moles of water mere diluted with ( S ) (a) A. W. Naumann, Ph.D. Dissertation, Iowa S t a t e College Library, Ames, Iowa, 1956; (b) R. E. Eberts, Ph.D. Dissertation, Iowa S t a t e College Library, Ames, Iowa, 1957. (9) B. 0. Ayers, Ph D. Dis?ertation, Iowa State College T,ibrary, Ames. Iowa, 1954.
X
grams of water. In determinations of the second type, samples containing n2“ moles of salt in nlRmoles of water were diluted by solutions resulting from determinations of the first type. The heat, q, evolved by these determinations was given by ql = - n ’ I ~ I -- 41,m,\l + QH (1) and i,,
‘12
= -
(W?’
+ r1”)4r + n?”@r Inis)
1711)
+
+ g~
n?’+um2)
(2,
In the expressions above, ml is the molality of the samples; m2,the molality following a dilution of the first type; m3, the molality following a dilution of the second type; 4 ~ the , relative apparent molal heat content of the solute; and q ~the , heat of opening of the same holders. The experimentally determined quantities were converted to intermediate integral heats of dilution by means of the relationships
and when n2’ m n z n ,as was the case for these experiments
The “short chord” method of Young and coworkers1° as extended by Wallace and Robinson1’ was used to analyze the igtermediate heats of dilution. In this treatment, Pi,the average slope of 41. zeYsus m’/P for the very dilute concentration range, is calculated by - = -AH$,J p, 1711’
(6)
=In equation of the form is derived for the concentration dependence of Pi for this concentration range. Equation 7 is then integrated to give +L(mk), the relative apparent molal heat content for the extremely dilute solutions of molality mk. The values of 4 ~ for . the solutions used are obtained from the expression #Lp,)
=
4L(rnr)
- hHl,k
(8)
where A H 1 , k = an intermediate heat of dilution corresponding to some A H l , n or A H I , ~ . Blank Experiments Forty-two measurements were made with water samples to determine the “heat of opening” of the sample holders. The results of these measurements were as Average heat of opening, cal. Standard deviation, cal.
1 2 . 3 X lo-“ 2 . 5 X lo-’
Results of Dilution Experiments The experimentally determined heats of dilution of the rare earth salt solutions a t 25’ are summarized in Table I and shown in Figs. 1 through 4. (10) (a) T. F. Young and 0. G . Vogel, THXSJOURNAL, 54, 3030 (b) T. F.Young and W. I,. Groenier, ibid., 68, 187 (1936). (11) W. E. Wallace and A. L. Robinson, i b i d . , 63, 9
