F. H. SPEDDING, M. J. PIKAL, AND B. 0. AYERS
2440
efficient, and the variations of the viscosity ratio with ionic radius at these concentrations may be interpreted using basically the same model and arguments presented when discussing the B coefficients. It may be noticed that the increase in the viscosity ratio with decreasing ionic radius becomes much more pronounced as the concentration increases. Although this phenomenon may seem surprising a t first, it is a direct result ~ ~(kl. ~ of the positive sign of the quantity, ( k l i i ) O)LSCL,, and of the concentration dependence of the obstruction effect (ie.,eq 2 or eq 3).
However, a t higher concentrations, the general shape of the viscosity ratio-ionic radius curve begins to change until at 3.6 m, shown in Figure 5 , it appears as through two distinct series exist, LaCh and NdC&forming one series and the rare earth chlorides from Sm through Er forming the other series. Figure 5 may also be interpreted as indicating the viscosity of NdCL is anomalously high, and the viscosities of the other rare earth chlorides form just one series. Viscosity data for concentrated solutions of CeC4 and PrCh are needed before it can be proved which interpretation is correct.
Apparent Molal Volumes of Some Aqueous Rare Earth Chloride and Nitrate Solutions at 2 5 O I
by F. H.Spedding, M. J. Pikal, and B. 0.Ayers Institute for Atomic Research and Departmmt of Chembtry, Iowa State University, Ames, Iowa (Received December 81, 1966)
The specific gravities and apparent molal volumes of aqueous solutions of 14 rare earth salts were determined over a concentration range of about 0.002-0.2 m. A magnetically controlled float apparatus was used to determine the specific gravities with an accuracy of about * 5 X lo-'. The apparent molal volumes showed significant deviations from the simple limiting law a t low concentrations. However, it was shown that, except for Nd(N03)3, these deviations are consistent with interionic attraction theory, provided the effect of the distance of closest approach parameter, a, is recognized. The partial molal volumes a t infinite dilution, Vz0, do not vary smoothly with ionic radius of the cation for either anion series. The Tz0values decrease with decreasing ionic radius from La to Nd and from T b to Yb, but from Nd to Tb the Vz0values increase with decreasing ionic radius. A change in preferred coordination number of the R3+-Hz0 species a t a critical cation radius is postulated to account for this behavior.
Introduction Although the concentration dependence of apparent molal volumes in dilute solution have been investigated for many 1-1 eleCtrOlYteS,2'3accurate data On higher valence type electrolytes are very scarce. Therefore, it W a s decided to determine the apparent molal vohmes of Wme rare earth chlorides and nitrates Over the concentration range 0.002-0.2 m. It W a s expected that The Journal of Physical Chemistry
these data would provide useful information on ionsolvent interactions, hniting behavior of 3-1 salts, and (1) Work was performed in the Ames Laboratory of the u. 8.Atomic Energy Commission. This paper is based, in part, on the Ph.D. dissertation of B. 0. Ayers submitted to the Graduate Faculty of Iowa State University of Science and Technology, Ames, Iowa, 1954, and on the Ph.D. dissertation of M. J. Pikal submitted to the Graduate Faculty of Iowa State University of Science and Technology, Ames, Iowa, 1966; Contribution NO. 1836.
APPARENTMOLALVOLUMES OF AQUEOUS RAREEARTH SALTSOLUTIONS AT 25"
additivity of ionic partial molal volumes at infinite dilution. The partial molal volume a t infinite dilution, VZo, may be written in the form
F'zo
=
V &4- AVH~O
(1)
V8is the volume occupied by one mole of solute, while AVH~O represents the effects of ion-solvent interactions and is the net change in the volume of water phase resulting from the addition of 1 mole of solute to an infinite quantity of water. Because of the regular decrease of ionic radii across the lanthanide series, the rare earth salts offer an ideal opportunity to study variation of the partial molal volume at infinite dilution with ionic radius. Therefore, accurately determined values of Vzofor the rare earth chlorides and nitrates should provide valuable information on ion-solvent interactions. I n 1931, Redlich and Rosenfeld4 derived an expression for the apparent molal volume, &, from the Debye-Huckel theory, which may be written as &. = $ J ~ ~ KW'/'C'/' (2)
+
where W is the valence factors, l / ~ c v i z ? and , K is a i
function of temperature, solvent properties, and fund* mental constants. I n the past there has been some uncertainty in K because of the uncertainty of the pressure derivative of the dielectric constant of water, b In D / b P , which appears in K. However, a recent review by Redlich and Meyerzb considers this problem in some detail and concludes, on the basis of recent measurements of b In D / b P by Owen and c o - ~ o r k e r sthat ,~ K = 1.868 at 25' for water as the solvent. Theoretically, eq 2 is limited to extremely low concentrations, and it has been well verified experimentally as a limiting law.2 I n fact, many salts obey this limiting law up to concentrations as high as a few tenths molar, although approximations made in deriving eq 2 are not justified at these concentrations. It seems certain that eq 2 will be valid for 3-1 electrolytes as a limiting law, but it is of interest to examine the deviations from eq 2 a t nonzero concentrations for 3-1 salts. Using the data of Baxter and Scott6bfound the partial molal volumes at ingnite dilution of the halides were additive properties of the individual ions. Although it is usually assumed that this additivity is valid for all valence types, experimental confirmation of this assumption is slight for 3-1 salts. Therefore, the additivity assumption will be investigated for the 3-1 salts studied in this research.
ExDerimental Section A . Preparation of Materials. The rare earth chlorides and nitrates used in this research were prepared
2441
by dissolving the oxides in pure acids. The oxides were obtained from the rare earth separation group of the Ames Laboratory of the U. S. Atomic Energy Commission. The rare earth oxides were analyzed for impurities due to other rare earths and common elements by emission spectrographic techniques. I n all cases, impurities due to other rare earths were less than 0.1% and impurities due to other elements (mostly iron and calcium) were less than 0.1%. I n preparing the rare earth chloride primary stock solutions, the dry oxides were added slowly to a slightly less than equivalent amount of approximately 6 N acids. The excess oxides were removed by filtering the solutions through a fine sintered glass filter. T h e solution in this form contained some colloid, which was readily detected by the formation of a Tyndall cone from a small beam of light passing through the solution. A small portion of the solution was removed and used to determine the equivalence point of the suspected hydrolysis reaction
R3+
+ HzO Jr R(OH)'+ + H f
(3)
by titration with 0.05 N HCI. Typical strong acidweak base titration curves were obtained, and the equivalence point was determined from a plot of pH against the volume of acid added. The equivalence pH values for the various rare earth solutions were usually around pH 2 for primary stock solutions of about 2.7 rn. The primary stock solution was then adjusted to the equivalence pH and heated for several hours to dissolve any oxychloride or colloidal oxide present. The solution was cooled, the pH adjusted again to the equivalence pH, and the solution was heated again for several hours. This process was carried out several times until the pH did not change from the equivalence pH. Solutions prepared in this way were found to be very stable and free of colloid. The rare earth nitrate solutions were prepared by the same procedure, except that nitric acid was used in place of the hydrochloric acid. Secondary stock solutions of low and moderate concentrations were prepared from weighed quantities of a (2) (a) 0. Redlich, J. Phys. Chem., 44, 619 (1940); (b) 0.Redlich and D. Meyer, Chem. Rev., 64, 221 (1964). (3) H. s. Harried and B, B, Owen, physical Chemistry of Electrolytic Solutions," 3rd ed, Reinhold Publishing Corp., New
York, N. Y.,1958. (4) 0.Redlich and P. Rosenfeld, Z . Physik. Chem., A155, 65 (1931). (5) B. B. Owen. R. C. Miller. C. E. Milner. and H. L. Conan. - . J. Phys. Chem., 65; 2065 (1961). (6) (a) G.P. Baxter and C. C. Wallace, J. Am. Chem. Sac., 38, 70 (1918); (b) A. F. Scott, J. Phys. Chem., 35, 2315 (1931). '
Volume 70, Number 8 August 1966
F. H. SPEDDING, M. J. PIKAL, AND B. 0. AYERS
2442
primary stock solution and conductivity water. The conductivity water had been prepared by redistillation of distilled water from an alkaline potassium permanganate solution and had a conductance of less than 10-6 mho/cm. The potassium chloride used in checking the apparatus was prepared by fusing reprecipitated potassium chloride in platinum crucibles at 800" under an atmosphere of dry argon. The potassium chloride solutions were prepared by adding weighed amounts of the fused potassium chloride to weighed quantities of conductivity water. The primary stock solutions were analyzed for rare earth concentration by one of two methods. 1. Sulfate Method. A quantity in 10% excess of 3N sulfuric acid was added to the rare earth solution, and then the sample was dried, heated in a gas burner, ignited to 500" in an electric furnace, and weighed as Rz(S04)3. Each analysis, made in triplicate, gave a mean deviation of less than 0.05%. This method was used for TbCl3 and PrC13. 2. Oxalate Precipitation Method. A 10% excess of oxalic acid was added to the solution in each crucible, and the resulting precipitates were then dried, ignited in an electric furnace at 950", and weighed as the oxide, R203. The mean deviation for a triplicate analysis was less than 0.05% in all cases. This method was used for all the rare earth solutions except PrC13 and TbC13. The rare earth chlorides were also analyzed for the chloride concentration by either the standard silver chloride gravimetric procedure or a potentiometric method using a silver-indicating electrode and a sleevetype reference electrode with an ammonium nitrate bridge to the inner calomel electrode. Both these methods gave mean deviations less than 0.1% for three samples. The chloride analysis agreed with the rare earth analysis within about 0.1% in all cases. All calculations were based on the rare earth analysis for LaC13, NdC13, YbC13, and the rare earth nitrates. For PrC13, SmC13, GdC13, TbC13, DyC13, HoCL, and ErC13, the averages of the rare earth and chloride analyses were used in the calculations. B. Apparatus. The apparent molal volumes may be calculated from the specific gravity of the solution, p / p o , the molar concentration, c, the molecular weight of the solute, MP, and the density of the solvent, PO, by the equation 4J" = (1 - P/Po)1ooo/c
+ MdPo
(4)
where PO = 0.99707 g/m1.7 Since the specific gravity is close to unity in dilute solutions, the apparent molal volumes of dilute soluT h e Journal of Physical Chemistry
tions are very sensitive to small errors in specific gravity. Therefore, an accuracy of better than i l x in the specific gravity is needed to obtain accurate data below about 0.02 M. Consequently, the method chosen for measuring the specific gravities was the magnetically controlled float method originated by Lamb and Lees and modified by other^.^^^^ This method consists of determining the current in a solenoid, which is just sufficient to balance a float of known weight in the solution through the interaction of the field of the solenoid with a permanent magnet in the float. This value of the current will be called the equilibrium current, Io. The interaction between the solenoid and the permanent magnet is empirically calibrated in terms of the weight equivalent of the current, \k. A specific gravity run consisted of first determining the equilibrium current for pure water, which in effect, calibrates for the volume of the float. Conductivity water prepared as described earlier was used for this purpose. Xext, portions of the appropriate stock solutions, sufficient to give solutions of the desired concentrations, were added to the cylinder containing the water and float. For each solution, platinum weights were added to the float until a solenoid current of several hundred milliamperes would balance the float, and the exact equilibrium solenoid current was determined. The platinum weights were then weighed on a microbalance to better than =kO.O1 mg and corrected to weight in the solution, using 21.428 g/cc for the density of platinum.1° From the weight of the float, weight of the platinum weights in solution, equilibrium current in solution, equilibrium current in pure water, and t8hecalibration factor, 'k, the specific gravity of the solution was calculated. About four or five different concentrations were measured during a single run. Temperature control was maintained within ~ 0 . 0 0 1 " . Two different methods of determining the equilibrium current were used. Method 1. The solenoid was designed so that a current through the solenoid resulted in a downward force on the float, and the equilibrium current was obtained by determining the minimum current necessary to prevent the float from rising. With this method, the equilibrium current could be determined (7) N. E. Dorsey, "Properties of Ordinary Water-Substance,'' Reinhold Publishing Corp., New York, N. Y.,1940. (8) A. B. Lamb and R.E. Lee, J. Am. Chem. Soc., 35, 1666 (1913). (9) W. Geffchen, C. Beckmann, and A . Kruis, 2. P h y s i k . Chem.,
B20, 398 (1933). (10) D. A. MacInnes, M. 0. Dayhoff, and B. Znstr., 22, 642 (1951).
R. Ray, Rev. Sei.
APPARENT MOLALVOLUMES OF AQUEOUS RAREEARTH SALTSOLUTIONS AT 25"
within about *0.2 ma. Due to difficulty in placing the cylinder containing the float and water in exactly the same position within the solenoid each time, it was necessary to calibrate for 9 before each specific gravity run. With method 2, this was not necessary, and even with method 1, the variation of 9 due to this problem seldom was more than twice the estimated experimental error in \k. Calibrations for \k gave values of about 0.1 mg/ma, with an uncertainty of less than *0.001 mg/ma. No variation of the equilibrium current wit.h atmospheric pressure was found for the cylindrical float used with method 1. Specific gravities of PrC13, SmC13, GdC18, TbCla, DyC13, HoC13, and ErCL were measured by this method. Method 2. The solenoid current resulted in an upward force here, and the equilibrium current was obtained by extrapolating the average rate of rise to zero velocity by use of a l / t 2 vs. I plot, where t is the time required for the float to pass between two marks and I is the current through the solenoid. This type of plot was found to be linear, except for high current values, and the range of extrapolation was very small. With this method, the equilibrium current could be determined within about *0.5 ma. Calibration for 9 gave a value of 0.05254 f 0.0002 mg/ma. The equilibrium current was found to be strongly dependent on the atmospheric pressure for the conical float used with this method. This pressure dependence was calibrated for, and an average value of A I o / A P = 1.08 f 0.01 ma,/mm was obtained. C. Experimental Errors. A serious limitation on the accurate determination of the apparent molal volumes was due to the uncertainties in the concentrations of the solutions. These uncertainties were due to two factors, errors made in weighing quantities of stock solutions into the cylinder, and the limitation in accuracy of the analytical method used. The uncertainties in the apparent molal volumes due to errors in the weights of stock solution were estimated to be less than *0.05 nil/mole. An analysis error results in a constant error in & of 0.25 ml/mole for each 0.1% error in concentration. The data for Nd(NO&, PrC13, GdC13, and DyCL, which were obtained using two independently prepared and analyzed primary stock solutions, indicate the analysis error is less than *0.05%. Therefore, the probable error in & resulting from an analysis error was estimated to be about f0.15 ml/mole. The probable error in specific gravity was estimated to be less than *5 X 10-7. This error contributes a significant error to &t only for concentrations below 0.01 m. The error in the apparent molal volume a t
2443
infinite dilution was estimated to be less than 1 0 . 2 ml/mole. D. Apparent Molal Volumes of Potassium Chloride. As a final check on the apparatus, apparent molal volumes of aqueous solutions of potassium chloride at 25" were measured. The specific gravities and apparent molal volumes obtained for potassium chloride are given in Table I. The apparent molal volumes obtained from the measurements in this laboratory were in excellent agreement with those by Geffchen and Price1' and by Kruis. l2 Table I: Apparent Molal Volumes of KCl a t 25" #V9
CVl
P/PQ
ml/mole
0 0.085719 0.119508 0.145207 0.164685 0.18101 0.25264 0.30171 0.44879 0.55886 0.64703
1.0003510 1.0006818 1,0010047 1.0012917 1.0015593 1.0030303 1.0043131 1.0094826 1.014637 1.019547
26,840 27.00 27.05 27.13 27.16 27.19 27.30 27.39 27.69 27.91 28.08
'Extrapolated by use of the extrapolation equation, 6,. = 26.84 1.868~~1' 0.08~.
+
+
Results The experimental data for the rare earth salts studied are given in Table 11. The experimental apparent molal volumes in ml/mole, (r$v)exptl, are given in the fourth column, and smoothed values, (&)cs~cd, are given in the fifth column. These smoothed values were calculated from eq 9 for Nd(NO& and from eq 6 for the other salts. The concentrations are given in units of molarity, c, and molality, m. The value of the apparent molal volume at infinite dilution, &", which is of great interest, must be obtained by extrapolating the experimental data to infinite dilution. Redlich and Meyer2b recommend that apparent molal volume data be extrapolated using the equation +y
=
&O
+ 1.868W"/'c'/*+ hc
(5)
where W is the valence factor defined earlier and h is an arbitrary parameter to be determined by the data. For a 3-1 electrolyte, 1.868Wa//"is equal to 27.44. ~~~~~
~
(11) W.Geffchen and D. Price, 2.Physik. Chem., B26, 81 (1934). (12) A. KN~s,ibid., B34, 1 (1936).
Volume 70, Number 8 August 1966
F. H. SPEDDING, M. J. PIKAL, AND B. 0. AYERS
2444
Table I1 : Specific Gravities and Apparent Molal Volumes m'/z
p/pa
(4v)erptl
0.031747 0.077677 0.10753 0.14782 0.20753 0,28557 0.36935 0.44744 0.51274 0.58169
LaCl3 1.0002324 1.0013816 1.0026400 1.0049727 1.0097570 1.018379 1.030573 1.044626 1.058325 1.074661
14.80 16.35 17.01 17.68 18.63 19.63 20.62 21.50 22.22 23.00
0.041695 0.068634 0.087385 0.13573 0.16644 0.23327 0.29613 0.36443 0.42354
PrC13 1.0004092 1,0011053 1.0017892 1.0042986 1.0064508 1.012611 1,020250 1.030528 1.041089
0.043602 0.059275 0.075892 0.11769 0.15078 0.24403 0.33733 0.40207 0.45515 0.49739 0.53817 0.59066
0.043667 0.059601 0.076007 0.11787 0.15102 0.24450 0.33813 0.40321 0.45664 0.49922 0.54039 0.59347
NdC13 1.0004564 1.0008488 1.0013785 1.0033057 1.0054145 1.014089 1.026795 1.037953 1.048514 1.057825 1.067553 1.081188
11.30 11.70 12.04 12.70 13.22 14.70 15.90 16.63 17.20 17.66 18.14 18.67
0.045036 0.046100 0.073046 0.095015 0.13175 0.16024 0.22644 0.28755 0.35857 0.41872
0.045103 0.046169 0.073157 0.095162 0.13196 0.16051 0.22687 0.28817 0.35949 0.41998
SmC18 1,0004971 1.0005210 1.0013056 1.0022054 1.0042297 1.0062459 1.012425 1.019975 1.030958 1.042106
12.38 12.32 12.78 13.18 13.81 14.23 15.15 15.89 16.68 17.32
0.043494 0.057520 0.090054 0.12334 0.15915 0.20390 0.29407 0.37189 0.42315
GdCla 1.0004718 1.0008245 1.0020160 1,0037713 1.0062666 1.010254 1.021222 1.033773 1.043613
e'/2
0.031700 0.077559 0.10737 0.14757 0.20714 0,28492 0.36829 0.44583 0.51050 0.57858 0.041633 0.068530 0.087251 0.13551 0.16616 0.23282 0.29549 0.36348 0.42226
0.043430 0.057433 0.089915 0.12314 0.15888 0.20353 0.29340 0.37085 0.42181
The Journal of Physical Chemistry
11.92 12.65 12.97 13.91 14.35 15.36 16.08 16.94 17.55
m'/z
P/PQ
(4v)expt 1
(4v)calcd
0.039062 0.070770 0.085471 0.13862 0.16029 0.22822 0.29238 0.36527 0.43056
0.039120 0.070878 0.085602 0.13885 0.16056 0.22866 0.29304 0.36626 0.43198
TbCla 1.0003839 1.0012586 1.0018328 1.0048054 1.0064137 1.012959 1.021193 1.032977 1.045679
14.46 14.77 15.18 15.99 16.44 17.27 18.16 18.90 19.66
14.22 14.89 15.17 16.06 16.38 17.31 18.10 18.93 19.66
0.041586 0.064935 0.086923 0.13661 0.16315 0.23848 0.27972 0.35331 0.40290
0.041647 0.065034 0.087057 0.13683 0.16342 0.23894 0.28032 0.35425 0.40412
DyCla 1.0004424 1.0010777 1.0019267 1.0047435 1.0067549 1.014373 1.019736 1.031379 1.040719
13.85 14.07 14.65 15.65 15.88 16.92 17.42 18.28 18.82
13.70 14.19 14.62 15.66 15.88 16.91 17.43 18.28 18.82
11.26 11.61 11.96 12.76 13.33 14.69 15.86 16.62 17.21 17.67 18.12 18.69
0.045283 0.065715 0.076195 0.093206 0.11052 0.15269 0.16191 0.19607 0.22756 0.28329 0,34586 0.36281 0.41869
0.045306 0.065813 0.076312 0.093350 0.11069 0.15285 0.16219 0.19642 0.22800 0.28390 0.34673 0.36376 0.41998
HOC13 1.0005306 1.0011176 1.0015012 1.0022439 1.0031499 1.0059894 1.0067421 1.0098644 1.013266 1.020505 1.030469 1.033504 1.044513
12.82 13.29 13.52 13.80 14.20 14.87 14.92 15.50 15.92 16.59 17.38 17.56 18.17
12.85 13.29 13.50 13.83 14.15 14.84 14.98 15.48 15.92 16.62 17.36 17.55 18.18
12.25 12.28 12.82 13.22 13.83 14.26 15.13 15.87 16.68 17.33
0.045679 0.067254 0.091134 0.14496 0.16076 0.23456 0.28131 0.35643 0.41841
0.045747 0.067355 0.091274 0.14519 0.16102 0.23500 0.28190 0.35732 0.41966
11.75 12.27 12.64 13.73 13.86 14.96 15.48 16.41 17.05
11.77 12.24 12.71 13.65 13.90 14.94 15.53 16.39 17.05
10.00 10.20 11.00 10.67 11.12 11.52 11.80 11.87 12.63
10.31 10.32 10.79 10.98 11.24 11.42 11.70 11.80 12.55
(4v)calcd
15.31 16.34 16.93 17.65 18.58 19.64 20.65 21.53 22.24 22.96 12.01 12.61 12.99 13.85 14.37 15.33 16.13 16.92 17.47
c'/1
ErC13 1.0005481 1.0011858 1.0021743 1.0054778 1.0067342 1.014276 1.020492 1.032779 1.045059 YbCla 14.25 14.43 15.03 15.67 16.15 16.84 17.87 18.82 19.26
14.15 14.44 15.08 15.64 16.19 16.81 17.91 18.75 19.30
0.041431 0.041962 0.063665 0.073942 0.080650 0.097085 0.11333 0.11864 0.16520
0.041492 0.042025 0.063761 0.074054 0.080773 0.097234 0.11351 0.11883 0.16547
1.0004638 1.0004756 1.0010913 1.0014740 1.0017505 1,0025328 1.0034470 1,0037769 1.0073203
APPARENTMOLALVOLUMESOF AQUEOUS RAREEARTHSALTSOLUTIONS AT 25’
2445
Table I1 (continued) m1/2
c1/2
(dv)axptl
(6v)oalod
C1/2
13.15 14.25 15.25 15.93 16.77
13.23 14.31 15.25 15.92 16.76
1.0013258 1.0019394 1.0042530 1.0088315 1.015965 1.019982 1,033430 1.058493
49.90 51.29 51.45 52.46 53.35 54.47 55.01 56.21 57.92
50.42 51.12 51.45 52,32 53.40 54.50 54.98 56.24 57.90
0.070916 0.071388 0.10601 0.10619 0.11013 0.13917 0.14233 0.15034 0.19302 0.19940 0.20302 0.26644 0.27116 0.27572 0.32668 0.34082 0.34150 0.39531 0.41853 0,42054 0.49051 0.50415 0.51675
0.071029 0.071503 0.10620 0.10638 0.11033 0.13945 0.14261 0.15065 0.19349 0,19990 0.20354 0.26733 0.27209 0.27669 0.32810 0.34239 0.34309 0.39760 0.42120 0.42324 0,49459 0.50857 0.52146
0.062677 0.097688 0.13662 0.18538 0.26557 0.33216 0.40407 0.45538
0.062775 0,097853 0.13688 0.18580 0,26641 0.33356 0.40631 0.45844
P/PQ
(Qdexptl
(4v)oalod
47.38 47.49 48.65 48.54 48.48 49.59 49.54 49.60 50,79 50.80 51.22 52.26 52.49 52.77 53.55 53.66 54.00 54.76 54.98 55.33 56.29 56.61 56.58
47.36 47 I37 48.47 48.48 48.59 49.43 49.52 49.73 50.82 50.97 51.05 52,43 52.53 52.62 53,58 53.83 53.84 54 I75 55.13 55.16 56.28 56.50 56.71
44.95 45.50 46.24 47.00 48.08 48.85 49.59 50.17
44.87 45.57 46.24 47.00 48.06 48.84 49.62 50.16
YbCls 1.012560 1.024905 1.040642 1.054617 1.074938
0.21688 0.30599 0.39163 0.45457 0.53331
0.21727 0.30664 0.39266 0.45600 0.53538
0,040273 0.069485 0.084062 0.12471 0.18001 0.24252 0.27160 0.35207 0.46720
0.040334 0,069596 0.084202 0.12495 0.18043 0,24327 0.27256 0.35384 0.47088
0.030997 0.058790 0.10670 0.14268 0.18591 0,25819 0.32930 0.39427 0.46407
0.031044 0.058883 0 ,10688 0.14296 0.18635 0.25901 0 33070 0,39643 0 46739
Er(N0a)a 1.0002959 1,0010361 1.0034914 1.0062330 1.010559 1.020300 1.032931 1.047098 1.065087
46.30 46.68 47.57 48.08 48.77 49.75 50.59 51.28 52.05
46.17 46.68 47.58 48.16 48.78 49.72 50.56 51.29 52.06
0.033484 0.035151 0.035495 0.059274
0,033534 0.035204 0.035549 0.059451
Nd(NOs)s 1.0003196 1.0003528 1,0003592 1IO009998
46.20 45.80 46.20 46.70
46.05 46.11 46.13 46.97
La (Nods
I.0004477
Yb(N0s)s
Unfortunately, plots of & - 27.44~”’against c show a great deal of curvature, making eq 5 unsatisfactory for extrapolating the rare earth salts. Owen and Brinkleyla derived an extrapolation function for the apparent molal volume which includes the effect of the ion size (the a parameter). For a 3-1 electrolyte with 8 theoretical limiting slope of 27.44, their result becomes
4,
+ 2 7 . 4 4 ~ ( ~ ~ +) ~ ’ / ’
=
‘/zvd(Ka)c
where
+ ‘/a&(6)
equals 0.8051dc”’ for a 3-1 electrolyte. ~ ( K u and ) ~ ( K U )approach unity as the concentration decreases and are defined by KU
+ In (1 + e(z) = ( 4 / ~ 4 ) [ ~ 2 / 2 2~ - 1 + ~(2= )
(3/z3)[s2/2 3 In (1
2
2)]
+ + 1/(1 + 41 X>
1.0014275 1.0014462 1.0031763 1,0031882 1.0034298 1.0054557 1.0057071 1.0063664 1,010449 1.011152 1.011543 1.019790 1.020499 1,021172 1,029637 1.032277 1,032335 1,043209 1.048399 1,048802 1.066158 1,069810 1,073355 1.0012379 1,0030024 1.0058586 1.010760 1.022008 1.034344 1.050700 1.064275
The distance of closest approach, a, may be evaluated from activity coefficient data, and although Wv may, in principle, be calculated from theory, it must be evaluated from the data due to the appearance of the unknown derivative, b In a/bP. K , is an empirical parameter that must be evaluated from the data. The apparent molal volumes of the solutions studied in this research were extrapolated using eq 6 . The values of the a parameter were evaluated from activity coefficient data for the rare earth chlorides and from conductivity data for the rare earth nitrates. The values of QLO, l/2Wv, and l/2Kv were determined from the data by the principle of least squares, using the inverse square of the probable error in 4, as the weight-
(7) (8)
(13) B. B. Owen and S. R. Brinkley, Jr., Ann. N . Y . Acad. Sci., 51, 753 (1949). See also, H. S. Harned and B. B. Owen, “The Physical Chemistry of Electrolytic Solutions,” 3rd ad, Reinhold Publishing Corp., New York, N. Y.,1958.
Volume 70, Number 8 August 1966
F. H. SPEDDING, M. J. PIICAL, AND B. 0. AYERS
2446
ing factor, and are given in Table 111, along with the values of the a parameter.
I n the last column, the root mean square deviations,
RMSD, of the calculated values from the observed values are given.
Table I11 : Parameters for Owen-Brinkley Equation Table IV: Parameters for the Equations 6,. = a0 azm 14.51 10.96 10.18 11,16 13.08 13.25 12.66 11.73 10.63 9.27 49.37 44,74 45.28 43.37
36.33 34.47 23.82 3.83 9.56 13.00 9.53 27.45 30.92 20.07 32.82
4.904 4.254 5.401 6.747 5.794 6.519 5.713 5.787 4,732 5.537 5.815
5.75" 5.73" 5 . 4gb 5.63" 5.63" 5 . 85d 5 . 32b 6 . 04b 5 . 92b 5 . 90b 4.46
...
...
...
8.29 32.41
6.539 4.821
5.6' 6.05'
' F. H. Spedding, P. E. Porter, and J. M. Wright, J . Am' Chem. Soc., 74, 2781 (1952). F. H. Spedding and J. L. Dye, ibid., 76, 879 (1954). F. H. Spedding and I. S. Jaffe, ibid., 74, 4751 (1952). R. Nelson, M.S. Thesis, Iowa State University of Science and Technology, Ames, Iowa, 1960. D. Heiser, Ph.D. Dissertation, Iowa State University of Science and Technology, Ames, Iowa, 1958.
'
The experimental data fit eq 6 within experimental error for all the rare earth salts studied except Nd( N o d 3. Empirical "least-squares" equations of the form
4,
= a0
+ alml/' + e m + a3m'/'
(9)
where m is the molal concentration, were found to represent the experimental apparent molal volumes within experimental error. I n spite of the disadvantages in using an empirical equation of this form for extrapolation, the data for Nd(N08)3 were extrapolated using eq 9. The value of +O, in Table I11 for Nd(N03)3refers to the extrapolation using eq 9. Although eq 6 is preferred for extrapolation, both eq 6 and eq 9 give essentially the same value of 4, above 0.01 m, so there is little reason to use the more cumbersome Owen-Brinkley equation for interpolation. Furthermore, the partial molal volumes may easily be calculated from the parameters in eq 9 by the equation
v2= a0 + 3/2aln~l/~+ 2a2m + 5/2a3ma/a (10) The parameters of eq 9 for the rare earth salts studied were determined by the principle of least squares, using the inverse square of the probable error in +, as the weighting factor, and are tabulated in Table IV. The Journal of Phy8ica.t Chemistry
+ a3m'/p and Vz
Salt
LaCl3 PrCls NdCls SmCla GdCls TbCl3 DyCla HOC13 ErC13 YbCls La( NO& Nd( NO,)a Er( N03)8 Yb(NOs)s
= a0
+ alml/a +
+ 8/zalm1/2+ 2a2m + 6/zaam'/2
ao
ai
az
aa
RMSD
14.38 10.96 10.48 11.42 13.30 13.51 12.82 11.83 10.69 9.22 49.08 44.74 45.59 43.60
27.83 26.58 21.15 20.56 21.72 21.02 22.90 24.38 25.33 26.64 32.19 40.42 20.28 22.31
-42.02 -42.55 -19.28 -21.81 -25.94 -23.02 -29.97 -35.72 -38.86 -45.10 -53.01 -54.02 -19.95 -25.72
33.97 39.22 11.63 14.90 18.92 16.70 24.97 32.58 35.01 40.81 52.21 39.39 13.05 17.62
0.07 0.04 0.03 0.02 0.04 0.06 0.04 0.03 0.04 0.12 0.11 0.13 0.03 0.03
Discussion 1. Interpretation of b ln a/bP. Although the apparent molal volumes studied in this research were well represented by the Owen-Brinkley equation, with the exception of Nd(NO&, any interpretation of b In a/bP values calculated from the W , parameters must be treated with caution. When W , is evaluated from the data, it seems likely that higher order effects, such as association and dielectric saturation, may contribute more to the parameter W , than the terms predicted by theory. However, since the OwenBrinkley equation in the form of eq 6 does fit the data very well and has the correct limiting slope, the equation is very useful for accurately extrapolating the data to determine the apparent molal volumes at infinite dilution. 2. Behavior of rp0 at Low Concentrations. The limiting behavior of the apparent molal volume is given by eq 2. Calculation of the valence factor for a 3-1 electrolyte gives +v
=
+vo
+ 27.44~"'
(11)
Equation 11 must certainly be valid as a limiting law. However, contrary to the behavior of many lower valence-type electrolytes, the rare earth salts studied showed significant deviations from the simple limiting law, given by eq 11, above a few thousandth molar. I n Figure 1, experimental values of +, are plotted against cl/* for NdC13 and Nd(N03)3. The circles represent experimental points, while the dashed line
APPARENT MOLALVOLUMESOF AQUEOUS RAREEARTHSALTSOLUTIONS AT 25"
I
58.0
-
1
1
Nd (NO,
/' 54.0
005
#/
Y
/
NdCI, 0
o
o
o
15.0
11.0 0
.I
.2
.3
.5
.4
.6
ct+ Figure 1. Comparison of data with theoretical limiting slope.
is the theoretical limiting slope drawn through the value of r$vO obtained from Table 111. The solid line represents the apparent molal volume of NdCL calculated from eq 13, which includes the effect of the a parameter to be discussed later. It should be noticed that NdCh shows a negative deviation from the theoretical limiting law throughout the concentration range studied, which results in the experimental slope always being less than the theoretical limiting slope. All the other salts studied, except Nd(N03)3, show similar behavior. Nd(N03)3 behaves differently in that the experimental slope is greater than the theoretical limiting slope in dilute solution. For example, in a 0.01 M solution, the experimental slopes of NdCh and Nd(N03)3 are 18 and 31, respectively. No satisfactory explanation of this singular behavior of Nd(NO3)t can be offered at this time. However, the negative deviations from the simple limiting law exhibited by the other rare earth salts at low concentrations seem to be consistent with the predictions of interionic attraction theory, provided the influence of the a parameter is considered. The first three terms on the right-hand side of eq 6, the OwenBrinkley equation, can be derived fron the DebyeHiickel expression for the mean ionic activity coefficient containing the a parameter, and therefore have theoretical justification. Retaining only these theoretical terms gives the equation
4"
=
4"' f 27.447(Ka)C1/'
+ '/iW,O(Ka)C
(12)
The success of the Debye-Hiickel theory for the mean
2447
ionic activity coefficient containing the a parameter in agreeing with data on rare earth chloride solution^^^-^^ suggests that eq 12 should be a good approximation up to about 0.05 M . A rigorous comparison of eq 12 with experimental data is difficult due to the presence of the pressure derivative of the a parameter in the definition of W,. It has been argued that the a parameter is effectively independent of pressure for aqueous electrolytes. 13,18 The a parameter includes the effect of any permanently coordinated water molecules, as well as the size of the ions. The compressibility of the water in the immediate vicinity of the ions may be expected to be small, since this water is already subjected to considerable pressure as a result of the strong ion-dipole forces. If the "effective hydration number" is independent of pressure, the pressure derivative of the a parameter should be small and may be neglected. Although it is not obvious that the "effective hydration number" will be independent of pressure, assuming the a parameter is effectively independent of pressure has some justification, and this simplifying assumption will be presumed valid for the following discussion. If the a parameter is effectively independent of pressure, eq 12 becomes independent of the term in W , for concentrations of the order of a few hundredths molar and reduces to the equation
+
4" = f#J"O 27*447(Ka)c1" (13) Since the function &a) is less than unity at nonzero concentrations, eq 13 predicts that the deviations from the simple limiting law should be negative and that the difference 4, - 2 7 . 4 4 ~ ( ~ cl/' a ) should be nearly constant in dilute solution, as indeed was observed for all the rare earth salts studied except Nd(N03)3. I n Figure 1, the apparent molal volumes of NdC13 predicted by eq 13 are shown by the solid curve. Equation 13 is in excellent agreement with the NdC13 data below about 0.03 M . Similar agreement was found for most of the salts studied. However, the positive deviations from the simple limiting law shown by Nd(N03)3are clearly not in agreement with eq 13. I n summary, it may be concluded that significant deviations from the simple limiting law do occur at low concentrations for the rare earth salts, but that, except for Nd(N03)3, these deviations seem to be consistent with interionic attraction theory, provided the effect of the a parameter is included. (14) See footnote a in Table 111.
(15) See footnote b in Table 111. (16) See footnote c in Table 111. (17) See footnote d i n Table 111. (18) J. Poirier, J. C h e n . Phys., 21, 965 (1953).
Volume YO,Number 8 August 1966
F. H. SPEDDING, ill. J. PIKAL, AND B. 0. AYERS
2448
3. Additivity Relationships. Assuming the solute is completely ionized at infinite dilution, the partial molal volumes of the rare earth chlorides and nitrates at infinite dilution should be additive properties of the individual ions, and we have additivity laws of the form
c
\
\
\
(~Zo>R(NOa)a- (pZo>RCia =
3[( Vzo)NOa-
( vZo>RXa -
- (V20),3-]
= constant
(14)
constant
(15)
(VZo)R'Xa = (V2')RBt
-
(VzO)Rta+ =
Thevaluesof 3[(f7Zo)Noa-- (Vzo)cl-]and (Vzo)~a+(Pzo)R)at were calculated from the partial molal given in volumes at infinite dilution, VZo ( = C#I~~)),
Table 111, and are listed in Table V. Since the quantity 3[(VZo)~oa- (vz0)c1-] should be independent of the cation, this quantity was also calculated from data on potassium chloride, potassium nitrate, ammonium chloride, and ammonium nitrate and compared in Table V with the values calculated from the rare earth salts. The values of Vzo used in the calculations were taken from Table I for potassium chloride and from the literature for ammonium chloridelg and ammonium nitrate." Apparent molal volumes of potassium nitrate were computed from the data of Gibson and KincaidZO and extrapolated, using eq 5, to obtain 38.41 ml/mole for the partial molal volume of potassium nitrate at infinite dilution.
Table V: Additivity Relationship 3[(?200)~0~-
Ion
-
(Vzo)c~-l R E a +
34.9 34.6 34.6 34.1 34.7 K+ 34.2 NH4+ Average = 34.5 La3 + Nd3+ Er3 + Yb3+
( f ' s o ) ~ ~ a + - (?$)Re's+
La%+ La3+ La3+ Er3+ Nd3+ Er3+
RE'at
Nds+ Er3 + Yb3+ Nd3+ Yb3+ Yb3+
yAnion-Chloride Nitrate
4.3 3.9 5.2 0.5 0.9 1.4
4.6 4.1 6.0 0.5 1.4 1.9
Keeping in mind that differences between quantities uncertain within f0.2 ml/mole are being compared, it can be seen from Table V that the additivity relationships are obeyed within experimental error. 4. Vzoas a Function of Ionic Radius. In Figure 2 are plotted values of the partial molal volumes at infinite dilution of some rare earth chlorides as a function of ionic radius of the rare earth ion. The ionic radii are those of Pauling.2L The dashed lines represent The Journal of Physical Chemistry
I
I
I
I
1.08
1.16
I
I
1.00
I
I
0.92
+r ( A )
Figure 2.
V20us.
rare earth ionic radius.
t,he trends shown by the data. It should be noticed that the Vza values do not vary smoothly with ionic radius. The partial molal volumes at infinite dilution decrease with decreasing ionic radius from La to Nd and from T b to Yb. However, in the region from Nd to Tb, the partial molal volumes at infinite dilution increase with decreasing ionic radius. Although a t present no accurate data exist for the rare earth nitrates between Nd and Er, the nitrates will show the same behavior as the chlorides, provided the additivity laws given by eq 14 and 15 are valid between Nd and Er. Various empirical and theoretical relations have been p r o p o ~ e d ~in~ -an ~ ~attempt to correlate the partial molal volumes at infinite dilution with ionic radius. These relations all predict that the partial molal volume at infinite dilution should smoothly decrease with a decrease in ionic radius for a given ionic charge. From our data, it is clear this is not the case for the rare earth chlorides or nitrates. I n eq 1, the partial molal volume a t infinite dilution was written as a sum of the two terms, V , and AVH,O. ~
~~
~~
~
~
(19) J. N. Pearce and G. G. Pumplin, J . Am. Chem. Soc., 59, 1221 (1937). (20) R. E. Gibson and J. F. Kincaid, ibid., 59, 25 (1937). (21) L. Pauling, "The Nature of the Chemical Bond," 3rd ed, Cornel1 University Press, Ithaca, N. Y., 1960. (22) A. M. Couture and K. J. Laidler, Can. J . Chem., 34, 1209 (1956). (23) L. G. Hepler, J . Phys. Chem., 61, 1426 (1957). (24) P. Mukerjee, ibid., 65, 740 (1961). (25) J. Padova, J . Chem. Phys., 39, 1552 (1963).
APPARENT MOLALVOLUMES OF AQUEOUS RAREEARTHSALTSOLUTIONS AT 25"
For a given coordination number of the R3+-H20 species, Vs and AVH,O should vary smoothly with changes in ionic radii, while a change in coordination number may result in sharp changes in both quantities with the major change occurring in the negative term, AVH~O.A shift to a lower coordination number would result in less breakdown of the water structure around the ion, decreasing the absolute magnitude of AVHI0 and increasing the value of V2O. If it is assumed that a rare earth ion in solution may exist in an equilibrium between two possible coordination numbers, where this equilibrium may be sharply displaced toward a lower coordination number below a critical ionic radius, the data may be qualitatively explained. According to this postulate, the equilibrium between the possible coordination numbers favors the higher coordination number for the rare earth ions between La and Nd. After Nd, a displacement of this equilibrium toward the lower coordination number begins to take place that results in the lower coordination number becoming increasingly more favorable for the rare earth ions from Nd to around Tb. The smooth decrease of the partial molal volumes at infinite dilution from T b to Yb indicates the shift toward the lower coordination number terminates around Tb, and the rare earth ions from around T b to Yb have essentially the same coordination number. On the basis of structural studies on rare earth hydrate crystals and aqueous rare earth salts, Morganze suggested that the principal coordination number for the R3+-H20 species in solution may vary across the lanthanide series. He suggests a coordination
2449
number of 9 a t the beginning of the series and coordination number of 6 a t the end, including Er3+ among the latter. From proton relaxation data on dilute (0.00030.02 M ) aqueous gadolinium perchlorate solutions, it was concluded that either coordination number 8 or 9 is acceptable for Gda+. Morgan's conclusions do not agree with our interpretation of the partial molal volume data since a coordination number of 6 for Era+would require the major change in coordination number to take place between Gd3+ and Er3+. However, Morgan's conclusions are based upon the X-ray diffraction work of Brady2' on aqueous solutions of ErCl3 and Err3. Brady found the principal solution species to be Er(H20)&12+ and Er(H20)sIz+ in concentrated (greater than 0.9 M ) solutions of ErCL and E&, respectively. However, in dilute solution where the degree of halide complexing is negligible, it seems quite possible that water molecules would replace the halide ions in the coordination sphere, giving the species Er(H20)83+. Coordination numbers of 9 for the rare earth ions from La3+to Nd3+ and of 8 for Gd3+ and Er3+ would agree with our interpretation of the partial molal volume data.
Acknowledgments. We wish to express our gratitude to Mr. Peter Cullen for assistance in making specific gravity measurements on ErCh and to other members of Physical and Inorganic Chemistry Group I for assistance in preparing the solutions.
ch.
(26) L.0.Morgan, J. P h m , 38, 2788 (1963). (27) G. W.Brady, {bid.. 33, 1079 (1960).
Volume YO, Number 8 Azcgust 1988
