APPARENTMOLAR REFRACTION OF LANTHANUM PERCHLORATE
April 20, 1957
1789
TABLE I11 COMPARISON OF CALCULATED WITH ACTUALVALUES Integral
4 [$I’m [slxz
x 2 an d x
Zdx
m
+ $lrxz $ dx] x2
-m
Exp. 1 Computed
0.446 0.448 + lzn6 x2 a n dx]
ism
2t
Actual
ax
Actual
Exp. 2 Computed
0.536
0.534
.627
,628
.757
,757
,621
,621
.757
.757
1.694
1.695
2.050
2.048
Actual
Exp. 3 Computed
1.655
1.615
3 . GOO
3.568
TABLE IV COMPARISON OF REDUCED FOURTH MOMENTS Exp. 1 Actual
D20 on
2.964 X 0 . 3 0 x 10-7
Exp. 2 Computed
2.951 X 0 . 2 7 X 10-
moments calculated for different portions of the curves are presented in Table 111. The computed values were obtained by the use of eq. 6 and 7. The last integral in eq. 6 was evaluated from the positions of fringes 96 and 98.’ The actual values were calculated using eq. 10.
x k is the weight fraction of component k. Equations 10b and c were solved numerically by double interpolation in the “Tables of Probability Functions.” Difficulties with signs for X and r are perhaps best avoided by considering all variables involved as being positive and separating any integrals crossing the zero axis into two integrals. Table IV compares the reduced fourth moments and the uD calculated from the eq. 8 and 9 with the actual values. (7) No definite rule can be given for choosing the optimum fringes for calculating t h e last integral of eq. 6. I n general one should use for t h e second fringe the highest numbered fringe or fractional fringe for which accurate measurements can be made.
[COXTRIBUTION FROM THE
Actual
4.325 X 0 . 3 5 x 10-7
Computed
4.252 X lo-” 0.23 x 10-7
Discussion Most of the error in the computation arises from the first and last integrals in eq. 6. The above results suggest that one can compute reduced second moments which are within 0.1% of the correct values for systems in which there is not too large a range of diffusion constants. It is also possible to obtain useful information about the amount of dispersion in the system by comparing the reduced second and fourth moments. Experiment 3 (see Table 11) corresponds to a highly improbable situation: e.g., a protein contaminated with 10% of a low molecular weight polypeptide. In this case the error is considerably larger than 0.1%. Preliminary experiments with polydisperse systemss indicated that data obtained a t different times during the run are reproducible to 0.1-0.2%. A final evaluation of the accuracy obtainable with actual polydisperse systems will have to be made on the basis of model experiments. Although the calculations involved are laborious, there will be systems for which the extra effort will be justified. It may be possible to make use of high speed calculators. (8) S. L. Burson, Jr., M. J. Fahrenbach, L. H. Frommhagen, B. A. Riccardi, R. A. Brown, J. A. Brockman, H. V. Lewry and E. L. R . Stokstad, THISJOURNAL, 78, 5874 (1956).
PEARL RIVER,N. Y.
DEPARTMENT O F CHEMISTRY,
UNIVERSITY OF MASSACHUSETTS]
The Apparent Molar Refraction of Lanthanum Perchlorate in Aqueous Solution BY JOHN E. ROBERTS AND NORMAN W. SILCOX’ RECEIVED ~SOVEMBER 29, 1956 The apparent molar refraction, dispersion, volume and t h e partial molal volume of lanthanum perchlorate in aqueous solution have been determined. The results have been interpreted in terms of t h e Fajans theory as well as by Bottcher’s modified refraction equation.
Introduction The chemistry of the lanthanon elements has assumed new importance by the recognition of their (1) Taken from the M.S. thesis of Norman W. Silcox, Univ. of Mass., June, 1955.
relationship to the actinides, and accurate measurem a t s of chemical and Physical Properties of the lanthanons has made possible helpful predictions and to the actinides* A quantity which has received little attention for these elements
17'30
JOHN
E.ItOBERTS AND N O R M A N
is molar refraction. Differences between adjacent members of the series may be expected to be small but any differences or trends within the series should be largely attributable to the differences in the 4f electron shells and to the accompanying change in nuclear charge. The rare-gas-type lanthanum ion is isoelectronic with the barium ion, can be compared readily with ions which have been subjected to considerable study and therefore makes possible an extension of the well-known theoretical interpretations of refraction developed by K. Fajans and co-workers.2 In 1925 Heydweiller3 reported the molar refraction of the aqueous lanthanum ion to be 1.61 cc. in LL nitrate solution. Extrapolation to infinite dilution from his data is unreliable. A value of 3.24 cc. for Rns for the lanthanum ion was found by Roberts* for a 3.1916 m nitrate solution but only one concentration was measured. No other refraction measureinents of aqueous solutions have been reported. The synimetrical structure, low deformability and non-complexing properties of the perchlorate ion suggested that lanthanum perchlorate would be a suitable compound for this study.
Experimental Materials.-The lanthanum material used in this work was isolated by recrystallization procedures from crudc monazite oxides. T r x e s of non-rare earth impurities wcre removed by precipitation with hydrogen sulfide followed by scvcral precipitations of lanthanum oxalate with recrystallized oxalic acid. T h e final oxalate precipitate was ignited t i l oxide in platinum. Spectrographic, spectrophotometric and chemical tests sliomed t h a t impurities could not be prescrit in excess of 0.0170 and probably were much less. T h c perchloric acid used was analytical reagent grade ( J . T . I h k c r ) . Water for dilution of the stock solution was triply distilled in a n all Pyrex still, once from alkaline permangaiiate and once from acidic solution. The specific resistivity was 4.4 X 10-6 ohm mi. Preparation of the Solutions.-The lanthanum oxide was slurried with water and treated with a n amount of concent rated perchloric acid insufficient to cause complete solution. 'Thc mixture was boiled, kept just below the boiling point for two days, cooled, filtered through a fine sintered glass funnel and the clear solution stored in a Pyrex flask. Dilutions were prepared using weight burets for both stock solution arid water. All weighings were done by transposition ir.it!i calibrated weights and tares. Vacuum corrccrions were applied, the air density being calculated from mcasurcd tcniperature, humidity and barometric pressure.5 The stock solution was analyzed by precipitation with oxalic acid and ignition of the oxalate t o oxide in the usual way. The concentrations of the dilute solutions were calculated from the dilution data. il check analysis of the most dilute solution established the validity of this procedure within 1.3 p.p.t. Density.-Solution densities were determined with bicapillary pycnometers of about 20-ml. capacity. These pycnometers were calibrated with water and permitted an accuracy of 1 X 10-6 in the density of the solutions. Temperature was controlled to 25.00 f 0.01'. The reported tlcnsitics arc the average of two independent fillings. Refractive Index.-The refraction measurements were tnade with a Zeiss Pulfrich Refractometer. Values for the refractive index of the prism for 25.00' and for the seven lielium spectral lines were calculated from the manufacturcr's values for 20' and other spectral lines. T h e resultant values wcrc shown to be accurate by measurement of mater a n d tcst pieces. The micrometer screw was calibrated (2) This theory is t o h e found in the series "Refractometric Investigations" b y I:a.ians, rl , ) I . See ref. (11) for a listing of many of these papers. (3) A. IIeydweiller, P h y s i k . Z.,2 6 , 526 (1925). ( 4 ) J. E, Roberts, M.S. thesis, Univ. of N e w Hampshire, 1964. ( 5 ) P. I;. Weatherill. THISJ O U R N A L , 62, 1035 (1930).
w.SILCOX
Vol. 7!J
against the graduated circle for three diffcrcrit positioiis arid found to have negligible error. The zero point corrcction was applied to all measurements. T h e glass cell was attached to the prism by Duco household cement and thermostatic water was circulated through the prism and cell jackets, the temperature of the sample being recorded as the average reading of two Beckmann thermometers placed in the water line on either side of t h e prism. Temperature was 0.005'. Samples were tratisferrcd controlled t o 25.00 from the pycnometers directly t o the cell by means of air pressure and the filled cell was closed immediately to prevent evaporation. T h e light source was a helium discharge tube operated at ten thousand volts. T h e entire experimental procedure was tested using analytical reagent quality potassium chloride. T h e molar refraction agreed within 0.01 cc. with values reported by Kruis and Geffcken6 for coinparablc concentrations.
*
TABLE I COMPOSITION, DENSITY, 1 b P A R E S T hfOLAR A N D P A R r I A L
MOLALVOLUMESOF LANTIIASUM PERCHLORATE SOI,I:TIOKS AT
Soh. Molarity
25.00" APP. molar VOI.. 0,(ml.)
Density, g./nil.
I
2.839 I1 2.109 I11 1.363 1%' 0.6815 V 0.0901 Extrap. t o c = Water
1.90435 f 2 . 5 X 10-6 1.67750 f 1 . 2 X 1.44314 =t 1 . 0 X 1.21397 =t 1 . 6 X 1.02759 I 1 . 0 X zcro 0.90708 (standard)
118.06 115.00 110.35 104.69 98.96 95.1
Partial molal vnl., V (ml.)
124.91 121.80 116.53 109.41 100.83 08.1
TABLE I1 REFRACTIVE INDEX
01' IdBNTHANUM PERCHLORATE S0l.U-
TIONS AYI)
WATERAT 25.00"
Wave length,
A.
4172 4713 4021 5016 5870 6678 io65
€120
1.33872 1.33724 1.33613 1,33565 1,33240 1.33027 1.32049
I 1.48870 I , 43695 1.43505 1,43507 1.43131 1.42891 1,42804
I1 1.11351 1. -I 141 Z 1.41287 1,412:35 1,4O8138
1.40li37 I.i0>18
111
IV
1'
1.39048 1.36451 1.34243 I 38892 I , 3020Ii 1.34094 I . ~ S ~ O 1D. 3 6 1 7 ~ 1,33080
1.3871.5 1.38364 1.38137 1.36049
1.36129 1,35790 1.85570 1.35101
I. 1.
1.33394 1.33314
TAELE I11 APPARENT&fOLAR REFRACTIOX OF
IdANTIIANUM PERCIILORATE, C C . / h f O L E
n'ave
length,
A.
I
I1
111
IV
V
c = zerub
43.69 43.68 4472 4 3 . 6 5 43.92 43.90 43.79 43.5; 43.79 43.79 43.66 (43.48) 43.61 4713 43.45 43.70 43.69 4 3 . 5 5 (43.29) 1 3 . 3 5 4921 43.49 43.36 5016 43.41 43.66 43.65 43.53 5876 43.14 43.30 43.37 43.27 (33.30) 3 3 . 1 7 43.10 43.19 43.14 43.38 43.87 43.26 5893" 43.04 43.01 4 2 . 9 8 43.24 43.23 43.11 6678 7065 42.92 43.17 4.3.16 33.07 (42.88) 42.93 42.40 Infinityb 42.43 42.70 42.67 42.56 42.49 a Graphical interpolation. Graphical extrapolation: values for infinite wave length by a plot of 1/R us. square of frequency; values for c = zero by graphical extrapolation as in Fig. 1.
Discussion of Results Lorentz-Lorenz Refraction of La(C104)a a s a Function of Concentration and Wave Length.The apparent inolnr refraction of lanthmuni perchlorate was calculated by the method of (0) A . Kruis and \V. Geffcken. 2. p h y s i k . Chein., B34, 1 (lOY6l
April 20, 1957
APPARENT MOLARREFRACTION OF LANTHANUM PERCHLORATE
Geffcken’ and the resulting values are shown in Table 111. When these results were plotted by the reciprocal plotting method of Wulffa a series of straight lines resulted from which the apparent molar refraction a t infinite wave length was found by extrapolation. These values for infinite wave length as well as those for selected finite wave lengths are plotted in Fig. 1 to show the concentration dependence. The accuracy of the results may be estimated by taking the difference between values for any two solutions and for each wave length. Such differences should be constant or show a regular change. The maximum ranges found for these solutions are: I11, 0.03 CC.; 11-111, 0.03 CC.; 111-IV, 0.07 CC.; IV-V, 0.05 cc.; V-zero, 0.11 cc. These values may be taken as maximum errors and the graphical processes may be expected to minimize them. The probable error in the extrapolated quantity may be reasonably taken as =t0.06 cc./mole. This also affects the value of the hydration effect. The possible accuracy decreases with decrease in concentration and some values for solution V, which is about a t the minimum concentration for which the method is applicable, contain relatively large errors. These values are enclosed in parentheses in Table I11 and were not used in the extrapolation. Further measurements in the very dilute range would be required to attain higher accuracy. I n terms of the Fajans theory, the slight positive slope, dR/dc in Fig. 1 for c between zero and 2 molar, may be interpreted as representing the displacement of water of hydration on the lanthanum ion. The negative slope between 2 and 2.8 molar may be due to interaction between lanthanum and perchlorate ions to form loosely bound ion pairs. Lorentz-Lorenz Refraction and Dispersion of Free and Hydrated La3+ Ions.-To evaluate the hydration effect for the lanthanum ion
42.6
1791
1 f-1J_- --\ -1-51 _-t-
---
.
3 2 Molarity. Fig. 1.-Concentration dependence of the apparent molar refraction of lanthanum perchlorate a t various wave lengths: (1) 4472 B.; (2) 5016 A.; (3) 5893 A.; (4) 6678 A.; ( 5 ) extrapolated to h = a. 0
1
- 2.669J2cc./mole, respectively. The change in hydration effect on going from Ba++ to La+++ may be expected to be less than 0.56 cc. and probably proportionally less, ;.e., less than (0.36) (0.56)/ 2.10 = 0.096 cc. Therefore the A R H y d for La+++ should certainly be less than 0.92 cc. and probably less than 0.46 cc. in absolute value. I n view of the uncertainty of =tO.O6 cc. in the extrapolation, the experimental value of -0.52 cc. is in satisfactory agreement with these estimates. The apparent molar dispersion may be evaluated from the data. R D - R, = 43.16 - 42.46 = 0.70 cc./mole. Taking 0.23 cc. as the molar dispersion of the perchlorate ion,” the apparent molar dispersion of the aqueous lanthanum ion is 0.01 cc./ A R H ~= ~ . Raq. - Rgtw mole. This is satisfactory in view of the value of its refractions in the infinitely dilute aqueous solu- 0.02 cc./mole reported for the aqueous barium ion.“ tion and in the “free gaseous ion” are compared, a t Calculations by Bottcher’s Method.-In the the same wave length (Na “D” line). Using 13.24 Fajans interpretation of the Lorentz-Lorenz refraccc. as the refraction of the aqueous perchlorate ion9 tions, deviations from additivity were associated with interactions of ions with each other and with RL.+++~~. = RL,,(CIO,)~ - 3Rc1oa- = 43.16 - 39.72 = water molecules. This interpretation has been 3.44 cc./mole questioned by B O t t ~ h e r ’ ~and J ~ it was claimed iniR L a f + f gas can be obtained by extrapolation of the tially that the deviations were completely elimigradation of the values for isoelectronic ionsI0as nated when a corrected equation was used. Later it l . l 5 J ? n a + + / R ~ , + + ’ = RC~/RB,’+ 1.351 was concluded that the “Fajans effect” still exists Hence R L a + + + g a s = 3.96 cc./mole. From this, the in potassium fluoride and aluminum chloride. The corrected equation considers that the internal field hydration effect A K H y d . = 3.44 - 3.96 = -0.52 a t the position of the molecules has a different cc.,/mole. The hydration effect for the triply-charged lan- value than in the intervening spaces and is different thanum ion may be expected to be greater in abso- for various kinds of particles. This equation takes lute value than that for the isoelectronic barium the form ion, i.e., more negative than -0.36 cc./mole.ll (n2 - 1)(2nz i- 1) - NOW* NaeS* The upper limit is less certain but may be estimated 12an2 by comparison with the Mg+f/Al+++ case for -2 a* = -e-.. sndf = 1 - x 2n2-which the hydration effects are -2.1012 and
+
(7) W. Geffcken,Z. p h y s i k . Chem., B6, 81 (1929). ( 8 ) P. Wulff, ibid., B21. 370 (1933). (9) IC. Fajans and R. Luhdeman, ibid., B29, 150 (1935), Table 11. (10) K. Fajans, ibid., B24, 103 (1934). Table I V modified t o include later data of G. Damkohler, ibid., B27, 130 (1934). (11) N. Bauer a n d K. Fajans, THISJOURNAL, 64, 3023 (1942). (12) K. Fajans, 2. p h r s i k . Chem., B24, 103 (1934).
1 -je
r8
2n2
+1
in which n is the refractive index, No and N , are concentrations of water and salt, respectively, CY is the polarizability and r is a constant best inter(13) C. J. P.Bottcher. Rea. Ira% c h i n . , 66, 39 (1946). (14) C. J. F. Bottcher and T. G. Scholte, ibid., 70, 209
(1951).
1702
JOHN
E. ROBERTS AND NORMAN W. SILCOX
preted as the distance of closest approach of the molecules or ions. Using 1.38 A. as the value of r for water,15 i t isofound from the present data that the value 3.04 A. for lanthanum perchlorate gives equal polarizabilities for extremes of concentration. The resultant values of a and the corresponding refraction R = 4/3a1JTa are shown in Table 11:. I
I
126 I-
the Lorentz-Lorenz equation which does not contain an arbitrary parameter is satisfactory. TABLE POLARIZABILITY Soh.
I I1 111
Iv V
118
0
0.4
0.8
1.2
1.6
d M o l a r i t y. Fig. 2.-Apparent molar ( 0 ) and partial molal ( A ) volumes of lanthanum perchlorate.
The slight deviations from constancy of the refraction values calculated by this method are in the same direction as those of the Lorentz-Lorenz refraction but of only about half the magnitude. Since the value of r must be adjusted to fit the data, this equation is essentially empirical and values calculated with i t are best interpreted as representing a lower limit of the polarizability. Furthermore, small changes in r have a relatively large effect on a. Brown’s conclusion16 that the success of Bottcher’s method is the result of cancellation of errors indicates that little significance can be attached to these values. For comparisons of similar materials, (15) L. Pauling. “The N a t u r e of t h e Chemical Bond,” Cornell Univ. Press, Ithaca, N. Y . . 1944, p. 304. (18) ‘A’. F. Brown, Jr., J. Chem. P h y s , 18, 1193, 1200 (1950).
VOl. 79
Iv
CALCULATED B Y
x CI
BOTTCHER’S EQUArION R
1023
inolecuI
