ANALYTICAL CHEMISTRY
1894 Table 11. Precision and Accuracy of Cerium Determination Standard Ce(II1) Ce(II1) Deviation KMnOn Taken, Found,= Error, 11 Jlg. llg. % lk. % 0.03445 0.01723 0.00689 0.003445 (1
88.73 29.60 11.84 5.921
88.77 29.64 11.84 5,926
+0.045 +0.13 0 00 $0.086
0.21 0.13 0.05 0.023
0.24 0.44 0.42 0.39
Average of 10 determinations done in pairs on 5 different days.
bias from nithin-day trends. The levels of cerium concentration studied ranged from about 6 to 89 mg. per 85 ml. of solution, and for each level a permanganate solution about 25 times as concentrated as the cerium solution was used. The results, which are summarized in Table 11. shon-ed no significant differences in accuracy or precision betn-een levels or between days. The over-all precision of the method under the conditions studied is best expressed by the coefficient of variation (standard deviation in per cent), which is 0.47,. .lutomatic performance of the titration using the apparatus of JLarple and Hume (6) n-as foiind to be satisfactory. ACKIVOWLEDGMEYT
cerium(II1) about 100 to 1. The method can therefore be recommended for the determination of traces of cerium(II1) in cerium(1V) salts soluble in neutral pyrophosphate.
This n-01k n as supported in part by the United States htoniic Energy Commission. E. P. Przybylowicz nishes to thank the Eastman Kodak Co. for a fellon-ship.
PRECISION AND ACCURACY
LITERATURE CITED
I n recognition of the fact that the agreement within a group of replicate samples all run at one time under identical conditions does not give a realistic estimate of the actual precision of an analytical method, an experiment was designed to determine the reproducibility of the method over a period of time and for different amounts of cerium. Samples of stock standard cerium(II1) solutions at four levels of concentration were analyzed in duplicate each day for 5 successive days. The order of titration of the eight samples run on any given day was randomized to minimize
(1) Goddu, R. F., Hume, D. K’.,-43.4~.CHEM.26, 1740 (1954). (2) Goffart, G., Anal. Chim. Acta 2, 140 (1948). (3) Latimer, W. M., “Oxidation Potentials,” Prentice Hail, Sew York, 1952. (4) Lingane, J . J., Karpius, R., IND. ENG.C H E Y . , BXAL.ED. 18, 191 (1946). (5) JIarple, T. L., Hume, D. S . ,A 3 . 4 ~ CHEM. . 28, 1116 (1956). (6) hleyer, R. J., Schweitzer, A , 2. anorg. Chenz. 54, 104 (1907). (7) TomiEek, O., Rec. trau. chim. 44, 410 (1925). (8) Weiss, L., Sieger, H., Z . anal. Chem. 113, 305 (1938).
RECEIVED for review May 19, 1956. bccepted July 25, 1956.
Differential Spectrophotometric Determination of Neodymium in Neodymium-Yttrium Mixtures CHARLES V. BANKS, JOHN L. SPOONER, r n d JEROME W. O’LAUGHLIN Institute for Atomic Research and Department o f Chemistry, Iowa State College, Amos, Iowa A differential spectrophotometric method for the determination of macro amounts of neodymium in neodymium-yttrium mixtures permits determination of neodymium in the presence of yttrium with errors in concentration of only 2 to 3 parts per thousand. A theoretical treatment is given of the corrections made necessary by differences in the lengths and absorbances of the cells.
B
ECAUSE the similar chemical properties of neodymium and yttrium make the analysis of mixtures of the two elements by classical methods extremely difficult, differences in physical properties are used whenever possible for the determination of these elements. Small amounts of neodymium have been determined in the presence of lanthanum, cerium, and praseodymium by spectrographic techniques ( 2 ) . Larger amounts have been determined by epectrophotomet~icmethods (1, 5 , 6, 8, Q ) , which involve measuring the radiant eneigy absorbed by neodymium in dilute acid solutions at the wave length of one of its absorption bands. The absorption spectrum of neodymium has a series of very narrox- bands in the visible region of the spectrum. Yttrium shows no absorption in this region of the spectrum and, therefore, does not interfere Kith the spectrophotometric determination of neodymium. The extreme narronmess of the absorption bands of neodymium necessitates special techniques for making spectrophotometric measurements. Very small slit widths are necessary. Because of slight inaccuracies in setting the wave length dial, the region near the absorption peak must be scanned until the wave length is found a t which maximum absorbance occurs. These
difficulties, coupled with the Ion. molar absorptivity of neodgmium, make relative errors of about 1%in concentration about the lowest that can be expected by conventional spectrophotometric methods. I n connection with a careful determination of certain ion exchange constants, it became necessary to analyze a number of neodymium-yttrium oxide mixtures. A4more accurate neodymium analysis was needed than could be obtained by the usual spectrophotometric methods. Reilley and Cranford ( 7 ) recently reviewed the general principles of spectrophotometry and suggested tn-o new methods. Their Method Is’, which seemed theoretically capable of yielding the desired accuracies, involves setting the spectrophotometer to read 0 and 100 Kith t v o standard refeience solutions of concentrations C, and C1in the light path. This method theoretically beconies more accurate as the difference between Cz and C1 becomes smaller. As the photometric error of a spectrophotometer is a minimum in reading an absorbance of 0.43, the best choice of concentrations for the refeience solutions is such that the absorbance of “
is approximately 0.43. 2 I n the course of this work it n a s found necessary to make cell corrections. Several treatments of cell corrections in differential spectrophotometi y appear in the literature ( 3 , 4). These methods refer, honever, to the technique in which a single reference solution is used to set the spectrophotometer a t 100 and darkness is used to set the spectrophotometer at 0. The present report is concerned with the application of Method I V of Reilley and Craaford ( 7 ) to the determination of neodymium in neodymium-yttrium mixtures. A method by which cell ~
+
V O L U M E 2 8 , NO. 1 2 , D E C E M B E R 1 9 5 6 corrections can be made when tn-o reference standards are employed is presented. APPARATUS
A Beckman Model D U spectrophotometer equipped with a photomultiplier attachment and a tungsten lamp was used. The lamp house was cooled and the cell compartment was thermostated a t 25" C. The solutions were read in three matched, ground-glass-stoppered Corex cells 0.998 em. long. R EAGEIVTS
Perchloric Acid, 10y0Solution. A stock solution of lOy0 perchloric acid was prepared by diluting 715 ml. of reagent grade, 70 to 727, perchloric acid (Baker and Adamson) to 8 liters with distilled water. Standard Neodymium Solutions. Neodymium oxide, XdpOa (Ames Laboratory stock, spectrographically free of other rare earths), was freed from small amounts of silica by evaporating to fumes of perchloric acid, diluting, and filtering. The neodymium was then precipitated with oxalic acid, filtered, and ignited to the oxide. It was stored in tightly capped bottles in a desiccator charged with anhydrous magnesium perchlorate. Samples of the oxide ranging from 0.7986 to 1.3559 grams n-ere weighed into recalibrated 100-ml. volumetric flasks. Approximately 90 ml. of the etock lOy0 perchloric acid was added to each flask. Upon standing, the neodymium oxide dissolved, after which the contents of the flasks were diluted to volume with 10% perchloric acid. The molar concentrations of these standard sdlctions are shon-n in Table I. Synthetic Neodymium-Yttrium Mixtures. These samples n-ere prepared in exactly the same way as the standard neodymium solutions, except that various amounts of yttrium oxide, Yz03 (Ames Laboratory stock, spectrographically free of other rare earths), were added a t the same time as the neodymium x i d e . The composition of these solutions is shown in Table 11. EXPERIMENTAL WORK
Spectrophotometric Measurement of Solutions. The cells were scrupulously cleaned by washing with a slurry of Dreft in water, thoroughly rinsed with water, and wiped dry with lintfree tissue. The optical faces were not touched or viiped during a series of readings. The two reference standards, C1 and Ct, were placed in cells 1 and 2, respectively. The wave length n-as set a t approximately 575 mp and the slit n-idth at 0.025 mm. The small slit width is made necessary by the narrowness of this absorption band of neodymium. The instrument was then balanced in the usual manner against solvent and darkness, and with one of the standards in the light path the wave length dial was carefully adjusted until the wave length of maximum absorbance was found. The instrument was rebalanced at 100 and 0 with solutions of concentrations C1 and C2, respectively, in the light path, by repeated adjustments of the dark current and sensitivity controls on the Beckman Model D U spectrophotometer and the necessary adjustments on the photomultiplier attachment. Solution CZwas then placed in cell 3 and the scale reading carefully determined. The same procedure was followed to obtain the scale reading for C1 in cell 3. These readings are usually not 0 and 100, because of slight differences in the lengths and absorbances of the cells. If the instrument cannot be balanced with CZin cell 3, the position of the cells can be exchanged. This may happen, because the scale on the Beckman Xodel DU spectrophotometer covers only the range from 0 to 110. By rearranging the cells, however, it is always possible to obtain a scale reading for both C1 and CZ in one of the cells with the instrument balanced on C1 and CZin the other two cells, Once this arrangement of the cells is found, it is used for all subsequent measurements. The scale readings ( R x and R.v) were found for C1 and CZ, respectively, when read in cell 3, after which the other standard solutions were read in cell 3. The instrument was rebalanced before every reading. R.11 and R v changed slowly \$ith time. Because all cell corrections arc based on these two measurements, they were redetermined frequently during a series of measuyements. Table I shows how Rir and Rv changed during one series of measurements. Cell Corrections. The fact that R.ir and R.v are not constant, eren during a series of measurements, makes the use of an empirical calibration curve unsatisfactory. The only reason that can be advanced for changes in RMor RN is a change in the absorbance of one or more cells. A change in cell length could hardly be postulated and the only two factors that are likely to
1895 affect RIIor RN are differences in the lengths and absorbances of the cells, if any reflectance from cell walls is neglected or assumed to be constant. It n-ould be desirable to correct the observed scale reading for a sample to the value that would have been observed if there were no differences in the lengths or absorbances of the cells. If the correction could be expressed as a function of R.u and RN, two measurements that could be made a t the Eame time the sample was read, it would be of maximum usefulness. This would permit the construction of a standard calibration curve independent of changes in the absorbances of the cells n-hich may occur while the measurements are made. One method of deriving a formula for making cell corrections is seen from the following considerations. Reilley and Cran-ford ( 7 ) relate the observed scale reading in this method to the intensities of light Z, Zl, and Iz issuing fiom samples C, C,, and C2, respectively, by the relationship
r*]
I =
R
f Z 2
It is apparent that Z is a linear function of R, if 11 and I2 are constant. Reilley and Crawford ( 7 ) then assumed that Z
ZolO-abc
Pa)
I,
ZolO-abCI
(2b)
12 =
1olO-Qbc2
(2c)
This is justified only if all three solutions are read in the same cell or in three cells perfectly matched for length; in either case, it assumes the cells themselves absorb no light.
Figure 1. Relationships among I , R , and R,
If reflectance from the cell walls is neglected, but it is assumed neither that the cells are of exactly the same length nor that they all have the same absorbance, it can be readily shown that
+ 8) ZI = ZolO-(ablC1 + Iz= zo10-(Qb2C2+ I
= ZolO-(abc
(3a)
'41)
(3b)
81)
(3c)
where b, bl, and bz are the lengths and A, -41,and AOare the absorbances of the cells actually used. If the relationships given by Equations 2a, 2b, and 2c are substituted in Equation 1, the following equation is obtained:
1896
ANALYTICAL CHEMISTRY
When Eqliations 3a, 3b, and 3c, are substituted in Equation 1-we obtain:
Table I. Observed and Calculated Values of R Nd SoluConcn., tion JI RO RJf Rs R Roalod . C1
1 2 3
4 Figure 1 3hom-s schematically the relationships among I , R, and R,. I N and ZN represent the light issuing from solutions CI and C, respectively, contained in cell 3 and corresponding t o the observed scale readings, RM and RN. The expressions for IM and Z.Vin terms of I Oare seen to be and
It is apparent from similar triangles in Figure 1 that
which can be essily rearranged to give
R
=
I-[
100
R, - Rh’ RM - RN
Equation 9 can be used to calculate the “true” scale reading from the experimental quantities R,, RM,and RN.
-6 A9 10
CZ
Io-EbC
0.45
040 V
n W
I
04750 05197 05478 05798 06037 06372 06719 06961 07447 07623 08018 08069
83’0 72 85 62.2 54 0 45 5 33 6 28 4 16 2 11 7 1 8
98:2 98.2 98.1 98 1 98 0 97.4 97 2 97.0 96 7 96 5
1:85 1,85 1.88 1.85 1 .so
1.70
1 ..55 1.55
l,l5 0.90
..
100 84.2 73.6 62.7 54.2 45.4 33.5 28.0 15.1 11.0 0.9 0
100 83.7 73.2 62.4 54.7 44.4 34.4 27.6 14.9 10.6 1.1 0
The mean deviation of the experimental points from the theoretical curve, a straight line defined by R = 0 a t 10-ebc*and R = 100 a t 10-abcl,in terms of R is h0.48, which corresponds to a relative error in concentration of 0.26%. The samples containing yttrium were read using two new reference solutions. This made construction of a new calibration curve necessary. As the calibration curve is a straight line for a new curve may and R = 100 a t which R = 0 a t be constructed immediately without reading additional standards. Table I1 shows the results obtained on known neodymium-yttrium mixtures, by using a calibration curve constructed in this manner. It is apparent that yttrium does not interfere with the method and the use of a calculated calibration curve is justified.
RESULTS
The results obtained when the series of standard neodymium solutions were read are given in Table I. R.v and RN were remeasured after every three to five readings.
0 0 0 0 0 0 0 0 0 0 0 0
RECOMMENDED PROCEDURE
Two reference standards are prepared as described and a calibration curve is constructed. Samples of the neodymiumyttrium oxide mixtures are weighed into recalibrated flasks. The sizes of the samples are chosen such that the neodymium concentrations in the final solutions are between those of the two standards. If necessar the approximate concentrations of neodymium are determined t y conventional spectrophotometric methods. Approximately 90 ml. of the stock 10% perchloric acid is added to each flask and after dissolution is complete the contents of the flasks are diluted to volume with 10% perchloric acid. The samples are then read on the spectrophotometer; the two standards are used to set the instrument a t 0 and 100 as previously described. RM and RN are determined frequently, if a number of measurements are made. The scale reading, R,, for the sample is corrected by use of Equation 9 and the concentration of neodymium is calculated from the calibration curve.
0035 Table 11. Determination of Neodymium in Known Neodymium-Yttrium Mixtures YPOS NdtOs NdzOs Added, Added, Found, % Solution G. G. G. Error
0.30 &I;C I V
,
11 12 13
Figure 2.
0 5289 1 0455 1 9963
1 0113 1 0196 1 0030
1 0142 1 0203 1 0062
0 29 0 07 0 32
Plot of 10-d~as a function of R for standard neodymium solutions DISCUSSIOS
Interpolated values of RM or RN were used in calculating R for samples read between measurements of RM or RN. Figure 2 is a plot of values of R for the series of neodymium samples as a function of An average value of 6.95 f 0.03 was used for the molar absorptivity, E , of neodymium a t its 575-mp absorption band. This is an average value of nine independent determinations. The cell length was taken as 0.998 cm. The value for c, the molar concentration of neodymium, is taken from Table I.
The proposed method permits the rapid and accurate determination of neodymium in neodymium-yttrium oxide mixtures. Difficult and time-consuming separations are avoided. Errors associated Kith setting the wave length dial a t the optimum position are minimized. Slight inaccuracies in setting the wave length dial affect the absorbances of the two reference solutions and the sample solution in a similar manner and the errors tend to cancel. An error in setting the wave length dial, that would cause
1897
V O L U M E 2 8 , NO. 1 2 , D E C E M B E R 1 9 5 6 approximately a 15% relative error in concentration by the usual spectrophotometric methods, would have comparatively little effect on the proposed method. It can be demonstrated that a t observed R values of less than 10 or greater than 90, an apparent, change of 15% in molar absorptivity would cause less than 0.2% relative error in concentration. The error would be greatest a t R values around 50, but even in this region the relative error in concentration would be less than 0.5%. The method can be used for very small samples. The sample solution can be prepared by weight and the only limiting factor would be the necessity of having a final volume great enough to fill a 1-cm. cell. If sample solutions are prepared by weight, it is necessary to determine the density of these sample solutions. APPLICATIONS
The proposed method was used for the analysis of a large number of neodymium-yttrium oxide mixtures. The neodymium content of the samples varied from 10 to SO’?&. Work on application of this method to other rare earth mixtures is being conducted. It should be generally applicable for the determination of larger amounts of many of the rare earths
in rare earth mixtures, where a wave length can be chosen a t which only the element being determined absorbs. ACKNOWLEDGMENT
The authors wish to express their appreciation to F. H. Spedding and his Rare Earth Group for supplying the pure rare earth oxides used in this study. They also wish to thank V. A. Fassel for spectrographically analyzing the various rare earth oxides for other rare earth impurities. LITERATURE CITED (1) Banks, C. V., Klingman, D. W., Anal. Chim. Acta 15, 356 (1956). (2) Fassel, V. rl., Cook, H. D., Krotz, L. C., Kehres, P W., Spectrochim. Acta 5 , 201 (1952). (3) Freeland, RI. Q., Fritz, J. S., ANAL.CHEW27, 1737 (1955). (4) Hiskey, C. F., Ibid., 21, 1440 (1949). (5) Holleck, L., Hartinger, L., Angaw. Chem. 67, 648 (1955). (6) hloeller, T., Brantley, J. C., ANAL.CHEM.22, 433 (1950). (7) Reilley, C. K.,Crawford, C. hf., Ibid., 27, 716 (1955). (8) Rodden, C. J., J . Research Natl. Bur. Standards 26, 557 (1941). (9) Wylie, A. W., J. SOC.Chem. Ind. 69, 143 (1950).
RECEIVED for review April 14, 1956. Accepted August 13, 1956. Contribution KO.468, Ames Laboratory, U . S. Atomic Energy Commission.
Spectrophotometric Method for Simultaneous Determination of Nickel and Cobalt R. D. WHEALY and S. 0.COLGATE West Texas State College, Canyon, rex.
Aqueous solutions of niclcelous and cobaltous nitrates react completely with excess diethylenetriamine to form Light absorption solutions of colored complexes. properties of these complexes permit the quantitative determination of both nickel and cobalt in the absence of interfering cations.
N
ICKEL nitrate reacts spontaneously with excess diethylenetriamine to form the violet complex Ni[ (C2HdNH2)2NH]2(K03)2 ( 1 ) . Aqueous solutions of this compound exhibit absorption maxima a t 850 and 540 mp (Figure 1). The absorption properties a t each Tvave length closely follow Beer’s law for initial nickelous ion concentrations of 0.01 to 0.06 gram-ion per liter. (Concentrations outside these limits were not studied.) The concentration of nickelous ions in solutions containing no interfering ions is readily obtained from absorption data a t either of the two maximum wave lengths. Solutions of cobaltous nitrate react with excess diethylenetriamine to form a yellow complex. The cobalt in this complex is apparently in the tripositive oxidation state. The cobaltous ion is easily oxidized by atmospheric oxygen. The reaction is hastened by bubbling air through the solution containing cobaltous ion and diethylenetriamine. The yellow complex has a single absorption maximum a t 460 mp (Figure 1). Behavior a t this wave length is in good agreement with Beer’s lam for initial cobaltous ion concentrations of 0.001 to 0.006 gram-ion per liter. Thus, cobalt can be determined in solutions containing no interfering ions. Figure 1 shows that nickel in solutions containing both nickel and cobalt ions can be determined by using the Beer’s law graph for the nickel complex a t 850 m9. The total absorbance a t 460 mp (cobalt complex maximum) represents the combined absorbance of the nickel complex and the cobalt complex. If the con-
centration of the nickel complex a t 850 mp is known, the absorbance due to this species a t 460 mp can be calculated. This value is subtracted from the total absorbance a t 460 mp to obtain the absorbance a t this mave length due to cobalt alone. Fortunately, diethylenetriamine exhibits no appreciable absorbance a t any of these absorption maxima. It can, therefore, be present in large excess to assure completeness of reaction. MATERIALS AND APPARATUS
All absorption measurements were taken with a Beckman Model B spectrophotometer equipped with 1-cm. Corex cells.
07
06
G I
04
SC3
C?
0
Figure 1. Absorption spectra of nickel nitrate and cobalt nitrate in presence of excess diethylenetriamine
