Anal. Chem. 1989, 61, 1667-1669
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Spectrophotometric Method for the Analysis of Plutonium and Nitric Acid Using Partial Least-Squares Regression W. Patrick Carey and Lawrence E. Wangen Chemical and Laser Science Division, G740, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
James T. Dyke* Material Science and Technology Division, E501, Los Alamos National Laboratory, Los Alamos, New Mexico 87545
A method for the determination of Pu(II1) and nitric acid concentrations uslng the multivariate calibration technique of partial least-squares (PLS) regression coupled with visible absorption spectra (500-880 nm) Is presented. Quantitation of plutonium using its visible spectrum is straightforward; however, the effects of nitric acid on the Pu( II I ) absorption spectra are subtle and nitric acid quantitation from the absorbance spectrum is more difficult. I n this study PLS regression is successfully applied to quantitate both plutonium and nitric acid udng the information contained In the absorption spectra of appropriate solutions. The calibration set, covering a range of Pu(II1) from 1.99 to 29.9 g/L was modeled with a standard error of 0.20 g/L. Similarly, nitric acid ranging from 0.44 to 3.08 M was successfully modeled with a standard error of 0.18 M. Evaluation of the calibration models, using test samples that span the range of the caiibration concentrations, gave predictions on the order of the standard error of the calibration models.
INTRODUCTION Plutonium can be precipitated from acidic solutions by forming an insoluble oxalate salt of Pu(II1). It has been shown that the concentrations of both nitric acid and oxalic acid affect the solubility of the Pu(II1) oxalate product (I, 2). The solubility of the plutonium(II1) oxalate is minimized under the conditions of 0.5-1.0 M nitric acid and 0.05-0.1 M excess oxalic acid. These concentrations result in a solubility of Pu(II1) between 2 and 20 mg/L. If the nitric acid is more concentrated, the solubility of Pu(II1) increases, i.e. in 2.0 M nitric acid the Pu(II1) concentration increases 10-fold. There are also indications that increasing the oxalic acid concentration above 0.2 M will lead to increased solubility of the plutonium. T o assist in the study of the precipitation reaction of plutonium(II1) oxalate, it would be beneficial to have a rapid analytical method for examining the initial solution to determine the concentrations of plutonium and nitric acid. In this study, a method for predicting both Pu(II1) and nitric acid from visible absorption spectra of solutions containing the species of interest using partial leastrsquares (PLS) regression was evaluated. Several techniques for estimating Pu(II1) based on visible absorption spectroscopy have been developed, and quantitation is fairly straightforward (3-6). The difficulty remains in the determination of the nitric acid concentration from the visible absorption spectra. In this paper we demonstrate the use of PLS for extracting the small signal of the nitric acid effect in the presence of a much larger signal due to the Pu(II1) absorption. This information provides a measure of nitric acid concentration that can be used in studying the precipitation reaction. The fundamental theory and applications of PLS have been investigated by several researchers (7-11). This technique, 0003-2700/89/0361-1687$01.50/0
which uses the full spectrum of data, correlates latent variables in the spectral responses to the analyte concentration vector. The latent variables, which are orthogonal vectors, account for the variance present in the spectral response data block or matrix. The PLS 2-block modeling used is based on the algorithm in which the scores are orthogonal. This method is similar to principal component regression in that the spectral responses are factor analyzed by orthogonal vectors, but it proceeds one step further and uses information from the analyte concentration vector in the construction of PLS latent variables. The correlation built by PLS between the spectral latent variables and the concentration variable discriminates between multiple analytes if their effects on the spectra are not fully collinear. By use of PLS in this study, two separate models were built, one each for Pu(II1) and nitric acid. Predictions of analyte concentrations in several unknown sample solutions were performed by using the models developed during calibration.
EXPERIMENTAL SECTION All chemicals used were reagent grade, except for the plutonium nitrate stock solutions. Plutonium nitrate stock solutions were obtained by dissolving PuOz in HNO,/HF followed by the removal of fluoride through ion exchange. The concentrations of these stock solutions were determined by standard radiochemical methods based on y-ray spectroscopy with a relative standard deviation of 0.5% (12). A calibration set, Figure 1, and a test sample set were prepared by performing volumetric dilutions of the stock solutions. During these dilutions, various amounts of nitric acid were added such that the calibration and test sets span the acid range encountered in the precipitation studies. Spectra between 500 and 880 nm were obtained on each sample by using a 0.2 cm path length flow cell. The spectrometer used for these experiments was an LT Industries Quantum 1200. This instrument allows for the remote placement of sample cell and detector in an isolated glovebox with a fiber optic bundle transporting the light. Resolution of this instrument is on the order of 1nm with the scan for the visible region requiring 200 ms. For each sample, 10 scans were acquired and averaged. Data analysis was performed by using a PLS 2-block routine developed at the University of Washington (13). This code was implemented on a VAX 11-780 where all the calibration models were constructed. Nitric Acid Determination. The nitric acid concentration of each sample was determined by a standard addition method (14) designed to avoid the formation of hydronium ion from hydrolysis of plutonium in the sample. One hundred microliters of sample was mixed with 10.0 mL of 1.0 M potassium thiocyanate used to complex plutonium. Then 100-pLstandard additions of 0.092M nitric acid were made, and the resulting pH was measured with a Ross combination semimicro-pH electrode (Orion) and a portable pH meter (SA250, Orion). The inclusion of an estimate of the hydronium ion activity coefficient was necessary for the acid range used in this study. Using the standard equation for the Debye-Huckel activity coefficient, a value of approximately 0.75 was estimated as the activity coefficient for hydronium ion. However, when this value was used to determine hydronium ion activity of 10 prepared acid samples whose total acidity had 0 1989 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 61, NO. 15, AUGUST 1, 1989
Table I. Variance Described by PLS Models for Plutoniurn(II1) and Nitric Acid spectral response each, % total, %
latent variable 1
2 1
2 3 4 5 6
94.53 3.61
94.53 98.14
94.35 1.81 3.51 0.14 0.05 0.02
94.35 96.17 99.68 99.82 99.87 99.90
350 30.0
total, %
98.80 1.16
98.80 99.96
I
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t
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I 0.790
v
._+.
I
t
t
8
-
each, %
total, %
5.78 29.55 1.17 28.12 16.91 11.52
5.78 35.34 36.51 64.63 81.55 93.07
t
1
/) fi
.. ..
20.0
.u
nitric acid
Pu(II1)
each, %
P'E (1, I ) 29.9g/L
15.04
13.3 g / L 10.0
6.0p / ?
..
0.0 0.0
2.0 g/L
0.5
10
1.5
2.0
Wavelength (nm) 2.5
3.0
3.5
" 0 3 Concentration (M)
~
Figure 2.
Absorbance spectra of Pu(II1) from 2.0 to 29.9 g/L.
Figure 1. Plot of
nitric acid concentration versus Pu(1I I) concentration in the calibration set.
previously been measured by sodium hydroxide titration, the known value was constantly underestimated. (Four of these samples contained a hydrolyzable metal, thorium nitrate.) We resorted to estimating the activity coefficient experimentally since the ionic strength and hydronium ion concentrations were not consistent with the DebyeHuckel theory. This procedure involves determining the activity coefficient by the following expression:
where the pH is the measured quantity of hydronium ion activity during the standard addition experiment and [H,O+] is the known concentration of added nitric acid after dilution. This procedure assumes complete dissociation of nitric acid. The mean value of this estimated activity coefficient, -fH@+, for the 10 standards was 0.93 f 0.01. By use of this estimated activity coefficient in the following equation, the initial acid concentration, [HsO+]i,in each calibration and test set sample can be estimated. vi[H~o+]iY~@ 4- V a [ H 3 0 + ] ~ ~ Y=~(vi s ~-k+ va)lo-pH(2) Vi and V, are the volumes of the initial sample and added standard respectively, and [Ha0+]smis the concentration of the standard. The estimation of nitric acid using the above method has a relative error of 2.4%.
RESULTS AND DISCUSSION Visible spectra of the plutonium species are presented in Figures 2 and 3. Figure 2 shows the sensitivity of several Pu(II1) absorption bands in solutions containing 2.0 to 29.9 g/L Pu(II1). The nitric acid concentration in these four samples is approximately 1.3 M. In high-precision analytical measurements, the bands a t 565 and 601 nm are commonly used to quantitate Pu(II1). The effect of nitric acid on plutonium(II1) nitrate complex absorption is presented in Figure 3. At a constant level of 6.0 g/L Pu(III), nitric acid was varied from 0.6 to 2.3 M. This effect is most readily observed at 565 nm, where the absorption peak tends to narrow or become more symmetrical with increasing nitric acid concentration, and between 750 and 825 nm, where a change in one or more
5000
550.0
6000
650.0
7000
7500
800.0
8500
Wavelength (nm)
Effect of nitric acid on Pu(II1)absorbance spectra. Nitric acid varies from 0.6 to 2.3 M with a constant 6.0 g/L Pu(II1) concentration. Figure 3.
underlying absorbance bands causes shifts in the spectra. Two separate models, one each for Pu(II1) and nitric acid, were built using PLS regression. For each regression model, the spectral responses from the 25-sample calibration set formed the X block (independent variables) and the concentrations of Pu(II1) or nitric acid formed the Y block (dependent variable). All variables were mean centered and scaled by their standard deviation as part of the model. For both models, the optimum number of latent variables to include in the calibration was determined by cross validation (alternating one sample removed method), and the models include all 25 samples. Table I shows the variance described by the PLS model for both Pu(II1) and nitric acid and the correlations of spectral responses to the Y-block information. The f i t latent variable of the X block corresponds to 94.35% of the variance in the spectral responses, which is primarily due to the large signal of changing Pu(II1) concentration as seen in Figure 1. This fist latent variable in Table I describes 99.80% of the information in the Y block containing Pu(II1). Therefore, Pu(II1) has a large signal-to-noise ratio, which is to be expected, and its modeling should be straightforward. Nitric acid, however, has only 5.78% of its variance described
ANALYTICAL CHEMISTRY, VOL. 61, NO. 15, AUGUST 1, 1989
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Table 11. Prediction Results for Test Set Samples 30 -25
Pu(III),g/L
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20
-
15
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1 2 3 4 5 6
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0
,
:
:
0
:
:
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:
10
:
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15
; 20
:
I 25
:
; 30
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.-D
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E
0.204 0.20
:
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:
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I 1.70
:
I 2.20
Actual HN03 Concentration
,
I 2.70
2.00 5.99 30.3 19.7 4.62 15.2
1.98 1.15 1.07 2.13 2.08 0.94
1.96 1.47 0.92 2.47 1.97 1.16
0.02 0.32 0.15 0.34 0.11 0.22 0.23'
Standard error of prediction.
Figure 4. Actual Pu(II1) concentration versus predicted Pu(II1) concentration based on a two latent variable PLS model.
v
1.99 5.97 29.9 19.9 4.67 15.6
0.25O
+
Actual Pu(ll1) Concentration (g/L)
-
0.01 0.02 0.4 0.2 0.05 0.4
differ-
sample true estimated
10 T
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ence
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:
3 0
(M)
Figure 5. Actual nitric acid concentration versus predicted nitric acid concentration from a six latent variable PLS model.
by the first latent variable. In subsequent latent variables, more of the nitric acid information is being correlated with spectral responses orthogonal to latent variable 1. Since very little spectral variance is being used to model nitric acid, one would expect a small signal-to-noise ratio and a model with a higher degree of error than the Pu(I11) model. The accuracy of a multivariate model can be visually examined by plotting the actual calibration concentrations versus the predicted values for each sample. For Pu(III), the 25 sample concentrations are plotted versus their estimated concentrations using a two latent variable model in Figure 4. As expected, Pu(II1) is easily modeled with an ? statistic of 1.00 and a standard error of 0.20 g/L. Figure 5 provides a similar plot of actual vewus predicted concentrations for nitric acid using a six latent variable model. In this case, the model describes the overall nitric acid effect on the spectra but with a greater degree of error than the Pu(II1) model. The r2 statistic for the nitric acid model was 0.93 with a standard error of 0.18 M. The best test for the validity of a calibration model is to examine the prediction capability of the model on samples not included in the calibration sample set. To validate the constructed models, a test set containing six samples with known Pu(II1) and nitric acid concentrations were analyzed in the same manner as the calibration set samples. Table I1 compares the resulting predictions with known values. The calibration model is proven to be valid if the predicted value of an unknown is within the standard error range of the model, which is a calculation of the standard deviation of the model residuals. For example approximately 95% of future samples
should fall within twice the standard error if the unknowns come from the same population as the standards. For Pu(III), with a standard error of 0.20 g/L, all of the predictions were within two standard errors with four of the six predictions within one standard error. For nitric acid all predicted values are within the two standard error limit (0.18 M "Os) estimated by the model, and half of these samples are within one standard error. The actual standard error of prediction was 0.25 g/L and 0.23 M for Pu(II1) and nitric acid, respectively, which is larger than the error for the calibration seta for both analytes. Although the number of samples was limited in both calibration and test sets, there was no statistical difference between the standard errors based on a F-test comparison. The results of this test set provide confidence that both the Pu(II1) and nitric acid models are valid over the range of concentrations normally encountered in the precipitation studies. We have demonstrated the use of the plutonium(1II)nitrate absorbance spectra coupled with PLS regression for the determination of Pu(II1) and nitric acid concentrations over the analyte ranges of 1.99 to 29.9 g of plutonium and 0.44 and 3.08 M nitric acid. The precision of these predictions is suitable for studying the effects of oxalic acid and nitric acid concentrations during the precipitation of plutonium oxalate. Although greater precision could be obtained from other analysis methods, the information gained from these spectral measurements is well suited for rapid analytical measurement. The coupling of multivariate regression techniques with absorbance spectroscopy provides quantitation of both Pu(II1) and nitric acid from a single spectral measurement, thereby simplifying the instrumentation used in studying the precipitation reaction. Registry No. Pu, 7440-07-5; nitric acid, 7697-37-2.
LITERATURE CITED (1) Burney, G. A.; Porter, J. A. Nucl. Chem. Lett. 1967,3 , 79-85. (2) Cleveland, J. M. The Chemistry of Plutonium; American Nuclear Society: La Grange Park, IL, 1979; pp 401-403. (3) Wangen, L. E.; Phllllps. M. V.; Walker, L. F. U S . Department of Energy Report LA-11297, 1988. (4) Hagan, P. G.; Miner. F. J. Atomic Energy Report, RFP-1391, 1969. (5) Van Hare D. R. U.S. Department of Energy Report, DP-1713. (6) Baldwin, D. L.; Stromatt, R. W. U S . Department of Energy Report PNL-SA-15318, 1987. (7) Lorber, A.; Wangen, L. E.; Kowalskl, 8. R. J . Chemom. 1987, 1 , 19-31. (8) Geladl, P.; Kowalskl, B. R. Anal. Chim. Acta l98S, 185, 1 and 19. (9) Haaland, D. M.; Thomas, E. V. Anal. Chem. 1988, 6 0 , 1193-1208, (IO) Otto, M.; Wegschelder, W. Anal. Chem. 1985. 57, 63. (11) Martens, M.; Martens, H. Appl. Spectrosc. 1986. 4 0 , 303. (12) Parker, J. L. U.S. Department of Energy Report LA-814&MS, 1980. (13) Vekkamp, D.; Kowalski, B. R. Center for Process Analytical Chemistry, BG10, University of Washington, Seattle, WA, PLS 2-Block Modeling, Version 3.0, 1988. (14) Baumann, E. W.; Torrey, 8. H. Anal. Chem. 1984,5 6 , 682-685.
RECEIVED for review January 23,1989. Accepted May 1,1989.
