ANALYTICAL CHEMISTRY, VOL. 51, NO. 7, JUNE 1979
LITERATURE CITED (1) R. A. Saunders and A. E. Williams, in "Mass Spectrometry of Organic Ions", F. W. McLafferty, Ed.. Academic Press, New York, 1963, Chap. 8. (2) J. T. Watson and K . Biemann, Anal. Chern., 37, 844 (1965). (3) W. J. McMurray, 8. N. Greene, and S.R. Lipsky. Anal. Chem., 38, 1194 (1966). (4) A. L. Burlingame, D. H. Smith, and R. W. Olsen, Anal. Chem., 40, 13 (1968). (5) M. L. Aspinal, K. R. Cornpson. A. A. D o w m n , R. N. Elliot, and D. Hazelby, Proceedings of the 23rd Annual Conference on Mass Spectrometry, Houston, Texas, 1975, p 73. (6) S.Evans, D. Hazelby, K. R. Compson, and A. E. Holme, Proceedings of the 24th Annual Conference on Mass SDectrometry, San Diepo, Calif., 1976, p 289. (7) D. F. Hunt, G. C. Stafford, J. Shabanowitz, and F. W. Crow, Anal.Chern., 49, 1884 (1977).
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(8)J. F. Holland, C. C. Sweeley, R. E. Thrush, R. E. Teets, and M. A. Bieber. Anal. Chem., 45, 308 (1973). (9) W. F. Holmes, W. H. Holland, B. L. Shore, D. M. Bier, and W. R. Sherman, Anal. Chern., 45, 2063 (1973). (10) W. A. Garland, R. J. Weinkam, and W. F. Trager, Chern. Instrum., 5,
271 (1974). (11) A. Savitsky and M. J. E. Golay, Anal. Chem., 38, 1627 (1964)
RECEIVED for review September 5, 1978. Accepted March 5, 1979. T h i s work was supported in part by Research Career Development Award GM 00007 (R.J.W.). Acquisition of computer and associated components was supported by Liver Research Center P-50 AM 18502 and Biotechnology Research Grant RR 05453.
Determination of Pentachlorophenol in Water by Mass Spectrometric Isotope Dilution Leonard L. Ingram, Jr.," Gary D. McGinnis, and Susmita V. Parikh Forest Products Utilization Laboratory, Post Office Drawer FP, Mississippi State, Mississippi 39 762
A mass spectrometric isotope dilution method using "0 labeled pentachlorophenol (PCP) has been developed for determining low levels of pentachlorophenol in water. A known amount of ''0 PCP is added to a measured volume of water and the combined solutions are extracted. The methyl ether derivatlve is prepared by reacting the extract with excess ethereal diaromethane solution and the fraction of "0 PCP is determined from the Ion intensities in the mass range m / e 278 to 290 in the GC/MS analysis. The lower useful limit is approximately 0.2 X lo-' g with a relative standard deviation of approximately 8 YO.
T h i s paper describes a GC-MS technique for t h e analysis of pentachlorophenol in water. Single ion monitoring (SIM) of mass 280 in the mass spectrum of pentachloroanisole (PCA) has been used routinely in this laboratory for several years. SIM is more specific than EC-GC ( 1 ) or colorimetric methods ( 2 ) b u t lacks the sensitivity of EC-GC. Another disadvantage of SIM is possible sample loss during extraction and methyl ether preparation. An isotope dilution method was developed t o obtain more reliable values on routine sample analysis and t o test t h e validity of t h e results obtained by other methods. The advantage of the isotope dilution method is accurate values may be obtained down t o concentrations of 1 wg/L of PCP. T h e major disadvantage is the analysis time is longer than required for other techniques because of t h e d a t a analysis required. EXPERIMENTAL Apparatus. Glassware which had not been subjected to a high concentration of PCP was used throughout the experiments and was cleaned by washing with Alconox detergent in warm water, 5 % sodium hydroxide solution, and finally deionized water. Gas Chromatograph-Mass Spectrometer. The gas chromatograph was a Varian Aerograph Model 2740 equipped with a 5-ft by 1/8-in.stainless steel column packed with 3% Dexsil 300 on Chromosorb WAW. The injector port, column, detector oven, and separator temperatures were 235 "C, 210 "C, 235 "C, and 250 "C, respectively. The helium flow was 30 cm3/min. The mass 0003-2700/79/0351-1077$01.00/0
spectrometer was a DuPont 21-490F low resolution instrument. The instrument was operated with an ionizing voltage of 70 eV a t 300 pA. The accelerating voltage was 1400 V and the source temperature was 250 "C. The mass spectra were recorded with a Bell and Howell Model 5-154 oscillographic recorder. Reagents. All chemicals were analytical reagent grade and the solvents were re-distilled in this laboratory. Deionized water was used for the preparation of standard solutions and no P C P could be detected in a blank determination on 1 L of water. Ethereal diazomethane was prepared from Diazald (N-methylN-nitroso-p-toluenesulfonamide) using a diazomethane generator kit purchased from Aldrich Chemical Company. The l80PCP was purchased from Key Isotope Company with a stated content of 69.0% l80PCP. Solutions. Stock solutions of PCP were prepared by dissolving a weighed amount of PCP in 0.1 N NaOH and diluting to volume with 0.1 N NaOH. The different concentrated solutions were prepared by dilution of measured volumes of the stock solutions to 50 mL with 0.1 N NaOH. The spike solution of l80PCP was prepared by dissolving a weighed amount in 0.1 N NaOH and diluting to volume with 0.1 N NaOH. Procedure. For the analysis of the 0.1 to 1.1 pg/mL PCP solution, 2.00 mL of a 9.36 wg/mL of " 0 PCP solution was added to 50.00 mL of each standard solution. The solution was mixed by shaking, and acidified to a pH of 2 with 4 M H2S04. For the 0.004 and 0.03 wg/mL solutions, 1.00 mL of a 0.900 pg/mL l80 PCP solution was added to 50.00 mL of sample. The acidified solution was extracted once with 25 mL of CHC1, which was then dried by filtering through approximately 2 g of anhydrous Na2S04. The CHCl, was evaporated with a rotary evaporator and the residue dissolved in 5 mL of CH2C12. Excess ethereal diazomethane solution was added and the mixture was allowed to stand for 30 min. The sample was evaporated to dryness and re-dissolved in 1 mL of benzene which could be evaporated to about 1 drop for the low concentration samples. The mass spectral data were obtained from 1-pL injections and the mass range from m / e 278 to 290 was scanned 5 or 6 times during the sample elution. For an average peak height error of less than 1% , six or more scans would be required (3) from a typical Gaussian GC Peak. However, the scan rate on this instrument is limited by the 1000-Hz recording oscillograph and only 5 or 6 spectra of significant intensity could be obtained on the nanogram samples. The peak intensities were determined manually and normalized. 'C' 1979 American Chemical Society
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ANALYTICAL CHEMISTRY, VOL. 51, NO. 7, JUNE 1979
Table I. Determination of I8O Pentachlorophenol in the Spike
Table 111. Analysis of 50-mL Standard Pentachlorophenol Samples
sample methoda l*O PCP, % probe 69.9 probe 69.9 probe 69.4 GC 67.4 GC 72.0 GC 70.0 Average value = 69.8 * 1.8 (95%). Relative standard deviation = 1.5. a Probe samples were pentachlorophenol and GC samples were pentachloroanisole. -___
Table 11. Results from the Analysis of 1.00 mL H,O Containing 1.OO pg/mL Pentachlorophenol determination no. results 1 2
1.02 1.07 0.90 0.96 1.07
3 4 5 Average = 1.004 r 0.09 (95%). Relative standard deviation = 0.074. A previously published ( 4 ) extraction procedure was used for sample preparation for single ion monitoring. A calibration graph was prepared by injecting 1yL of PCA standard sample in benzene and monitoring mass 280. A plot of peak height vs. concentration yields a linear calibration plot.
RESULTS AND DISCUSSION T h e fraction of l80PCA was determined using all peak intensities from mass 278 to mass 290 with the computer program MIMS (5,6). In the present application, the program utilizes a multinomial distribution algorithm to calculate the ion intensities for the 12C, 13C, 35Cl, '3 :1, l60,ISO, and 'H present. T h e program was modified to iterate from 0.0 to 100% l80PCA a t 0.1% increments. T h e minimum point in the plot of the root mean square deviation vs. percent isotopic enrichment corresponded to the percent of l80PCA in the sample (6). The computer program was modified to determine this minimum by comparison of each value. Test data for the computer technique for 0.0, 10.0,25.0,50.0, a n d 75.0% l*O PCA gave absolute agreement. Comparison of the computer results with values obtained by subtracting the l60spectrum showed differences of less than 2% in over 20 samples. T h e methods and applications of the computer program MIMS for determining isotopic abundances have been discussed by the original author (6). T h e fraction of l80P C P in the spike material shown in Table I was determined from a P C P sample by direct probe insertion and from the G C / M S of PCA. T h e average value was 69.8 [C.I. (95%) = =k1.8%] and was in agreement with the Key Isotopes Company stated l80P C P content of 69.0%. T h e concentration of PCP in the sample was calculated fom Equation 1,
sample no. 1
2 3 4 5 6 7 8 9
concentration of stock d m L 1.1 0.88
0.44
concentration found, aimL 1.07 0.86 0.36 0.16
0.20 0.11 0.010
0.0090
0.0307 0.0153
0.0315 0.0150
0.0046
0.0051
0.11
error, % -2.5 -1.8 -17.2
-21.0
-
3.6 -10.0 2.6 -2.0 A 10.8
Average error = 7.9%. a Samples 1-6 and 7-9 were prepared from separate stock solutions, Table IV. Wood Treatment Plant Water Samples single ion sample monitoring, isotope dilution, no. PigimL PdmL 1 0.28 0.38 2 0.003 0.0046 3 0.20 0.43 4 4.4 8.6 5 440 619 6 0.002 0.0022 spike used in this analysis was 0.90 yg l80P C P , or a total of 1.9 yg of material. Sufficient material for the GC/MS analysis can be easily recovered from this amount of sample. T h e average of five determinations was 1.004pg/mL k 0.09 (95%). This value indicates that the precision and the accuracy of the method are approximately the same b u t are less than normally achieved with the isotopic dilution technique (7). The results of single analyses of stock solutions of P C P are shown in Table 111. T h e average observed error from the prepared concentration was about the same as that observed for the data in Table I. Several samples containing less than 0.2 ,ug of P C P were analyzed, but insufficient material was recovered to obtain usable mass spectral data. T h e results of the analysis of P C P in wastewater from a wood treating plant are shown in Table IV. In all samples where PCP was determined by single-ion monitoring and isotope dilution, the isotope dilution analysis was always higher. Since the results of the isotope-dilution method depend on the ratio of the two isotopes and not on total sample recovery, it appears that P C P is being lost during the extraction or methylation procedure. Extraction efficiencies of 95 to 10070 were reported with this extraction procedure ( 4 ) , but the treatment plant samples contained 1 to 10% other organic material which could possibly interfere with extraction or methylation. In the analysis of the wastewater samples, no other compounds were observed with the same mass ion intensities and the same retention time as PCA. With a computer interfaced to the mass spectrometer, the data analysis could be completely automated with a great reduction in the total analysis time of the isotope dilution samples.
LITERATURE CITED where Co = concentration of P C P in pg/mL, R = ratio of the molecular weight of l60PCA to l80PCA, F,= fraction of l80 P C P in the spike, F,,, = fraction of l8O P C P in the spiked sample extract, F, = fraction of naturally occurring lSO, W , = the weight of the spike in pg, and Vo = the sample volume. T h e results of the analysis of a stock solution of 1.00 yg/mL pentachlorophenol are shown in Table 11. T h e amount of
(1) Morris Crammer and Joseph Freai. Life Sci., 9, 121 (1970). (2) W . T. Hosklns. Anal. Chem., 23, 1672 (1951). (3) P. E . Matthews and J. M. Hayes, Anal. Chem., 48, 1375 (1976). (4) Donald R. Buhler, M. E. Rosmussan, and H. S. Nakave, Environ. Sci. Technoi., 7, 929 (1973). (5) E. McLaughlin and R. W. Rozett. J . Organomet. Chem., 52, 261 (1973). (6) R. W . Rozett, Ana;,. Chem., 46, 2085 (1974). (7) Author J. A h e a r n , Trace Analysis by Mass Spectrometry", Academic Press, N ew York and London, 1972.
ANALYTICAL CHEMISTRY, VOL. 51, NO. 7 , JUNE 1979
RECEIVED for review May 30,1978. Accepted March 7,1979. This research was supported by the Environmental Protection
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Agency and presented to the 173rd National Meeting, American Chemical Society, New Orleans, La., March 2@25,1977.
CORRESPONDENCE Maximum Likelihood Estimation Evaluation of a Material with Unequal Number of Replicates Sir: As noted by Mandel and Paule (I),a frequent problem in the interlaboratory evaluation of a material is that each participating laboratory is not always able to make the same number of replicate determinations. They note that this lack of balance introduces some difficulties in the estimation of the two variance components and in the determination of the “best” overall average. Mandel a n d Paule also criticize the “usual” formulas and propose a n iterative procedure for estimating the three parameters. It is demonstrated in this paper that maximum likelihood estimates (MLE) of the three parameters may be obtained using an iteratively-reweighted Gauss-Newton algorithm for nonlinear least squares. Using the example from ( I ) , the MLEs are compared with those of Mandel and Paule. EXPERIMENTAL
The Model. L e t y,, represent the j t h result obtained in the ith laboratory. If the number of laboratories is k , we have i = 1, 2 , . . ., k Supposing that the number of measurements contributed by the ith laboratory is ni,then j = 1,.. . , ni for laboratory i T h e assumed model is: yi] = p
+ Li + ti,
(1)
where p is a constant representing the “true value”; L, is the “laboratory effect” (or bias) of the ith laboratory; and ti, is “the replication error” (or “within laboratory” error) due to the j t h measurement of laboratory i. T h e values of Li are assumed to represent a random sample from a normal population of mean zero and standard deviation (B for between laboratories). T h e values of e;, (all i and all j ) are also assumed to be a random sample from a normal population of zero mean. T h e standard deviation of this population is denoted by ow (w for within laboratories). Note that this model assumes the “replication error“ does not vary among the laboratories.
PROCEDURE T o obtain the MLEs of the parameters, let jj, denote the average of results for lab i and jj, the weighted overall average. Let OA= ( p , oB2,owz)denote the vector of unknown parameters a n d 8, the M L E of B. Also let
Table I. Sufficient Statistics statistic, z expectation, f ( e )
variance, l / w
The MSW, term represents the within laboratory mean square for the zth laboratory, while MSB represents the between laboratory mean square. Then Jennrich and Moore ( 2 ) have noted the set of yL,i = 1, 2, . . . k ; is sufficient for p and the set of pairs (n,(g,- M ) ’ , MSW,), z = 1, 2 , . . . k ; is sufficient for (oB2,uw2). Expections and variances of the sufficient statistic are given in Table I. Note that the relative weights for the pi are identical to those in Mandel and Paule (I). It has been shown ( 2 ) that maximum likelihood estimation in such a case can be accomplished using the (iteratively reweighted) Gauss-Newton algorithm for nonlinear least squares. To do this, the expected values f(O) are fitted to the observations t using weights b. Note that weights are recomputed a t each iteration. T h e iterative procedure is outlined below. T h e weighted overall average may be used as an initial estimate of p ; the mean of the MSW, for ow2and k 0 ‘ ~=~ ( k ( M S B ) -
k
2 MSW,)/ C n, 1 = 1
(4)
1 = 1
The iteratively reweighted Gauss-Newton algorithm may be viewed as an iterated application of weighted linear least squares. Consider z = f(0)
+e
(5)
Now f ( 0 ) can be approximated locally by
T h u s replacing f ( 0 ) with its local linear approximation in Equation 5 gives
(7)
n,
MSW, = {
c
]=I
( y ; ]- y1)2/(n; - l),ni
>
1
(2)
and
0003-2700179/0351-1079$01 OO/O
which may be viewed as a weighted multiple linear regression problem with the df(B)/dO playing the role of independent variables, the A0 as the regression coefficients, z - f ( 0 ) the role of the dependent variable, e the random errors, and u the weights. Then proceed as follows: (1) Determine initial estimates, Bo. C 1979 American Chemical Society
