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ANALYTICAL CHEMISTRY, VOL. 51, NO. 2, FEBRUARY 1 9 7 9
The minimum detectable activity for an N peak region with a 0.003 cpm background and a detector with 2 2 % counting efficiency is 0.01 pCi for a 1000-min counting time. A 10-g sample with a 50% chemical yield would then give a 0.002 pCi/g minimum detectable limit for an americium or curium determination.
LITERATURE CITED (1) R. Bojanowski, H. D. Livingston, D. L. Scheider, and D. R. Mann, "A Procedure fw the Anatysis of Americium in Marine Environmental Samples", Reference Methods for Marine Radioactivity Studies 11, InternationalAtomic Energy Agency, Vienna, Technical Report Series No. 169 (1973). (2) M. C. de Bortoli, Anal. Chem., 39, 375 (1967). (3) E. L. Hampson and D. Tennant, Analyst (London), 98, 873 (1973). (4) S. A. Reynolds and T. G. Scott, Radiochem. Radioanal. Lett., 23 (4), 269 (1975). (5) T. G. Scott and S. A. Reynolds, Radiochem. Radioanal. Lett.. 23 (4), 275 (1975).
(6) C. W. Sill, K. W. Puphal, and F. D. Hindman, Anal. Chem., 46, 1725 (1974). (7) N. A. Talvitie, Anal. Chem.. 43, 1827 (1971). (8) U.S. Atomic Energy Commission, "Measurement of Radionuclides in the Environment-Sampling and Analysis of Plutonium in Soil", U.S. AEC Regulatory Guide 4.5 (1974). (9) C. W. Sill, Anal. Chem. 46, 1426 (1974). (10) P. B. Hahn, E. W. Bretthauer, P. B. ARringer, and N. F. Mathews, "Fusion Method for the Measurement of Plutonium in Soil: Single-Laboratory Evaluation and Interlaboratory Collaborative Test", Office of Research and Development, U S . Environmental Protection Agency, EPA-BOO/ 7-77-078 (1977). (11) C. W. Sill and R. D. Hindman, Anal. Chem., 46, 113 (1974). (12) T. D. Filer, Anal. Chem., 46, 608 (1974). (13) N. A. Taivitie, Anal. Chem. 44, 280 (1972). (14) C. W . Sill, Health Phys., 29, 619 (1975). (15) F. Nelson, T. Murase, and K . A. Krause. J . Chromatogr.. 13, 503 (1964).
RECEIIFDfor review September 14,1978. Accepted November 21, 1978.
CORRESPONDENCE Regression Line That Starts at the Origin Sir. When analytical results for experimental measurements of a dependent variable, y , are theoretically obtained with an independent variable, x , it is customary to calculate the "best straight line" using the equation
y=a+bx
C
(1)
through the region of experimental points by the method of least squares, where a is the intercept on the y axis ( 1 ) . However, theoretical, graphical representation of some analytical measurements, especially Beer's law, consists of a straight line that begins at the origin. In spectrophotometry, this would be expected t o occur if corrections have been carefully made for blank absorptions and cell differences. In view of this contradiction, it would seem appropriate, for a system that has been well tested, to determine instead t h e best straight line through t h e experimental points, commencing at t h e origin:
A
C
0
(2)
y = bx
This will unavoidably reduce the precision slightly, but could increase the accuracy. If forced to choose, most analytical chemists would place accuracy above precision. T h e derivation of t h e method for calculating such a best straight line is considerably simpler than that for the determination of a and b. Following the same procedure as for
from y i will be
S = Z(yi - b x J 2
(4)
= Z ( y I 2- 2 b x y 1 + b2XI2)
+ 2 b x I 2 )= 0
bBx12= Z x y l b = Zx~,/2xL2
02
--L
Though S is a measure of the total deviation of points from the best line, it is more common to use the standard error of estimate
(5)
Taking the derivative of S with respect to b , setting it equal to zero for a minimum, and solving for b,
aS/ab = Z ( - 2 x j 1
mg N / d
(6)
(7) (8)
0003-2700/79/0351-0298so1 O O / O
which puts it on an individual basis like standard deviation. A practical application of the proposed procedure is given by some analyses that are part of a paper being submitted to another journal for publication (2). Each of eight samples of brown rice was divided into two parts; one part was milled, the other left unmilled. The sixteen samples were then ,C 1979 American Chemical Society
ANALYTICAL CHEMISTRY, VOL. 51, NO. 2, FEBRUARY 1 9 7 9
Table I. Comparison of Absorptivities of Two Sets of Solutions Calculated from the Best Straight Lines and from the Best Straight Lines through the Origin" rice equation s, equation s, brown A = 2 . 3 5 ~- 0.011 0 . 0 0 3 A = 2 . 3 0 ~ 0.003 milledb A = 2 . 0 6 ~+ 0.051 0.008 A = 2 . 3 0 ~ 0 . 0 1 2 Another publication of Cell thickness 1.000 cm. protein determination in brown and milled rice b y the Kjeldahl reaction also shows a larger standard error of estimate for milled rice ( 3 ) .
299
The results calculated from the two equations are shown in Table I, the most striking being the different absorptivities using Equation 10 (2.35 and 2.06) and identical ones (2.30) using Equation 11. A slight difference in the two absorptivities might be expected, since the layer removed by milling contains a small amount of protein that might be different in nature. However, there should then also be a difference when using Equation 11, but there is not. Hence, the identity of absorptivities from best straight lines through the origin demonstrates the desirability of the proposed method.
LITERATURE CITED analyzed for total nitrogen by the Kjeldahl method (1.170 to 1.886% N and 1.051to 1.864% N for the two sets, respectively) and used to test a procedure developed by the authors for determining protein nitrogen by the biuret reaction. The absorbances of the solutions of the copper-nitrogen complex for the two sets of samples are shown plotted vs. the nitrogen concentration in Figure 1. Introducing symbols for spectrophotometry into Equations 1 and 2 gives, respectively,
A = a,
+ abc
(10)
and
A = abc
(11)
(1) "Official Methods of Analysis of the A.O.A.C.", William Horwitz, Ed., 12th ed., Association of Official Analytical Chemists, Washington, D.C., 1975, xvi-xvii. (2) "A Moderately Rapid, Accurate, Room-Temperature Method for the Spectrophotometric Determination of Protein in Rice by the Biuret Reaction", F. C. Strong 111and P. Theis-Maimone, submitted for publication. (35 L. C. Parial, L. W. Rooney, and B. C. Webb, Cer. Chem.,47, 38-43 (1970).
Frederick C. Strong I11 Faculdade de Engenharia de Alimentos e Agricola Universidade Estadual de Campinas Caixa Postal No. 1170 13100 Campinas, S.P., Brasil
RECEIVED for review May 24,1978. Accepted October 30,1978.
Exchange of Comments: Analytical Methods of Bis(chloromethy1) Ether in Air Sir: Since the carcinogenicity of bis(chloromethy1) ether (BCME) was established, its potential presence in the industrial environment became a grave concern (1-4). T o ascertain its actual existence and level in suspected industries and to protect the workers from this occupational hazard, air monitoring is essential. Thus, various quantitative analytical procedures for BCME have been reported. Among them are: (A) Direct gas chromatography (GC) (B) On-Column Concentration-GC. The BCME, together with some of the other contaminants, is first allowed to adsorb on the front section of the column a t room temperature and then analyzed a t a programmed higher temperature ( 5 ) . (C) Adsorber-GC combination. The BCME, together with some of the other contaminants, is first allowed to adsorb on the packing in B trapping tube and then thermally flashed onto a GC analytical column or a set of analytical columns (6, 7 ) . (D) Adsorber-mass spectrometry (MS) combination. The BCME, together with some of the other contaminants, is first allowed to adsorb on the packing in a trapping tube, and then is thermally eluted into the reservior of a high-resolution mass spectrometer (8). (E) Adsorber-GC-MS combination. The BCME, together with some of the other contaminants, is first allowed to adsorb on the packing in a trapping tube, then thermally flashed onto a GC analytical column, and finally the BCME fraction is gated into a mass spectrometer (9, I O ) . The preceding methods are all technically sound and straightforward in application. They differ in sensitivity, selectivity, cost of equipment, and requirement for trained personnel. In addition to the above methods, there is a unique derivatization method which first appeared in this journal (Analytical Chemistry) in 1975, followed by a modified version a year later (11, 12). 0003-2700/79/0351-0299$01.00/0
This derivatization method involves the conversion of BCME, by means of trichlorophenol and methoxide in methanol, into a derivative which is then to be assayed by GC. The stock reagent consists of 25 g of sodium methoxide and 5 g of trichlorophenol in 1 L of methanol. In other words, methoxide is more than 18-fold in molar excess. The derivative was identified, as stated in the article, as C13CsH2OCH20CH20CH,but no spectral or other evidence was given to substantiate its identity. An 86 to 115% recovery was reported according to the data in Table I1 of the original article. (Data in Table I11 of the same article show an 84 to 160% variation.) No reason was offered for an 18-fold molar excess of sodium methoxide, in spite of the fact that BCME undergoes extensive decomposition in the presence of methoxide, and that it has been used in scrubbers to destroy BCME. At the end of the original article, a statement was made to the effect that the sensitivity could be increased 6or 8-fold by using stoichiometric quantities of sodium methoxide and trichlorophenol, with recoveries varying from 82 to 100%. This realization of the basic principle of chemical stoichiometry did not, however, prompt a re-examination of the experiments, nor promote a critical evaluation of the chemistry involved. T h e derivatization apparently involves the following equilibrium:
OH
+
CH30Na
ci
._ C I CI
Both the methoxide and the trichlorophenoxide then react with BCME and can give one unsymmetric derivative and two symmetrical derivatives as follows: 'C 1979 American Chemical Society
