separate tellurium from selenium may find some special application. A more practical application involved a direct precipitation of tellurium from a solution of a reactor-fuel specimen. The gamma-ray spectra of the composite and precipitate are shown in Figure 2. The latter spectrum clearly shows the 230 keV photon of tellurium with some loaRu (490 keV) and 1321, the daughter of tellurium. From the spectra, it is seen that tellurium was separated from many fission products sufficiently pure for analytical purposes. Zirconium, niobium, and protactinium can be complexed with fluoride and thus retained in the supernatant liquid. When looking for trace amounts of selenium, it may become necessary to remove gross amounts of tellurium. We have used several precipitations with phenanthroline in order to reduce the number of distillations, selective reductions, and hydroxide scavenges that would otherwise be required to obtain a few milligrams of selenium free of tellurium, and other ions. This works expecially well when trying to obtain ’9Se free of other radionuclides found in nuclear fission products.
R. R. RICKARD E. I. WYATT
t-
I (00
I 700 PHOTON E N E R G Y , k e V I
I
500
500
I 900
1
Figure 2. Separation of tellurium from mixed fission products
Oak Ridge National Laboratory Post Office Box X Oak Ridge, Tenn. 37831
RECEIVED for review September 24, 1971. Accepted January 6, 1972.
Criterion for Judging the Acceptability of Analytical Methods SIR: E. A. McFarren, J. R. Lishka, and J. H. Parker (I) recommended the following characteristic as a criterion of the acceptability of analytical methods total error
=
+
d 2s 100 P
where d is the absolute value of the mean error, s the standard deviation, and p is the correct value. Here the absolute value of the mean error is substituted in relation (A) without regard to its statistical significance-Le., irrespective of whether it represents the actual systematic error or is statistically insignificant. In this latter case, the absolute value of the mean error would only be the result of accidental variation of individual results around the true value. However, in the criterion (A), this oscillation within the limits of variability is already characterized by the value of the standard deviation, s. T. J. Farrell ( 2 ) also used the criterion (A) in his remark on the study ( I ) . I therefore suggest the use of a similar criterion total error
=
100
da
+ 2s
~
P
(1) E. A. McFarren, R. J. Lishka, J. H. Parker, ANAL.CHEM., 42, 358 (1970). (2) T. J. Farrell, ibid., 43, 156 (1971). 878
ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
where, however, dA is the vzlue of the absolute mean error which is statistically significantly different from zero. When the absolute value of the mean error does not significantly differ from zero, dA = 0 is substituted and criterion (B) converts to 100 2 4 , ~ . Statistical significance of the difference of d~ from zero must first be tested by means of Student’s t-test on the significance level CY = 0.05 for the number of degrees of freedom v = n - 1 (3). Here n is the number of determinations from which the absolute mean error and standard deviation were obtained. The significance level for testing the statistical significance of the mean error must be prescribed strictly. The reason is, that if selection of the significance level were left to the discretion of individual authors, the criterion (B) could not become a generally acceptable means of comparison. In assessing the acceptability of analytical methods, the criterion (B) takes into the consideration the variability of results (2s) as well as the value of the mean error, provided of course that the latter is statistically significant (dA). This also satisfies the demand expressed by Ch. Eisenhart (4)--i.e., that when the uncertainty of results obtained by measurement is being expressed, cases in which the results (3) K. Eckschlager “Errors, Measurements and Results in Chemical Analysis,” van Nostrand-Reinhold Co., London, 1969. (4) Ch. Eisenhart, Science, 160,1201 (1968).
Table I. Summary of Data on Metals by Atomic Absorption Spectrophotometry
Sample
True value
Number of results
Average
Mean error
0.055 0.502 1.030
+0.005 +o .002 $0.030
0.067 0.271 1.034
+0.017 +0.021 +Os 034
1 2 3
0.05 0.50
1 .oo
51 48 49
1 2 3
0.05 0.25 1 .oo
57 58 53
Standard deviation Absolute Relative Zinc 0.023 0.041 0.108 Copper 0.031 0.065 0.116
Total error
f
fk
41.8 8.2 10.5
1.55 0.31 1.94
2.009 2.012 2.011
92.0 16.4 21.6
47.3 11.2
4.14 2.46 2.11
2.003 2.002 2.007
158.0 60.4 26.6
17.5 10.7 7.6
1.32 1.86 2.33
2.447 2.447 2.447
40.0 20.0 17.0
2.0
Silver 1 2 3
0.05 0.10 0.20
7 7 7
0.055 0.093 0.215
+O .005 -0.007 +0.015
are subject to a systematic error should be separated from cases where there is no systematic error. The systematic error may be understood to be involved in cases where the absolute value of the mean error statistically differs from zero on a selected significance level. According to criterion (B), results of the determination of Zn, Cu, and Ag by atomic absorption photometry stated in the study (I) would then have to be assessed as shown in Table I. In this table, t k is the critical value of the Student’s t-distribution on the Significance level CY = 0.05. It is evident that the total error of the determination of Zn and Ag is lower than stated in (I) when the criterion (A) is applied. The mean error here is statistically insignificant on the significance level a = 0.05 and, therefore, it is not included in the total error value da according to criterion (B). The result of assessing the results of the method of determining Cu are the same as in the study ( I ) , since the mean error significantly differs from zero on the significance level of a = 0.05 and, therefore, is not included in the total error. Assessment of the applicability of an analytical method with the use of a criterion which includes the standard devia-
0.010 0.010 0.017
tion should, however, always be based on an approximately equal, and sufficiently large number of determinations. For example, however, in ( I ) the determination of Ag by atomic absorption photometry is based on seven results while assessment of the determination of Zn with the use of the same method is done from 51 results. This means that the relative width of the reliability interval of the standard deviation estimate is 160% in the first case, and only 40% in the second. Under these conditions, however, it is difficult to compare the total error of the determination of two elements by means of the same method. KARELECKSCHLAGER
Institute of Inorganic Chemistry Czechoslovak Academy of Sciences Prague, Czechoslovakia
RECEIVED for review March 29, 1971. Accepted January 6,1972.
Aromatic Hydroxylation as an Analytical Reaction SIR: The phenyl group has not attracted much analytical attention as a functional group, though it offers the possibility of a general approach to the detection and determination of aromatic compounds. Nitration and bromination have found limited use (I). Aromatic hydroxylation is an attractive reaction because the product, a phenol, is amenable to detection and measurement by many methods. Little prior use has been made of aromatic hydroxylation. Benzoic acid can be determined in foods by conversion to salicylic acid (12% yield) upon treatment with a reagent of ferric ion, hydrogen peroxide, and sulfuric acid (2, 3 ) ; the salicylic acid is removed by extraction and is determined colorimetrically. Bartos (4) determined several aromatic compounds colori(1) N. D. Cheronis and T. S. Ma, “Organic Functional Group Analysis by Micro and Semimicro Methods,” Interscience Publishers, New York, N. Y., 1964, p 443. (2) J. R. Nicholls, Analyst (London),53, 19 (1928). (3) N. L. Allport and J. E. Brocksopp, “Colorimetric Analysis,” Vol. II,2nd ed., Chapman and Hall, London, 1963, p 52. (4) J. Bartos, Ann. Pharm. Fr., 27,759 (1969).
metrically through formation of o-nitrosophenols by means of a cupric ion-hydrogen peroxide-hydroxylamine reagent. Of the several hydroxylating agents that have been proposed (usually as model systems for enzymes), that ofHamilton seemed to provide advantages of simplicity, yield, and speed (5,6). The Hamilton system consists of an aqueous solution of ferric ion, hydrogen peroxide, and catechol (or another enediol). Hamilton et af. (5,6) studied the hydroxylation of some monosubstituted benzenes, measuring the kinetics of the loss of peroxide when the aromatic substrate was in excess. Anisole and nitrobenzene were found to undergo hydroxylation at comparable rates, ruling out an electrophilic substitution as the mechanism. The present paper reports the application of this system to the quantitative determination of some aromatic compounds. ( 5 ) G. A. Hamilton, J. P. Friedman, and P. M. Campbell, J. Amer. Chem. Soc., 88,5266 (1966).
(6) G. A. Hamilton, J. W. Hanifin, and J. P. Friedman, ibid., p 5269. ANALYTICAL CHEMISTRY, VOL. 44, NO. 4, APRIL 1972
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