Statistical Method in Isotope Analysis Sir: Genty recently published an article on the application of statistical method to isotope analysis ( I ) . It contains an elaborate and valuable discussion on the number of isotopic variants of molecules, the probability of obtaining each variant, and gives expressions for determining isotope ratios. Since reading the article, I have been puzzled by the discrepancy between some of his equations and those used in our laboratory (2, 3 ) . Recently, I have come to the conclusion that several of Genty's equations contain an extra term. The major equations of the article are correct, so Genty's methods of verification did not uncover the extra term. The basic flaw occurs in an unnumbered equation following his equation ( 4 ) : Or,
PI = F , [ A " ' ]
. . .[A"']
'. . .[A'"] '
His Equation 5 elaborates ( I ): P i -
. . [A"']Orp
(3) N is the multinomial coefficient. Since most of Genty's equations use ratios of (1) or (21, the extra term is eliminated; the equations concerned with isotope ratios are correct. Fourteen equations, each introduced by Pi, should be modified. The number within the parentheses in the following list refers to the number of the equation in Genty's article: Pi, pi (51, p2(8), P3(14), P4(16), p5(17), p6, p7, p8, pg, Pg, PI 0, and Plo. Except for P1 and the numerical examples, simple deletion of the p n term is sufficient to correct the expression. LITERATURE CITED (1)C.Genty, Anal. Chem., 45, 505 (1973). (2)E. McLaughlin and R. W. Rozett, J. Organomet., 52, 261 (1973). (3)R. W. Rozett, Anal. Chem., 46, 2085 (1974). (4) W. Feller, "Probability Theory and Its Applications," 3rd ed., Wiley and Sons, New York, N.Y., 1970,Vol. 1, p 167.
Richard W. Rozettl
?Z ! l x a , ! . ..ai!. . .CYP! p"
P , = N,[A'i']Ori. .[A"']='.
. . ,[A"'] '. . .[A'"'] '
The symbols are Genty's. The term l / p n should not be present. If it is removed, the equation correctly defines the binomial distribution when two isotopes are present, and the multinomial distribution in the general case ( 4 ) . Equation 1 should read:
Chemistry Department Fordham University Bronx, New York 10458
RECEIVEDfor review August 14, 1974. Accepted October 31, 1974.
Present temporary address, Research Division, Center for Experimental Design & Data Analysis, Environmental Data Service, 3300 Whitehaven St., N.W., Washington, D.C. 20235.
AIDS FOR ANALYTICAL CHEMISTS Reusable Glass-Bound pH Indicators G. Bruce Harper' Department of Chemistry, Brock University, St. Catharines, Ontario, Can Ontario, Canada
For many years, enzymes have been insolubilized on various carriers. The binding of enzymes to highly porous glass was pioneered by H. Weetall of Corning Glass. The binding modes used are included in a brochure "Corning Biomaterial Supports" available from Pierce Chemical Co., Rockford Ill. 61105. In the process of activating high-surface area glass in the binding of enzymes, this author produced a pale orange sintered glass funnel (Kimax 350-ml-80F). Attempts to wash out the color were unsuccessful. The funnel turned reversibly deep red when washed with acids, a discovery which led to the development of further glass-bound pH indicators. Conventionally, indicators have been used by dissolving the indicator chemical entity in the liquid to be tested, or by coating paper with the chemical entity and then contacting the coated carrier with the liquid to be tested. In Present address, Department of Chemistry, University of Toronto, Toronto, M5S ZAl,Canada. 348
nd Department of Chemistry, University of Toronto, Toronto,
whatever form indicators are presently used, a quantity of the indicator is required for each test. The amount of indicators consumed in an industry or in an active laboratory can be both substantial and costly. Furthermore, bound indicators are superior in the determination of pH's of weakly or nonbuffered solutions. Typical pH papers in nonbuffered solutions need long immersions for color change and dyes bleed into solutions. Also, a chromatographic effect causes free dyes to creep on paper, forming zones of uneven color. The use of bound indicators removes such difficulties. Glass-bound pH indicators have several advantages over soluble indicators: 1) They can be used indefinitely with quantitative recovery of indicator. They exhibit continued and apparently constant activity, as indicated by the intensity of color changes, over a period of at least one year a t room temperature, upon exposure to most organic and aqueous assay conditions. 2) They are unsusceptible to mi-
ANALYTICAL CHEMISTRY, VOL. 47, NO. 2, FEBRUARY 1975
crobial attack. 3) They are insoluble and, hence, do not contaminate systems. 4) They may be made in a form which is especially convenient for particular laboratory operations, e.g., glass wool, glass stirring rods, filter sticks, disks, or glass fragments. Bound indicators are very useful in analytical procedures and may also be used in the preparation of many foodstuffs, chemicals, and pharmaceuticals. Recently, E. Merck Company has marketed non-bleeding pH papers in which 2-sulfoxyethylsulfonyl derivatives of indicators are covalently bound to cellulose. While these have the same advantages as glass-bound indicators, they may prove to have inferior longevity, as cellulose is subject to slow bacterial attack and has been reported to be less acid and base stable than glass ( 1 ). Silane coupling agents are necessary to activate the porous glass. They are molecules which are characterized by two different kinds of reactivity. These are organofunctional, and silicon-functional, so characterized that the silicon portion of the molecule has an affinity for glass, while the organic portion of the molecule is an indicator or is tailored to combine with indicators. The function of the coupling agent is to provide a bond between the indicator and the carrier. The variety of useful organofunctional silanes is limited only by the number of organofunctional groups which bind to silicon to give a stable coupling agent, by the stability of the bonds to the carrier and to the indicator, and by the available sites in the organic species which yield an active bound indicator. The inexpensive coupling agent used in the experiments here reported is 3-aminopropyltriethoxysilane (APTSI). The idealized silylation mechanism is (2): R
where R = (CH2)3NHz. This alkylamine porous glass was then bound to suitable organic species to give indicator glasses. For example, alkylamine glass is facilely coupled to cyanuric chloride in refluxing chloroform and to this mixture of activated glass containing a halo-s- triazine ring, any indicator or mixture of indicators having amino, phenolic, or alcholic moieties may be bound. ( 3 ) . Idealized mechanism: C N CI