Comment on Calculator Program Yielding Confidence Limits for Least Squares Straight Line Sir: In their article (I)Blaedel and Iverson use a polynomial approximation to Student‘s t. Gardiner and Bombay (2) have shown that a much better approximation for t is of the form
t=
.f
+ P + rf-’
f + 6
+ Et-’
f
,
where f is degree of freedom ( N - 1)and the coefficients are shown below. Quantile Coefficient 0.950 0.975 0.995 a 1.6449 1.9600 2.5758 0.60033 -0.82847 P 3.5283 0.95910 1.8745 7 0.85602 -0.90259 -2.23 11 6 1.2209 0.11588 1.5631 e -1.5162 The value o f t obtained from the above approximation differs
from tabulated values by no more than one in the fourth decimal place. If a programmable calculator is used, this approximation is as easily used as the polynomial and provides better precision.
LITERATURE CITED (1) W. J. Blaedel and D. G. Iverson, Anal. Chem., 48, 2027 (1976). (2) D. A. Gardiner and B. F. Bombay, “An Approximation to Student’s t ” , Technometrics, 7, 71 (1965).
William F. Chambers Division 5822 Sandia Laboratories Albuquerque, New Mexico 87115
RECEIVED for review January 17,1977. Accepted February 14, 1977.
Determination of Chlorine, Bromine, Phosphorus, and Sulfur in Organic Molecules by Ion Chromatography Sir: The simplicity of the Schoniger or oxygen flask technique ( I ) for the preparation of organic compounds for heteroatom analysis has led to its wide application. Once the sample is combusted, a variety of techniques, gravimetric, volumetric, colorimetric, and x-ray fluorescence have been used to quantitatively determine the heteroatom of interest. We have applied Ion Chromatography (IC) to the problem of determining the heteroatom content of organic molecules thereby offering a faster and simpler alternative to the other methods. IC is a technique of ion-exchange chromatography developed by Small, Stevens, and Bauman (2,3) which uses the speed of liquid chromatography coupled with a unique combination of eluents and resins so that conductance can be used as the mode of detection. IC becomes an even more powerful tool when applied to the problem of simultaneous multielement analysis, for example, in molecules that contain both chlorine and bromine. The data reported were obtained with a Dionex Corporation Model 10 Ion Chromatograph. Samples of 5 to 10 mg were combusted in 500-mL Schoniger flasks containing an absorption solution of 10 mL of distilled water and 3 drops of 30% HzOz. After combustion, the absorption solution was diluted to 100 mL with distilled water and a portion of the sample loaded into the ion chromatograph sample loop. Table I lists the chromatographic conditions. Blanks of sample wrapper and absorption solution were analyzed just as the samples. Small blanks due to residual chloride in the sample wrapper and distilled water had to be subtracted from peak heights or areas due to chloride from samples. The carbonate generated from the carbonaceous portion of the organic sample plus the sample wrapper caused a small carbonate peak over and above the background carbonate eluent. This interfered slightly with the bromide peak but was reproducible and simply subtracted out as a blank. The carbonate blank was reproducible even though different organic molecules have 884
e
ANALYTICAL CHEMISTRY, VOL. 49, NO. 6, MAY 1977
Table I. Chromatographic Conditions Eluent: 0.003 M NaHCOJ0.0024 M Na,CO, Flow rate: 1.5 mL/min Sample loop: 0.1 mL Separator column: 3 mm i.d. X 500 mm Separator resin: Dionex low capacity anion exchange resin DA-X5-0.656 surface agglomerated to Dionex surface sulfonated polystyrene divinyl benzene copolymer DCS-X2-55 Suppressor column: 9 mm i.d. x 500 mm Suppressor resin : Dionex high capacity cation exchange resin DC-X12-55 Detection: conductivity Table 11. Retention Times (RT) and Peak Width at Half Height ( 1 / 2 H ) Ion Chloride Bromide Phosphate Sulfate
RT, min 6.5 10.5 11.5 18.7
1/%H,min 0.5 1.1 1.5 2.5
more or less carbon and sample wrappers do not always weigh exactly the same. This is because carbonate emerges from the suppressor column as carbonic acid which is only feebly dissociated and, therefore, the conductivity detector is relatively insensitive to changes in the carbonate blank. It should be noted that the carbonate peak interfered with the bromide peak under the conditions used. The position of the carbonate peak is affected by both the pH of the eluent and the volume and length of the suppressor column, as it is a weak base. Standards were made from reagent grade sodium salts of chloride, bromide, phosphate, and sulfate. The stock standards were standardized volumetrically with AgN03for
