1550
Anal. Chem. 1984, 56,1550-1551
Table I. Comparison of Exact Solution and Taylor’s Series Approximation for the 1:1 Complexing Examplea LtiIM
[LIi/M approximate
exact
0.005 0.01 0.02
0.04 0.06 0.08 0.10
0.004 564 0.009 161
0.004 563 0.009 160
0.018 44 0.037 28 0.056 39
0.018 0.037 0.056 0.075
0.20 0.50
0.075 69 0.095 1 2 0.193 4 1 0.491 7
1.00
0.990 9
M.
44
28 39 69
0.095 12 0.193 41 0.491 7 0.990 9
a Using K,, = 10.0 M - l , St = 0.010 M. With eq 7 .
* With eq 5.
conjugate acid and base substrate species, eq 8 and 9 correspond to eq 1 and 2.
ApK, = log
1 + Klla[LIi
+
The derivative g’(Lti) is
g’(L,J = 1 +
StK11a + stKllb (lo) 2(1 + K11aLtJ2 2(1 + KllbLti)’
Substituting eq 10 into eq 3 gives
[L]i = Lti - -
StKIlaLti 2(1 + KllaLti)
+
This method for calculating free ligand concentration is general, accurate, and simple to introduce into iterative calculations. We have found it useful in treating spectrophotometric and potentiometric data on a-cyclodextrin complexes of aromatic compounds, for which we have used both linear and nonlinear least-squares regression. A further advantage is that convergence in nonlinear regression occurred more rapidly with the Taylor’s series calculation of [LIi then with the alternative procedure (c). It is useful not only when other calculations are difficult or impossible but also for simple systems, such as the 1:l complexing system discussed as an example.
LITERATURE CITED (1)
+ Kllb[Lli
Lti = [L]i + s,
Its accuracy was evaluated by means of simulated stability constants and assumed values of [LIi, which with eq 9 give the corresponding L,i values. Then the Taylor’s series approximation, eq 11, was used to estimate the free ligand concentration. Agreement between the assumed and computed values was within 0.1% a t 0.01 M and 0.01% a t 0.05
2(1 + KllbLti)
(11) This technique was also applied to potentiometric systems requiring three stability constants for their description (15).
Benesi, H.; Hildebrand, J. H. J . Am. Chem. SOC.1949, Keefer, R. M.; Andrews, L. J. J . Am. Chem. SOC. 1952,
71, 2703. (2) 74, 1891. (3) Rose, N. J.; Drago, R. S. J . Am. Chem. SOC. 1959, 81, 6138. (4) Tamres, M. J . Phys. Chem. 1981, 65, 654. (5) Lang, R. P. J . Am. Chem. SOC. 1982, 8 4 , 1185. (6) Jurinski, N. B.; de Maine, P. A. D. J . Am. Chem. SOC. 1984, 86, 3217. (7) Wentworth, W. E.; Hirsch, W.; Chen, E. J . f h y s . Chem. 1987, 71, 218. (6) Christian, S.D. J . Chem. Educ. 1988, 4 5 , 713. (9) Grundnes, J.; Christian, S. D. J . Am. Chem. SOC.1968, 90, 2239. (IO) Moriguchi, I.; Kaneniwa, N. Chem. Pharm. Bull. 1969, 17, 2173. (11) Kakeml, K.; Sezaki, H.; Suzuki, E.; Nakano, M. Chem. Pharm. Bull. 1989. 17. 242. (12) Nakano, M.; Nakano, N. I.; Higuchi, T. J . fhys. Chem. 1967, 71, 3954. (13) Connors, K. A.; Lin, S.-F.; Wong, A. B. J . Pharm. Sci. 1982, 71, 217 (14) Lin, S.-F.;Connors, K. A. J . Pharm. Sci. 1983, 72, 1333. (15) Pendergast, D. D. Ph.D. Thesis, University of Wisconsin-Madison, 1983.
RECEIVED for review December 19,1983. Accepted March 8, 1984. This work was supported by a grant from the Upjohn
co.
Technique for Storage of Breath Samples for Hydrogen Determination Anita R. Tierney and Donald P. Kotler*
Gastrointestinal Division, Medical Service, St. Luke’s-Roosevelt Hospital Center and the Department Columbia University College of Physicians & Surgeons, New York, New York 10025 In recent years breath tests have been developed as noninvasive tools to measure small intestinal absorption in man. The analysis of postprandial breath hydrogen (H,) excretion to detect carbohydrate malabsorption is based upon the knowledge that molecular H, is a metabolic product of bacterial carbohydrate fermentation in the colon and is not a product of mammalian metabolism ( I ) . Breath Hz analysis is being used clinically in the detection of intestinal hypolactasia (2). Although breath H2 excretion tests are safe and simple to perform, Hz analysis by gas chromatography is more complicated. Several methods for the determination of H2 concentration in expired air are available. All require analysis soon after sample collection. The ability to store and transport large numbers of samples to a central location for analysis would facilitate screening of individuals in field situations. For this reason, a method has been developed to store breath
of
Medicine,
samples in which H, concentration is stable for at least 3 weeks.
EXPERIMENTAL SECTION Samples of H2gas (115 ppm by analysis, Matheson, East Rutherford, NJ) were collected in plastic Leur-lok syringes fitted with three-way metal stopcocks. Twenty-five milliliters of gas were injected through a 22 gauge needle into 70 nonsilicone coated, nonsterile 10-mL evacuated tubes (Venoject T-200 U, Terumo Medical Corp., Elkton, MD). Positive pressure was applied as the needle was inserted and withdrawn from the evacuated tube to minimize contamination by room air. These samples were analyzed in groups of 10 on days 0,1, 3, 5,7, 14, and 2 1 following preparation. Samples were stored at room temperature until analysis and then injected into a Carle gas chromatograph (Carle Industries, Fullerton, CA) by impaling the stopper onto an 18 gauge needle
0 1984 American Chemical Society 0003-2700/84/0356-1550$01.50/0
1551
Anal. Chem. 1984, 56,1551-1552
Table I. H, Recovery after Storage for Different Time Intervalsa9b 1 day 3 days
a
5 days
7 days
14 days
21 days
mean recovery of H, stds std dev
102.1 1.4
101.3 1.3
101.3 1.5
100.0
99.5 0.6
103.1
1.6
mean recovery of breath samples std dev
104.5 7.4
94.6 3.0
101.5 8.0
95.3 6.7
103.6 5.3
99.8 4.9
H, recovery determined as described in the Experimental Section.
attached to the inlet tube. The inlet tube led to a 3-mL stainless steel sampling loop, a 5A molecular sieve, and a thermistor for detection of thermal conductivity. Samples were run at 40 O C with argon (18 mL/min) as the carrier gas. The output was transcribed onto a chart recorder (Model 9176, Varian Associates Inc., Walnut Creek, CA). Hydrogen concentration was calculated by comparing the peak height of the sample to the peak height obtained from the H2standard injected directly from the syringe. In preliminary studies, calculation of Hz concentration from the peak height and from the area under the Hz peak (obtained by triangulation) did not differ. In a separate trial, three normal human subjects ingested 10 g of lactulose (Cephulac Syrup, Merrell Dow Pharmaceuticals, Inc., Cincinnati, OH), a nonabsorbable carbohydrate which was dissolved in 250 mL of water. Breath samples were obtained at 30-min intervals with a Priestley-Haldane tube (I,3) until excess Hzexcretion was noted. Thereafter, eight samples were collected at several time points. Breath H2 concentration was determined immediatelyfrom one fresh sample, and the six remaining samples were injected into evacuated tubes, stored, and analyzed in the same way as the standard samples.
RESULTS AND DISCUSSION Comparison of Hz concentrations in syringes and evacuated tubes analyzed on day 0 showed that the recovery of Hz from the standards was 88.0 f 1.3% ( n = 10, mean f standard deviation) and that the recoveries of H2from breath samples were 89.7 f 2.4% ( n = 10, mean f standard deviation). Comparison of tube samples analyzed a t the six storage periods to tube samples analyzed on day 0 gave recoveries of 101.2 f 4.1% (n = 60, mean f standard deviation) for the hydrogen standards and 99.9 f 12.9% ( n = 60, mean f standard deviation) for human samples (Table I). The results in the breath samples were more variable than the results in the standard gas samples in part because of the variability in Hz concentration in repeated breath samples (approximately 3%) (1). Statistical analysis of recoveries by one way analysis of variance ( 4 ) showed no differences between samples stored
1.0
n = 1 0 for each time point.
in Vacutainers and run immediately and samples stored for up to 21 days. There appears to be a decrease in Hzconcentration which occurs a t the time of initial injection into the evacuated tube. This loss is due in part to dilution of the gas sample by the small amount of gas initially present in the evacuated tube, although there may have been some contamination by room air. The use of positive pressure (25 mL into a 10 mL tube) acts to minimize sample dilution by endogenous gas. Positive pressure also is necessary for the direct injection of gas into the chromatograph from the Vacutainer tube without other manipulation. Several types of evacuated tubes were tested in preliminary studies. All sterile tubes had unacceptably high levels of endogenous H2. Hydrogen may be released from the rubber stopper during sterilization (5). Other nonsterile evacuated tubes (e.g., Vacutainer 3200 U, Becton-Dickinson, Columbus, NB) gave acceptable results. In summary, this study demonstrates that breath samples can be stored in nonsterile evacuated tubes for at least 3 weeks without progressive loss of Hz. The method described allows for testing of carbohydrate malabsorption by breath H2 analysis to be performed a t sites distant from laboratory facilities.
Registry No. Hydrogen, 1333-74-0. LITERATURE CITED (1) Kotler, Donald P.; Holt, Peter R.; Rosensweig, Norton S. J. Lab. Clln. Med. 1982, 100, 798-805. (2) Newcomer, Albert D.; McGIII, Douglas G.; Thomas, Peter J.; Hofmann, Alan F. New Engl. J . Med. 1975, 293, 1232-1236. (3) Metz, G.; Gassull, M. A.; Leeds, A. R.; Blendis, L. R.; Jenkins, D. J. A. Clin. Sci. Mol. Med. 1976. 50 237-243. (4) Klugh, Hugh E. "Statistics: 'The 'Essentials for Research"; Wiley: New York. 1974: DO 303-304. (5) Personal cdmmunlcation, Becton-Dickinson, Columbus, NB, 1982.
RECEIVED for review December 9, 1982. Resubmitted February 21, 1984. Accepted February 21, 1984.
Electron Paramagnetic Resonance Spectra of Samples Immobilized on Solid Substrates Kundalika M. More and Gareth R. Eaton* Department of Chemistry, University of Denver, Denver, Colorado 80208 Sandra S . Eaton Department of Chemistry, University of Colorado at Denver, Denver, Colorado 80202 In many applications it would be useful to have a method to obtain EPR spectra of magnetically dilute, immobilized samples a t or near room temperature. For some compounds this can be done by doping the paramagnetic species into a diamagnetic host and examining the powder or single-crystal EPR spectrum. However this approach necessitates finding a suitable host and carries the risk that the conformation of 0003-2700/84/0356-1551$01.50/0
the paramagnetic species will be altered by the steric requirements of the host. If frozen solution spectra are used in place of room-temperature spectra, it may be difficult to assess the impact of the temperature change. In addition, even when samples are frozen rapidly, some molecules are prone to intermolecular aggregation. We were therefore interested in examining possible substrates for obtaining immobilized 0 1984 American Chemical Society
