Anal. Chem. 2009, 81, 5833–5839
Development of a Measurement System for Certifying Ethanol Mass Fraction in Aqueous Solutions Daniel G. Burke,* Lindsey G. Mackay, Richard Myors, Judith Cuthbertson, Jeremy Richardson, Nigel Sousou, David Saxby, Shane Askew, and Rebecca O’Brien National Measurement Institute, 1 Suakin Street, Pymble, New South Wales 2073, Australia In response to the sovereign requirement for national standards the National Measurement Institute, Australia (NMIA) has developed a measuring system using isotope dilution mass spectrometry (IDMS) to certify forensic aqueous ethanol solutions. NMIA participated in an international study, CCQM-K27, organized under the auspices of the International Committee for Weights and Measures to compare our measuring system with the techniques being used for certifying aqueous ethanol solutions in other metrology institutes. This comparison provided objective evidence that the measuring system developed was fit for the purpose of certifying aqueous ethanol solutions that ranged in concentration from 0.8 mg/g to 120 mg/g. A complete measurement uncertainty budget is presented and shows that the largest contribution to measurement uncertainty was from method precision followed by the contribution from the calibration solution. The fundamental technology of the measuring system was gas chromatography of the aqueous ethanol solutions using porous layer open tubular columns, and this effectively produced peak area measurements with both GC/MS and GC-FID. It was found that deactivation of the chromatographic system was critical for obtaining reproducible peak shapes and peak area measurements. A range of measuring systems, all using this gas chromatographic technology, was investigated. When conditions were carefully controlled there was no difference in measurement results from GC-IDMS, GC/ MS or GC-FID. There was also no difference in results from on-column or split injection systems. A significant issue with the IDMS system was the fragmentation of 13C2ethanol to produce an ion with the same mass as the molecular ion of ethanol which lead to isobaric interference; careful measurement of this fragmentation ratio was necessary to calculate accurate mass fraction values. NMIA has adopted the GC-IDMS split measuring system to certify aqueous ethanol solutions for Australian legal requirements since this measuring system provided higher analytical specificity than GCFID, accuracy that was fit for purpose and was operationally less stringent than on-column techniques. * To whom correspondence should be addressed. Fax: +61 2 9449 1653. E-mail:
[email protected].
Certified ethanol in water reference materials that have mass fraction values obtained by titrimetry and by GC-FID are commercially available; however, there is a specific legal requirement in Australia that the reference materials used in this jurisdiction must be national standards. This placed a requirement on NMIA to develop a capability for the certification of aqueous ethanol solutions used for calibrating breath alcohol measuring instruments used in this country. King and Lawn reviewed the results from an international interlaboratory study of forensic ethanol standards and found that only 6 of the 16 participating laboratories had results that were within 1% of the certified value.1 These authors concluded that gravimetric preparation of reference solutions provided the highest accuracy for certification and that GC methods appeared to be less than adequate for this purpose. The advantage of GC methods however is increased analytical specificity leading to a more rigorous characterization of bias from interfering substances especially when combined with mass spectrometry. A GC-IDMS measuring system based on that published by Wolff Briche et al. 20002 using 13C2-ethanol as internal standard was developed and validated at NMIA and by participation in an international intercomparison organized by the Consultative Committee for the Amount of Substance (CCQM) of the International Bureau of Weights and Measures. A similar gas chromatographic system, but without combustion before IDMS measurements, was used in our system. The measurement of the intact ethanol molecule initiated a re-examination of the traditional IDMS measurement equation that lead to publication of an improved equation for the measurement of organic molecules.3 The new equation allows for a difference in the relative abundance of naturally occurring stable isotopes between test and reference material and does not require correction of the observed isotope ratio for difference from “true” isotope amount ratio as required by Wolfe Briche et al.2 A range of measuring systems was investigated that combined the same gas chromatographic technology with different injection and detector systems and different internal standards. In all cases the technique of exact matching was used. An internal standard solution was mixed with the test solution to produce a blend containing both ethanol and the internal standard. A calibration (1) King, B.; Lawn, R. Analyst 1999, 124, 1123–1130. (2) Briche, C. S. J. W.; O’Connor, G.; Webb, K. S.; Catterick, T.; Herna´ndez, H. Analyst 2000, 125, 2189–2195. (3) Burke, D. G.; Mackay, L. G. Anal. Chem. 2008, 80, 5071–5078.
10.1021/ac900806y CCC: $40.75 Published 2009 by the American Chemical Society Published on Web 06/16/2009
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Table 1. Percentage of Total Ion Current and Mass Values for Major Ions ion +
M [M-H]+ [M-CH3]+
ethanol 7.2%, m/z 46 18.4%, m/z 45 65.2%, m/z 31
13
C2-ethanol
3.8%, m/z 48 13.0%, m/z 47 61.9%, m/z 32
blend
ethanol, µmol
13 C2 -ethanol, µmol
mole ratio ethanol/13C2-ethanol
peak area ratio m/z 46/48
sample calibration ratio S/Ca
8.612b 8.552 1.0069
8.575 8.445 1.0154
1.0043 1.0127 0.9917
1.2819 1.2990 0.9869
2-propanol 0.4%, m/z 60 2.9%, m/z 59 68.0%, m/z 45
blend was prepared using a solution of ethanol reference material, at a concentration similar to that found in the sample solution, mixed with the same internal standard solution to produce the same peak area ratio as the test solution blend. When peak area ratios in the calibration blend are sufficiently matched to the same peak area ratio in the test solution blend and when the matrix of the calibration solution is the same as the test solution, termed exact matching, very accurate measurements are possible.3-5 To provide independent validation of this measuring system, NMIA participated in an international key comparison organized by the CCQM of the CIPM. Key comparison number 27 (CCQMK27) consisted of distribution and analysis of three different aqueous ethanol solutions: sample A was an aqueous ethanol solution at a concentration of about 1 mg/g, sample B was an aqueous ethanol solution at a concentration of about 100 mg/g, and sample C was a red wine also with a concentration of about 100 mg/g. This work shows that with careful attention to important parameters, fit-for-purpose accuracy enabling certification of aqueous ethanol solutions can be achieved using either GC/MS with 13C2-ethanol internal standard, GC/MS with 2-propanol internal standard, or GC-FID with 2-propanol internal standard. MATERIALS AND METHODS Ethanol Calibration Solutions. Water used for preparation of calibration solutions and dilution was from a Millipore Element water purification system with UV disinfection, reverse osmosis, ion exchange, activated carbon filtration delivering minimum 18 Mohm.cm-1 resistivity. Ethanol used as reference standard was obtained from Fluka (Product no. 02851) specified >99.8% and less than or equal to 0.0005% residue on evaporation. Analysis by GC-FID did not detect any extraneous compounds (estimated detection limit 0.01 g/100 g). Karl Fischer (KF) moisture determination, performed at the same time as the preparation of standard solutions, gave duplicate values of 0.030 g/100 g. This agreed closely with the batch certificate value of 0.028 g/100 g from the supplier. A purity value of 99.96 g/100 g was assigned to this batch of reference material which included an allowance for impurities (0.01 g/100 g) in combination with the KF moisture value (0.03 g/100 g). A standard uncertainty of 0.02 g/100 g was estimated for this purity value. Calibration solutions were prepared by addition of ethanol reference standard (measured with a five-figure analytical balance calibrated to the Australian standard kilogram) directly into water. Aqueous Ethanol Solution Certified Reference Materials. Standard Reference Material SRM1828a was obtained from National Institute of Standards and Technology, Gaithersburg, (4) Mackay, L. G.; Taylor, C. P.; Myors, R. B.; Hearn, R.; King, B. Accredit. Qual. Assur. 2003, 8, 191–194. (5) Henrion, A. Fresenius’ J. Anal. Chem. 1994, 350, 657–658.
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Table 2. Typical Peak Area Ratio Matching for Sample A Obtained for GC-IDMS with Split Injection
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a S/C denotes the ratio of the value in the sample blend divided by the value in the calibration blend. b The amount of ethanol in the sample blend was calculated from the measured mass fraction.
USA. The reference material is provided as a package of ampules with four different mass fraction levels that were certified using GC-FID measurements. Certified Reference Material 5401 was obtained from LGC, Teddington, United Kingdom with values certified by titration measurements. Ethanol concentrations in this paper will be given as mass fraction mg/g for consistency with CCQM-K27 requirements; aqueous ethanol solution reference materials are certified as either mass fraction percentage (NIST) or mass concentration (LGC) and were converted to mass fraction mg/g (Table 4) for ease of comparison. Exact Matching IDMS (13C2-Ethanol Internal Standard). The method of exact matching was used; calibration blends were prepared with mole ratios of reference material to internal standard to match the mole ratio in the sample blend.4-6 Since CCQMK27 sample A had the lowest concentration of ethanol, our measuring system was optimized for this sample concentration. Sample blends were gravimetrically prepared using a five-figure balance calibrated to the Australian standard kilogram by mixing 0.5 g aqueous 13C2-ethanol (1 mg/g) and 0.5 g sample solution; calibration blends were prepared by mixing the same amounts of internal standard solution and reference material solution. This gave sample and calibration blends with an ethanol concentration of approximately 0.5 mg/g. For on-column analysis, blends were diluted volumetrically to give an ethanol concentration of 0.05 mg/g. In order to conserve 13C2-ethanol, the higher concentration samples CCQM-K27 B and K27 C were gravimetrically diluted before blend preparation; this introduced a step where potential bias could occur so a number of blends were also prepared using the neat sample then diluted volumetrically prior to instrumental analysis to give similar concentrations to the diluted samples. Exact Matching Non-IDMS (2-Propanol Internal Standard). The difference between IDMS and non-IDMS measurements was investigated by preparing additional sample and calibration blends using 2-propanol as the internal standard. These blends were analyzed by GC/MS as well as by GC-FID to enable isolation of potential biases that may have been due to the detector type. The ions used for GC/MS measurements of ethanol and 2-propanol had a different molar response from the FID to these molecules which lead to peak area ratios that were a factor of 3 higher for GC-FID when the same blends were measured by both techniques. For CCQM-K27 sample A, blends were prepared as for IDMS but with 2-propanol (0.34 mg/g) as internal standard solution. For (6) Webb, K. S.; Briche, C. S. J. W. Metrologia 2004, 41, 08002-08002.
Table 3. Matching for Sample A by GC/MS with Split Injection and GC-FID with on-Column blend
ethanol, µmol
2-propanol, µmol
mole ratio ethanol/2-propanol
peak area ratio GC/MS
peak area ratio GC-FID
sample calibration ratio S/Ca
8.802b 8.957 0.9827
2.706 2.768 0.9774
3.2532 3.2354 1.0055
0.7919 0.7860 1.0076
2.2944 2.2880 1.0028
a S/C denotes the ratio of the value in the sample blend divided by the value in the calibration blend. b The amount of ethanol in the sample blend was calculated from the measured mass fraction.
Table 4. Values Obtained for Certified Reference Materials during Analysis of CCQM-K27 Study Materials
c
LGC 5401 NIST SRM 1828a
certified value
uncertaintya
ethanol, mg/g
bias, mg/gb
RSD
n
0.8006 0.9480
0.0060 0.0036
0.8037 0.9450
0.0031 -0.0030
0.38% 0.37%
6 5
a Uncertainty is given as the expanded uncertainty at the 95% confidence level. b The difference between the NMIA measured value and the certified value is given as the bias. c Density values used to convert the LGC material were 0.9982 g/cm3 for water and 0.7905 g/cm3 for ethanol both at 20 °C.8
CCQM-K27 samples B and C, sample and calibration blends were prepared using high concentration standards and internal standards then volumetrically diluted before analysis to an ethanol concentration matching sample A. Since 2-propanol may evaporate from aqueous solutions at a higher rate than ethanol, it was necessary to subsample calibration blends that were used for an entire analysis batch into multiple vials and that each vial was then only used for about a 2 h period. Optimisation of Chromatographic Conditions. All the measuring systems used in this work were based on gas chromatography with water as the sample solvent, and this placed peculiar requirements on the chemistry of the analytical column. A porous layer open tubular column with a stationary phase consisting of styrene-divinylbenzene copolymer beads bonded to the inner fused silica surface was used (Varian Chrompack). This stationary phase is hydrophobic; however, it is readily hydrolyzed to reveal active sites that cause loss of analyte and degradation of chromatographic peak shape. Thus chromatographic active sites must be effectively deactivated for best peak shape and reproducible peak area measurements. Deactivation was achieved by drawing 1 mL of 2.5 g/L carbowax 20 M through the column while it was connected to the mass spectrometer source. For GC-FID columns, a retention gap consisting of 3-5 m of a carbowax 20 M column provided a continuous bleed of this material thus maintaining inert chromatographic conditions despite repeated aqueous injections. The best chromatographic peak shapes were obtained using cool-on-column injection with a retention gap. Careful attention was needed to eliminate dead volume in the retention gap connections and to deactivation of active sites. Excellent peak shapes with asymmetry factors (AS) of 1.2 were obtained when chromatographic conditions were optimized. The peak shape for 2-propanol was similar to ethanol. Peak shapes from the GC/MS split injection method were initially very similar to the cool-on-column system with AS of 1.2, but columns deteriorated with repeated aqueous injections and ethanol peaks with AS of 2 to 3 were generally obtained. However, even though split injection lead to poorer peak shapes with As of up to 3, reproducible results could still be obtained and instrument operation was much simpler than for cool-on-column systems.
Selection of Mass Spectral Ions. There was a significant molecular ion for ethanol and 13C2-ethanol but not for 2-propanol. For ethanol the base peak was due to the loss of a methyl group (CH3-), and there was a characteristic fragmentation pattern due to losses of one to five hydrogen atoms. This fragmentation pattern meant that there were significant contributions to all ions in the range m/z 40 to m/z 46 in ethanol from 13C2-ethanol. The contribution of the interfering ion from the internal standard to the selected ion from ethanol was controlled by the use of the full IDMS equation and required accurate measurement of the fragmentation ratio of the internal standard, R′Y. The proportion of ion current in the molecular ion, the M-H]+ and the M-CH3]+ ions in ethanol was different from the corresponding ions in 13C2-ethanol which resulted in a significant difference between ion abundance ratios and mole ratios. Table 1 illustrates the differences in ion current proportions measured in our laboratory. For IDMS measurements, 13C2-ethanol was used as internal standard, and the ions m/z 45 and m/z 46 from ethanol and m/z 47 and m/z 48 from 13C2-ethanol were monitored. For nonIDMS GC/MS measurements, 2-propanol was used as internal standard and the ions m/z 45 from both ethanol and 2-propanol were monitored, but under the conditions used for Table 1 this ion carried 3.7 times more of the ion current in 2-propanol compared to ethanol. GC-FID Conditions. Hewlett-Packard 5890 with autosampler, on-column injector at 60 °C, injection volume 0.3 or 0.5 µL, 100 kPa He constant pressure, analytical column Chrompack 27.5 m × 0.32 mm i.d. PoraPLOT Q, retention gap 3.6 m × 0.53 mm i.d. BPX20 (SGE), temperature program 50 °C 0.5 min, 60 °C/min to 180 °C, hold 4.8 min, detector temperature 300 °C, air 300 mL/ min, hydrogen 50 mL/min. Chromatograms were integrated with standard Agilent Chemstation software. GC/MS with Cool-on-Column Injection. Hewlett-Packard 6890 with CTC A200S autosampler, injector: on-column at 60 °C, injection volume: 0.1 µL, 100 kPa He constant pressure, column: Chrompack 27.5 m × 0.32 mm i.d. PoraPLOT Q (Varian), retention Analytical Chemistry, Vol. 81, No. 14, July 15, 2009
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gap: 3.6 m × 0.53 mm i.d. BPX20 (SGE), oven temperature program: 40 °C 1 min, 60 °C/min to 160 °C, hold 2 min. The column was directly connected to a Finnigan MAT 95 mass spectrometer; transfer line 200 °C, ion source temp 200 °C, electron impact, 70 V electron energy, 1 mA filament current, 2.2 kV electron multiplier voltage, resolution 2000 (10% valley). Multiple ion detection lock mode, m/z 40 lock mass, m/z 69 calibration mass, monitored ions m/z 45.034 (C2H5O), 46.042 (C2H6O), 47.041 (13C2H5O), 48.049 (13C2H6O), dwell time for lock and calibration masses 4.1 msec and for analyte ions 21.8 msec, cycle time 0.2 s. Mass chromatograms were manually integrated by dragging the integration baseline from peak start to peak end, and the resulting peak area value was manually entered into a spreadsheet for further processing. GC/MS with Split Injection. Hewlett-Packard 6890 with Agilent 7683 autosampler, split/splitless injector 200 °C, constant pressure 27.5 kPa He, split ratio 50:1, tapered focus-linear 4 mm i.d. (Scientific Glass Engineering, Melbourne, Australia), injection volume 0.2 µL, column: Chrompack 25 m × 0.32 mm i.d. Porabond Q (Varian), column oven 120 °C isothermal. The column was directly connected to an Agilent 5973 mass selective detector, transfer line 200 °C, ion source 230 °C, electron impact, 70 V electron energy, 35 µA filament current, 2400 V electron multiplier voltage. The mass selective detector was operated in selected ion monitoring mode; ions m/z 45, 46, 47, 48 were selected with a dwell time 50 ms each for IDMS and m/z 45 only with dwell time 100 ms for non-IDMS measurements. Mass chromatograms were integrated with standard Agilent Chemstation software. Calculation of Ethanol Mass Fraction. In all measuring systems, sample blends were analyzed 5 times bracketed by calibration blends, and thus the mass fraction value for each blend was the average of the 5 individual mass fraction calculations of the 5 replicates. For IDMS measurements, eq 1 was used to calculate the ethanol mass fraction for each replicate analysis since overlapping ions were present in blend solutions.3 For non-IDMS measurements, eq 2 was used. Additional mass dilution factors, not shown in eqs 1 or 2, were included for samples B and C when necessary. In both equations the FX term incorporates yield factors relating to the difference between sample blend and calibration blend matrices that may lead to measurement bias. For these measurements it was not necessary to explicitly evaluate the FX term since sample and calibration blend matrices were nominally identical (except for sample C) an assumption that was validated by measurement of the certified reference materials. For sample C (red wine) an additional factor to account for the difference between sample and calibration matrices was included in the uncertainty budget wX ) wZ ·
mY mZ (R′Y - R′B) · (R′B,c - R′Z) · R′X · ·F mX mY,c (R′B - R′X) · (R′Y - R′B,c) · R′Z X (1) wX ) wZ ·
mY mZ R′B · ·F mX mY,c R′B,c X
(2)
where wX ) mass fraction of ethanol in test material, wZ ) mass fraction of reference substance in calibration solution, mY ) 5836
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mass of internal standard solution added to sample blend, mZ ) mass of calibration solution added to calibration blend, mX ) mass of test material in sample blend, mY,c ) mass of internal standard solution added to calibration blend, R′B ) measured peak area ratio of selected ions in sample blend, R′B,c ) measured peak area ratio of selected ions in calibration blend, R′X ) measured peak area ratio of selected ions in analyte molecule, R′Y ) measured peak area ratio of selected ions in internal standard molecule, R′Z ) measured peak area ratio of selected ions in reference standard molecule, and FX ) measuring system factor. To determine R′X, R′Y, and R′Z replicate measurements at m/z 45, 46, 47, and 48 of the sample (R′X), ethanol reference material (R′Z) and 13C2-ethanol solutions (R′Y) were taken. The low absolute abundance of the denominator ions resulted in R′X and R′Z measurements with a standard deviation of 5%. Higher precision was obtained when ethanol concentrations used for this measurement were higher (by up to 4-fold) than the regular sample blend concentration. However, in order for a conservative estimation of uncertainty, the higher standard deviation was used in the subsequent uncertainty analysis. Significant differences between the theoretically calculated and observed values for R′Y for both ion pairs indicated that interference from fragment ions was present so theoretical values could not be used. Values for R′Y obtained close to the time of sample analysis were used in mass fraction calculations. The mass fraction results for all IDMS measuring systems were calculated using the abundance ratio of ion m/z 46 to m/z 48. RESULTS Comparison of Ethanol Mass Fraction in Test Samples Using Different Measuring Systems. As a first approximation, measuring systems were evaluated by comparing precision estimates only. This proved to be a reasonable guide to measurement uncertainty since when total uncertainty was estimated for one of the measuring systems the major contributor was measurement precision. However, additional factors such as bias that may be due to isobaric interference must also be included in the total uncertainty estimation. Thus even though precision estimates from different measuring systems may be similar, total uncertainty may be different. CCQM-K27 sample A was analyzed using 4 different measuring systems each employing the same basic gas chromatographic column technology but with different injection systems, detectors, and internal standards. The results from these different measuring systems are summarized in Figure 1 and show that there was no significant difference between any of these methods (ANOVA, R ) 0.05). That is, it was not possible to distinguish between measuring systems using precision alone. The mass fraction values are the average of separate analyses of two sample bottles and n is the total number of separate blends prepared; the average value from all the measuring systems was 0.8041 mg/g (shown as the x-axis), and the error bars represent two times the standard deviation. CCQM-K27 sample B was analyzed using 6 different measuring systems shown in Figure 2, and again there was no significant difference between results from any of these systems (ANOVA, R ) 0.05). The mass fraction values were the average of separate analyses of two sample bottles, and n is the total number of
Figure 1. Measuring systems for CCQM-K27 sample A. Two different internal standards were used; blends with 13C2-ethanol internal standard (IDMS) were analyzed by GC/MS with either split injection (split) or on-column injection; blends with 2-propanol internal standard (ISTD) were analyzed by either GC/MS with split injection or GC-FID with on-column injection.
Figure 2. Measuring systems for sample B. This sample was greater than 100 times more concentrated than sample A and so was gravimetrically diluted before (Diluted) or volumetrically diluted after (Neat) blends were made. Blends with 2-propanol internal standard (ISTD) were analyzed by either GC/MS with split injection or GC-FID with on-column injection.
separate blends prepared; the average value from all the measuring systems was 120.92 mg/g (shown as the x-axis), and the error bars represent two times the standard deviation. CCQM-K27 sample C was measured using 3 different measuring systems shown in Figure 3, and again there was no significant difference between results from these systems (ANOVA, R ) 0.05). The mass fraction values were the average of separate analyses of two sample bottles, and n is the total number of separate blends prepared; the average value from all the measur-
ing systems was 81.41 mg/g (shown as the x-axis), and the error bars represent two times the standard deviation. Matching. Close matching of peak area ratios between sample and calibration blends was obtained for both IDMS and non-IDMS methodologies. Tables 2 and 3 illustrate the typical matching obtained for mole ratios and peak area ratios in IDMS and nonIDMS measuring systems. The critical matching factor is that between sample and calibration blends denoted as ratio S/C in these tables.3 For both types of measuring systems the peak area Analytical Chemistry, Vol. 81, No. 14, July 15, 2009
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Figure 3. Measuring systems for sample C. This sample was also considerably more concentrated than sample A and so was gravimetrically diluted before blends were made. Both IDMS and non-IDMS measurements were made.
ratios had the same degree of matching as the mole ratios between sample and calibration blends and were matched to within 0.5% or better and this was within the standard deviation of the peak area values. This degree of matching ensured that all error types were minimized and was adequate to give highly accurate results.3 Control Measurements of Aqueous Ethanol Certified Reference Materials. Two commercially available, high quality certified reference materials were used to provide a comparison point that was independent of the CCQM study. These were also used to ensure our measuring system was under control during the study; one of the commercially available reference materials was measured with each batch of test samples. The results of these control measurements are summarized in Table 4 and show that our methodology gave precise results that were consistent with the certified values. Comparison of Different Reference Standard Solutions. Four separate calibration solutions were prepared from the ethanol reference standard (Fluka) at a nominal value of 1 mg/g and were then used to calibrate a single test solution of LGC 5401 with the certified value of 0.8006 mg/g and expanded uncertainty at the 95% confidence level of ±0.0060 mg/g. The differences between standard solutions were not significant (ANOVA, 95% confidence interval), and all were within the uncertainty of the certified reference value. Comparison of IDMS Results from Different Ion Pairs. Method specificity can be assessed by calculating mass fraction results from different ions since interfering compounds would most likely have different ion abundance ratios from ethanol. The difference in calculated mass fraction values when using the two different ion pairs was not significant (t test, 95% confidence level) for any IDMS measuring system. CCQM-K27 Study Results. The measuring system comprising GC-IDMS with split injection was chosen for analysis of CCQM-K27 study materials as it gave an effective balance of analytical specificity, accuracy, and laboratory efficiency. In addition, isobaric interference could be evaluated by comparison of results from different ion pairs, a procedure this is not possible with GC-FID. Study participants were supplied with duplicate bottles of samples A, B, and C and were required to take two aliquots from 5838
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each sample bottle and analyze each aliquot in two instrumental runs (8 measurements in all for each sample). The study results have been reported elsewhere, and for ease of reference comparative results for sample A are reproduced in Figure 4.6 In order to determine accuracy, a key comparison reference value (KCRV) was assigned to each sample; the KCRV for samples A and B were the gravimetrically prepared value with the standard deviation of the mean of the results taken as the standard uncertainty of the KCRV. For sample C, it was proposed that the KCRV should be calculated as the mean of the results with the standard deviation of the mean taken as the standard uncertainty of the KCRV. The results for sample A from all participants are presented in Figure 4; the midline represents the KCRV and the dashed lines upper and lower limits of the 95% confidence interval of the KCRV and the error bars represent expanded uncertainty reported by the participant. The National Analytical Reference Laboratory (NARL) formed part of what is now NMIA, so the results for NMIA are shown as NARL; other laboratories’ identities may be found in the published study results.6 NMIA’s result for each sample was very close to the KCRV providing further validation of the measuring system. Measurement Uncertainty. For each sample (A, B, and C), uncertainties for all components in the measurement equation (eq 1) based on the GC-IDMS split injection measuring system were estimated and combined using sensitivity coefficients as described in the Guide to the Expression of Uncertainty in Measurement.7 Standard uncertainties were calculated for the following: method precision, calibration solution concentration (wZ), blend masses, mX, mY, mZ, mY,c (an additional term for dilution masses was included for samples B and C when needed) ion abundance ratios in the analyte, reference material, and 13C2-ethanol (R′X,R′Y,R′Z) and peak area ratios in sample and calibration blends (R′B,R′B,c). The standard deviation of replicate measurements of sample blends over a 14 day period was used to estimate the standard uncertainty of method precision. Estimation of standard uncer(7) Guide to the expression of uncertainty in measurement; ISO, 1995. (8) Handbook of Chemistry and Physics, 86th ed.; CRC Press: Cleveland, Ohio, USA, 2005.
Figure 4. Sample A results from all participants. KCRV 0.8040 mg/g, expanded uncertainty 0.0080 mg/g. Table 5. Uncertainty Budget for CCQM-K27 Sample A Measured by IDMS parameter1
value
standard uncertainty
method precision wZ mX mY mZ mY,c R′Y R′X
1.0000 0.9889 0.4994 0.4663 0.3987 0.4618 0.137 424
0.0017 0.0005 0.00004 0.00004 0.00004 0.00004 0.021 22
1
sensitivity coefficient
units
0.805 0.841 -1.911 1.725 2.018 -1.742 0.00193 -0.00001
mg/g mg/g g g g g none none
Table 6. Results of Uncertainty Analysis for CCQM-K27 parameter
sample A
sample B
sample C
ethanol, mg/g combined standard uncertainty, mg/g total effective degrees of freedom coverage factor (95% CI) expanded uncertainty, mg/g relative expanded uncertainty
0.8045 0.0015
120.88 0.27
81.29 0.34
8.57
8.81
8.29
2.31
2.31
2.31
0.0034
0.63
0.78
0.42%
0.52%
0.96%
Parameter pronumerals are as given in eq 1.
tainty of purity of the reference ethanol is given in the materials section and was included in the estimation of ethanol reference solution uncertainty. Standard uncertainties of blend masses and masses of ethanol reference solution components were based on values from the balance calibration certificate. The standard uncertainties for the parameters R′B and R′B,c were considered to have been included in the estimates of method precision, and so these factors do not appear separately in the uncertainty budget. The standard uncertainties of R′X, R′Y, and R′Z were obtained from the standard deviations of replicate measurements. For sample C, an additional uncertainty factor to account for the matrix difference between the calibration solution (water) and the sample solution (red wine) was estimated based on the difference between R′X and R′Z. The standard uncertainties were combined as the sum of the squares of the product of the sensitivity coefficient (obtained by partial differentiation of the measurement equation) and standard uncertainty to give the square of the combined uncertainty. The square root of this value was multiplied by a coverage factor (95% confidence interval) from the t-distribution at the total effective degrees of freedom obtained from the Welch-Satterthwaite equation to give the expanded uncertainty. A complete uncertainty budget for CCQM-K27 sample A is presented in Table 5, and the results of the uncertainty analysis for all samples are summarized in Table 6. The major contributor to measurement uncertainty for all measuring systems was the precision of replicate results measured
over a 14 day period. For sample C, the additional uncertainty factor to account for the matrix difference between the calibration solution (water) and the sample solution (red wine) was the major contributor to total uncertainty for this sample. Since the expanded uncertainties were less than 1% of the measured value and were thus fit for purpose, no further investigation of the major source of uncertainty was undertaken.1 CONCLUSIONS A range of measuring systems has been shown to provide comparable measurements of the mass fraction of ethanol in water, and each measuring system had sufficient accuracy to certify these materials for forensic use. NMIA has selected the GC-IDMS split injection system as offering the best combination of analytical specificity, accuracy, and laboratory efficiency for our purposes. This measuring system was validated by NMIA and independently assessed through participation in the CCQM-K27 key comparison. Since the expanded uncertainty was less than 1% of the measured value, this measuring system has the accuracy needed for certification of aqueous ethanol solutions for forensic applications and provides measurements that are traceable to the SI through the Australian standard kilogram. Received for review April 14, 2009. Accepted May 29, 2009. AC900806Y Analytical Chemistry, Vol. 81, No. 14, July 15, 2009
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