High accuracy isotope dilution analysis for the determination of ethanol using gas chromatography-combustion-isotope ratio mass spectrometry

Transcription

1 High accuracy isotope dilution analysis for the determination of ethanol using gas chromatography-combustion-isotope ratio mass spectrometry Céline S. J. Wolff Briche,* a Helena Hernández, b Gavin O Connor, a Ken S. Webb a and Tim Catterick a a LGC, Queens Road, Teddington, Middlesex, UK TW11 0LY. cwb@lgc.co.uk b Oxford Centre for Molecular Sciences, New Chemistry Laboratory, Oxford University, South Parks Road, Oxford, UK OX1 3QT Received 0th July 000, Accepted 4th October 000 First published as an Advance Article on the web 1st November 000 A procedure was established for the determination of ethanol in water samples by isotope dilution analysis. After spiking the sample with labelled [ 13 C ]ethanol, it was analysed by gas chromatography-combustion-isotope ratio mass spectrometry. Results are reported for two certified reference materials and also ethanol solutions prepared for a CITAC (Co-operation on International Traceability in Analytical Chemistry) interlaboratory comparison. The certified reference materials were certified using the dichromate titration method at nominal levels of 80 and 00 mg per 100 ml. The CITAC solutions were prepared gravimetrically at nominal levels of 50, 80 and 00 mg per 100 ml. The results of the analysis agree well to within 0.5% of the gravimetric values of the different samples. The relative expanded standard uncertainties (with a coverage factor equal to ) associated with the results varied between 0.18 and 0.37%, a range that encompassed the gravimetric values for the different samples. A complete uncertainty budget was also drawn up so that the different contributions could be identified and quantified. The main contributions were due to variations in the measured isotope amount ratios and a between blend component introduced to quantify the contribution of factors such as the degree of matching of the isotope amount ratios between standards and samples used in the isotope dilution analysis. Introduction Routine chemical analysis is playing an ever-increasing role in international trade and industry. Therefore, the confidence and reliability of analytical results must play a major part in world trade. Ethanol is a prime example of a high impacting analyte. Its routine determination in biological fluids has forensic implications, whilst its measurement in food, beverages and perfumes determines the excise duty paid on the product. Certified reference materials (CRMs) play an important role in developing and proving the confidence of laboratories analytical results. Hence the production and certification of CRMs must use a variety of independent technology and skills to ensure the integrity of the product. Isotope dilution mass spectrometry (IDMS) has the potential of being a primary method of measurement with proven capability in providing high accuracy measurements. 1 It is traceable to SI units and is therefore well suited for the certification of reference materials. Conventional gas chromatography-mass spectrometry (GC- MS) instruments are capable of performing the isotope amount ratio measurements for IDMS. However, they have a number of limiting factors, which include variation of isotope amount ratio due to ionisation and fragmentation, contributions of other isotopomers on the monitored ions, background contamination and sensitivity changes. Moreover, in single collector instruments, the mass spectrometric conditions are not completely identical when switching between the recorded isotope ions. Instruments for isotope ratio mass spectrometry (IRMS) have been specifically designed with a multi-collector and constructed to yield high precision isotope amount ratio measurements on stable isotopes. The coupling of IRMS to gas Copyright LGC (Teddington) Ltd chromatography (GC) via a combustion interface allows the measurements of compound specific isotope amount ratios with a precision between 10 and 10 3 times better than conventional instrumentation. This is achieved by first converting the sample to CO, which reduces the effect of isotopomers on the recorded ion intensity in each channel. The ions of m/z 44, 45 and 46 are recorded simultaneously (no beam switching) using a fixed accelerating voltage, magnet field strength and Faraday cup detectors. This type of analysis has almost exclusively been applied to the measurement of natural variations of carbon isotopes. However, a recent study investigated the use of IRMS for isotope dilution (ID) analysis. 3 While the isotope amount ratios measured for enriched samples were not as precise as for natural samples, they were still a vast improvement over conventional GC-MS techniques. Experimental Reagents and standards Absolute ethanol (AR, 99.99%) (Fisher, Loughborough, UK) was used to prepare gravimetrically primary standard solutions of ethanol in water. The data given by the International Union for Pure and Applied Chemistry (IUPAC) were used to calculate the isotope amount ratio of carbon in the prepared primary standard solutions Z as R Z = n( 13 C)/n( 1 C). The molar mass used for natural ethanol was ± g mol 1. The ethanol spike was prepared from [ 13 C ]ethanol (99%) (Cambridge Isotope Laboratories, Andover, MA, USA). The information given on the certificate for the isotopic composition of the material merely stated 99% 13 C. The corresponding molar mass of labelled ethanol was calculated as ± 0.01 g mol 1. DOI: /b005878p Analyst, 000, 15, This journal is The Royal Society of Chemistry 000

2 The calibration solutions were prepared with high purity deionised water (18 MΩ) (Elga, High Wycombe, UK). The samples analysed were two CRMs, LGC 5401 and LGC 5403 (LGC Teddington, Teddington, UK), and three solutions used for an international interlaboratory study initiated by CITAC (Co-operation on International Traceability in Analytical Chemistry) for forensic ethanol determination in water. 4 These solutions had nominal ethanol mass concentrations in water of 50, 80 and 00 mg of ethanol per 100 ml of water. The details of the concentrations and mass fractions of the different solutions analysed are given in Table 1. Instrumentation All solutions were prepared gravimetrically and the weighings were performed on a Sartorius RC 103 balance (Sartorius, Germany). All isotope amount ratio measurements were performed using a commercially available instrument for gas chromatography combustion isotope ratio mass spectrometry (GC-C- IRMS) (MAT 5, Finnigan MAT, Bremen, Germany) with the combustion interface ConFlo II. Details of the instrumentation have been described elsewhere. 5 Gas chromatography. The GC system was an HP5890 series II instrument (Hewlett-Packard, Berkshire, UK), with electronic pressure control. Sample introduction was performed using on-column injection by an A00S autosampler (CTC Analytics, Zwingen, Switzerland). Mass spectrometer. The MAT 5 isotope ratio mass spectrometer was operated with an accelerating voltage of 10 kv. A set of six Faraday cups and amplifiers were available for ion recording. The cup configuration selected determined the m/z values that were detected for a particular magnet field strength. For isotope dilution analysis, the Faraday cups 3 and 4 (m/z 44 and 45) were set to have the same sensitivity, i.e., both were set with a resistor of Ω, so that isotope amount ratios equal to 1 could be measured. A third detector (cup 5) was used to monitor m/z 46, with a resistor of Ω; however, this was only used for instrument checks. The voltages generated by the ion currents were digitised and processed by ISODAT software (Finnigan MAT). The experimental conditions used are given in Table. m/z 44. The intensity recorded at m/z 44 corresponds to 1C 16 O 16 O, which reflects the amount of 1 C in the analyte, but the intensity recorded at m/z 45 corresponds to three different isotopomers, 13 C 16 O 16 O, 1 C 17 O 16 O and 1 C 16 O 17 O. Therefore a correction must be made to correct the measured isotope amount ratio n( 45 CO )/n( 44 CO ) and to convert it into n( 13 C)/ n( 1 C). 6 When natural compounds are analysed, the measured isotope amount ratio n( 46 CO )/n( 44 CO ) is used to correct the isotope amount ratio n( 45 CO )/n( 44 CO ) for the 17 O contribution. For ID measurements, a 13 C-labelled compound was used, which could contain up to 1% of 18 O according to the supplier, and which also had a non-natural 17 O amount fraction. As a consequence, it becomes very complex to calculate a correction factor, and the correction used when analysing natural samples can no longer be used to do the correction on the isotope dilution samples. An easier approach is to try to reproduce the same oxygen isotopic composition in the different blends measured so that it can compensate for the effects of the oxygen contribution. Optimisation of the experimental conditions The factors that influenced the accuracy and precision of the IDMS measurements using GC-C-IRMS can be briefly outlined. The system required samples of approximately nmol of carbon per analyte to be loaded on to the analytical column. The amplifier configuration directly influenced the column loading and ion precision. The peak shape was an important factor owing to the effect of the combustion interface on peak broadening and adsorption. As all compounds are combusted into CO, the GC column bleed was minimised. Isothermal conditions during peak elution were preferable, as the background signal, due to column bleed, was more stable. Good chromatographic resolution was important, as the peaks had to be pure analyte. The combustion had to be quantitative to avoid isotopic fractionation and the efficiency of nitrogen oxide and water removal had at least to be repeatable from run to run. The integration and background subtraction procedures influence the isotope amount ratios measured and their precision and had to be carefully optimised. On-column injection was found to be more appropriate than split or splitless injection in terms of response, peak shape and linearity and signal intensity. 7 Oxygen correction for CO measurements The measured isotope amount ratios correspond to the ratios of the intensities measured at the mass-to-charge ratio m/z 45 to Table 1 Ethanol mass concentrations and mass fractions for the CITAC solutions, based on their gravimetric preparation. 4 Titrimetric certified ethanol mass concentrations for the LGC CRMs. The associated uncertainties are standard uncertainties Solution Certified mass concentration/mg per 100 ml Mass fraction (mg g 1 ) conversion of the concentration Mass fraction (mg g 1 ) gravimetric value LGC ± a a LGC ± a.0090 a CITAC ± ± CITAC ± ± CITAC ± ± a The mass fractions from the gravimetric preparation and conversion of the concentration are indicative and do not have quoted uncertainties. Table Experimental conditions for the determination of ethanol by GC C IRMS Column 7.5 m mm id, 10 mm film thickness, PoraPLOT-Q HT (Chrompack, Loughborough, UK) Retention gap 3 m mm id PEG-deactivated Head pressure bar, constant flow mode On-column injector temperature 60 C Injection volume 0.10 ml GC oven programme 1 min at 60 C Ramp at 30 C min 1 13 min at 140 C Ramp at 30 C min 1 5 min at 180 C Total run time 30 min Backflush time 400 s Helium interface pressure 1.4 bar Emission 1.49 ma Analyser pressure 10 6 mbar Source pressure mbar Acceleration voltage 10 kv Integration time 0.50 s Integration parameters 0.4 mv s 1 start, 0.05 mv s 1 end Background subtraction Individual 190 Analyst, 000, 15,

3 Measurement protocol During the optimisation of the measurement procedure, a drift in the measured isotope amount ratios was observed. In order to avoid any bias due to this drift, the sequence was started with five injections of pure water (18 MΩ) so that the baseline level due to water could reach a stable level. A further 10 injections were then used to stabilise the system, before recording usable data. An example showing the results of a measurement sequence is shown in Fig. 1. The measurements obtained after the first 10 injections showed more constant measured isotope amount ratios. For the analysis, 10 injections of each sample blend were performed, bracketed by a calibration blend for each sample injection. The IDMS procedure The IDMS protocol used follows that described by Catterick et al. 8 It consists in performing a double IDMS, in which the influence and contribution of the spike on the results and uncertainties were minimised. The uncertainty calculation follows the recommendations given by ISO and EURA- CHEM. 9,10 A detailed description of the application of the double IDMS analysis with the exact matching isotope amount ratio technique was originally reported by Henrion. 11 The exact matching refers to matching the isotope amount ratios of the different blends used for the IDMS analysis. This protocol was followed for the determination of the ethanol mass fraction in the different samples. The double IDMS equation [eqn. (1)] was used for the calculation of the ethanol mass fraction in the samples, for which the representative IUPAC isotopic composition of carbon was used for both the sample X and the primary standard Z: 1 w w m Y mzc RY - RB - RZ X = Z mx myc RB - RZ RY - R (1) where w X is the mass fraction of ethanol in sample X and w Z the mass fraction of ethanol in the primary standard Z; m Yc is the mass of spike Y added to m Zc, the mass of primary standard Z, to prepare the blend (= Z + Y); R is the isotope amount ratio of the calibration blend (= Z + Y); m Y is the mass of spike Y added to m X, the mass of sample X, to prepare the blend B (= X + Y); R B is the isotope amount ratio of the sample blend B (= X +Y); R Z is the isotope amount ratio of natural carbon in the primary standard Z (and sample X, i.e., IUPAC value) and R Y the isotope amount ratio of spike Y. Mass discrimination effects which may occur at different stages of the measurement procedure, which affect the response of different isotopes measured, were accounted for by using a correction factor K. This factor can be defined as the ratio between the true value R (i.e., the ratio of the exact amounts of isotope 13 C to 1 C) and the measured value RA of the same isotope amount ratio. The isotope amount ratio R of blend is well known as it was gravimetrically prepared, and is measured bracketing (i.e., before and after) every sample during the analysis, so it was used to calculate the mass discrimination factor K: Rtrue K = = R measured R () Consequently, the unknown true value of the sample isotope amount ratio R B can be expressed as a function of the measured isotope amount ratio of the sample blend RA B, the gravimetric value R and the measured value RA of isotope amount ratio of the calibration blend according to RB = R R B (3) By combining eqns. (1) and (3), the mass fraction of ethanol in the sample X can be expressed by eqn. (4), in which all the variables can be fully described: w w m X = Z m Y X m m Zc Yc R R R Y - B R R R R R R B - Z R Y - R - R As R B and R are well matched, any effect occurring during the measurement will affect both measured isotope amount ratios equally, so that the mass bias correction effects are minimised compared with the use of non-matching isotope amount ratios for the correction factor K determination. To avoid further bias due to the enrichment in 17 O in the labelled ethanol spike, the masses of spike added to the primary standard and sample, m Y and m Yc, were matched to obtain the same amount of labelled ethanol in both blends B and. When this condition is fulfilled, the correction made using the K factor also allowed the elimination of any effect from a non-natural 17 O contribution. Evaluation of the measurement uncertainty All the variables present in eqn. (4) have associated standard uncertainties and contribute to the combined standard uncertainty of the mass fraction of ethanol in the sample. A detailed description of the calculation of all these variables standard uncertainties is given in the Appendix. An example of data is given in Table 3, describing all variables with their associated standard uncertainties for the measurement of a blend prepared from the CITAC solution containing 50 mg of ethanol per 100 ml of solution. Z (4) Fig. 1 Variation of the measured isotope amount ratio with the number of replicated injections for a measurement sequence performed for the CITAC 50 solution. Calculation of the measurement combined standard uncertainty. The combined standard uncertainty on the mass fraction of ethanol in the samples was calculated by applying the uncertainty propagation law to eqn. (4), as recommended in the EURACHEM Guide. 10 As the different variables x i occurring in eqn. (4) are non-correlated, only the variance terms had to be considered: wx uc( wx) = Ê u ( xi) Ë Á ˆ S (5) xi An uncertainty budget can then be drawn up, once all the standard uncertainties were combined to give the combined standard uncertainty of ethanol amount fraction in the sample. The budget was drawn up by comparing the variance of each variable [terms appearing in the sum in eqn. (5)] to the square of Analyst, 000, 15,

4 the combined standard uncertainty of the result. The uncertainty budget obtained using the data in Table 3 is given in Fig.. Replicate analysis of the sample. Three aliquots of the sample X were spiked with the solution Y and measured under the same conditions. This replication of the analysis incorporated factors not directly linked to the variation of the different variables involved in the calculation, but with variations occurring between the different blends of the sample, such as the degree of matching between the isotope amount ratios of the sample and the calibration blends. The resulting mass fractions of ethanol of three aliquots are given in Table 4, for the CITAC 50 sample. The standard deviation of the mean (standard deviation of the three results divided by A3) can be considered as an estimate of the between blend variation and was used as a between blend uncertainty component u between. As the results reported were the mean of the three mass fractions w Xi (i = 1 3), a within blend uncertainty contribution u within was calculated as given in eqn. (6) by applying the uncertainty propagation law to the expression of the mean: uc wxi uwithin = S ( ) n (6) with n = 3. The within and between blend uncertainty contributions were then combined by adding their square, and the square root of this sum was taken as the final result s combined standard uncertainty. If only the standard deviation of the mean u between was used as the result s uncertainty, the standard uncertainty of each variable used to calculate w X would be completely ignored along with their respective contributions. If it was not included in the result s uncertainty, then the aspects not covered by the variation of the different variables (e.g., the degree of matching of the isotope amount ratios) would also be ignored. Results and discussion As the carbon in all eluting compounds was combusted to CO, good chromatographic resolution was essential so that only the ethanol was combusted when the isotope amount ratios were being measured. It was found initially that acetonitrile was eluting in the tail of the ethanol peak, leading to bias in the results. As a consequence, the preparation and storage of all solutions prior to their analysis were performed in a solvent free environment. Special care was also spent on avoiding contamination and checking the samples for the presence of this interfering peak. The results of IDMS of ethanol in the different samples are given in Table 5. The mass fractions and mass concentrations in Table 1 for the CITAC solutions correspond to the gravimetric value. For the LGC CRMs, the mass concentrations were certified using the dichromate oxidation method. This method consists in adding in excess a known amount of potassium dichromate to oxidise the ethanol contained in the sample. The unreacted dichromate is then determined by potentiometric titration using ammonium ferrous sulfate. These concentrations were converted into mass fractions, using a density of , to give mg g 1 for LGC 5401 and mg g 1 for LGC The gravimetric values of the mass fractions for the CRMs were and.0090 mg g 1 for LGC 5401 and 5403 respectively (Table 1). No standard uncertainty can be quoted for these mass fractions, as not enough information was available on the density used to combine them. These values were nevertheless used to compare the results of the IDMS analysis of ethanol with those obtained using the dichromate oxidation method and the gravimetric value. The deviations of the IDMS analysis from the gravimetric values are given in Table 6. The deviation between the IDMS results and the gravimetric values are well within 0.3% of the gravimetric value. In addition, the expanded standard uncertainty (with a coverage factor k equal to ) always encompasses the observed deviation between the IDMS results and the gravimetric values. The dichromate oxidation method is considered to be the most accurate and precise method for the determination of ethanol for forensic purposes. The CITAC intercomparison report 4 quotes a precision range of 1.1% for the dichromate oxidation method and 3.% for GC (headspace) analysis. The same report mentions a maximum possible bias for the dichromate method of % ( % for the GC methods). It also quotes a desirable relative standard uncertainty of less than 1% on the certified value of ethanol in water standards in order to be able to achieve acceptable uncertainty for the measurement of ethanol in blood (i.e.,.9% in the UK for a single measurement). The method developed for the determination of ethanol in water by IDMS meets these requirements. The relative expanded standard uncertainty achieved for all samples is < 0.5% and in most cases is around %, with a coverage factor k =, which would give a 95% confidence interval. The Fig. Uncertainty budget for the measurement performed on a blend prepared from CITAC 50 sample (which represent a calculated measurement uncertainty u c = mg g 1 ). Table 3 Summary of the values and associated standard uncertainties of each variable and their contribution to the result s uncertainty for one blend prepared for the CITAC 50 analysis Variable Symbol Value Standard uncertainty Mass fraction of primary standard Z w Z mg g mg g 1 Mass fraction of spike Y w Y mg g mg g 1 Mass of sample X m X g g Mass of spike Y added to sample X m Y g g Mass of primary standard Z m Zc g g Mass of spike Y added to primary Standard Z m Yc g g n( 13 C)/n( 1 C) for Z R Z n( 13 C)/n( 1 C) for Y R Y Measured isotope amount ratio of B RA B Measured isotope amount ratio of RA Prepared isotope amount ratio of R Analyst, 000, 15,

5 relative deviation observed between the IDMS results and the gravimetric values was < 0.3% and was always within the stated relative expanded standard uncertainty of the IDMS result, which did not exceed 0.5% (with a coverage factor k = ). However, for the purpose of certifying aqueous ethanol standards, this method can be reasonably easily used and provides an independent unrelated method to the traditional dichromate titration. Because of the time required per analysis, IDMS cannot be used routinely for a high turnover of samples. It was not tested in matrices other than water (e.g., spirits, blood). IDMS has the potential of being a primary ratio method of measurement. This study also demonstrates the possibility of obtaining ethanol mass fractions traceable to the SI system. This is of importance when certifying reference materials to be used by laboratories as quality control/quality assurance checks or validation for their methods of analysis. Two analysts performed the analysis independently, and no differences were noticed between their respective results. This provides extra evidence of the robustness of the method employed compared with more conventional certification approaches. The IDMS analysis requires only the weighing of the sample and spike addition. The risk of analyst mishandling the sample preparation or misinterpretation is thus minimal. Conclusions The combination of an exact matching double IDMS approach and GC-C-IRMS isotope amount ratio measurements have proved capable of supplying highly accurate and precise mass fraction determinations of ethanol in water. The difference observed between the measured mass fraction and that of the gravimetrically prepared value was < 0.3%, well within a relative expanded standard uncertainty of 0.5%. The possible bias was much smaller than that achieved using titrimetry, which has been the method of choice for the certification of ethanol CRMs, and was even not significant with regard to the stated expanded standard uncertainties. However, whilst the method outlined was fairly simplistic, it did require wellcharacterised pure materials. The demanding nature of this high accuracy IDMS procedure will be best justified for characterising very select primary certified reference materials. Table 4 Results of the analysis of three separate blends of the CITAC 50 sample (the combined standard uncertainties stated are not expanded) Sample Mass fraction/ mg g 1 u within /mg g 1 CITAC 50-B CITAC 50-B CITAC 50-B Gravimetric value Acknowledgements This study was supported under contract with the Department of Trade and Industry as part of the National Measurement System Valid Analytical Measurement (VAM) programme. Appendix: calculation of the standard uncertainties of the different parameters for the calculation of the mass fraction of ethanol in the samples Standard uncertainty of the isotope amount ratios of the materials: R Z and R Y For the sample X and the primary standard Z, the isotopic composition recommended by IUPAC was used to calculate the isotope amount ratio R Z = ± The uncertainties recommended by IUPAC for the isotope abundances of carbon isotopes were considered having a rectangular distribution and were divided by A3 to obtain their respective standard uncertainties. For a rigorous calculation, covariances should be considered to get a better estimate of the uncertainty of the isotope amount ratios, as the abundances are correlated together. However, a more accurately known value of the standard uncertainty was not required as it does not contribute significantly to the results. The values of R X and R Z could be measured using the IRMS and would have smaller standard uncertainties than the IUPAC value used. This determination was not done because of memory effects encountered when switching the measurement modes, i.e., changing the cup configuration in the detector. The isotope amount ratios measured for the IDMS analysis are close to 1, while the natural one is 100 times less. In practice, it takes 3 days before measurements can be accurately performed after switching modes. The consideration of R X = R Z also allows the IDMS equation to be slightly simplified. However, the values of R X and R Z do not affect the results of the analysis, and even when the large IUPAC standard uncertainty is used it does not affect the uncertainty budget. For the enriched [ 13 C ]ethanol material, the only information provided was a 13 C specification of 99%. As R Y does not influence the result at all using the double IDMS, the isotope amount ratio n( 13 C)/n( 1 C) considered for this material was R Y = 99 ± 5, corresponding to a relative standard uncertainty of 5% on the isotope amount fractions of 0.99 for 13 C and 0.01 for 1C. No information was given concerning the molar mass and its associated standard uncertainty of the labelled [ 13 C ]ethanol. If only oxygen with natural isotopic composition is contained in the labelled ethanol, its molar mass is then g mol 1, and the corresponding standard uncertainty is g mol 1. Unfortunately, the labelled ethanol could also be enriched in 18O, and as a consequence the standard uncertainty calculated Table 5 Results of the IDMS analysis for the different samples, with their total combined standard uncertainties, and the repartition between the within and between blend uncertainty contributions Sample Mass fraction/ mg g 1 u within contribution/ mg g 1 u between contribution/ mg g 1 Combined uncertainty, u c (w X )/mg g 1 Expanded uncertainty, U (k = )/ mg g 1 TCITAC CITAC CITAC LGC LGC Analyst, 000, 15,

6 was increased by a factor 10 to reach 0.01 g mol 1, but the molar mass was kept equal to g mol 1. Standard uncertainty of the masses: m Zc, m Yc, m X, m Y Each weighing was repeated at least four times and the mean of the replicates was used to calculate the masses involved in the different blends. As the masses were calculated by difference, their standard uncertainties were calculated by combining contributions for the linearity and the repeatability of the weighing. The balance certificate quoted a maximum error for linearity of g. This value was considered having a rectangular distribution and was divided by A3. It was then combined with the standard deviation of the mean (s m ) of the repeated weighings. Standard uncertainty of the mass fractions w Z and w Y The primary standard solution used for this analysis was prepared by diluting gravimetrically absolute ethanol into water and then further gravimetrically diluting to reach the desired mass fraction. The mass fraction w Z was calculated according to w p m EtOH m1 z = (7) m(s 1) m(s ) where p is the purity of the absolute ethanol, m EtOH is the mass of absolute ethanol dissolved into a mass of water m(s 1 ) and m 1 is the mass of the solution S 1 further diluted in mass m(s ) to obtain the diluted solution S. The absolute ethanol was stated as being 99.99% ethanol by assay, but no overall standard uncertainty was quoted for the purity. Considering the amount of different impurities stated on the certificate, and a water content analysis performed on the absolute ethanol, the purity was considered as with a standard uncertainty u(p) = The resulting mass fractions of the different primary standards Z prepared were then equal to w Z =.0095 ± , ± and ± mg g 1 with the combined standard uncertainties u c (w Z ) calculated according to eqn. (8), which corresponds to the uncertainty propagation law applied on the expression of w Z [as given in eqn. (7)]: u ( w ) = w c Z Z Èux ( i) SÍ Î xi where x i represents the different variables involved in eqn. (7). The spike s mass fraction was calculated similarly. Its purity could not be assessed as accurately as for the natural absolute ethanol as only 0.5 ml was available. Its purity was considered equal to with a standard uncertainty of (8) Standard uncertainty of the prepared isotope amount ratio of the blend: R The isotope amount ratio of the calibration blend is calculated from the data of the spike Y and the primary standard Z, that are gravimetrically mixed as described in the following eqn. (9): RZmZcvZ( 1+ RY) + RYmYcvY( 1+ RZ) = (9) mzc vz ( 1+ RY ) myc vy ( 1+ RZ ) The amount contents v Y and v Z must be used to calculate R. The mass fractions w Y and w Z were converted into amount contents by multiplying them with the respective molar masses M Y and M Z of ethanol in Y and Z [M Y = mol g 1, u(m Y ) = mol g 1 and M Z = mol g 1, u(m Z ) = mol g 1 ]. The amount contents were then equal to n Y = ± mmol g 1 and v Z = ± mmol g 1. All the necessary data to calculate R are given in Table 3 for one example. The prepared isotope amount ratio R was then equal to The different standard uncertainties were then combined according to the uncertainty propagation law 10 to obtain a combined standard uncertainty u c (R ) = 0.005, which is used as the standard uncertainty of R in further calculation. Standard uncertainty of the measured isotope amount ratios of the blends: RA B and RA The sample and calibration blend solutions were injected alternately into the GC-C-IRMS system. For each measured sample blend isotope amount ratio RA B, the associated calibration blend isotope amount ratio RA was calculated as the average value of the two values obtained for the injections made just before and after the sample blend. The standard uncertainties associated with these isotope amount ratios were calculated as the standard deviation (s) calculated for the measured 10 and 11 values given by the instrument for RA B and RA, respectively. The standard deviation, and not the standard deviation of the mean, was used as standard uncertainty because the mass fraction of ethanol in the sample X was calculated for each injection made for the sample blend and not from the average of the measured isotope amount ratios. The resulting mass fraction for the blend analysed was then calculated as the average of the 10 mass fractions calculated for each sample blend injection. This is to allow the bracketing correction to be performed more accurately when a drift in the measurement of the isotope amount ratios occurs. When there is no significant drift, the difference between the mass fraction calculated using eqn. (3), with the average isotope amount ratios for RA B and RA, and the average mass fraction calculated from the 10 individual ones, is not significant and stays well within the calculated combined standard uncertainty of the mass fraction of ethanol in the sample. Table 6 values Comparison of the IDMS analysis results with the gravimetric Sample Mass fraction by gravimetry/ mg g 1 Mass fraction by IDMS/ mg g 1 Relative expanded uncertainty for IDMS, U (k = ) (%) Relative deviation between the two values (%) CITAC CITAC CITAC LGC LGC References 1 P. De Bièvre, R. Kaarls, H. S. Peiser, S. D. Rasberry and W. D. Reed, Accred. Qual. Assur., 1996, 1, 3. H. Craig, Geochim. Cosmochim. Acta, 1957, 1, G. Dube, A. Henrion, R. Ohlendorf and W. Richter, Rapid Commun. Mass Spectrom., 1998, 1, 8. 4 B. King and R. Lawn, Analyst, 1999, 14, D. A. Merritt, K. H. Freeman, M. P. Ricci, S. A. Studley and J. M. Hayes, Anal. Chem., 1995, 67, J. Santrock, S. A. Studley and J. M. Hayes, Anal. Chem., 1985, 57, Analyst, 000, 15,

7 7 VAM report Interim Assessment of the Factors Which Influence the Accuracy of IDMS Data from GC/C/IRMS and GC/MS, LGC/VAM/ 1998/09, LGC Teddington, Teddington, T. Catterick, B. Fairman and C. Harrington, J. Anal. At. Spectrom., 1998, 13, Guide to Expression of Uncertainty in Measurement, ISO, Geneva, Quantifying Uncertainty in Analytical Measurements, EURACHEM Guide, LGC, Teddington, A. Henrion, Fresenius J. Anal. Chem., 1994, 350, K. J. R. Rosman and P. D. P. Taylor, Pure Appl. Chem., 1998, 70, P. Roper, Office of Reference Materials, LGC Teddington, Teddington, personal communication. Analyst, 000, 15,