Supporting Material
Stable chlorine isotope analysis of chlorinated acetic acids using gaschromatography quadrupole mass spectrometry
Milena E. Miska1, Orfan Shouakar-Stash2, 3, Henry Holmstrand1*
1
Department of Applied Environmental Science, Stockholm University, Stockholm, Sweden
2
Department of Earth and Environmental Sciences, University of Waterloo, Waterloo Ontario,
Canada
3
Isotope Tracer Technologies Inc., Waterloo, Ontario, Canada
*Correspondence to: Henry Holmstrand, Dept. Environmental Science and Analytical
Chemistry, Stockholm University, 106 91 Stockholm, Sweden.
E-mail: henry.holmstrand@aces.su.se
Content: 6 pages
S-1 Dataset for the external calibration of the GC/qMS method for referencing to SMOC
S-2 Simple linear regression on the calibration data
S-3 Estimation of the uncertainty of 37Cl values derived by the GC/qMS method
S-4 Day-to-day variations of the GC/qMS system
1
S-1 Dataset for the external calibration of the GC/qMS method for referencing to SMOC
Table S-1: Data for the N = 6 pairs of Std1/Std2 used for external calibration of the GC/qMS method.
Difference in 37Cl
obtained using GC/qMS
N
Std1
Std2
37ClStd1, SMOC
37ClStd2, SMOC
37ClStd1/Std2, SMOC
37ClStd1/Std2, (GCqMS)
[‰ vs SMOC]
[‰ vs SMOC]
[‰]
[‰]
2.9 ± 0.6
-0.3 ± 0.3
3.5 ± 0.7
1a
PCE #1
PCE
3.2 ± 0.7
(n=3)
(n=5)
(n=10)
1.7 ± 0.7
-0.3 ± 0.3
1.6 ± 0.6
2a
PCE #2
PCE
2.0 ±0.8
(n=3)
(n=5)
(n=10)
-1.5 ± 0.4
-0.3 ± 0.3
-2.2 ± 0.7
3a
PCE PPG
PCE
-1.2 ±0.5
(n=3)
(n=5)
(n=8)
-5.4 ± 0.6
-4.4 ± 0.5
-1.0 ± 1.1
4a
DDT BDH
DDT Aldrich
-1.0 ±0.7
(n=2)
(n=5)
(n=9)
-1.3 ± 0.7
-1.0 ± 0.7
0.1 ± 1.1
5a
PCP Supelco
PCP Aldrich
-0.3 ±1.0
(n=2)
(n=5)
(n=9)
-6.0 ± 0.2
-0.7 ± 0.1
-4.3 ± 0.2
6b
mDCA [B]
mDCA [A]
-5.2 ±0.2
(n=8)
(n=2)
(n=35)
a
[1]
Data of the Std1/Std2-pairs 1 to 5 were published in Aeppli et al. . The measurements were performed on a GC/qMS-system consisting of the
same GC- and qMS-parts as in this study. Samples and standards were SMOC-characterized offline by conversion to CsCl followed by TIMSanalysis. b Std1/Std2-set 6 was analyzed within this study by GC/qMS and SMOC-referenced by conversion to CH3Cl followed by GC/IRMS
analysis.
Std1/Std2-pairs
Values for 37Cl obtained using TIMS or IRMS
2
S-2 Simple linear regression on the calibration data
Plotting 37ClStd1/Std2, SMOC vs 37ClStd1/Std2, (GCqMS) showed a linear relationship of the
variables. Employing simple linear regression on the N = 6 data pairs resulted in a calibration
curve of the form:
Δ 37 Cl Smp/Std, (GCqMS)  a  Δ 37 Cl Smp/Std, SMOC  b
(Eq. S-1)
with a slope a of 0.92 (±0.29) and an intercept b of 0.01 (±0.80). The slope and intercept 95 %
confidence intervals, calculated following common statistical approaches, are given in
parentheses. First the uncertainty of the regression, the residual standard deviation sr, was
calculated:
N
sr 
 ( yi  yˆi )2
(Eq. S-2)
i 1
N 2
with yi the observed values on the y-axis and ŷ i the predicted y value for a given x. The
standard deviations of the slope (sa) and intercept (sb) were then calculated as:
sa 
sr
(Eq. S-3)
N
 (x i  x avg ) 2
i 1
N
 x i2
sb  s r 
i 1
N
N   (x i  x avg )
(Eq. S-4)
2
i 1
with the values on the x-axis xi and their average value xavg. The confidence intervals for the
slope and intercept were calculated by multiplication of the t-distribution with the standard
deviation of the slope and intercept, respectively. For a 95 % confidence interval,
corresponding to =0.05, and N-2 degrees of freedom the t-distribution is:
t α/2, N  2  t 0.025,
4
 2.78
(Eq. S-5)
The 95 % confidence interval for the slope was consequently:
a  t α/2, N  2  0.92  0.29
(Eq. S-6)
and for the intercept, it was:
3
b  t α/2, N  2  0.01  0.80
(Eq. S-7)
S-3 Estimation of the uncertainty of 37Cl values derived by the GC/qMS method
A confidence interval can also be calculated for values predicted by the calibration curve. The
uncertainty of a SMOC-converted isotopic difference (37ClSmp/Std, SMOC) of a sample from its
isotopic standard from multiple (n) measurements of the sample versus the standard can be
estimated by calculation of its standard deviation, here denoted as Sx0:
Sx 0
(y 0  y avg ) 2
 Sr  1 1



 
N
a n N
 
a 2  (x i  x avg ) 2
(Eq. S-8)
i 1
with the residual standard deviation Sr, the slope of the calibration curve a, the number of
calibration pairs N, the number of replicate measurements n, the average y0 of the measured
y value to be calculated, the average y value of the calibration standards yavg, the x values of
the calibrations standards xi and their average xavg. The 95 % confidence interval for predicted
values can then be calculated by multiplication of Sx0 with the t-distribution. This prediction
interval gives an estimate of the uncertainty of predicted values and is illustrated in Fig. S-3.
Following equation 5 in the paper, the final GC/qMS-derived 37Cl values (37Cl(GCqMS)) were
calculated from 37ClSmp/Std, SMOC and the IRMS-derived 37Cl values of the isotopic standards
37ClStd, SMOC (with their precision SStd as one standard deviation). The final published
standard deviations of the 37Cl(GCqMS) values were estimated by error propagation:
Sfinal  (S x0 ) 2  (SStd ) 2
(Eq. S-9)
4
y0
x0
Figure S-3: Illustration of a calibration plot using N=5 calibration pairs (black squares). The
standard deviation of the instrumental response from n measurements is illustrated by the
error bars. A calibration curve (grey line) was fitted using linear regression. The 95 %
confidence interval of the calibration curve is marked by the dashed line, and the 95 %
confidence interval of predicted values (i.e. the prediction interval) by the black solid line.
The true value x0 can be predicted for an instrumental response y0, with an uncertainty that
can be estimated from the prediction interval shaded red). Thus, the prediction interval leads
to a larger uncertainty than that of the calibration curve alone.
5
S-4 Day-to-day variations of the GC/qMS system
Figure S-4: Isotopic difference 37ClStd1/Std2, (GCqMS) of mDCA[A] vs mDCA[B] measured on
the GC/qMS system. Eight sequences with n=5 to 7 single Std1/Std2-pairs (grey circles) were
run to determine the variation of the instrument-obtained isotopic difference of mDCA[A] to
mDCA[B]. The average of the isotopic difference for each sequence was illustrated (black
circles) with its corresponding standard deviation (error bars). The measurements were spread
out throughout a year.
REFERENCES
[1]
C. Aeppli, H. Holmstrand, P. Andersson, O. Gustafsson. Direct compoundspecific stable chlorine isotope analysis of organic compounds with quadrupole
GC/MS using standard isotope bracketing. Anal. Chem. 2010, 82, 420.
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