International Key Comparison APMP.QM-S1
Draft B
Field – Gas standards
Subject - Comparison of primary standards of nitrogen in helium
Participants
Angelique Botha (CSIR, South Africa), Damian Smeulders (NMIA, Australia), Kenji Kato
(NMIJ, Japan), Sang Hyub Oh and Byung Moon Kim (KRISS, Korea)
1. Table of Contents
Introduction ………………………………………………………………………..….1
Work Carried out by the Coordinating Laboratory……………………………………2
Preparation of Gravimetric Standards……………………………………………….2
Consistency of Standards and Measurement Uncertainty…………………………...2
Calculation of the Key Comparison Reference Value ……………………………...2
Results Submitted by Participating Laboratories…………………………………….. 3
Conclusions…………………………………………………………………………....4
Degrees of Equivalence………………………………………………………………..5
Annexes………………………………………………………………………………..6
Introduction
Gravimetry has been used as the primary method for the preparation of primary standard
gas mixtures in most of NMIs. In the uncertainty evaluation of primary standard gas mixtures,
the purity analysis and the weighing of gases are very important. In general Key Comparison,
the uncertainty of analysis is bigger than that of preparation, and accurate comparison about
the capability of preparation of primary standard gas mixtures is significantly difficult.
In this comparison, the concentration of nitrogen has been chosen as that easily to be
analyzed using GC-TCD with small uncertainty and to be weighed in the almost same range
for component and balance gases. Participants sent primary standard gas mixture composed
of about 12.5 %mol/mol nitrogen in helium to the coordinating laboratory with the report of
the purity analysis and the gravimetric preparation including raw data. Coordination
laboratory analysed each standard gases cylinder with GC-TCD and compared with reported
concentration values.
1
Preparation of Gravimetric Standards
Pure N2 and He were purchased from Deokyang Energen (Korea). The impurities of each
pure gas were analyzed using Gas MS, FTIR, dew point meter and GCs. The results of the
purity analysis are shown in Table1.
Table 1. Purity of N2 and He gases.
Nitrogen
Deokyang Energen
Purity
(µmol/mol)
999966.6
Helium
Deokyang Energen
999998.76
Gas name
Source
Uncertainty(k=2)
(µmol/mol)
1.74
0.12
The hierarchy of gravimetric standards prepared by KRISS for this comparison is shown in
Figure 1. 10 L Aluminium cylinders from Luxfer were used for all standards. Six cylinders in
the range of 12.2445~12.5612 % mol/mol were prepared by two persons (Mr. K. Kim and
Mr. B. Kim) and compared each other. And YA000990 cylinder was used as the reference
standard in this comparison.
Pure N2 + He
YA000381
12.2445
%mol/mol
YA001174
12.4741
%mol/mol
YA001009
12.5171
%mol/mol
B. Kim
K. Kim
K. Kim
YA000990
12.5202
%mol/mol
Reference
K. Kim
YA000608
12.5203
%mol/mol
YA000944
12.5612
%mol/mol
B. Kim
K. Kim
Figure 1. The hierarchy of the gravimetric standards of N2 / He prepared by KRISS.
Consistency of the Standards and Measurement Uncertainty
The consistency of the standards in the hierarchy shown in Figure 1 was validated by the
comparison with YA000990 cylinder. Analytical conditions are as follows:
GC-µTCD (Agilent 6890)
Column : Molecular sieve 5A (packed type)
Oven temp. : 115 oC
Sample loop : 0.5 ml
2
% difference [measured/gravimetric concentraion]
Figure 2 shows the percent difference between the analytical amount fraction and the
gravimetric amount fraction when YA000990 cylinder was used as a reference cylinder. As
can be seen, in the range of 12.2445 ~ 12.5612 %mol/mol, the percent differences of five
cylinders were within 0.02 % (relative to value). This measurement was carried out five
times. We assumed that this value means the relative measurement uncertainty of KRISS on
this comparison.
0.10
0.08
0.06
0.04
0.02
0.00
-0.02
-0.04
-0.06
-0.08
-0.10
12.20
12.25
12.30
12.35
12.40
12.45
12.50
12.55
12.60
Concentration of PRMs [%mol/mol]
Figure 2. The percent difference of five cylinders prepared by KRISS. YA000990 cylinder
was used as a reference standard. ● and ■ represent cylinders prepared by Mr. K. Kim and
Mr. B. Kim, respectively.
Calculation of the Key Comparison Reference Value
Since a gravimetric value from each participant was not available, a reference cylinder was
used to determine for the Key Comparison Reference Value (KCRV). A new PRM cylinder
from KRISS was used as a reference cylinder, and analysed with participant’s cylinders. The
response from the participant’s cylinder ( rp ) and the response from reference ( rref ) were
measured and the response ratio calculated according to the following equation.
ri =
rp
rref
(1)
To calculate the KCRV, the reported value from each participant was divided by response
ratio according to the equation (2).
3
X i ,R =
Xi
ri
(2)
Where X i is the gravimetric value reported by the participant, ri is the response ratio, and
X i ,R is the concentration of the reference cylinder when each participant’s cylinder was used
as a standard cylinder.
Table 2 summarizes the reported values from the participants and the concentration of the
reference cylinder. This data is also graphically represented in Figure 3.
Table 2. Summary of values.
Participants
Reported value
(%mol/mol)
Xi
NMIJ
NMIA
KRISS
CSIR
12.1039
12.4926
12.4313
12.5104
Response ratio
U (Xi )
(k = 2)
0.0024
0.0016
0.0021
0.0017
ri
0.9670
0.9980
0.9930
0.9992
U (ri )
(k = 2)
0.0003
0.0003
0.0003
0.0003
Reference cylinder
concentration
(%mol/mol)
U ( X i ,R )
X i ,R
(k = 2)
12.5165
0.0045
12.5174
0.0041
12.5192
0.0043
12.5204
0.0042
12.540
Concentration (% mol/mol)
12.535
12.530
12.525
12.520
12.515
12.510
12.505
12.500
NMIJ
NMIA
KRISS
CSIR
Laboratory
Figure 3. Graph of results.
From the results shown in Figure 2, it is clear that there is not outlier in this comparison.
Consequently, the distribution of the results is regarded as a normal distribution and a
arithmetic mean was used as a KCRV ( X KCRV ). To conform this result, the value of the
4
arithmetic mean and mean from Robust statistics were calculated, and the difference was very
small as 0.0001.
Degree of Equivalence
The degree of equivalence for each participating laboratory was calculated with the equation
(3).
Di = X i ,R − X KCRV
(3)
The uncertainty of the degree of equivalence was calculated using the equation (4).
U ( Di ) = 2 u ( X i ,R ) 2 + u ( X KCRV ) 2
(4)
The degree of equivalence and uncertainty is summarized in Table 3, and graphically
represented in Figure 4.
Table 3. Degree of equivalence
Participants
Calculated reference
value (%mol/mol)
X i ,R
NMIJ
NMIA
KRISS
CSIR
12.5165
12.5174
12.5192
12.5204
U ( X i ,R )
(k = 2)
0.0045
0.0041
0.0043
0.0042
Degree of
equivalence
(%mol/mol)
U ( X KCRV )
U ( Di )
Di
(k = 2)
(k = 2)
0.0018
-0.0019
0.0097
0.0018
-0.0010
0.0089
0.0018
0.0008
0.0097
0.0018
0.0020
0.0091
KCRV(%mol/mol)
X KCRV
12.5184
12.5184
12.5184
12.5184
5
0.020
Degree of equivalence (% mol/mol)
0.015
0.010
0.005
0.000
-0.005
-0.010
-0.015
-0.020
NMIJ
NMIA
KRISS
CSIR
Laboratory
Figure. 3. Degree of Equivalence.
* NMIJ reported two results. One is corrected value in consideration of the cylinder
expansion effect based on ISO 6142 and the other is not corrected value. Corrected value was
used in this comparison.
References
1. International Standard ISO 6142: Gas analysis -- Preparation of calibration gas mixtures - Gravimetric Method, Geneva, International Organization for Standardization, 2001.
2. Milton M. J. T., Woods P. T., Holland P., Uncertainty reduction due to correlation effects
in weighing during the preparation of primary gas standards, Metrologia, 2002, 39, 9799.
3. Analytical Methods Committee of the Royal Society of Chemistry, Technical Brief 6 (April
2001), Robust statistics: a method of coping with outliers,
www.rsc.org/Membership/Networking/InterestGroups/Analytical/AMC/TechnicalBriefs.as
p
4. S. Ellison, Robust Statistics Toolkit (RobStat.xla) Excel add-in,
www.rsc.org/Membership/Networking/InterestGroups/Analytical/AMC/Software/RobustS
tatistics.asp
5. P. Ciarlini, M. Cox, F. Pavese. G. Regoliosi, The use of a mixture of probability
distributions in temperature interlaboratory comparisons, Metrologia, 2002, 41, 116-121.
6. D.L. Duewer, A Robust Approach for the Determination of CCQM Key Comparison
Reference Values and Uncertainties, Working document CCQM/04-15, BIPM, 2004.
7. F. R. Guenther et al., International Comparison CCQM-K41 :Hydrogen sulfide in
nitrogen, Metrologia, 2007, 44. 08004.
Coordinators
6
Sang-Hyub Oh
Korea Research Institute of Standards and Science (KRISS)
1 Doryong Dong, Yuseong Gu, Daejeon 305-340, Korea
7
Results for nitrogen in helium
Participant : NMIJ
Sample cylinder identification : CPB30893
1.
Purity of nitrogen
Table 1. Purity table for high-purity nitrogen gas.
He
O2
H2 O
CO
CO2
CH4
N2
2.
Standard
uncertainty
1.3
0.47
0.25
0.032
0.019
0.0054
1.4
Mole fraction
10-6 mol/mol
1.8
0.82
0.44
0.056
0.033
0.0094
999996.9
Component
Purity of helium
Table 2. Purity table for high-purity helium gas.
Component
Mole fraction
10-6 mol/mol
N2
O2
Ar
He
3.
Standard
uncertainty
0.22
0.105
0.136
999999.54
0.12
0.061
0.079
0.16
Preparation Data
(i) Specification of Balance (Model No., Readability, Resolution, etc.,)
Model No. : Mettler-Toledo Model: KA10-3/P
Resolution : 1 mg
Pooled experimental standard deviation for weighing, sp=2.6 mg,
(ii) Weighing method (A-B-A, Substitution method, etc.,)
A-B-B-A method was used. “A” and “B” corresponded to a reference cylinder (10 L Aluminum
cylinder) and a sample cylinder, respectively. The scheme ”A-B-B-A” was automatically repeated
5 times per 1 measurement. The differences of readings between reference cylinder and sample
cylinder were always adjusted within ±1 g, by using calibrated standard mass pieces (OIML E2
class). These mass pieces were traceable to the National Standards at NMIJ’s mass force standard
group.
(iii) Weight of nitrogen, mN
2
The weight of nitrogen and its standard uncertainty were 120.1936 g and 2.5 mg.
These values have been corrected in consideration of the cylinder expansion effect.
8
( If the expansion effect was ignored, the weight of nitrogen and its standard uncertainty will be
120.1898 g and 1.7 mg. )
(iv) Weight of helium, mHe
The weight of helium and its standard uncertainty were 124.711 g and 14 mg.
These values have been corrected in consideration of the cylinder expansion effect.
( If the expansion effect was ignored, the weight of helium and its standard uncertainty will
be 124.6833 g and 1.7 mg. )
(v) Concentration
The mole fraction of N2 and its expanded uncertainty [k=2] were 121039 µmol/mol and 24
µmol/mol.
(If the correction is not made, the mole fraction of N2 and its expanded uncertainty [k=2] will be
121058.9 µmol/mol and 5.6 µmol/mol. )
Table 3. Uncertainty table for concentration of N2 in the sample gas mixture. The concentration was calculated
by using the equation (3) in ISO6142:2001.
Uncertainty
source
Mass of nitrogen gas
(mg)
Mass of
helium gas (mg)
Molar mass of N2
(mg/mol)
Molar mass of He
(mg/mol)
Purity of nitrogen gas
(µmol/mol)
Purity of helium
gas (µmol/mol)
Conc. of nitrogen in
helium gas
(µmol/mol)
Conc. of helium in
nitrogen gas
(µmol/mol)
Other impuritires in
nitrogen gas and
helium gas
Conc. of nitrogen in
gas mixture, xN
2
Estimate
xi
Assumed
distribution
Standard
uncertainty
u(xi)
Sensitivity
coefficient
ci
Contribution
to standard
uncertainty
u(yi)
120193.6
Normal
2.5
0.89
2.2
124711
Normal
14
-0.85
12
28013.40
Rectangular
0.23
3.8
0.88
4002.602
Rectangular
0.0012
-27
0.031
999996.9
1.4
-0.0010
0.0014
999999.54
0.16
0.0010
0.00016
0.22
Rectangular
0.12
0.0070
0.00087
1.8
Rectangular
1.3
-0.00014
0.00019
negligible
-
-
-
-
12
121039
( µmol/mol )
9
Tables 4 and 5 are shown as optional data. The mass of gas filled into the sample cylinder, mgas, are calculated
by using the following formula ;
m gas = ∆I a − ∆I b + (Wa − Wb )(1 − ρ air / ρ w ) + ρ air ⋅ ∆Vexp ,
(1)
where,
∆Ia : Difference of readings between reference cylinder and sample cylinder after filling,
∆Ib : Difference of readings between reference cylinder and sample cylinder before filling,
Wa : Calibrated standard mass pieces used for minimizing the ∆Ia within 1 g,
Wb : Calibrated standard mass pieces used for minimizing the ∆Ib within 1 g,
ρair : Air density,
ρw : Conventional density of mass pieces ( = 8000 kg/m3 ),
∆Vexp : Volume of expansion of the sample cylinder by filling gas ( The method of estimate for this value is
described below table 5. ) .
Table 4. Uncertainty table for mass of high-purity nitrogen gas in the sample gas mixture.
Uncertainty
source
Difference
of readings
before
filling ,
∆Ib
Mass pieces
before
filling,
Wb
Difference
of readings
before
filling,
∆Ia
Mass pieces
after filling,
Wa
(Assumed)
Cylinder
expansion
effect after
filling,
ρair·∆Vexp
Mass
of
nitrogen,
mgas
Estimate
xi
Assumed
distribution
Standard
uncertainty
u(xi)
Sensitivity
coefficient
ci
Contribution
to standard
uncertainty
u(yi)
-150.9 mg
Normal
1.2 mg
1
1.2 mg
-25996.17
mg
Rectangular
0.083 mg
1
0.083 mg
58.0 mg
Normal
1.2 mg
1
1.2 mg
93986.192
mg
Rectangular
0.085 mg
1
0.085 mg
3.8 mg
Rectangular
1.9 mg
1
1.9 mg
120193.6 mg
2.5 mg
10
Table 5. Uncertainty table for mass of high-purity helium gas in the sample gas mixture.
Uncertainty
source
Readability of
balance
(before
filling) ,
∆Ib
Mass pieces
(before filling)
Wb
Readability of
balance (after
filling), ∆Ia
Mass pieces
(after
filling) Wa
(Assumed)
Cylinder
expansion
effect,
ρair·∆Vexp
Mass of
helium, mgas
Estimate
xi
Assumed
distribution
Standard
uncertainty
u(xi)
Sensitivity
codfficient
ci
Contribution
to standard
uncertainty
u(yi)
58.0
Normal
1.2
1
1.2
93986.192
Rectangular
0.085
1
0.085
-242.2
Normal
1.2
1
1.2
218968.30
Rectangular
0.12
1
0.12
28
Rectangular
14
1
14
124711
14
Reference [1] claims that there is no contribution of cylinder expansion to measurements of mass fractions in
‘typical’ practical preparations of reference gas mixtures. In the reference, ‘typical practical preparations’ means
the preparations of mixtures, which the major component is nitrogen with the mass of 1600 g and the minor
component with the mass of 80 g is SO2, CO2, C3H8, NO, CO, or, CH4. However, in this comparion, He is
dilution gas and the difference of molar mass between N2 and He is relatively large. We estimate a contribution
of the cylinder expansion.
We have never measured an expansion of our 10 L aluminum cylinder by filling gases. Then, the cylinder
expansion effect, (ρair·∆Vexp), was simply calculated by the following method.
In the section A.5.2.3 of ISO6142 annex A, it is described that an expansion of the cylinder by filling gas with
the pressure of 15 MPa is about 0.02 L (for 5 L cylinder). By using this example data, we assumed that the
expansion of our 10 L aluminum cylinder by filling up to 15 MPa was 0.04 L.
For our sample cylinder, it was estimated by using the equation of state (for ideal gas) and the masses of nitrogen
and helium shown in the tables 4 and 5 that the partial pressures of the nitrogen and the helium were calculated
as 1.1 MPa and 8.2 MPa, respectively.
11
Based on the assumption that the ∆Vexp was proportional to the inner pressure of the sample cylinder, it was
estimated that the volumes of expansion by filling were ∆V = 3.2 x 10-6 m3 for nitrogen and ∆V = 2.3 x 10exp
5
m3
exp
for helium.
During the weighings of these gases, the (maximum) value of air density in our balance room was ρair = 1.18
kg/m3 , which were calculated using the observed atomospheric values on a Fortin mercury barometer and a
electronic thermohygrometer.
As conclusion, it was estimated that the values of (ρair·∆Vexp ) were 3.8 mg for the filling of nitrogen and 28 mg
for the filling of helium. We regarded its standard uncertainty as half value of the ∆mexp , i.e., the values of
u(∆mexp) were 1.9 mg for the nitrogen and 14 mg for the helium.
Reference
[1] M.J.T. Milton, P.T. Woods, and, P.E. Holland, ‘Uncertainty reduction due to correlation effects in weighing
during the preparation of primary gas standards’, Metrologia 39, 97-9 (2002).
End
12
Results for nitrogen in helium
Participant : KRISS
Cylinder No : YA000937
1.
Purity of nitrogen
Table 1. Purity table for nitrogen gas.
Component
Mole fraction
-6
10-6 mol/mol
10 mol/mol
H2
0.2
0.029
O2
0.0379
0.00058
CO
<0.01
0.0029
CO2
<0.01
0.0029
Ar
31.2
1.73
H2O
1.0
0.115
C1~C5
0.98
0.058
N2
2.
Standard Uncertainty
999966.6
1.74
Purity of helium
Table 2. Purity table for helium gas.
Component
Mole fraction
-6
10 mol/mol
10-6 mol/mol
O2
0.44
0.029
CO2
0.05
0.006
H2O
0.75
0.058
He
3.
Standard Uncertainty
999998.76
0.065
Preparation Data
Balance
Model : Mettler Toledo KA10-3/P
Resolution : 1 mg
Weighing method
A-B-A method was used. A and B mean reference and sample cylinder respectively. A-B-A
cycle was repeated 5 times in a measurement and temperature, pressure and relative humidity
are recorded.
13
Model Equation:
xi = nc / n * 100 ;
nc = mc / Mc ;
nb = mb / Mb ;
n = nc + nb + nimpurity ;
nimpurity = Wc / Mc * (1 - Pc / 100) + Wb / Mb * (1 - Pb / 100) ;
mc = Wc * PWc/100 ;
mb = Wb * PWb/100 ;
Wc = ((WDc - WDempty) - (WDrefc - WDrefempty)) + Um ;
Wb = ((WDb - WDc) - (WDrefb - WDrefc)) + Um + Ubuoy;
Mc = N * 2 ;
Mb = He ;
List of Quantities:
Quantity
Unit
Definition
xi
%
Conc of nitrogen
nc
mole
Mole of nitrogen
nb
mole
Mole of helium
n
mole
Total mole of gas
nimpurity
mole
Mole of total impurity
mc
g
Weight of nitrogen
mb
g
Weight of helium
Mc
g/mol
MW of nitrogen
Mb
g/mol
MW of helium
PWc
%
Weight percentage of pure nitrogen
PWb
%
Weight percentage of pure helium
Wc
g
Weight of nitrogen introduced
Wb
g
Weight of helium introduced
WDrefempty
g
Weight of reference cylinder empty
WDempty
g
Weight of sample cylinder empty
WDrefc
g
Weight of reference cylinder after nitrogen introducing
WDc
g
Weight of sample cylinder after nitrogen introducing
WDrefb
g
Weight of reference cylinder after helium introducing
WDb
g
Weight of sample cylinder after helium introducing
Um
g
Uncertainty for cylinder weighing process
N
g/mol
Molar mass of nitrogen
He
g/mol
Molar mass of nitrogen
Pc
%
Mole percentage of nitrogen
Pb
%
Mole percentage of helium
Ubuoy
g
Uncertainty for buoyancy by cylinder expansion
14
Uncertainty Budgets:
Quantity
Value
Standard
Uncertainty
nc
5.094918 mole
170·10-6 mole
nb
35.88941 mole
3.43·10-3 mole
n
40.98454 mole
3.47·10-3 mole
nimpurity
214.87·10-6 mole
9.15·10-6 mole
mc
142.7264 g
4.74·10-3 g
mb
143.6510 g
0.0137 g
Mc
28.01348 g/mol
70.0·10-6 g/mol
Mb
4.002602 g/mol
1.00·10-6 g/mol
PWc
99.995233 %
PWb
Distributio
n
Sensitivity
Coefficient
Uncertainty
Contribution
248·10-6 %
0.11
27·10-6 %
99.999241 %
34.8·10-6 %
-0.11
-3.8·10-6 %
Wc
142.7332 g
4.72·10-3 g
Wb
143.6521 g
0.0137 g
WDrefempty
9929.3186 g
696·10-6 g
normal
0.076
53·10-6 %
WDempty
9760.4119 g
1.24·10-3 g
normal
-0.076
-94·10-6 %
WDrefc
9929.3052 g
1.74·10-3 g
normal
-0.15
-270·10-6 %
WDc
9903.1317 g
1.12·10-3 g
normal
0.15
170·10-6 %
WDrefb
9929.3457 g
1.81·10-3 g
normal
0.076
140·10-6 %
WDb
10046.8243 g
2.02·10-3 g
normal
-0.076
-150·10-6 %
Um
0.0 g
4.00·10-3 g
490·10-6
2.0·10-6 %
N
14.00674 g/mol
35.0·10-6 g/mol
normal
-0.78
-27·10-6 %
He
4.002602 g/mol
1.00·10-6 g/mol
normal
2.7
2.7·10-6 %
Pc
99.996656 %
174·10-6 %
0.015
2.7·10-6 %
Pb
99.999876 %
6.48·10-6 %
0.11
710·10-9 %
Ubuoy
0.0 g
0.0127 g
-0.076
-960·10-6 %
xi
12.43132 %
1.04·10-3 %
rectangular
Results:
Quantity
Value
Expanded
Uncertainty
Coverage factor
Coverage
xi
12.4313 %
0.0021 %
2.00
95% (normal)
15
Results for nitrogen in helium (APMP.QM-S1)
Participant : CSIR
Cylinder No : 6625E
1.
Purity of nitrogen
Component
O2
H2O
N2
2.
Mole fraction
10-6 mol/mol
31.2
5
999963.8
Uncertainty
ppm
6.2
1
7.2
Mole fraction
10-6 mol/mol
0.55
1.4
3
999982.45
Uncertainty
ppm
0.11
0.28
0.6
1
Purity of helium
Component
O2
N2
H2O
He
3.
Preparation Data
(i) Specification of Balance
Mass Comparator: Sartorius CC10000S.
Resolution 0.1mg.
Readability 0.1mg
Reproducibility 0.25mg
Uncertainty of 0.5mg
(ii) Weighing method
ABBA
An ABBA weighing scheme is used to minimise the effect of instrument and environmental
drift. This involves weighing a reference mass (cylinder) prior to and after two weighings of
the sample mass.
45 data points are collected for each weighing of a cylinder, but only the last 16 data points
are used in the calculations.
During the weighing process, the air temperature, pressure and relative humidity are
measured during each reading on the mass comparator to calculate the air density. The air
density is used to correct for changes in the buoyancy of cylinders and rings.
(iii) Weight of nitrogen
85.0366 g (Pure nitrogen)
Please note that masses and composition details are also shown in Table 3.1.
16
(iv) Weight of helium
85.1080 g (Pure helium)
(v) Concentration
Nitrogen concentration: 124.926 mmol/mol
Expanded uncertainty :0.016 mmol/mol (k = 2.13)
Helium concentration: 875.066 mmol/mol
4.
Preparation Uncertainty
The following components are considered in determining the uncertainty of the gravimetric
mixtures:
•
•
•
•
•
Uncertainty of the mass comparator
Uncertainty due to buoyancy of cylinders (A,B), tare masses, cylinder expansion
Uncertainty due to the use of tare masses
Uncertainty due to cylinder expansion
Uncertainty due to impurities in source gases.
Each of these components has differing impacts on the total amount of uncertainty of the final
gravimetric mixture, with buoyancy contributing the largest fraction. The contribution of each
type of uncertainty is outlined in Table 4.1.
17
Table 3.1: Composition details for nitrogen in helium gas mixture.
Chemical Name
Helium
Nitrogen
Oxygen
Water
Formula
He
N2
O2
H2O
Amount of
Substance
(mol)
21.2631632
3.035561726
0.000106407
8.11328E-05
Table 4.1 : Uncertainty contributions for gravimetric mixture.
Uncertainty
Estimate
source
xi
(mmol/mol
)
Uncertainty of balance
Buoyancy of reference cylinder (A)
Buoyancy of sample cylinder (B)
Buoyancy (expansion of cylinder)
Buoyancy of rings on sample cylinder
Different rings on sample cylinder
Impurity
Expanded uncertainty: 0.016 mmol/mol
Mass of
Mixture Concentration
Substance (g)
85.10797957
85.03664769
0.003404891
0.001461631
(mmol/mol)
875.0664554
124.9258266
0.004379078
0.00333895
(%mol)
87.5066455
12.4925827
0.00043791
0.00033389
(µmol/mol)
875066.455
124925.827
4.3790776
3.33894958
Assumed
distribution
Standard
uncertainty
u(xi)g
Sensitivity
coefficient
ci
Normal
Normal
Normal
Normal
Normal
Normal
Normal
0.0005
0.00268
0.00268
0.00021
0.000112
0.000427
0.000604
1
1
1
1
1
1
1
Coverage factor: 2.13
4_5_APMP_QM-S1 Draft B 0803211
Page 18 of 4
Contribution
to standard
uncertainty
u(yi)%
1.65
47.19
47.15
0.29
0.08
1.20
2.4
Results for nitrogen in helium
Participant : NMIA
Cylinder No : ME2637
1.
Purity of nitrogen
Component
CO
CO2
H2
H 2O
HCn
O2
N2
2.
Standard
uncertainty
(x10^-6)
mol.mol-1
0,01
0,0235
0,288675135
0,005773503
0,028867513
0,002886751
0,291308399
Expanded
uncertainty
(x10^-6)
mol.mol-1
0,02
0,047
0,577350269
0,011547005
0,057735027
0,005773503
0,582616798
Specifications
(x10^-6)
mol.mol-1
1
0,02
0,1
0,01
Distribution
normal
normal
rectangular
rectangular
rectangular
rectangular
Purity of helium
Component
CO
CO2
H 2O
CHn
(Hydrocarbons)
N2
O2
Helium
3.
Mole
fraction
(x10^-6)
mol.mol-1
0,032
0,021
0,5
0,01
0,05
0,005
999999,382
Mole fraction
(x10^-6)
mol.mol-1
0,25
0,25
0,5
Standard
uncertainty
(x10^-6)
mol.mol-1
0,144337567
0,144337567
0,288675135
Expanded
uncertainty
(x10^-6)
mol.mol-1
0,288675135
0,288675135
0,577350269
0,25
0,1539
1
999997,5961
0,144337567
1,5448
0,577350269
1,692800551
0,288675135
3.0896
1,154700538
3,385601103
Specifications
(x10^-6)
mol.mol-1
0,5
0,5
1
0,5
2
Preparation Data
(vi) Specification of Balance(Model No., Readability, Resolution, etc.,)
Mettler Toledo PR 10003, Readability: 0,01 mg, Resolution: 0,01 mg
(vii) Weighing method (A-B-A, Substitution method, etc.,)
Substitution method
4_5_APMP_QM-S1 Draft B 0803211
Page 19 of 4
Distribution
rectangular
rectangular
rectangular
rectangular
normal
rectangular
(viii) Vacuum weighing
Parameter
Sensitivity
Weighing
difference
Mass pieces
Air density
Volume expansion
Density of mass
pieces (stainless
steel)
Mass (g)
Standard
uncertainty (mg)
-
Parameter
Sensitivity
Weighing
difference
Mass pieces
Air density
Volume expansion
Density of mass
pieces (stainless
steel)
Mass (g)
Standard
uncertainty (mg)
(ix)
Parameter
Sensitivity
Weigh difference
Mass pieces
Air density
Volume expansion
Density of the mass
pieces (stainless
steel)
Mass (g)
Standard
uncertainty (mg)
Estimate
1,000115013
Standard
uncertainty (u)
0,001185011
Sensitivity
coefficient (c)
0,9710000000
Uncertainty
contribution
(c x u)
0,001150645
0,9710000000
2,0000000000
1,027987952
-0,00025
0,0019962741
0,0000100000
0,000186407
1,33621E-06
1,000115013
0,999871502
-0,0005
1,0279879521
0,001996504
9,99872E-06
-9,32034E-08
1,37361E-06
8000
2,970597684
0,002
-3,21246E-08
-6,42492E-11
Estimate
0,99896607
Standard
uncertainty (u)
0,001935006
Sensitivity
coefficient (c)
0,0327400000
Uncertainty
contribution
(c x u)
6,33521E-05
0,0327400000
76,9999300000
1,026441597
-0,009624991
0,0021295177
0,0000254951
0,000216267
4,48372E-06
0,99896607
0,999871695
-0,019249983
1,0264415973
0,002127316
2,54918E-05
-4,16313E-06
4,60227E-06
8000
77,01287717
0,002
-1,23494E-06
-2,46987E-09
Standard
uncertainty
(u)
0,000650019
0,0020629199
0,0000524404
0,000200735
0,003
Sensitivity
coefficient (c)
0,0026166667
0,998253057
0,999870329
-0,015874979
1,0373645428
Uncertainty
contribution
(c x u)
1,70088E-06
0,002059316
5,24336E-05
-3,18666E-06
0,003112094
0,002
-2,44753E-06
-4,89506E-09
Type
A/B
Degrees
of
freedom
A
1
A
B
B
B
2
infinity
infinity
infinity
B
infinity
2,304368311
Weight after Nitrogen addition
Type
A/B
Degrees
of
freedom
A
1
A
B
B
B
2
infinity
infinity
infinity
B
infinity
2,128420739
Weight after helium addition
Estimate
0,998253057
0,0026166667
150,9998300000
1,037364543
0,015
8000
150,9984223
3,732113567
4_5_APMP_QM-S1 Draft B 0803211
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Type
A/B
A
A
B
B
B
B
Degrees of
freedom
1
2
infinity
infinity
infinity
infinity
_
Weights of nitrogen and helium
Component
N2
He
(x)
Component
O2
CH (Hydrocarbons)
N2
CO2
H 2O
CO
H2
Helium
Weight (g)
74,04227949
73,98554513
Combined Standard uncertainty (mg)
3,13692336
4,29637598
Concentration
Mole fraction
(x10^-6) mol.mol-1
0,875521347
0,224979165
125104,2312
0,221351144
0,438698955
0,22272729
0,062552087
874893,723
Standard uncertainty
(x10^-6) mol.mol-1
0,505121475
0,126331967
8,413384064
0,126314554
0,252561706
0,06960228
0,036114465
69,15138658
Coverage factor :2 ; level of confidence = 95.45% ; ν eff = ∞
Expanded uncertainty : 16.82676813 (x10^-6) mol.mol-1
4_5_APMP_QM-S1 Draft B 0803211
Page 21 of 4
Expanded uncertainty
(x10^-6) mol.mol-1
1,010242949
0,252663934
16,82676813
0,252629109
0,505123411
0,139204561
0,072228929
138,3027732