Determination of the amount fo lead in water using double isotope dilution and inductively coupled plasma mass spectrometry

This is the example A7 of the EURACHEM / CITAC Guide "Quantifying Uncertainty in Analytical Measurement", Second Edition.

The amount content of lead in water is measured using Isotope Dilution Mass Spectrometry (IDMS) and Inductively Coupled Plasma Mass Spectrometry (ICP-MS)

In this case a 'double' isotope dilution is applied. It uses a well characterised (ideally certified) material of natural isotopic composition as a primary assay standard. Two blends are then prepared: blend b, which is a blend between known masses of the sample and the enriched spike, and blend b', which is the blend between the enriched spike and the primary assay standard. The isotope ratios of the primary assay standard, the spike, the sample and the two blends are measured using ICP-MS. Together with the weighing data of the blends, the amount content of lead in the sample can be calculated.

Model Equation:

{equation for the double isotope dilution}

cx = (cz * my1 / mx *mz / my2 * (Ky1 * Ry1 - Kb1 * Rb1) / (Kb1 * Rb1 - Kx1 * Rx1) * (Kb2 * Rb2 - Kz1 * Rz1) / (Ky1 * Ry1 - Kb2 * Rb2) / (ΣKziRzi) * (ΣKxiRxi)) - cblank;

ΣKxiRxi = Kx1 * Rx1 + Kx2 * Rx2 + Kx3 * Rx3 + Kx4 * Rx4;

ΣKziRzi = Kz1 * Rz1 + Kz2 * Rz2 + Kz3 * Rz3 + Kz4 * Rz4;

{calculation of the molar mass of the lead of the primary assay standard 1}

MPb Assay1 = (Kz1 * Rz1 * Mz1 + Kz2 * Rz2 * Mz2 + Kz3 * Rz3 * Mz3 + Kz4 * Rz4 * Mz4) / (ΣKziRzi);

{concentration of the primary assay standard z which is used for the double IDMS}

cz =m2 / d2 * m1 * w / d1 / MPb Assay1 * kmol;

{calculation of the K-factors for the various isotope ratios measured}

Kb1 = K0_b1 + Kbias_b1;

Kb2 = K0_b2 + Kbias_b2;

Kx1 = K0_x1 + Kbias_x1;

Kx2 = K0_x2 + Kbias_x2;

Kx3 = K0_x3 + Kbias_x3;

Kx4 = K0_x4 + Kbias_x4;

Ky1 = K0_y1 + Kbias_y1;

Kz1 = K0_z1 + Kbias_z1;

Kz2 = K0_z2 + Kbias_z2;

Kz3 = K0_z3 + Kbias_z3;

Kz4 = K0_z4 + Kbias_z4;

List of Quantities:

Quantity Unit Definition
cx µmol/g amount content of the sample x
cz µmol/g amount content of the primary assay standard z
my1 g mass of enriched spike in blend b
mx g mass of sample in blend b
mz g mass of primary assay standard in blend b'
my2 g mass of enriched spike in blend b'
Ky1   mass bias correction of Ry1
Ry1   measured ratio of enriched isotope to reference isotope in the enriched spike, n(208Pb)/n(206Pb)
Kb1   mass bias correction of Rb1
Rb1   measured ratio of blend b, n(208Pb)/n(206Pb)
Kx1   mass bias correction of Rx1
Rx1   measured ratio of enriched isotope to reference isotope in the sample x, n(208Pb)/n(206Pb)
Kb2   mass bias correction of Rb2
Rb2   measured ratio of blend b', n(208Pb)/n(206Pb)
Kz1   mass bias correction of Rz1
Rz1   measured ratio of enriched isotope to reference isotope in the primary assay standard z, n(208Pb)/n(206Pb)
ΣKziRzi   sum of all mass bias corrected ratios of the primary assay standard
ΣKxiRxi   sum of all mass bias corrected ratios of the sample
cblank µmol/g observed amount content in procedure blank
Kx2   mass bias correction of Rx2
Rx2   measured ratio of sample, n(206Pb)/n(206Pb)
Kx3   mass bias correction of Rx3
Rx3   measured ratio of sample, n(207Pb)/n(206Pb)
Kx4   mass bias correction of Rx4
Rx4   measured ratio of sample, n(204Pb)/n(206Pb)
Kz2   mass bias correction of Rz2
Rz2   measured ratio of sample, n(206Pb)/n(206Pb)
Kz3   mass bias correction of Rz3
Rz3   measured ratio of sample, n(207Pb)/n(206Pb)
Kz4   mass bias correction of Rz4
Rz4   measured ratio of sample, n(204Pb)/n(206Pb)
MPb Assay1 g/mol molar mass of the primary assay standard
Mz1 g/mol nuclidic mass of 208Pb
Mz2 g/mol nuclidic mass of 206Pb
Mz3 g/mol nuclidic mass of 207Pb
Mz4 g/mol nuclidic mass of 204Pb
m2 g aliquot of the first dilution of the primary assay standard
d2 g total mass of the second dilution of the primary assay standard
m1 g mass of the lead piece for primary assay standard
w g/g purity of the metallic lead piece, expressed as mass fraction
d1 g total mass of first dilution of the primary assay standard
kmol µmol/mol conversion factor 106 µmol = 1 mol
K0_b1   mass bias correction of Rb1 as determined at time 0
Kbias_b1   other contributions to the mass bias of Rb1
K0_b2   mass bias correction of Rb2 as determined at time 0
Kbias_b2   other contributions to the mass bias of Rb2
K0_x1   mass bias correction of Rx1 as determined at time 0
Kbias_x1   other contributions to the mass bias of Rx1
K0_x2   mass bias correction of Rx2 as determined at time 0
Kbias_x2   other contributions to the mass bias of Rx2
K0_x3   mass bias correction of Rx3 as determined at time 0
Kbias_x3   other contributions to the mass bias of Rx3
K0_x4   mass bias correction of Rx4 as determined at time 0
Kbias_x4   other contributions to the mass bias of Rx4
K0_y1   mass bias correction of Ry1 as determined at time 0
Kbias_y1   other contributions to the mass bias of Ry1
K0_z1   mass bias correction of Rz1 as determined at time 0
Kbias_z1   other contributions to the mass bias of Rz1
K0_z2   mass bias correction of Rz2 as determined at time 0
Kbias_z2   other contributions to the mass bias of Rz2
K0_z3   mass bias correction of Rz3 as determined at time 0
Kbias_z3   other contributions to the mass bias of Rz3
K0_z4   mass bias correction of Rz4 as determined at time 0
Kbias_z4   other contributions to the mass bias of Rz4

my1: Type B normal distribution
Value: 1.1360 g
Expanded Uncertainty: 0.0002 g
Coverage Factor: 1
Weighings are performed by a dedicated mass metrology lab. The procedure applied was a bracketing technique using calibrated weights and a comparator. The bracketing technique was repeated at least six times for every sample mass determination. Buoyancy correction was applied. The uncertainties from the weighing certificates were treated as standard uncertainties, Type B.

mx: Type B normal distribution
Value: 1.0440 g
Expanded Uncertainty: 0.0002 g
Coverage Factor: 1
Weighings are performed by a dedicated mass metrology lab. The procedure applied was a bracketing technique using calibrated weights and a comparator. The bracketing technique was repeated at least six times for every sample mass determination. Buoyancy correction was applied. The uncertainties from the weighing certificates were treated as standard uncertainties, Type B.

mz: Type B normal distribution
Value: 1.1029 g
Expanded Uncertainty: 0.0002 g
Coverage Factor: 1
Weighings are performed by a dedicated mass metrology lab. The procedure applied was a bracketing technique using calibrated weights and a comparator. The bracketing technique was repeated at least six times for every sample mass determination. Buoyancy correction was applied. The uncertainties from the weighing certificates were treated as standard uncertainties, Type B.

my2: Type B normal distribution
Value: 1.0654 g
Expanded Uncertainty: 0.0002 g
Coverage Factor: 1
Weighings are performed by a dedicated mass metrology lab. The procedure applied was a bracketing technique using calibrated weights and a comparator. The bracketing technique was repeated at least six times for every sample mass determination. Buoyancy correction was applied. The uncertainties from the weighing certificates were treated as standard uncertainties, Type B.

Ry1: Type A summarized
Mean: 0.00064
Standard Deviation of the Mean: =0.00004/sqrt(8)
Degrees of Freedom: 7
Each ratio has been measured 8 times. The experimental uncertainty is therefore divided by sqrt(8).

Rb1: Type A summarized
Mean: 0.29360
Standard Deviation of the Mean: =0.00073/sqrt(8)
Degrees of Freedom: 7
Each ratio has been measured 8 times. The experimental uncertainty is therefore divided by sqrt(8).

Rx1: Type A summarized
Mean: 2.1402
Standard Deviation of the Mean: =0.0054/sqrt(8)
Degrees of Freedom: 7
Each ratio has been measured 8 times. The experimental uncertainty is therefore divided by sqrt(8).

Rb2: Type A summarized
Mean: 0.5050
Standard Deviation of the Mean: =0.0013/sqrt(8)
Degrees of Freedom: 7
Each ratio has been measured 8 times. The experimental uncertainty is therefore divided by sqrt(8).

Rz1: Type A summarized
Mean: 2.1429
Standard Deviation of the Mean: =0.0054/sqrt(8)
Degrees of Freedom: 7
Each ratio has been measured 8 times. The experimental uncertainty is therefore divided by sqrt(8).

cblank: Type A summarized
Mean: 4.5·10-7 µmol/g
Standard Deviation of the Mean: =4.0e-7/sqrt(4)
Degrees of Freedom: 3
The procedure blank was measured using external calibration. The procedure blank was measured four times. The experimental standard deviation is divided by sqrt(4) to obtain the standard uncertainty.

Rx2: Constant
Value: 1
This is the ratio of n(206Pb)/n(206Pb), which is by definition equal to 1.

Rx3: Type A summarized
Mean: 0.9142
Standard Deviation of the Mean: =0.0032/sqrt(8)
Degrees of Freedom: 7
Each ratio has been measured 8 times. The experimental uncertainty is therefore divided by sqrt(8).

Rx4: Type A summarized
Mean: 0.05901
Standard Deviation of the Mean: =0.00035/sqrt(8)
Degrees of Freedom: 7
Each ratio has been measured 8 times. The experimental uncertainty is therefore divided by sqrt(8).

Rz2: Constant
Value: 1
This is the ratio of n(206Pb)/n(206Pb), which is by definition equal to 1.

Rz3: Type A summarized
Mean: 0.9147
Standard Deviation of the Mean: =0.0032/sqrt(8)
Degrees of Freedom: 7
Each ratio has been measured 8 times. The experimental uncertainty is therefore divided by sqrt(8).

Rz4: Type A summarized
Mean: 0.05870
Standard Deviation of the Mean: =0.00035/sqrt(8)
Degrees of Freedom: 7
Each ratio has been measured 8 times. The experimental uncertainty is therefore divided by sqrt(8).

Mz1: Type B normal distribution
Value: 207.976636 g/mol
Expanded Uncertainty: 0.000003 g/mol
Coverage Factor: 1
The nuclidic masses and their respective uncertainties are taken from literature. G. Audi and A. H. Wapstra, Nuclear Physics, A565 (1993).

Mz2: Type B normal distribution
Value: 205.974449 g/mol
Expanded Uncertainty: 0.000003 g/mol
Coverage Factor: 1
The nuclidic masses and their respective uncertainties are taken from literature. G. Audi and A. H. Wapstra, Nuclear Physics, A565 (1993).

Mz3: Type B normal distribution
Value: 206.975880 g/mol
Expanded Uncertainty: 0.000003 g/mol
Coverage Factor: 1
The nuclidic masses and their respective uncertainties are taken from literature. G. Audi and A. H. Wapstra, Nuclear Physics, A565 (1993).

Mz4: Type B normal distribution
Value: 203.973028 g/mol
Expanded Uncertainty: 0.000003 g/mol
Coverage Factor: 1
The nuclidic masses and their respective uncertainties are taken from literature. G. Audi and A. H. Wapstra, Nuclear Physics, A565 (1993).

m2: Type B normal distribution
Value: 1.0292 g
Expanded Uncertainty: 0.0002 g
Coverage Factor: 1
Weighings are performed by a dedicated mass metrology lab. The procedure applied was a bracketing technique using calibrated weights and a comparator. The bracketing technique was repeated at least six times for every sample mass determination. Buoyancy correction was applied. The uncertainties from the weighing certificates were treated as standard uncertainties, Type B.

d2: Type B normal distribution
Value: 99.931 g
Expanded Uncertainty: 0.01 g
Coverage Factor: 1
Weighings are performed by a dedicated mass metrology lab. The procedure applied was a bracketing technique using calibrated weights and a comparator. The bracketing technique was repeated at least six times for every sample mass determination. Buoyancy correction was applied. The uncertainties from the weighing certificates were treated as standard uncertainties, Type B.

m1: Type B normal distribution
Value: 0.36544 g
Expanded Uncertainty: 0.00005 g
Coverage Factor: 1
Weighings are performed by a dedicated mass metrology lab. The procedure applied was a bracketing technique using calibrated weights and a comparator. The bracketing technique was repeated at least six times for every sample mass determination. Buoyancy correction was applied. The uncertainties from the weighing certificates were treated as standard uncertainties, Type B.

w: Type B normal distribution
Value: 0.99999 g/g
Expanded Uncertainty: 0.000005 g/g
Coverage Factor: 1
The purity of the metalic lead can be obtained through analysis or a supplier's certificate.

d1: Type B normal distribution
Value: 196.14 g
Expanded Uncertainty: 0.03 g
Coverage Factor: 1
Weighings are performed by a dedicated mass metrology lab. The procedure applied was a bracketing technique using calibrated weights and a comparator. The bracketing technique was repeated at least six times for every sample mass determination. Buoyancy correction was applied. The uncertainties from the weighing certificates were treated as standard uncertainties, Type B.

kmol: Constant
Value: 1·106 µmol/mol
K0_b1: Type A summarized
Mean: 0.9987
Standard Deviation of the Mean: =0.0025/sqrt(8)
Degrees of Freedom: 7
The K0's are measured using a certfied isotopic reference material, and they are calculated according to the following equation:

K0 = Rcertified/Robserved

When looking at the uncertainty contributions of Rcertified and Robserved, it is clear that the contribution of Rcertified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, Robserved, are used for the uncertainties on K0.

The original measurement data for the determination of K0 is not shown in this example.

Kbias_b1: Type B normal distribution
Value: 0
Expanded Uncertainty: 0.001
Coverage Factor: 1
This bias factor is introduced to account for possible deviations in the value of the mass discrimination factor (these could be variations over time, as well as other sources of bias, such as multiplier dead time correction, matrix effects etc.). The values of these biases are not known in this case, but they are assumed to be around 0, therefore a value of 0 is applied. An uncertainty is associated to this bias, which is estimated from experience. In this case a standard uncertainty of 0.001 is considered to be sufficient to cover all effects.

K0_b2: Type A summarized
Mean: 0.9983
Standard Deviation of the Mean: =0.0025/sqrt(8)
Degrees of Freedom: 7
The K0's are measured using a certfied isotopic reference material, and they are calculated according to the following equation:

K0 = Rcertified/Robserved

When looking at the uncertainty contributions of Rcertified and Robserved, it is clear that the contribution of Rcertified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, Robserved, are used for the uncertainties on K0.

The original measurement data for the determination of K0 is not shown in this example.

Kbias_b2: Type B normal distribution
Value: 0
Expanded Uncertainty: 0.001
Coverage Factor: 1
This bias factor is introduced to account for possible deviations in the value of the mass discrimination factor (these could be variations over time, as well as other sources of bias, such as multiplier dead time correction, matrix effects etc.). The values of these biases are not known in this case, but they are assumed to be around 0, therefore a value of 0 is applied. An uncertainty is associated to this bias, which is estimated from experience. In this case a standard uncertainty of 0.001 is considered to be sufficient to cover all effects.

K0_x1: Type A summarized
Mean: 0.9992
Standard Deviation of the Mean: =0.0025/sqrt(8)
Degrees of Freedom: 7
The K0's are measured using a certfied isotopic reference material, and they are calculated according to the following equation:

K0 = Rcertified/Robserved

When looking at the uncertainty contributions of Rcertified and Robserved, it is clear that the contribution of Rcertified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, Robserved, are used for the uncertainties on K0.

The original measurement data for the determination of K0 is not shown in this example.

Kbias_x1: Type B normal distribution
Value: 0
Expanded Uncertainty: 0.001
Coverage Factor: 1
This bias factor is introduced to account for possible deviations in the value of the mass discrimination factor (these could be variations over time, as well as other sources of bias, such as multiplier dead time correction, matrix effects etc.). The values of these biases are not known in this case, but they are assumed to be around 0, therefore a value of 0 is applied. An uncertainty is associated to this bias, which is estimated from experience. In this case a standard uncertainty of 0.001 is considered to be sufficient to cover all effects.

K0_x2: Constant
Value: 1
This mass bias correction refers to the ratio of n(206Pb)/n(206Pb), which is by definition equal to 1 and not measured. Therefore no mass bias correction is needed, the factor is equal to 1.

Kbias_x2: Constant
Value: 0
This mass bias correction refers to the ratio of n(206Pb)/n(206Pb), which is by definition equal to 1 and not measured. Therefore no mass bias correction is needed, this factor is equal to 0.

K0_x3: Type A summarized
Mean: 1.0004
Standard Deviation of the Mean: =0.0035/sqrt(8)
Degrees of Freedom: 7
The K0's are measured using a certfied isotopic reference material, and they are calculated according to the following equation:

K0 = Rcertified/Robserved

When looking at the uncertainty contributions of Rcertified and Robserved, it is clear that the contribution of Rcertified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, Robserved, are used for the uncertainties on K0.

The original measurement data for the determination of K0 is not shown in this example.

Kbias_x3: Type B normal distribution
Value: 0
Expanded Uncertainty: 0.001
Coverage Factor: 1
This bias factor is introduced to account for possible deviations in the value of the mass discrimination factor (these could be variations over time, as well as other sources of bias, such as multiplier dead time correction, matrix effects etc.). The values of these biases are not known in this case, but they are assumed to be around 0, therefore a value of 0 is applied. An uncertainty is associated to this bias, which is estimated from experience. In this case a standard uncertainty of 0.001 is considered to be sufficient to cover all effects.

K0_x4: Type A summarized
Mean: 1.001
Standard Deviation of the Mean: =0.006/sqrt(8)
Degrees of Freedom: 7
The K0's are measured using a certfied isotopic reference material, and they are calculated according to the following equation:

K0 = Rcertified/Robserved

When looking at the uncertainty contributions of Rcertified and Robserved, it is clear that the contribution of Rcertified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, Robserved, are used for the uncertainties on K0.

The original measurement data for the determination of K0 is not shown in this example.

Kbias_x4: Type B normal distribution
Value: 0
Expanded Uncertainty: 0.001
Coverage Factor: 1
This bias factor is introduced to account for possible deviations in the value of the mass discrimination factor (these could be variations over time, as well as other sources of bias, such as multiplier dead time correction, matrix effects etc.). The values of these biases are not known in this case, but they are assumed to be around 0, therefore a value of 0 is applied. An uncertainty is associated to this bias, which is estimated from experience. In this case a standard uncertainty of 0.001 is considered to be sufficient to cover all effects.

K0_y1: Type A summarized
Mean: 0.9999
Standard Deviation of the Mean: =0.0025/sqrt(8)
Degrees of Freedom: 7
The K0's are measured using a certfied isotopic reference material, and they are calculated according to the following equation:

K0 = Rcertified/Robserved

When looking at the uncertainty contributions of Rcertified and Robserved, it is clear that the contribution of Rcertified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, Robserved, are used for the uncertainties on K0.

The original measurement data for the determination of K0 is not shown in this example.

Kbias_y1: Type B normal distribution
Value: 0
Expanded Uncertainty: 0.001
Coverage Factor: 1
This bias factor is introduced to account for possible deviations in the value of the mass discrimination factor (these could be variations over time, as well as other sources of bias, such as multiplier dead time correction, matrix effects etc.). The values of these biases are not known in this case, but they are assumed to be around 0, therefore a value of 0 is applied. An uncertainty is associated to this bias, which is estimated from experience. In this case a standard uncertainty of 0.001 is considered to be sufficient to cover all effects.

K0_z1: Type A summarized
Mean: 0.9989
Standard Deviation of the Mean: =0.0025/sqrt(8)
Degrees of Freedom: 7
The K0's are measured using a certfied isotopic reference material, and they are calculated according to the following equation:

K0 = Rcertified/Robserved

When looking at the uncertainty contributions of Rcertified and Robserved, it is clear that the contribution of Rcertified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, Robserved, are used for the uncertainties on K0.

The original measurement data for the determination of K0 is not shown in this example.

Kbias_z1: Type B normal distribution
Value: 0
Expanded Uncertainty: 0.001
Coverage Factor: 1
This bias factor is introduced to account for possible deviations in the value of the mass discrimination factor (these could be variations over time, as well as other sources of bias, such as multiplier dead time correction, matrix effects etc.). The values of these biases are not known in this case, but they are assumed to be around 0, therefore a value of 0 is applied. An uncertainty is associated to this bias, which is estimated from experience. In this case a standard uncertainty of 0.001 is considered to be sufficient to cover all effects.

K0_z2: Constant
Value: 1
This mass bias correction refers to the ratio of n(206Pb)/n(206Pb), which is by definition equal to 1 and not measured. Therefore no mass bias correction is needed, the factor is equal to 1.

Kbias_z2: Constant
Value: 0
This mass bias correction refers to the ratio of n(206Pb)/n(206Pb), which is by definition equal to 1 and not measured. Therefore no mass bias correction is needed, this factor is equal to 0.

K0_z3: Type A summarized
Mean: 0.9993
Standard Deviation of the Mean: =0.0035/sqrt(8)
Degrees of Freedom: 7
The K0's are measured using a certfied isotopic reference material, and they are calculated according to the following equation:

K0 = Rcertified/Robserved

When looking at the uncertainty contributions of Rcertified and Robserved, it is clear that the contribution of Rcertified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, Robserved, are used for the uncertainties on K0.

The original measurement data for the determination of K0 is not shown in this example.

Kbias_z3: Type B normal distribution
Value: 0
Expanded Uncertainty: 0.001
Coverage Factor: 1
This bias factor is introduced to account for possible deviations in the value of the mass discrimination factor (these could be variations over time, as well as other sources of bias, such as multiplier dead time correction, matrix effects etc.). The values of these biases are not known in this case, but they are assumed to be around 0, therefore a value of 0 is applied. An uncertainty is associated to this bias, which is estimated from experience. In this case a standard uncertainty of 0.001 is considered to be sufficient to cover all effects.

K0_z4: Type A summarized
Mean: 1.0002
Standard Deviation of the Mean: =0.006/sqrt(8)
Degrees of Freedom: 7
The K0's are measured using a certfied isotopic reference material, and they are calculated according to the following equation:

K0 = Rcertified/Robserved

When looking at the uncertainty contributions of Rcertified and Robserved, it is clear that the contribution of Rcertified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, Robserved, are used for the uncertainties on K0.

The original measurement data for the determination of K0 is not shown in this example.

Kbias_z4: Type B normal distribution
Value: 0
Expanded Uncertainty: 0.001
Coverage Factor: 1
This bias factor is introduced to account for possible deviations in the value of the mass discrimination factor (these could be variations over time, as well as other sources of bias, such as multiplier dead time correction, matrix effects etc.). The values of these biases are not known in this case, but they are assumed to be around 0, therefore a value of 0 is applied. An uncertainty is associated to this bias, which is estimated from experience. In this case a standard uncertainty of 0.001 is considered to be sufficient to cover all effects.

Interim Results:

Quantity Value Standard
Uncertainty
cz 0.0926048 µmol/g 27.8·10-6 µmol/g
Ky1 0.99990 1.33·10-3
Kb1 0.99870 1.33·10-3
Kx1 0.99920 1.33·10-3
Kb2 0.99830 1.33·10-3
Kz1 0.99890 1.33·10-3
ΣKziRzi 4.11331 3.90·10-3
ΣKxiRxi 4.11212 3.90·10-3
Kx2 1.0 not valid!
Kx3 1.00040 1.59·10-3
Kx4 1.00100 2.35·10-3
Kz2 1.0 not valid!
Kz3 0.99930 1.59·10-3
Kz4 1.00020 2.35·10-3
MPb Assay1 207.210345 g/mol 665·10-6 g/mol

Uncertainty Budgets:

cx: amount content of the sample x
Quantity Value Standard
Uncertainty
Distribution Sensitivity
Coefficient
Uncertainty
Contribution
Index
my1 1.136000 g 200·10-6 g normal 0.047 9.5·10-6 µmol/g 0.3 %
mx 1.044000 g 200·10-6 g normal -0.051 -10·10-6 µmol/g 0.3 %
mz 1.102900 g 200·10-6 g normal 0.049 9.7·10-6 µmol/g 0.3 %
my2 1.065400 g 200·10-6 g normal -0.050 -10·10-6 µmol/g 0.3 %
Ry1 640.0·10-6 14.1·10-6 normal -0.077 -1.1·10-6 µmol/g 0.0 %
Rb1 0.293600 258·10-6 normal 0.21 55·10-6 µmol/g 9.3 %
Rx1 2.14020 1.91·10-3 normal -0.016 -31·10-6 µmol/g 2.9 %
Rb2 0.505000 460·10-6 normal -0.14 -64·10-6 µmol/g 12.7 %
Rz1 2.14290 1.91·10-3 normal 0.020 38·10-6 µmol/g 4.4 %
cblank 450·10-9 µmol/g 200·10-9 µmol/g normal -1.0 -200·10-9 µmol/g 0.0 %
Rx2 1.0          
Rx3 0.91420 1.13·10-3 normal 0.013 15·10-6 µmol/g 0.7 %
Rx4 0.059010 124·10-6 normal 0.013 1.6·10-6 µmol/g 0.0 %
Rz2 1.0          
Rz3 0.91470 1.13·10-3 normal -0.013 -15·10-6 µmol/g 0.7 %
Rz4 0.058700 124·10-6 normal -0.013 -1.6·10-6 µmol/g 0.0 %
Mz1 207.97663600 g/mol 3.00·10-6 g/mol normal -130·10-6 -400·10-12 µmol/g 0.0 %
Mz2 205.97444900 g/mol 3.00·10-6 g/mol normal -63·10-6 -190·10-12 µmol/g 0.0 %
Mz3 206.97588000 g/mol 3.00·10-6 g/mol normal -58·10-6 -170·10-12 µmol/g 0.0 %
Mz4 203.97302800 g/mol 3.00·10-6 g/mol normal -3.7·10-6 -11·10-12 µmol/g 0.0 %
m2 1.029200 g 200·10-6 g normal 0.052 10·10-6 µmol/g 0.3 %
d2 99.9310 g 0.0100 g normal -540·10-6 -5.4·10-6 µmol/g 0.0 %
m1 0.3654400 g 50.0·10-6 g normal 0.15 7.4·10-6 µmol/g 0.2 %
w 0.99999000 g/g 5.00·10-6 g/g normal 0.054 270·10-9 µmol/g 0.0 %
d1 196.1400 g 0.0300 g normal -270·10-6 -8.2·10-6 µmol/g 0.2 %
kmol 1.0·106 µmol/mol          
K0_b1 0.998700 884·10-6 normal 0.062 55·10-6 µmol/g 9.4 %
Kbias_b1 0.0 1.00·10-3 normal 0.062 62·10-6 µmol/g 12.1 %
K0_b2 0.998300 884·10-6 normal -0.070 -62·10-6 µmol/g 12.0 %
Kbias_b2 0.0 1.00·10-3 normal -0.070 -70·10-6 µmol/g 15.3 %
K0_x1 0.999200 884·10-6 normal -0.034 -30·10-6 µmol/g 2.8 %
Kbias_x1 0.0 1.00·10-3 normal -0.034 -34·10-6 µmol/g 3.6 %
K0_x2 1.0          
Kbias_x2 0.0          
K0_x3 1.00040 1.24·10-3 normal 0.012 15·10-6 µmol/g 0.7 %
Kbias_x3 0.0 1.00·10-3 normal 0.012 12·10-6 µmol/g 0.4 %
K0_x4 1.00100 2.12·10-3 normal 770·10-6 1.6·10-6 µmol/g 0.0 %
Kbias_x4 0.0 1.00·10-3 normal 770·10-6 770·10-9 µmol/g 0.0 %
K0_y1 0.999900 884·10-6 normal -49·10-6 -44·10-9 µmol/g 0.0 %
Kbias_y1 0.0 1.00·10-3 normal -49·10-6 -49·10-9 µmol/g 0.0 %
K0_z1 0.998900 884·10-6 normal 0.042 37·10-6 µmol/g 4.3 %
Kbias_z1 0.0 1.00·10-3 normal 0.042 42·10-6 µmol/g 5.5 %
K0_z2 1.0          
Kbias_z2 0.0          
K0_z3 0.99930 1.24·10-3 normal -0.012 -15·10-6 µmol/g 0.7 %
Kbias_z3 0.0 1.00·10-3 normal -0.012 -12·10-6 µmol/g 0.4 %
K0_z4 1.00020 2.12·10-3 normal -750·10-6 -1.6·10-6 µmol/g 0.0 %
Kbias_z4 0.0 1.00·10-3 normal -750·10-6 -750·10-9 µmol/g 0.0 %
cx 0.053737 µmol/g 180·10-6 µmol/g

Results:

Quantity Value Expanded
Uncertainty
Coverage
factor
Coverage
cx 0.05374 µmol/g 180·10-6 µmol/g 1.00 manual

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