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 = K0b1 + Kbiasb1;
Kb2 = K0b2 + Kbiasb2;
Kx1 = K0x1 + Kbiasx1;
Kx2 = K0x2 + Kbiasx2;
Kx3 = K0x3 + Kbiasx3;
Kx4 = K0x4 + Kbiasx4;
Ky1 = K0y1 + Kbiasy1;
Kz1 = K0z1 + Kbiasz1;
Kz2 = K0z2 + Kbiasz2;
Kz3 = K0z3 + Kbiasz3;
Kz4 = K0z4 + Kbiasz4;
|
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 |
| K0b1 | mass bias correction of Rb1 as determined at time 0 | |
| Kbiasb1 | other contributions to the mass bias of Rb1 | |
| K0b2 | mass bias correction of Rb2 as determined at time 0 | |
| Kbiasb2 | other contributions to the mass bias of Rb2 | |
| K0x1 | mass bias correction of Rx1 as determined at time 0 | |
| Kbiasx1 | other contributions to the mass bias of Rx1 | |
| K0x2 | mass bias correction of Rx2 as determined at time 0 | |
| Kbiasx2 | other contributions to the mass bias of Rx2 | |
| K0x3 | mass bias correction of Rx3 as determined at time 0 | |
| Kbiasx3 | other contributions to the mass bias of Rx3 | |
| K0x4 | mass bias correction of Rx4 as determined at time 0 | |
| Kbiasx4 | other contributions to the mass bias of Rx4 | |
| K0y1 | mass bias correction of Ry1 as determined at time 0 | |
| Kbiasy1 | other contributions to the mass bias of Ry1 | |
| K0z1 | mass bias correction of Rz1 as determined at time 0 | |
| Kbiasz1 | other contributions to the mass bias of Rz1 | |
| K0z2 | mass bias correction of Rz2 as determined at time 0 | |
| Kbiasz2 | other contributions to the mass bias of Rz2 | |
| K0z3 | mass bias correction of Rz3 as determined at time 0 | |
| Kbiasz3 | other contributions to the mass bias of Rz3 | |
| K0z4 | mass bias correction of Rz4 as determined at time 0 | |
| Kbiasz4 | 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 | |||||
| K0b1 | 0.998700 | 884·10-6 | normal | 0.062 | 55·10-6 µmol/g | 9.4 % |
| Kbiasb1 | 0.0 | 1.00·10-3 | normal | 0.062 | 62·10-6 µmol/g | 12.1 % |
| K0b2 | 0.998300 | 884·10-6 | normal | -0.070 | -62·10-6 µmol/g | 12.0 % |
| Kbiasb2 | 0.0 | 1.00·10-3 | normal | -0.070 | -70·10-6 µmol/g | 15.3 % |
| K0x1 | 0.999200 | 884·10-6 | normal | -0.034 | -30·10-6 µmol/g | 2.8 % |
| Kbiasx1 | 0.0 | 1.00·10-3 | normal | -0.034 | -34·10-6 µmol/g | 3.6 % |
| K0x2 | 1.0 | |||||
| Kbiasx2 | 0.0 | |||||
| K0x3 | 1.00040 | 1.24·10-3 | normal | 0.012 | 15·10-6 µmol/g | 0.7 % |
| Kbiasx3 | 0.0 | 1.00·10-3 | normal | 0.012 | 12·10-6 µmol/g | 0.4 % |
| K0x4 | 1.00100 | 2.12·10-3 | normal | 770·10-6 | 1.6·10-6 µmol/g | 0.0 % |
| Kbiasx4 | 0.0 | 1.00·10-3 | normal | 770·10-6 | 770·10-9 µmol/g | 0.0 % |
| K0y1 | 0.999900 | 884·10-6 | normal | -49·10-6 | -44·10-9 µmol/g | 0.0 % |
| Kbiasy1 | 0.0 | 1.00·10-3 | normal | -49·10-6 | -49·10-9 µmol/g | 0.0 % |
| K0z1 | 0.998900 | 884·10-6 | normal | 0.042 | 37·10-6 µmol/g | 4.3 % |
| Kbiasz1 | 0.0 | 1.00·10-3 | normal | 0.042 | 42·10-6 µmol/g | 5.5 % |
| K0z2 | 1.0 | |||||
| Kbiasz2 | 0.0 | |||||
| K0z3 | 0.99930 | 1.24·10-3 | normal | -0.012 | -15·10-6 µmol/g | 0.7 % |
| Kbiasz3 | 0.0 | 1.00·10-3 | normal | -0.012 | -12·10-6 µmol/g | 0.4 % |
| K0z4 | 1.00020 | 2.12·10-3 | normal | -750·10-6 | -1.6·10-6 µmol/g | 0.0 % |
| Kbiasz4 | 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 |