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) / (SKziRzi) * (SKxiRxi)) - cblank; SKxiRxi = Kx1 * Rx1 + Kx2 * Rx2 + Kx3 * Rx3 + Kx4 * Rx4; SKziRzi = 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) / (SKziRzi); {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)
SKziRzi		sum of all mass bias corrected ratios of the primary assay standard
SKxiRxi		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 Uncertainty: =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 Uncertainty: =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 Uncertainty: =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 Uncertainty: =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 Uncertainty: =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 Uncertainty: =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 Uncertainty: =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 Uncertainty: =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 Uncertainty: =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 Uncertainty: =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 Uncertainty: =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 = R_certified/R_observed

When looking at the uncertainty contributions of R_certified and R_observed, it is clear that the contribution of R_certified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, R_observed, are used for the uncertainties on K_0.

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 Uncertainty: =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 = R_certified/R_observed

When looking at the uncertainty contributions of R_certified and R_observed, it is clear that the contribution of R_certified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, R_observed, are used for the uncertainties on K_0.

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 Uncertainty: =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 = R_certified/R_observed

When looking at the uncertainty contributions of R_certified and R_observed, it is clear that the contribution of R_certified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, R_observed, are used for the uncertainties on K_0.

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 Uncertainty: =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 = R_certified/R_observed

When looking at the uncertainty contributions of R_certified and R_observed, it is clear that the contribution of R_certified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, R_observed, are used for the uncertainties on K_0.

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 Uncertainty: =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 = R_certified/R_observed

When looking at the uncertainty contributions of R_certified and R_observed, it is clear that the contribution of R_certified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, R_observed, are used for the uncertainties on K_0.

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 Uncertainty: =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 = R_certified/R_observed

When looking at the uncertainty contributions of R_certified and R_observed, it is clear that the contribution of R_certified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, R_observed, are used for the uncertainties on K_0.

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 Uncertainty: =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 = R_certified/R_observed

When looking at the uncertainty contributions of R_certified and R_observed, it is clear that the contribution of R_certified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, R_observed, are used for the uncertainties on K_0.

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 Uncertainty: =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 = R_certified/R_observed

When looking at the uncertainty contributions of R_certified and R_observed, it is clear that the contribution of R_certified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, R_observed, are used for the uncertainties on K_0.

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 Uncertainty: =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 = R_certified/R_observed

When looking at the uncertainty contributions of R_certified and R_observed, it is clear that the contribution of R_certified can be neglected for this example. Henceforth, the uncertainties on the measured ratios, R_observed, are used for the uncertainties on K_0.

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.

Uncertainty Budgets:
c_x: amount content of the sample x

Quantity	Value	Standard Uncertainty	Distribution	Sensitivity Coefficient	Uncertainty Contribution	Index
cz	0.09260484 µmol/g	27.77·10-6 µmol/g
my1	1.1360000 g	200.0·10-6 g	normal	0.047	9.5·10-6 µmol/g	0.3 %
mx	1.0440000 g	200.0·10-6 g	normal	-0.051	-10·10-6 µmol/g	0.3 %
mz	1.1029000 g	200.0·10-6 g	normal	0.049	9.7·10-6 µmol/g	0.3 %
my2	1.0654000 g	200.0·10-6 g	normal	-0.050	-10·10-6 µmol/g	0.3 %
Ky1	0.999900	1.335·10-3
Ry1	640.00·10-6	14.14·10-6	normal	-0.077	-1.1·10-6 µmol/g	0.0 %
Kb1	0.998700	1.335·10-3
Rb1	0.2936000	258.1·10-6	normal	0.21	55·10-6 µmol/g	9.3 %
Kx1	0.999200	1.335·10-3
Rx1	2.140200	1.909·10-3	normal	-0.016	-31·10-6 µmol/g	2.9 %
Kb2	0.998300	1.335·10-3
Rb2	0.5050000	459.6·10-6	normal	-0.14	-64·10-6 µmol/g	12.7 %
Kz1	0.998900	1.335·10-3
Rz1	2.142900	1.909·10-3	normal	0.020	38·10-6 µmol/g	4.4 %
SKziRzi	4.113314	3.905·10-3
SKxiRxi	4.112123	3.902·10-3
cblank	450.0·10-9 µmol/g	200.0·10-9 µmol/g	normal	-1.0	-200·10-9 µmol/g	0.0 %
Kx2	1.0	0.0
Rx2	1.0
Kx3	1.000400	1.591·10-3
Rx3	0.914200	1.131·10-3	normal	0.013	15·10-6 µmol/g	0.7 %
Kx4	1.001000	2.345·10-3
Rx4	0.0590100	123.7·10-6	normal	0.013	1.6·10-6 µmol/g	0.0 %
Kz2	1.0	0.0
Rz2	1.0
Kz3	0.999300	1.591·10-3
Rz3	0.914700	1.131·10-3	normal	-0.013	-15·10-6 µmol/g	0.7 %
Kz4	1.000200	2.345·10-3
Rz4	0.0587000	123.7·10-6	normal	-0.013	-1.6·10-6 µmol/g	0.0 %
MPb Assay1	207.2103448 g/mol	665.1·10-6 g/mol
Mz1	207.976636000 g/mol	3.000·10-6 g/mol	normal	-130·10-6	-400·10-12 µmol/g	0.0 %
Mz2	205.974449000 g/mol	3.000·10-6 g/mol	normal	-63·10-6	-190·10-12 µmol/g	0.0 %
Mz3	206.975880000 g/mol	3.000·10-6 g/mol	normal	-58·10-6	-170·10-12 µmol/g	0.0 %
Mz4	203.973028000 g/mol	3.000·10-6 g/mol	normal	-3.7·10-6	-11·10-12 µmol/g	0.0 %
m2	1.0292000 g	200.0·10-6 g	normal	0.052	10·10-6 µmol/g	0.3 %
d2	99.93100 g	0.01000 g	normal	-540·10-6	-5.4·10-6 µmol/g	0.0 %
m1	0.36544000 g	50.00·10-6 g	normal	0.15	7.4·10-6 µmol/g	0.2 %
w	0.999990000 g/g	5.000·10-6 g/g	normal	0.054	270·10-9 µmol/g	0.0 %
d1	196.14000 g	0.03000 g	normal	-270·10-6	-8.2·10-6 µmol/g	0.2 %
kmol	1.0·106 µmol/mol
K0_b1	0.9987000	883.9·10-6	normal	0.062	55·10-6 µmol/g	9.4 %
Kbias_b1	0.0	1.000·10-3	normal	0.062	62·10-6 µmol/g	12.1 %
K0_b2	0.9983000	883.9·10-6	normal	-0.070	-62·10-6 µmol/g	12.0 %
Kbias_b2	0.0	1.000·10-3	normal	-0.070	-70·10-6 µmol/g	15.3 %
K0_x1	0.9992000	883.9·10-6	normal	-0.034	-30·10-6 µmol/g	2.8 %
Kbias_x1	0.0	1.000·10-3	normal	-0.034	-34·10-6 µmol/g	3.6 %
K0_x2	1.0
Kbias_x2	0.0
K0_x3	1.000400	1.237·10-3	normal	0.012	15·10-6 µmol/g	0.7 %
Kbias_x3	0.0	1.000·10-3	normal	0.012	12·10-6 µmol/g	0.4 %
K0_x4	1.001000	2.121·10-3	normal	770·10-6	1.6·10-6 µmol/g	0.0 %
Kbias_x4	0.0	1.000·10-3	normal	770·10-6	770·10-9 µmol/g	0.0 %
K0_y1	0.9999000	883.9·10-6	normal	-49·10-6	-44·10-9 µmol/g	0.0 %
Kbias_y1	0.0	1.000·10-3	normal	-49·10-6	-49·10-9 µmol/g	0.0 %
K0_z1	0.9989000	883.9·10-6	normal	0.042	37·10-6 µmol/g	4.3 %
Kbias_z1	0.0	1.000·10-3	normal	0.042	42·10-6 µmol/g	5.5 %
K0_z2	1.0
Kbias_z2	0.0
K0_z3	0.999300	1.237·10-3	normal	-0.012	-15·10-6 µmol/g	0.7 %
Kbias_z3	0.0	1.000·10-3	normal	-0.012	-12·10-6 µmol/g	0.4 %
K0_z4	1.000200	2.121·10-3	normal	-750·10-6	-1.6·10-6 µmol/g	0.0 %
Kbias_z4	0.0	1.000·10-3	normal	-750·10-6	-750·10-9 µmol/g	0.0 %
cx	0.0537374 µmol/g	179.9·10-6 µmol/g

Results:

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