Measurement of Concentration of Nitrate in Drinking Water

Abstract

For nitrate we have here below text extracts of an ISO method and also the requirements in the directive for nitrate.

Appendices

Exercise 1: Establishing Traceability in Analytical Chemistry

1. :

Specifying the analyte and measurand

Analyte	Nitrate
Measurand	Nitrate in drinking water, rain water, ground water and surface water
Units	mg L−1

2. :

Choosing a suitable measurement procedure with associated model equation

Measurement procedure	EN ISO 10304-1 Water quality – Water quality – Determination of dissolved anions by liquid chromatography of ions – Determination of bromide, chloride fluoride, nitrate, nitrite, phosphate and sulphate.
Type of calibration	Standard curve	Standard addition	Internal standard

Model equation

The concentration of nitrate, C, is calculated by:

$$C_{{}} = \frac{{A - B_{0} }}{{B_{1} }}$$

where A, B₁ and B₀ are measured area of the sample chromatographic peak, slope of the linear least square calibration curve and calculated blank. Slope of the linear least square calibration curve B₁ and calculated blank B₀ are calculated from equations:

$$B_{1} = \frac{{\sum\limits_{i = 1}^{n} {(C_{i} - \bar{C}) \cdot (A_{i} - \bar{A})} }}{{\sum\limits_{i = 1}^{n} {(C_{i} - \bar{C})^{2} } }}$$

$$B_{0} = \bar{A} - B_{1} \cdot \bar{C}_{{}}$$

$$\bar{A} = \frac{1}{n}\sum\limits_{i = 1}^{n} {A_{i} }$$

$$\bar{C}_{{}} = \frac{1}{n}\sum\limits_{i = 1}^{n} {C_{i} }$$

where C_i and A_i are concentration of reference solution on ith level (C₁, …, C_i, …, C_n) and areas of chromatographic peaks of ith reference solution (A₁, …, A_i, …, A_n), respectively.

3. :

List the input quantities according to their influence on the uncertainty of the result of the measurement (first the most important ones). At this point, your judgement should be based on your previous experience only

1	Uncertainty of concentration of reference solutions
2	Uncertainty of volumes
3	Uncertainty of weighing
4	–
5	–

4. :

List the reference standards needed and state the information regarding traceability of the reference value

For the analyte

1	Name/ChemicalFormula/producer:	NIST Standard Reference Material 3185 ‘Nitrate anion solution’
2	Name/ChemicalFormula/producer:	–

For the other input quantities

1	Quantity/Equipment/calibration: e.g. mass/balance/calibrated by NMI, U = xx (k = 2), see also data yellow sheet	Volume/calibrated glassware and pipettes/with established traceability
2	Quantity/Equipment/calibration:	Mass/calibrated balance/with established traceability
3	Quantity/Equipment/calibration:
4	Quantity/Equipment/calibration:

5. :

Estimating uncertainty associated with the measurement

Are all important parameters included in the model equation?	Yes	No
Other important parameters are:	Matrix effects

6. :

How would you prove traceability of your result?

1	Analysis of matrix CRM
2	Participation in a proficiency testing scheme (Aquacheck,…)
3	–

7. :

Any other comments, questions …

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Exercise 2: Single Laboratory Validation of Measurement Procedures

2.1 Part I: General Issues

1. :

Specify the measurement procedure, analyte, measurand and units

The measurement procedure	Measurement procedure is based on EN ISO 10304-1 Water quality – Determination of dissolved fluoride, chloride, nitrite, orthophosphate, bromide, nitrate and sulphate ions, using liquid chromatography of ions – Part I: Method for water with low contamination
Analyte	nitrate
The measurand	Nitrate in drinking water
Unit	mg L−1

2. :

Specify the scope

Matrix	Drinking water
Measuring range	>0.1 mg L−1

3. :

Requirement on the measurement procedure

Intended use of the results
Mark the customer’s requirements and give their values	Parameters to be validated		Value requested by the customer
		LOD	5 mg L−1
		LOQ
		Repeatability
		Within-lab reproducibility	5 mg L−1
		Trueness
		Measurement uncertainty	5 mg L−1
		Other-state

4. :

Origin of the Measurement Procedure

		Validation
New In-House Method		Full
Modified Validated Method		Partial
Official Standard Method		Confirmation/Verification

2.2 Part II: Parameters to be Validated

5. :

Selectivity/Interference/Recovery

Where yes, please give further information e.g. which CRM, reference method

	CRM/RM: analysis of available CRM or RM
	Further information: Promochem QCP 051 – Anions
	Spike of pure substance
	spiking of samples with pure substances and calculation of recovery
	Compare with a reference method
	.
	Selectivity, interferences
	.
	Test with different matrices
	.
	Other – please specify
	.

6. :

Measuring range

	Linearity
	Upper limit
	LOD
	LOQ

7. :

Spread – Precision

	Repeatability
	Reproducibility (within Lab)
	Reproducibility (between Lab)

8. :

Robustness

Variation of parameters

9. :

Quality Control

	Control charts
	Participation in PT schemes

10. :

Other parameters to be tested

	Working range and testing of homogeneity of variances
	R square
	Residual standard deviation
	Standard deviation of the analytical procedure
	Coefficient of variation of the analytical procedure
	Measurement uncertainty

2.3 Part III: Some Calculations and Conclusions

11. :

Calculation of parameters requested by the customer

Parameters requested to be validated		Calculations
	LOD	LOD = 0.5 mg L−1
		Calculations
		Abl (aver)	33,869
		Sbl	915.4294
		ALOD = Abl + 3Sbl	36615.29
		LOD	0.5 mg L−1
	LOQ
	Repeatability
	Within-lab reproducibilty	s = 0.06 mg L−1
		Calculations
		c (aver)		5.40
		s		0.06 mg L−1
	Trueness	R = 1.005 Significant test was used to show that R is not significantly different from 1
	Measurement uncertainty
	Other-please state

12. :

Does the analytical procedure fulfil the requirement(s) for the intended use?

Parameter	Value requested by the customer (the same as stated in question 3)	Value obtained during validation	The requirement is fulfilled Yes/No
LOD	5 mg L−1	0.5 mg L−1
LOQ	–	–
Repeatability	–	–
Within-lab reproducibility	5 mg L−1	0.06 mg L−1
Trueness	5 mg L−1	0 (R = 1)
Measurement uncertainty	–	–
Other	–	–

The analytical procedure is fit for the intended use:

Yes No

For Measurement Uncertainty and Traceability refer to the corresponding sheets.

Exercise 3: Building an Uncertainty Budget

1. :

Specify the measurand and units

Measurand	Nitrate in drinking water
Unit	mg L−1

2. :

Describe the measurement procedure and provide the associated model equation

Measurement procedure:

Concentration of nitrate in water is measured by liquid chromatography (calibration curve).

For the final result, recovery is taken into account.

Model equation:

$$C_{{NO_{3} }} = \frac{{A - B_{0} }}{{B_{1} \cdot R}}$$

where A, B₁, B₀ and R are measured area of the sample chromatographic peak, slope of the linear least square calibration curve, calculated blank and method recovery, respectively. Slope of the linear least square calibration curve B₁ and calculated blank B₀ are calculated from eqns:

$$B_{1} = \frac{{\sum\limits_{i = 1}^{n} {(C_{i} - \bar{C}) \cdot (A_{i} - \bar{A})} }}{{\sum\limits_{i = 1}^{n} {(C_{i} - \bar{C})^{2} } }}\quad \quad B_{0} = \bar{A} - B_{1} \cdot \bar{C}_{{}}$$

$$\bar{A} = \frac{1}{n}\sum\limits_{i = 1}^{n} {A_{i} } \quad \quad \bar{C} = \frac{1}{n}\sum\limits_{i = 1}^{n} {C_{i} }$$

$$R = \frac{{c_{observed} - c_{matrix} }}{{c_{spiked} }}$$

where C_i and A_i are concentration of reference solution on ith level (C₁, …, C_i, …, C_n) and areas of chromatographic peaks of ith reference solution (A₁, …, A_i, …, A_n), respectively.

3. :

Identify (all possible) sources of uncertainty

	Uncertainty of concentration of reference solutions
	Uncertainty of measurements of peak area
	Method bias
	Matrix effect
	Other:
	Other:

4. :

Evaluate values of each input quantity

Input quantity	Value	Unit	Remark
A	594,350	–
B0	−14,967	–
B1	112,837	–
R	1	–
$\bar{C}$	3.4770	mg L−1
$\bar{A}$	377,367	–

5. :

Evaluate the standard uncertainty of each input quantity

Input quantity	Standard uncertainty	Unit	Remark
A	4220	–
B0	3410	–
B1	831	–
R	0.01	–
$\bar{C}$	0.016	mg L−1
$\bar{A}$	146	–

$$\begin{aligned} \frac{{u\left( {B_{1} \times \bar{C}} \right)}}{{B_{1} \times \bar{C}}} & = \sqrt {\left( {\frac{{u(B_{1} )}}{{B_{1} }}} \right)^{2} + \left( {\frac{{u(\bar{C})}}{{\bar{C}}}} \right)^{2} } = \sqrt {\left( {\frac{831}{112837}} \right)^{2} + \left( {\frac{0.016}{3.4770}} \right)^{2} } \\ & = \sqrt {5.4237 \times 10^{ - 5} + 2.1175 \times 10^{ - 5} } = \sqrt {7.5412 \times 10^{ - 5} } \\ \end{aligned}$$

$$u(B_{1} \times \bar{C}) = 112837 \times 3.4770 \times \sqrt {7.5412 \times 10^{ - 5} } = 3407$$

$$u(B_{0} ) = \sqrt {u(\bar{A})^{2} + u(B_{1} \times \bar{C})^{2} } = \sqrt {146^{2} + 3407^{2} } = 3410$$

6. :

Calculate the value of the measurand, using the model equation

$$C_{{NO_{3} }} = \frac{{A - B_{0} }}{{B_{1} \cdot R}}\quad \quad {\text{C}}_{\text{NO3}} = 5.4\,{\text{mg}}\,{\text{L}}^{ - 1}$$

7. :

Calculate the combined standard uncertainty (u _c ) of the result & specify units

Using: Mathematical solution; Spreadsheet Approach; Commercial Software

Input quantity	Value	Standard uncertainty	Unit	Remark
A	594,350	4220	–	Included in the MU data sheet
B0	−14967	−130	–	To be calculated by the participants (for details see xls green sheet)
B1	112,837	831	–	Included in the MU data sheet
R	1	0.01	–	Included in the MU data sheet

$$\begin{aligned} \frac{u\left( c \right)}{c} & = \sqrt {\left( {\frac{{u(B_{1} )}}{{B_{1} }}} \right)^{2} + \left( {\frac{u(R)}{R}} \right)^{2} + \left( {\frac{{u(A - B_{0} )}}{{A - B_{0} }}} \right)^{2} } = \sqrt {\left( {\frac{831}{112837}} \right)^{2} + \left( {\frac{0.01}{1}} \right)^{2} + \left( {\frac{5425.54}{594350 + 14967}} \right)^{2} } \\ & = \sqrt {23.35235 \times 10^{ - 5} } \\ \end{aligned}$$

$$u(A - B_{0} ) = \sqrt {u(A)^{2} + u(B_{0} )^{2} } = \sqrt {4220^{2} + 3410^{2} } = 5425.54$$

$$u(c) = 0.015281475 \times 5.4 = 0.082\,{\text{mg}}\,{\text{L}}^{ - 1}$$

u(c) = 0.082 mg L⁻¹

8. :

Calculate expanded uncertainty (U _c ) & specify the coverage factor k and the units

${\mathbf{U}}_{{\mathbf{c}}} = {\mathbf{0}}.{\mathbf{2}}\,{\text{mg}}\,{\text{L}}^{ - 1} \,\,({\mathbf{k}} = {\mathbf{2}})$

9. :

Analyse the uncertainty contribution & specify the main three input quantities contributing the most to U _c

1	Method recovery
2	Calibration curve
3	Measurement of the peak area of the sample

10. :

Prepare your Uncertainty Budget Report

3.1 Addendum I: Measurement Uncertainty Calculation: Spreadsheet Approach (Excel)