# Assessment of the determination of heavy metals in organic soil improvers by ICP–OES

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## Abstract

Directive 86/278/EEC sets maximum levels of heavy metals in sewage sludge used in agriculture to regulate the risk of using these organic soil improvers. The assessment of the compliance of soil improvers with this legislation should be supported on measurements with adequately low uncertainty. This work presents a strategy for assessing the performance of the determination of aqua regia extractable Cu, Zn and Cr in organic soil improvers and urban sewage sludges following EN 13650 standard. The measurement procedure validation involves checking the adequacy of the linear weighted regression model for ICP–OES calibration, the determination of the limit of quantification, the assessment of measurement repeatability, intermediate precision and trueness, and the evaluation of the measurement uncertainty using the differential approach. Routine tests quality control, including the estimated measurement uncertainty, is checked through the analysis of control standards, equivalent to calibrators, and reference materials from proficiency tests. Since the estimated relative expanded uncertainty is smaller than the defined target value (40 %), measurements are fit for assessing compliance of the mass fraction of heavy metals in organic soil improvers with the council directive.

### Keywords

Measurement uncertainty Differential approach Heavy metals Soil improvers ICP–OES### Abbreviations

- CC
Calibration control

- CRM
Certificated reference material

- ICP–OES
Inductively coupled plasma with optical emission spectrometry

- LoD
Limit of detection

- LoQ
Limit of quantification

- RM
Reference material (RM

*j*the*j*th analysed reference material)

### List of symbols

*A*Intercept of the linear unweighted regression line of the standard deviation of the mass concentration of analyte versus mass concentration of analyte (mg L

^{−1})*a*_{W}Intercept of the linear weighted regression line of the indication (instrumental signal) versus mass concentration of analyte

*B*Slope of the linear unweighted regression line of the standard deviation of the mass concentration of analyte versus mass concentration of analyte

*b*_{W}Slope of the linear weighted regression line of the indication versus mass concentration of analyte (L mg

^{−1})*f*_{d}Dilution factor of sample extract

*F*_{tab}Critical

*F*value for one-tailed test*i*Week of analysis of the RM (

*i*= 1, \(\ldots\),*l*)*j*Identification of analysed RM (

*j*= 1, \(\ldots\),*p*)*k*Coverage factor

*l*Number of replicated analyses of RM

*j*for estimating \( s'_{\text{Z}} \)*m*Mass of the analytical portion (g)

*n*Number of indications of the calibration curve

*p*Number of RM analysed for estimating \( s'_{\text{Z}} \)

*q*Indication of the calibration curve (

*q*= 1, \(\ldots\),*n*)*r*_{P}Pearson's linear correlation coefficient

- \( \overline{R} \)
Mean analyte recovery

*s*Standard deviation of measurement intermediate imprecision

*s*′relative standard deviation of measurement intermediate imprecision

- \( s'_{\text{d}} \)
Standard deviation of the relative difference of duplicate measurements

*s*_{LoD}Standard deviation of replicated measurements at the

*γ*_{LoD}*s*_{LoQ}Standard deviation of replicated measurements at the

*γ*_{LoQ}*s*_{q}Standard deviation of indication intermediate imprecision of calibrator indication

*q**s*_{r}standard deviation of measurement repeatability

- \( s'_{\text{r}} \)
Relative standard deviation of measurement repeatability

- \( s'_{{\text{r}}(m)} \)
Relative standard deviation of weighing repeatability

*s*_{(y/γ)W}Residual standard deviation of the linear weighted regression line

- \( s'_{\text{Z}} \)
Relative standard deviation of the intermediate imprecision of analyte mass fraction in soil improvers

- \( s'_{y} \)
relative standard deviation of indication intermediate imprecision

- \( u'_{\text{Co}} \)
Relative standard uncertainty associated with complex uncertainty components

- \( u'_{f{\text{d}}} \)
Relative standard uncertainty associated with the dilution factor

- \( u'_{\text{Int}} \)
Relative standard uncertainty associated with the interpolation of an indication in the calibration curve

- \( u'_{j+} \)
Maximum relative standard uncertainty of the reference values of RM

- \( u'_{m} \)
Relative standard uncertainty of analytical portion mass

- \( u_{{\overline{R} }} \)
Standard uncertainty of the mean analyte recovery

- \( u'_{\text{Rcal}} \)
Maximum relative standard uncertainty of the ratio of calibrators’ mass concentrations

- \( u'_{\text{Stk}} \)
Relative standard uncertainty of stock solution mass concentration

- \( u'_{w} \)
Combined relative standard uncertainty of

*w**U*_{w}Expanded uncertainty of

*w*- \( u'_{\gamma } \)
Relative standard uncertainty of sample extract mass concentration

*V*_{1}*, V*_{2}Volumes used to estimate

*f*_{d}(*f*_{d}=*V*_{1}/*V*_{2})*V*_{ext}Sample extract volume

*w*Mass fraction of sample (mg kg

^{−1})*W*_{0}Weighting factor of \( \bar{y}_{0} \)

- \( \overline{w}_{ij} \)
Mean of duplicate measurement results of RM

*j*obtained under repeatability conditions, in week*i*(independent digestion)- \( \overline{w}_{j} \)
Mean

*w*estimated from the analysis of the RM*j*- \( W_{q} \)
Weighting factor of calibrator indication

*q**w*_{RMj}Reference mass fraction of RM

*j*- \( \bar{y}_{0} \)
Interpolated sample mean indication

*y*_{q}Indication of calibrator measurement

*q*- \( \bar{y}_{\text{W}} \)
Weighted mean of

*y*_{q}values- γ
Mass concentration of the sample extract (mg L

^{−1})- \( \bar{\gamma }_{0} \)
Interpolated mean mass concentration of sample extract

*γ*_{1}Minimum mass concentration of ICP–OES calibrators excluding blank solutions

*γ*_{2}Maximum mass concentration of ICP–OES calibrators

*γ*_{LoD}Mass concentration of ICP–OES limit of detection

*γ*_{LoQ}Mass concentration of ICP–OES limit of quantification

*γ*_{q}Calibrator mass concentration of measurement

*q*(mg L^{−1})- \( \bar{\gamma }_{W} \)
Weighted mean of

*γ*_{q}values- \( \phi_{\text{Co}} \)
Fraction of the combined uncertainty attributed to complex uncertainty components (reported in percentage)

- \( \phi_{{\bar{R}}} \)
Fraction of the combined uncertainty attributed to the mean recovery (reported in percentage)

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