Determination of lanthanides in international geochemical reference materials by reversed-phase high-performance liquid chromatography using error propagation theory to estimate total analysis uncertainties

The weighted least-squares (WLS) regression method was successfully applied to establish calibration curves with variable amounts of lanthanides ranging from 0.002 to 0.430 μg. These curves were employed for the analysis of 13 lanthanides (La-Nd, Sm-Tb, and Ho-Lu) in 12 international geochemical reference materials (IGRM). The separation of the lanthanide group was achieved in ∼15 min. Dysprosium could not be determined in IGRM because of its co-elution with Yttrium. A linear gradient program of α-HIBA eluent with a concentration ranging from 0.05 to 0.5 M (0.1 M OS, pH 3.8 with NH4OH, and a flow-rate of 1.0 ml/min) was employed. The detection was performed with a UV–vis system at 658 nm using a post-column reagent of Arsenazo III (0.5 ml/min). With this set of RP-HPLC conditions together with the use of both the ordinary least-squares (OLS) and the WLS regressions, we report the results of the measurements along with the total propagated uncertainties in individual concentration values. The uncertainties were obtained by combining standard errors in both regression parameters (slope and intercept) with those related to the chromatographic peak areas. The straight-line slopes and intercepts calculated by the WLS method provided not only considerably smaller errors than the conventional OLS method but also a much better estimation of the limits of detection. The concentrations calculated were compared with the “most probable” concentration values of these reference materials reported in the literature. Statistically significant agreement was consistently observed between the HPLC data and the literature values. The total uncertainties in estimated concentration values for the WLS were consistently smaller than the respective errors for the OLS.