Gravimetric preparation and characterization of primary reference solutions of molybdenum and rhodium

Abstract

Gravimetrically prepared mono-elemental reference solutions having a well-known mass fraction of approximately 1 g/kg (or a mass concentration of 1 g/L) define the very basis of virtually all measurements in inorganic analysis. Serving as the starting materials of all standard/calibration solutions, they link virtually all measurements of inorganic analytes (regardless of the method applied) to the purity of the solid materials (high-purity metals or salts) they were prepared from. In case these solid materials are characterized comprehensively with respect to their purity, this link also establishes direct metrological traceability to The International System of Units (SI). This, in turn, ensures the comparability of all results on the highest level achievable. Several national metrology institutes (NMIs) and designated institutes (DIs) have been working for nearly two decades in close cooperation with commercial producers on making an increasing number of traceable reference solutions available. Besides the comprehensive characterization of the solid starting materials, dissolving them both loss-free and completely under strict gravimetric control is a challenging problem in the case of several elements like molybdenum and rhodium. Within the framework of the European Metrology Research Programme (EMRP), in the Joint Research Project (JRP) called SIB09 Primary standards for challenging elements, reference solutions of molybdenum and rhodium were prepared directly from the respective metals with a relative expanded uncertainty associated with the mass fraction of U _rel(w) < 0.05 %. To achieve this, a microwave-assisted digestion procedure for Rh and a hotplate digestion procedure for Mo were developed along with highly accurate and precise inductively coupled plasma optical emission spectrometry (ICP OES) and multicollector inductively coupled plasma mass spectrometry (MC-ICP-MS) methods required to assist with the preparation and as dissemination tools.

Appendix

Bracketing plus internal standard method

In the case of a linear relationship of the measured signal intensity I of an element E or isotope I and the amount of substance n of this element or isotope carried into the measurement device (e.g., ICP OES), a straight line connecting the two standard solutions (bracket) can be assumed. Its parameters slope tanα and y-intercept R ₀ can then be applied to calculate the mass fraction w _x of the element in the original sample. If all solutions were additionally doped with an internal standard Y, having a mass fraction of w _y, the straight line can be expressed via signal intensity and amount of substance ratios, respectively (Fig. 6).

Fig. 6

Relationship between signal intensity ratios R and amount of substance ratios r used to derive Eq. (10) for the calculation of the mass fraction of the analyte element in the original sample (x)

$$ \begin{array}{l}{r}_{\mathrm{bx}}=\frac{n_{\mathrm{bx}}\left(\mathrm{Y}\right)}{n_{\mathrm{bx}}\left(\mathrm{E}\right)}=\frac{M_{\mathrm{x}}\left(\mathrm{E}\right)\times {w}_{\mathrm{y}}\times {m}_{\mathrm{y}\mathrm{x}}}{M\left(\mathrm{Y}\right)\times {w}_{\mathrm{x}}\times {m}_{\mathrm{x}}}\\ {}{r}_1=\frac{n_1\left(\mathrm{Y}\right)}{n_1\left(\mathrm{E}\right)}=\frac{M_{\mathrm{z}}\left(\mathrm{E}\right)\times {w}_{\mathrm{y}}\times {m}_{\mathrm{y}1}}{M\left(\mathrm{Y}\right)\times {w}_{\mathrm{z}}\times {m}_{\mathrm{z}1}}\\ {}{r}_2=\frac{n_2\left(\mathrm{Y}\right)}{n_2\left(\mathrm{E}\right)}=\frac{M_{\mathrm{z}}\left(\mathrm{E}\right)\times {w}_{\mathrm{y}}\times {m}_{\mathrm{y}2}}{M\left(\mathrm{Y}\right)\times {w}_{\mathrm{z}}\times {m}_{\mathrm{z}2}}\\ {}{R}_{\mathrm{bx}}=\frac{I_{\mathrm{bx}}\left(\mathrm{Y}\right)}{I_{\mathrm{bx}}\left(\mathrm{E}\right)},\kern0.5em {R}_1=\frac{I_1\left(\mathrm{Y}\right)}{I_1\left(\mathrm{E}\right)},\kern0.5em {R}_2=\frac{I_2\left(\mathrm{Y}\right)}{I_2\left(\mathrm{E}\right)}\\ {} \tan \alpha =\frac{R_1-{R}_2}{r_1-{r}_2}\\ {}{R}_0={R}_2-\left({r}_2-0\right)\times \frac{R_1-{R}_2}{r_1-{r}_2}\\ {}{R}_{\mathrm{bx}}={R}_0+\left( \tan \alpha \right)\times {r}_{\mathrm{bx}}\\ {}{r}_{\mathrm{bx}}=\frac{R_{\mathrm{bx}}-{R}_0}{ \tan \alpha }=\frac{R_{\mathrm{x}}-{R}_2+{r}_2\times \frac{R_1-{R}_2}{r_1-{r}_2}}{\frac{R_1-{R}_2}{r_1-{r}_2}}\\ {}{r}_{\mathrm{bx}}=\frac{R_{\mathrm{bx}}\times \left({r}_1-{r}_2\right)-{R}_2\times \left({r}_1-{r}_2\right)+{r}_2\times \left({R}_1-{R}_2\right)}{R_1-{R}_2}\\ {}{r}_{\mathrm{bx}}=\frac{R_{\mathrm{bx}}\times {r}_1-{R}_{\mathrm{bx}}\times {r}_2-{R}_2\times {r}_1+{R}_2\times {r}_2+{r}_2\times {R}_1-{r}_2\times {R}_2}{R_1-{R}_2}\\ {}{r}_{\mathrm{bx}}=\frac{r_1\times \left({R}_{\mathrm{bx}}-{R}_2\right)+{r}_2\times \left({R}_1-{R}_{\mathrm{bx}}\right)}{R_1-{R}_2}\\ {}\frac{M_{\mathrm{x}}\left(\mathrm{E}\right)\times {w}_{\mathrm{y}}\times {m}_{\mathrm{y}\mathrm{x}}}{M\left(\mathrm{Y}\right)\times {w}_{\mathrm{x}}\times {m}_{\mathrm{x}}}=\frac{M_{\mathrm{z}}\left(\mathrm{E}\right)\times {w}_{\mathrm{y}}}{M\left(\mathrm{Y}\right)\times {w}_{\mathrm{z}}}\times \frac{\frac{m_{\mathrm{y}1}}{m_{\mathrm{z}1}}\times \left({R}_{\mathrm{bx}}-{R}_2\right)+\frac{m_{\mathrm{y}2}}{m_{\mathrm{z}2}}\times \left({R}_1-{R}_{\mathrm{bx}}\right)}{R_1-{R}_2}\\ {}{w}_{\mathrm{x}}={w}_{\mathrm{z}}\times \frac{M_{\mathrm{x}}\left(\mathrm{E}\right)}{M_{\mathrm{z}}\left(\mathrm{E}\right)}\times \frac{m_{\mathrm{y}\mathrm{x}}}{m_{\mathrm{x}}}\times \frac{R_1-{R}_2}{\frac{m_{\mathrm{y}1}}{m_{\mathrm{z}1}}\times \left({R}_{\mathrm{bx}}-{R}_2\right)+\frac{m_{\mathrm{y}2}}{m_{\mathrm{z}2}}\times \left({R}_1-{R}_{\mathrm{bx}}\right)}\end{array} $$

In case the isotopic composition of the element of interest is the same in the sample and in the standard, the ratio of the molar masses cancels from the last equation.

$$ {w}_{\mathrm{x}}={w}_{\mathrm{z}}\times \frac{m_{\mathrm{y}\mathrm{x}}}{m_{\mathrm{x}}}\times \frac{R_1-{R}_2}{\frac{m_{\mathrm{y}1}}{m_{\mathrm{z}1}}\times \left({R}_{\mathrm{bx}}-{R}_2\right)+\frac{m_{\mathrm{y}2}}{m_{\mathrm{z}2}}\times \left({R}_1-{R}_{\mathrm{bx}}\right)} $$

In case a mass spectrometer is used and the element of interest has at least two isotopes, the amount of substance fractions x of the isotope of the analyte element measured in sample x and in standard z have to be taken into account.

$$ {w}_{\mathrm{x}}={w}_{\mathrm{z}}\times \frac{x_{\mathrm{z}}\left(\mathrm{I}\right)}{x_{\mathrm{x}}\left(\mathrm{I}\right)}\times \frac{M_{\mathrm{x}}\left(\mathrm{E}\right)}{M_{\mathrm{z}}\left(\mathrm{E}\right)}\times \frac{m_{\mathrm{y}\mathrm{x}}}{m_{\mathrm{x}}}\times \frac{R_1-{R}_2}{\frac{m_{\mathrm{y}1}}{m_{\mathrm{z}1}}\times \left({R}_{\mathrm{bx}}-{R}_2\right)+\frac{m_{\mathrm{y}2}}{m_{\mathrm{z}2}}\times \left({R}_1-{R}_{\mathrm{bx}}\right)} $$

Quantities, indices, and other symbols

Table 3 summarizes all quantities, indices, and additional symbols used throughout the document.

Table 3 List of all symbols