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Chapter 5: Problem 8
What is the difference between a false positive and a false negative?
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An unknown sample of \(\mathrm{Cu}^{2+}\) gave an absorbance of \(0.262\) in an atomic absorption analysis. Then \(1.00 \mathrm{~mL}\) of solution containing \(100.0 \mathrm{ppm}(=\mu \mathrm{g} / \mathrm{mL}) \mathrm{Cu}^{2+}\) was mixed with \(95.0 \mathrm{~mL}\) of unknown, and the mixture was diluted to \(100.0 \mathrm{~mL}\) in a volumetric flask. The absorbance of the new solution was \(0.500\). (a) Denoting the initial, unknown concentration as \(\left[\mathrm{Cu}^{2+}\right]_{\mathrm{i}}\), write an expression for the final concentration, \(\left[\mathrm{Cu}^{2+}\right]_{\mathrm{f}}\), after dilution. Units of concentration are ppm. (b) In a similar manner, write the final concentration of added standard \(\mathrm{Cu}^{2+}\), designated as \([\mathrm{S}]_{\mathrm{f}}\). (c) Find \(\left[\mathrm{Cu}^{2+}\right]_{\mathrm{i}}\) in the unknown.
A solution containing \(3.47 \mathrm{mM} \mathrm{X}\) (analyte) and \(1.72 \mathrm{mM} \mathrm{S}\) (standard) gave peak areas of 3473 and 10222 , respectively, in a chromatographic analysis. Then \(1.00 \mathrm{~mL}\) of \(8.47 \mathrm{mM} \mathrm{S}\) was added to \(5.00 \mathrm{~mL}\) of unknown \(\mathrm{X}\), and the mixture was diluted to \(10.0 \mathrm{~mL}\). This solution gave peak areas of 5428 and 4431 for \(\mathrm{X}\) and \(\mathrm{S}\), respectively. (a) Calculate the response factor for the analyte. (b) Find the concentration of \(\mathrm{S}(\mathrm{mM})\) in the \(10.0 \mathrm{~mL}\) of mixed solution. (c) Find the concentration of \(\mathrm{X}(\mathrm{mM})\) in the \(10.0 \mathrm{~mL}\) of mixed solution. (d) Find the concentration of \(\mathrm{X}\) in the original unknown.
Verifying constant response for an internal standard. When we develop a method using an internal standard, it is important to verify that the response factor is constant over the calibration range. Data are shown below for a chromatographic analysis of naphthalene \(\left(\mathrm{C}_{10} \mathrm{H}_{8}\right)\), using deuterated naphthalene \(\left(\mathrm{C}_{10} \mathrm{D}_{8}\right.\) in which \(\mathrm{D}\) is the isotope \({ }^{2} \mathrm{H}\) ) as an internal standard. The two compounds emerge from the column at almost identical times and are measured by a mass spectrometer, which distinguishes them by molecular mass. From the definition of response factor in Equation 5-11, we can write $$ \frac{\text { Area of analyte signal }}{\text { Area of standard signal }}=F\left(\frac{\text { concentration of analyte }}{\text { concentration of standard }}\right) $$ Prepare a graph of peak area ratio \(\left(\mathrm{C}_{10} \mathrm{H}_{8} / \mathrm{C}_{10} \mathrm{D}_{8}\right)\) versus concentration ratio \(\left(\left[\mathrm{C}_{10} \mathrm{H}_{8}\right] /\left[\mathrm{C}_{10} \mathrm{D}_{8}\right]\right)\) and find the slope, which is the response factor. Evaluate \(F\) for each of the three samples and find the standard deviation of \(F\) to see how "constant" it is. $$ \begin{array}{ccccc} \text { Sample } & \begin{array}{c} \mathrm{C}_{10} \mathrm{H}_{8} \\ (\mathrm{ppm}) \end{array} & \begin{array}{c} \mathrm{C}_{10} \mathrm{D}_{8} \\ (\mathrm{ppm}) \end{array} & \begin{array}{c} \mathrm{C}_{10} \mathrm{H}_{8} \\ \text { peak area } \end{array} & \begin{array}{c} \mathrm{C}_{10} \mathrm{D}_{8} \\ \text { peak area } \end{array} \\ \hline 1 & 1.0 & 10.0 & 303 & 2992 \\ 2 & 5.0 & 10.0 & 3519 & 6141 \\ 3 & 10.0 & 10.0 & 3023 & 2819 \\ \hline \end{array} $$
Correcting for matrix effects with an internal standard. The appearance of pharmaceuticals in municipal wastewater (sewage) is an increasing problem that is likely to have adverse effects on our drinking water supply. Sewage is a complex matrix. When the drug carbamazepine was spiked into sewage at a concentration of \(5 \mathrm{ppb}\), chromatographic analysis gave an apparent spike recovery of \(154 \%{5}^{15}\) When deuterated carbamazepine was used as an internal standard for the analysis, the apparent recovery was \(98 \%\). Explain how the internal standard is used in this analysis and rationalize why it works so well to correct for matrix effects. Experimental Design
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