15.5: Problems
- Page ID
- 138795
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)1. Make a list of good laboratory practices for the lab that accompanies this course, or another lab if this course does not have an associated laboratory. Explain the rationale for each item on your list.
2. Write directives outlining good measurement practices for (a) a buret, for (b) a pH meter, and for (c) a spectrophotometer.
3. A atomic absorption method for the analysis of lead in an industrial wastewater has a method detection limit of 10 ppb. The relationship between the absorbance and the concentration of lead, as determined from a calibration curve, is
\[A=0.349 \times(\text{ppm Pb}) \nonumber\]
Analysis of a sample in duplicate gives absorbance values of 0.554 and 0.516. Is the precision between these two duplicates acceptable based on the limits in Table 15.3.1?
4. The following data were obtained for the duplicate analysis of a 5.00 ppm NO3– standard.
| sample | \(X_1\) (ppm) | \(X_2\) (ppm) |
|---|---|---|
| 1 | 5.02 | 4.90 |
| 2 | 5.10 | 5.18 |
| 3 | 5.07 | 4.95 |
| 4 | 4.96 | 5.01 |
| 5 | 4.88 | 4.98 |
| 6 | 5.04 | 4.97 |
Calculate the standard deviation for these duplicate samples. If the maximum limit for the relative standard deviation is 1.5%, are these results acceptable?
5. Gonzalez and colleagues developed a voltammetric method for the determination of tert-butylhydroxyanisole (BHA) in chewing gum [Gonzalez, A.; Ruiz, M. A.; Yanez-Sedeno, P.; Pingarron, J. M. Anal. Chim. Acta 1994, 285, 63–71.]. Analysis of a commercial chewing gum gave a result of 0.20 mg/g. To evaluate the accuracy of this results, the authors performed five spike recoveries, adding an amount of BHA equivalent to 0.135 mg/g to each sample. The experimentally determined concentrations of BHA in these samples were reported as 0.342, 0.340, 0.340, 0.324, and 0.322 mg/g. Determine the percent recovery for each sample and the mean percent recovery.
6. A sample is analyzed following the protocol shown in Figure 15.4.1 using a method with a detection limit of 0.05 ppm. The relationship between the analytical signal, Smeas, and the concentration of the analyte in parts per million, CA, as determined from a calibration curve, is
\[S_{meas}=0.273 \times C_{A} \nonumber\]
Answer the following questions if the limit for a successful spike recovery is ±10%:
(a) A field blank is spiked with the analyte to a concentration of 2.00 ppm and returned to the lab. Analysis of the spiked field blank gives a signal of 0.573. Is the spike recovery for the field blank acceptable?
(b) The analysis of a spiked field blank is unacceptable. To determine the source of the problem, a spiked method blank is prepared by spiking distilled water with the analyte to a concentration of 2.00 ppm. Analysis of the spiked method blank gives a signal of 0.464. Is the source of the problem in the laboratory or in the field?
(c) The analysis for a spiked field sample, BSF, is unacceptable. To determine the source of the problem, the sample is spiked in the laboratory by adding sufficient analyte to increase the concentration by 2.00 ppm. Analysis of the sample before and after the spike gives signals of 0.456 for B and a signal of 1.03 for BSL. Considering this data, what is the most likely source of the systematic error?
7. The following data were obtained for the repetitive analysis of a stable standard [Standard Methods for the Analysis of Waters and Wastewaters, American Public Health Association: Washington, D. C., 18th Ed., 1992. The data is from Table 1030:I].
| sample | \(X_i\) (ppm) | sample | \(X_i\) (ppm) | sample | \(X_i\) (ppm) |
|---|---|---|---|---|---|
| 1 | 35.1 | 10 | 35.0 |
18 |
36.4 |
| 2 | 33.2 | 11 | 31.4 | 19 | 32.1 |
| 3 | 33.7 | 12 | 35.6 | 20 | 38.2 |
| 4 | 35.9 | 13 | 30.2 | 21 | 33.1 |
| 5 | 33.5 | 14 | 32.7 | 22 | 34.9 |
| 6 | 34.5 | 15 | 31.1 | 23 | 36.2 |
| 7 | 34.4 | 16 | 34.8 | 24 | 34.0 |
| 8 | 34.3 | 17 | 34.3 | 25 | 33.8 |
| 9 | 31.8 |
Construct a property control chart for these data and evaluate the state of statistical control.
8. The following data were obtained for the repetitive spike recoveries of field samples [Standard Methods for the Analysis of Waters and Wastewaters, American Public Health Association: Washington, D. C., 18th Ed., 1992. The data is from Table 1030:II].
| sample | % recovery | sample | % recovery | sample | % recovery |
|---|---|---|---|---|---|
| 1 | 94.6 | 10 | 104.6 |
18 |
104.6 |
| 2 | 93.1 | 11 | 123.8 | 19 | 91.5 |
| 3 | 100.0 | 12 | 93.8 | 20 | 83.1 |
| 4 | 122.3 | 13 | 80.0 | 21 | 100.8 |
| 5 | 120.8 | 14 | 99.2 | 22 | 123.1 |
| 6 | 93.1 | 15 | 101.5 | 23 | 96.2 |
| 7 | 117.7 | 16 | 74.6 | 24 | 96.9 |
| 8 | 96.2 | 17 | 108.5 | 25 | 102.3 |
| 9 | 73.8 |
Construct a property control chart for these data and evaluate the state of statistical control.
9. The following data were obtained for the duplicate analysis of a stable standard [Standard Methods for the Analysis of Waters and Wastewaters, American Public Health Association: Washington, D. C., 18th Ed., 1992. The data is from Table 1030:I].
| sample | \(X_1\) (ppm) | \(X_2\) (ppm) | sample | \(X_1\) (ppm) | \(X_2\) (ppm) |
|---|---|---|---|---|---|
| 1 | 50 | 46 | 14 | 36 | 36 |
| 2 | 37 | 36 | 15 | 47 | 45 |
| 3 | 22 | 19 | 16 | 16 | 20 |
| 4 | 17 | 20 | 17 | 18 | 21 |
| 5 | 32 | 34 | 18 | 26 | 22 |
| 6 | 46 | 46 | 19 | 35 | 36 |
| 7 | 26 | 28 | 20 | 36 | 25 |
| 8 | 26 | 30 | 21 | 49 | 51 |
| 9 | 61 | 58 | 22 | 33 | 32 |
| 10 | 44 | 45 | 23 | 40 | 38 |
| 11 | 40 | 44 | 24 | 16 | 13 |
| 12 | 36 | 35 | 25 | 39 | 42 |
| 13 | 29 | 31 |