Page 148 - Modern Analytical Chemistry

1400-CH05 9/8/99 3:59 PM Page 131

Chapter 5 Calibrations, Standardizations, and Blank Corrections 131

5H PROBLEMS

1. In calibrating a 10-mL pipet, a measured volume of water was 9. An appropriate standard additions calibration curve based on
transferred to a tared flask and weighed, yielding a mass of equation 5.8 plots S spike (V o + V s ) on the y-axis and C s V s on
9.9814 g. (a) Calculate, with and without correcting for the x-axis. Clearly explain why you cannot plot S spike on the y-
buoyancy, the volume of water delivered by the pipet. Assume axis and C s [V s /(V o + V s )] on the x-axis. Derive equations for
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that the density of water is 0.99707 g/cm and that the density the slope and y-intercept, and explain how the amount of
3
of the weights is 8.40 g/cm . (b) What are the absolute and analyte in a sample can be determined from the calibration
relative errors introduced by failing to account for the effect curve.
of buoyancy? Is this a significant source of determinate error 10. A standard sample was prepared containing 10.0 ppm of an
for the calibration of a pipet? Explain. analyte and 15.0 ppm of an internal standard. Analysis of the
2. Repeat the questions in problem 1 for the case when a sample gave signals for the analyte and internal standard of
mass of 0.2500 g is measured for a solid that has a density 0.155 and 0.233 (arbitrary units), respectively. Sufficient
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of 2.50 g/cm . internal standard was added to a sample to make it 15.0 ppm
3. Is the failure to correct for buoyancy a constant or in the internal standard. Analysis of the sample yielded signals
proportional source of determinate error? for the analyte and internal standard of 0.274 and 0.198,
respectively. Report the concentration of analyte in the
4. What is the minimum density of a substance necessary to sample.
keep the buoyancy correction to less than 0.01% when using
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brass calibration weights with a density of 8.40 g/cm ? 11. For each of the pairs of calibration curves in Figure 5.13
on page 132, select the calibration curve with the better
5. Describe how you would use a serial dilution to prepare 100 set of standards. Briefly explain the reasons for your
mL each of a series of standards with concentrations of selections. The scales for the x-axes and y-axes are the same
–2
–5
–3
–4
1.000 ´10 , 1.000 ´10 , 1.000 ´10 , and 1.000 ´10 M
for each pair.
from a 0.1000 M stock solution. Calculate the uncertainty for
each solution using a propagation of uncertainty, and 12. The following standardization data were provided for a series
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compare to the uncertainty if each solution was prepared by a of external standards of Cd that had been buffered to a pH
single dilution of the stock solution. Tolerances for different of 4.6. 14
types of volumetric glassware and digital pipets are found in
[Cd ] (nM) 15.4 30.4 44.9 59.0 72.7 86.0
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Tables 4.2 and 4.4. Assume that the uncertainty in the
S meas (nA) 4.8 11.4 18.2 26.6 32.3 37.7
molarity of the stock solution is ±0.0002.
6. Three replicate determinations of the signal for a standard
(a) Determine the standardization relationship by a linear
solution of an analyte at a concentration of 10.0 ppm give values
regression analysis, and report the confidence intervals for the
of 0.163, 0.157, and 0.161 (arbitrary units), respectively. The
slope and y-intercept. (b) Construct a plot of the residuals,
signal for a method blank was found to be 0.002. Calculate the
and comment on their significance.
concentration of analyte in a sample that gives a signal of 0.118.
At a pH of 3.7 the following data were recorded
7. A 10.00-g sample containing an analyte was transferred to a
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250-mL volumetric flask and diluted to volume. When a [Cd ] (nM) 15.4 30.4 44.9 59.0 72.7 86.0
10.00-mL aliquot of the resulting solution was diluted to 25.00 S meas (nA) 15.0 42.7 58.5 77.0 101 118
mL it was found to give a signal of 0.235 (arbitrary units). A
second 10.00-mL aliquot was spiked with 10.00 mL of a 1.00- (c) How much more or less sensitive is this method at the
ppm standard solution of the analyte and diluted to 25.00 mL. lower pH? (d) A single sample is buffered to a pH of 3.7 and
The signal for the spiked sample was found to be 0.502. analyzed for cadmium, yielding a signal of 66.3. Report the
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Calculate the weight percent of analyte in the original sample. concentration of Cd in the sample and its 95% confidence
8. A 50.00-mL sample containing an analyte gives a signal of interval.
11.5 (arbitrary units). A second 50-mL aliquot of the sample, 13. To determine the concentration of analyte in a sample, a
which is spiked with 1.00-mL of a 10.0-ppm standard solution standard additions was performed. A 5.00-mL portion
of the analyte, gives a signal of 23.1. What is the concentration of the sample was analyzed and then successive
of analyte in the original sample? 0.10-mL spikes of a 600.0-ppb standard of the analyte