Page 244 - Modern Analytical Chemistry

1400-CH07 9/8/99 4:04 PM Page 227

Chapter 7 Obtaining and Preparing Samples for Analysis 227

2. A shipment of 100 barrels of an organic solvent is to be determine if the population is homogeneous or
evaluated by collecting and analyzing single samples from 10 heterogeneous?
of the barrels. A random number table is used to determine 7. Examine equation 7.6 for sampling a heterogeneous
the barrels to be sampled. From which barrels should the population. (a) Explain why the contribution of heterogeneity
samples be drawn if the first barrel is given by the twelfth to the overall sampling variance can be minimized by
entry in the random number table in Appendix 1E, with increasing the number of samples, but not the mass of the
subsequent barrels given by every third entry? individual samples. (b) Explain why the contribution of
3. The concentration of dissolved O 2 in a lake shows a daily cycle homogeneity to the overall sampling variance can be
due to the effect of photosynthesis and a yearly cycle due to minimized by increasing both the number of samples and the
seasonal changes in temperature. Suggest an appropriate mass of individual samples.
systematic sampling plan for monitoring the daily changes in 8. Show that equation 7.5 can be derived from equation 7.4.
dissolved O 2 . Suggest an appropriate systematic sampling plan Assume that the particles are spherical with a radius of r and a
for monitoring the yearly changes in dissolved O 2 . density of d.
4. The following data were collected during a preliminary study 9. The sampling constant for the radioisotope Na in a sample of
24
of the pH of an industrial wastewater stream homogenized human liver has been reported as approximately
25
35 g. (a) What is the expected relative standard deviation for
Time Time
(h) pH (h) pH sampling if 1.0-g samples are analyzed? (b) How many 1.0-g
samples need to be analyzed to obtain a maximum sampling
0.5 4.4 9.0 5.7 error of ±5% at the 95% confidence level?
1.0 4.8 9.5 5.5 10. Engels and Ingamells reported the following results for the
1.5 5.2 10.0 6.5 %w/w K 2 O in a mixture of amphibolite and orthoclase. 26
2.0 5.2 10.5 6.0
0.247 0.300 0.236 0.258 0.304 0.330
2.5 5.6 11.0 5.8
0.247 0.275 0.212 0.311 0.258 0.187
3.0 5.4 11.5 6.0
Each of the 12 samples had a nominal weight of 0.1 g.
3.5 5.4 12.0 5.6
Determine the approximate value for K s , and the mass of
4.0 4.4 12.5 5.6
sample needed to achieve a percent relative standard
4.5 4.8 13.0 5.4
deviation of 2%.
5.0 4.8 13.5 4.9
11. The following data have been reported for the determination
5.5 4.2 14.0 5.2
of KH 2 PO 4 in a mixture of KH 2 PO 4 and NaCl. 27
6.0 4.2 14.5 4.4
6.5 3.8 15.0 4.0 Nominal Mass Actual Mass %w/w KH 2 PO 4
7.0 4.0 15.5 4.5 (g) (g)
7.5 4.0 16.0 4.0
0.10 0.1039 0.085
8.0 3.9 16.5 5.0
0.1015 1.078
8.5 4.7 17.0 5.0
0.1012 0.413
Construct a graph of pH as a function of time, and suggest an 0.1010 1.248
appropriate sampling frequency for a long-term monitoring 0.1060 0.654
program. 0.0997 0.507
5. Suppose you have been asked to monitor the daily
fluctuations in atmospheric ozone levels in the downtown 0.25 0.2515 0.847
area of a city to determine the relationship between daily 0.2465 0.598
traffic patterns and ozone levels. (a) Describe the sampling
0.2770 0.431
plan you would choose (random, systematic, judgmental,
0.2460 0.842
systematic–judgmental, or stratified). (b) Would you choose
0.2485 0.964
to collect and analyze a series of grab samples or form a
0.2590 1.178
single composite sample? (c) How would your answers to
these questions change if the purpose of your work is to
determine if the average daily ozone level exceeds a threshold 0.50 0.5084 1.009
value? 0.4954 0.947
6. The best sampling plan for collecting samples depends 0.5286 0.618
on whether the population is homogeneous or 0.5232 0.744
heterogeneous. (a) Define homogeneous and heterogeneous. 0.4965 0.572
(b) If you collect and analyze a single sample, can you 0.4995 0.709