Page 116 - Modern Analytical Chemistry

1400-CH04 9/8/99 3:55 PM Page 99

Chapter 4 Evaluating Analytical Data 99

g = 0.118 (±0.002) 13. Obtain a sample of a metal from your instructor, and
R = 0.082056 (±0.000001) determine its density by one or both of the following
T = 298.2 (±0.1) methods:
P = 0.724 (±0.005)
Method A: Obtain the sample’s mass with a balance.
V = 0.250 (±0.005)
Calculate the sample’s volume using appropriate linear
(a) What is the compound’s formula weight and its estimated dimensions.
uncertainty? (b) To which variable(s) should you direct your Method B: Obtain the sample’s mass with a balance.
attention if you wish to improve the uncertainty in the Calculate the sample’s volume by measuring the amount of
compound’s molecular weight? water that it displaces. This can be done by adding water to a
2+
6. A standard solution of Mn was prepared by dissolving graduated cylinder, reading the volume, adding the object,
0.250 g of Mn in 10 mL of concentrated HNO 3 (measured and reading the new volume. The difference in volumes is
with a graduated cylinder). The resulting solution was equal to the object’s volume.
quantitatively transferred to a 100-mL volumetric flask
Determine the density at least five times. (a) Report the mean,
and diluted to volume with distilled water. A 10-mL
the standard deviation, and the 95% confidence interval for
aliquot of the solution was pipeted into a 500-mL volumetric
your results. (b) Find the accepted value for the density of
flask and diluted to volume. (a) Express the concentration
your metal, and determine the absolute and relative error for
of Mn in parts per million, and estimate uncertainty by a
your experimentally determined density. (c) Use the
propagation of uncertainty calculation. (b) Would the
propagation of uncertainty to determine the uncertainty for
uncertainty in the solution’s concentration be improved
your chosen method. Are the results of this calculation
by using a pipet to measure the HNO 3 , instead of a
consistent with your experimental results? If not, suggest
graduated cylinder?
some possible reasons for this disagreement.
7. Hydroscopic materials often are measured by the technique of
14. How many carbon atoms must a molecule have if the mean
weighing by difference. In this technique the material is
13
number of C atoms per molecule is 1.00? What percent of
placed in a sealed container and weighed. A portion of the
13
such molecules will have no atoms of C?
material is removed, and the container and the remaining
material are reweighed. The difference between the two 15. In Example 4.10 we determined the probability that a
13
masses gives the amount of material that was sampled. A molecule of cholesterol, C 27H 44 O, had no atoms of C.
solution of a hydroscopic material with a gram formula (a) Calculate the probability that a molecule of cholesterol,
13
weight of 121.34 (±0.01) was prepared in the following has one atom of C. (b) What is the probability that a
13
manner. A sample of the compound and its container has a molecule of cholesterol will have two or more atoms of C?
mass of 23.5811 g. A portion of the compound was 16. Berglund and Wichart investigated the quantitative
transferred to a 100-mL volumetric flask and diluted to determination of Cr in high-alloy steels by a potentiometric
6+ 21
volume. The mass of the compound and container after the titration of Cr . Before titrating the steel was dissolved in
6+
transfer is 22.1559 g. Calculate the molarity of the solution, acid and the chromium oxidized to Cr by peroxydisulfate.
and estimate its uncertainty by a propagation of uncertainty Following are their results (%w/w Cr) for the analysis of a
calculation. single reference steel.
8. Show by a propagation of uncertainty calculation that the
16.968 16.922 16.840 16.883
standard error of the mean for n determinations is given as
— 16.887 16.977 16.857 16.728
s/Ön.
Calculate the mean, the standard deviation, and the 95%
9. What is the smallest mass that can be measured on an
confidence interval about the mean. What does this
analytical balance with a tolerance of ±0.1 mg, such that the
confidence interval mean?
relative error is less than 0.1%?
17. Ketkar and co-workers developed a new analytical method
10. Which of the following is the best way to dispense 100.0 mL
22
for measuring trace levels of atmospheric gases. The
of a reagent: (a) use a 50-mL pipet twice; (b) use a 25-mL
analysis of a sample containing 40.0 parts per thousand (ppt)
pipet four times; or (c) use a 10-mL pipet ten times?
2-chloroethylsulfide yielded the following results
11. A solution can be diluted by a factor of 200 using readily
available pipets (1-mL to 100-mL) and volumetric flasks 43.3 34.8 31.9 37.8 34.4 31.9 42.1 33.6 35.3
(10-mL to 1000-mL) in either one, two, or three steps. (a)Determine whether there is a significant difference between
Limiting yourself to glassware listed in Table 4.2, determine the experimental mean and the expected value at a= 0.05.
the proper combination of glassware to accomplish each (b) As part of this study a reagent blank was analyzed 12
dilution, and rank them in order of their most probable times, giving a mean of 0.16 ppt and a standard deviation of
uncertainties. 1.20 ppt. What are the IUPAC detection limit, the limit of
12. Explain why changing all values in a data set by a constant identification, and limit of quantitation for this method
–
amount will change X but will have no effect on s. assuming a= 0.05?