-
![]()
Problems
3-1. Explain the difference between
*(a) random and systematic error.
(b) constant and proportional error.
*(c) absolute and relative error.
(d) mean and median.
*3-2. Suggest two sources of systematic error and two sources
of random error in measuring the length of a 3-m table
with a 1-m metal rule.
3-3. Name three types of systematic errors.
*3-4. Describe at least three systematic errors that might
occur while weighing a solid on an analytical balance.
*3-5. Describe at least three ways in which a systematic error
might occur while using a pipet to transfer a known
volume of liquid.
3-6. Describe how systematic method errors may be
detected.
*3-7. What kind of systematic errors are detected by varying
the sample size?
3-8. A method of analysis yields masses of gold that are low
by 0.4 mg. Calculate the percent
relative error caused
by this result if the mass of gold in the sample is
(a) 500 mg.
(b) 250 mg.
V(c) 125 mg.
(d) 60 mg.
3-9. The method described in Problem 3-8 is to be used for
the analysis of ores that assay about 1.2% gold. What
minimum sample mass should be taken if the relative
érror resulting from a 0.4-mg loss is not to exceed
*(a) -0.1%?
(b) -0.4%?
(c) -0.8%?
(d) - 1.1%?
3-10. The color change of a chemical indicator requires an
overtitration of 0.03 mL. Calculate the
error if the total volume of titrant is
percent
relative
(a) 50.00 mL.
(c) 25.0 mL.
3-11. A loss of 0.4 mg of Zn occurs in the course of an
percent relative
analysis for that element. Calculate the
error due to this loss if the mass of Zn in the sample is
*(b) 10.0 mL.
(d) 30.0 mL.
190
(c) 188
(d) 4.52 x 103
4.63 x 103
4.53 x 10 ³
√6
*(a) 30 mg.
(b) 100 mg.
*(c) 300 mg.
(d) 500 mg.
3-12. Find the mean and median of each of the following sets
of data. Determine the deviation from the mean for
each data point within the sets, and find the mean devi-
Vation for each set. Use a spreadsheet if it is convenient.
*(a) 0.0110
0.0105
(b) 24.53
0.0104
24.68
24.81
24.77
39.61
862
(f) 850
MA
3-13. Challenge Problem: Richards and W
the molar mass of lithium and colle
data.
24.73
Experiment
1
2
3
4
5
6
194
447 X 10
7
448 X 107
4.58 X 10
(a) Find the mean molar t
workers.
(b) Find the median molar ma
(c) Assuming that the cam
molar mass of lithium is
the absolute ertor and
of the mean value demi
Willard.
(d) Find in the chemical
ues for the molar mus
since 1910, and ag
a table or spreadshera
1817 given in the a
Richards and Willd. Com
mass versus year to la
of lithium has chang
Suggest possible
abruptly about 18 ant
de
(e) The incredibly deals
Richards and W
that major changes
will occur. Disc
calculation in pat
(f) What factors ha
since 1910?
(g) How would you
mass?
6See Chapter 2 of Applications of Microsoft Excel in Analytical Chemistry, 4th ed., for information about statistical
7T. W. Richards and H. H. Willard, J. Am. Chem. Soc., 1910, 32, 4, DOI: 10.1021/ja01919a002.
built-in statistical functions.
"Answers are provided at the end of the book for questions and problems marked with an asterisk
The I
of ₂
or inc
rce of
able vas
error c
often in
individu
ate resul
data in
rtainties.
dimensio
andom e
analysts
The result
