Fundamentals of Analytical Chemistry: 8th ed.
Chapter 5
Chapter 5
5-1
(a) Constant errors are the same magnitude regardless of sample size. Proportional
errors are proportional in size to sample size.
(b) Random error causes data to be scattered more or less symmetrically around a mean
value. Systematic error causes the mean of a data set to differ from the accepted value.
(c) The mean is the sum of the results in a set divided by the number of results. The
median is the central value for a set of data.
(d) The absolute error of a measurement is the difference between the measured value
and the true value. The relative error is the absolute error divided by the true value.
5-2
(1) Random temperature fluctuations causing random changes in the length of the metal
rule; (2) uncertainties from moving and positioning the rule twice; (3) personal judgment
in reading the rule; (4) vibrations in the table and/or rule; (5) uncertainty in locating the
rule perpendicular to the edge of the table.
5-3
(1) Instrumental errors
(2) Method errors
(3) Personal errors
5-4
(1) The analytical balance is miscalibrated; (2) after weighing an empty vial, fingerprints
are placed on the vial while adding sample to the vial; (3) a hygroscopic sample absorbs
water from the atmosphere while placing it in a weighing vial.
5-5
(1) Incorrect calibration of the pipet; (2) temperature different from calibration
temperature; (3) incorrect filling of the pipet (overshooting or undershooting the mark).
Fundamentals of Analytical Chemistry: 8th ed.
5-6
Chapter 5
Systematic method errors are detected by application of the method to the analysis of a
standard reference material having one or more analytes at exactly known concentrations.
5-7
Constant and proportional errors.
5-8
(a) (– 0.4/700) × 100% = – 0.06%
As in part (a)
(b) – 0.09%
(c) – 0.2%
(d) – 1%
5-9
(a) First determine how much gold is needed to achieve the desired relative error.
(– 0.4/– 0.2%) × 100% = 200 mg gold
Then determine how much ore is needed to yield the required amount of gold.
(200/1.2%) × 100% = 17,000 mg ore or 17 g ore
(b) 7 g ore
(c) 4 g ore
(d) 3 g ore
5-10
(a) (0.04/50.00) × 100% = 0.08%
As in part (a)
(b) 0.4%
(c) 0.16%
(d) 0.1%
Fundamentals of Analytical Chemistry: 8th ed.
5-11
(a) (– 0.4/40) × 100% = – 1.0%
As in part (a)
(b) – 0.23%
(c) – 0.10%
(d) – 0.07%
5-12
 0.0110 + 0.0104 + 0.0105 
mean = 
 = 0.01063 ≈ 0.0106
3


Arranging the numbers in increasing value the median is:
0.0104
0.0105
← median
0.0110
The deviations from the mean are:
0.0104 − 0.0106 = 0.0002
0.0105 − 0.0106 = 0.0001
0.0110 − 0.0106 = 0.0004
 0.0002 + 0.0001 + 0.0004 
mean deviation = 
 = 0.00023 ≈ 0.0002
3


Chapter 5
Fundamentals of Analytical Chemistry: 8th ed.
Chapter 5
(b) Using a spreadsheet
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
A
B
Data
24.53
24.68
24.73
24.77
24.81
C
Deviation
0.174
0.024
0.026
0.066
0.106
Mean =
Median =
24.704
24.73
0.0792
Spreadsheet Documentation
B8=AVERAGE(B2:B6)
B9=MEDIAN(B2:B6)
C2=ABS(B2-$B$8)
C8=AVERAGE(C2:C6)
Tabulating the results for (a) through (f) gives:
Mean
Median
Deviation from the Mean
Mean Deviation
(a)
0.0106
0.0105
0.0002, 0.0001, 0.0004
0.0002
(b)
24.70
24.73
0.17, 0.02, 0.03, 0.07, 0.11
0.08
(c)
190
189
2, 0, 4, 3
2
(d)
4.54×10-3
4.52×10-3
0.02×10-3, 0.07×10-3, 0.09×10-3,
0.05×10-3
0.06×10-3, 0.01×10-3, 0.04×10-3
(e)
39.59
39.64
0.24, 0.02, 0.34, 0.09
0.17
(f)
859
862
9, 3, 10, 10, 6
8