INSTRUCTOR'S
MANUAL
Instrumental
Measurements
2
General Comments
This experiment is critical for using instruments, recording data, and understanding uncertainty and
significant digits in a measurement. It is helpful for the entire class to do one procedure at a time;
that is, a short discussion/demonstration followed by lab work, and then regroup for a discussion of
the next procedure. That is, demonstrate to the class how to use the metric rulers in the lab manual,
have students take length measurements, and then regroup for the next explanation of mass
measurements.
Checking each student’s Data Table before leaving class is painstaking, but pays dividends.
This experiment is crucial for generating conscientious attitudes that persist throughout the course.
A. Length Measurement
It is helpful to make an overhead transparency of Figures 2.1 and 2.2 to demonstrate
length measurements using Metric Rulers A and B.
B. Mass Measurement
It is desirable to have a large number of balances available so as to avoid a bottleneck.
C. Mass and Volume of an Unknown Solid
The Instructor has the option to eliminate one or more mass readings according to the
precision of the balances available.
Suggested Unknowns: Recommended rectangular solids have an identifying number
with approximate dimensions 5.0 cm × 2.5 cm × 1.0 cm. The solids can be made from
aluminum, brass, copper, steel, or other materials.
D. Volume Measurement
This procedure is a good exercise for becoming proficient in using a graduated cylinder.
Check the uncertainty (± 0.5 mL) and the precision of the three measurements.
E. Temperature Measurement
Setting up a boiling waterbath and using the thermometer should be closely supervised.
To avoid breakage, the thermometer should not touch the bottom of the hot beaker.
9
EXPERIMENT 2
DATE
NAME
SECTION
SELECT THE SINGLE BEST ANSWER FOR EACH OF THE FOLLOWING.
1. Which of the following terms is a metric unit of length?
(a) centimeter (cm)
(b) gram (g)
(c) milliliter (mL)
(d) all of the above
(e) none of the above
2. Which of the following terms is a metric unit of mass?
(a) centimeter (cm)
(b) gram (g)
(c) milliliter (mL)
(d) all of the above
(e) none of the above
3. Which of the following terms is a metric unit of volume for a liquid?
(a) centimeter (cm)
(b) gram (g)
(c) milliliter (mL)
(d) all of the above
(e) none of the above
4. Which of the following terms is a metric unit of volume for a solid?
(a) centimeter (cm)
(b) cubic centimeter (cm3 )
(c) square centimeter (cm2 )
(d) all of the above
(e) none of the above
5. What is the term for a clear lens at the surface of the liquid inside a narrow piece of glassware
such as a graduated cylinder?
(a) crescent
(b) meniscus
(c) monocle
(d) parallax
(e) none of the above
6. What is the term for a decimal system of measurement that uses prefixes and basic units to
express length, mass, and volume?
(a) English system
(b) metric system
(c) troy system
(d) all of the above
(e) none of the above
10
7. What is the term for the degree of inexactness in an instrumental measurement?
(a) accuracy
(b) error
(c) precision
(d) uncertainty
(e) none of the above
8. What is the name of the laboratory equipment shown in the diagram?
(a) casserole and cover
(b) crucible and cover
(c) evaporating dish and lid
(d) ignition crucible
(e) mortar and pestle
9.
What is the name of the laboratory equipment shown in the diagram?
(a) beaker
(b) Erlenmeyer flask
(c) Florence flask
(d) volumetric flask
(e) wash bottle
10. What is the name of the laboratory equipment shown in the diagram?
(a) calibrated cylinder
(b) Erlenmeyer flask
(c) Florence flask
(d) graduated cylinder
(e) Pyrex cylinder
11
11. What is the name of the laboratory equipment shown in the diagram?
(a) casserole
(b) crucible
(c) evaporating dish
(d) glass disk
(e) watchglass
12. What is the name of the laboratory equipment shown in the diagram?
(a) casserole
(b) crucible
(c) evaporating dish
(d) mortar
(e) watchglass
13. What is the physical quantity expressed by the following measurement: 10.0 cm?
(a) length
(b) mass
(c) temperature
(d) time
(e) volume
14. What is the physical quantity expressed by the following measurement: 10.0 g?
(a) length
(b) mass
(c) temperature
(d) time
(e) volume
15. What is the physical quantity expressed by the following measurement: 10.0 mL?
(a) length
(b) mass
(c) temperature
(d) time
(e) volume
16. What is the physical quantity expressed by the following measurement: 10.0 s?
(a) length
(b) mass
(c) temperature
(d) time
(e) volume
17. What is the physical quantity expressed by the following measurement: 10.0 °C?
(a) length
(b) mass
(c) temperature
(d) time
(e) volume
12
18. What is the uncertainty of a measurement using a metric ruler with 1 cm divisions?
(a) ± 1 cm
(b) ± 0.1 cm
(c) ± 0.5 cm
(d) ± 0.01 cm
(e) ± 0.05 cm
19. What is the uncertainty of a measurement using a metric ruler with 1 mm divisions?
(a) ± 1 cm
(b) ± 0.1 cm
(c) ± 0.5 cm
(d) ± 0.01 cm
(e) ± 0.05 cm
20. What is the uncertainty of a measurement using a decigram balance?
(a) ± 1 g
(b) ± 0.1 g
(c) ± 0.01 g
(d) ± 0.001 g
(e) ± 0.0001 g
21. What is the uncertainty of a measurement using a centigram balance?
(a) ± 1 g
(b) ± 0.1 g
(c) ± 0.01 g
(d) ± 0.001 g
(e) ± 0.0001 g
22. What is the uncertainty of a measurement using a milligram balance?
(a) ± 1 g
(b) ± 0.1 g
(c) ± 0.01 g
(d) ± 0.001 g
(e) ± 0.0001 g
23. What is the uncertainty of a measurement using a 100-mL graduated cylinder?
(a) ± 1 mL
(b) ± 0.5 mL
(c) ± 0.1 mL
(d) ± 0.05 mL
(e) ± 0.01 mL
24. What is the uncertainty of a measurement using a 110 °C thermometer?
(a) ± 1 °C
(b) ± 0.5 °C
(c) ± 0.1 °C
(d) ± 0.05 °C
(e) ± 0.01 °C
13
25. What is the length of the object shown on the metric ruler?
(a) 0.75 cm
(b) 0.8 cm
(c) 0.80 cm
(d) 7.5 cm
1
2
3
4
5
(e) 7.50 cm
6
7
8
9
10
26. What is the length of the object shown on the metric ruler?
(a) 6 cm
(b) 6.0 cm
(c) 6.6 cm
(d) 6.60 cm
(e) 6.55 cm
1
2
3
4
5
6
7
8
9
10
27. What is the length of the object shown on the metric ruler?
(a) 6 cm
(b) 6.0 cm
(c) 6.5 cm
(d) 6.00 cm
(e) 6.05 cm
1
2
3
4
5
6
7
8
9
10
28. What is the length of the object shown on the metric ruler?
(a) 3 cm
(b) 3.1 cm
(c) 3.05 cm
(d) 31 cm
(e) 30.1 cm
1
2
3
4
5
29. What is the length of the object shown on the metric ruler?
(a) 7.0 cm
(b) 7.5 cm
(c) 7.55 cm
(d) 7.6 cm
1
2
3
4
5
(e) 7.65 cm
14
6
6
7
7
8
8
9
9
10
10
30. What is the length of the object shown on the metric ruler?
(a) 0.5 cm
(b) 0.05 cm
(c) 0.55 cm
(d) 5.5 cm
(e) 5.50 cm
1
2
3
4
5
31. What is the volume of liquid shown in the graduated cylinder?
(a) 10.5 mL
(b) 15 mL
(c) 15.5 mL
(d) 24.5 mL
(e) 25.0 mL
6
7
8
9
10
20
10
32. What is the volume of liquid shown in the graduated cylinder?
(a) 80 mL
(b) 80.5 mL
(c) 81 mL
(d) 81.0 mL
(e) 81.5 mL
90
80
33. What is the temperature shown by the thermometer?
(a) 0.5 °C
(b) 0.50 °C
(c) 5.0 °C
(d) 5.5 °C
(e) 5.50 °C
10
0
15
34. What is the temperature shown by the thermometer?
(a) 23 °C
(b) 20.3 °C
(c) 23.0 °C
(d) 23.5 °C
(e) 23.50 °C
30
20
35. What is the volume of a rectangular solid that measures 3.0 cm by 2.5 cm by 1.2 cm?
(a) 7.5 cm3
(b) 7.50 cm3
(c) 9 cm3
(d) 9.0 cm3
(e) 9.00 cm3
36. What is the volume of a rectangular solid that measures 3.8 cm by 2.4 cm by 1.0 cm?
(a) 9 cm3
(b) 9.0 cm3
(c) 9.1 cm3
(d) 9.2 cm3
(e) 9.12 cm3
37. What is the volume of a rectangular solid that measures 5.00 cm by 2.25 cm by 1.10 cm?
(a) 12 cm3
(b) 12.0 cm3
(c) 12.375 cm3
(d) 12.38 cm3
(e) 12.4 cm3
38. What is the volume of a rectangular solid that measures 5.05 cm by 2.50 cm by 1.20 cm?
(a) 15 cm3
(b) 15.0 cm3
(c) 15.1 cm3
(d) 15.2 cm3
(e) 15.15 cm3
39. Which of the following safety precautions is advisable?
(a) light a laboratory burner carefully
(b) operate an electronic balance carefully
(c) handle the boiling waterbath carefully
(d) use a thermometer carefully
(e) all of the above
16
EXPERIMENT 2
DATE
NAME
SAMPLE DATA
SECTION
DATA TABLE
A. Length Measurement
length of a 13 × 100 mm test tube
METRIC RULER A
± 0.1 cm
10.0
cm
METRIC RULER B
± 0.05 cm
10.05
cm
METRIC RULER A
± 0.1 cm
9.9
cm
METRIC RULER B
± 0.05 cm
9.95
cm
METRIC RULER A
± 0.1 cm
8.2
cm
METRIC RULER B
± 0.05 cm
8.20
cm
diameter of a watchglass
diameter of an evaporating dish
B. Mass Measurement
mass of an evaporating dish
decigram balance
± 0.1 g
43.5
g
centigram balance
± 0.01 g
43.55
g
milligram balance
± 0.001 g
43.546
g
decigram balance
± 0.1 g
29.2
g
centigram balance
± 0.01 g
29.20
g
milligram balance
± 0.001 g
29.205
g
decigram balance
± 0.1 g
77.6
g
centigram balance
± 0.01 g
77.56
g
milligram balance
± 0.001 g
77.546
g
mass of a crucible and cover
mass of a 125-mL Erlenmeyer flask
17
C. Mass and Volume of an Unknown Solid
UNKNOWN #
mass of unknown solid
decigram balance
± 0.1 g
130.1
g
centigram balance
± 0.01 g
130.95
g
milligram balance
± 0.001 g
130.961
g
volume of unknown solid (METRIC RULER A)
length of solid
± 0.1 cm
5.1
cm
width of solid
± 0.1 cm
2.5
cm
thickness of solid
± 0.1 cm
1.2
cm
Show the calculation for the volume of the rectangular solid (see Example Exercise 2.3).
(5.1 cm) (2.5 cm) (1.2 cm) = 15.3 = 15 cm3
15
cm3
volume of unknown solid (METRIC RULER B)
length of solid
± 0.05 cm
5.15
cm
width of solid
± 0.05 cm
2.50
cm
thickness of solid
± 0.05 cm
1.25
cm
Show the calculation for the volume of the rectangular solid (see Example Exercise 2.4).
(5.15 cm) (2.50 cm) (1.25 cm) = 16.09 = 16.1 cm3
16.1
cm3
D. Volume Measurement
volume of water in a graduated cylinder
± 0.5 mL
100.0
mL
volume minus one test tube of water
± 0.5 mL
89.5
mL
volume minus two test tubes of water
± 0.5 mL
78.5
mL
room temperature
± 0.5 °C
22.0
°C
melting point temperature of ice
± 0.5 °C
0.5
°C
boiling point temperature of water
± 0.5 °C
99.5
°C
E. Temperature Measurement
18
EXPERIMENT 2
NAME
DATE
ANSWER KEY
SECTION
POSTLABORATORY ASSIGNMENT
1. State the basic unit in the metric system for each of the following.
(a) length
(c) volume
meter (m)
liter (L)
(b)
mass
(d)
temperature
gram (g)
d e g r ee Celsius (°C)
2. State a common laboratory instrument for measuring each of the following.
(a) diameter of beaker
(c) volume of water
(b)
mass of a sample
_ balance__
graduated cylinder (d)
temperature of air
thermometer_
metric ruler _
3. State the metric unit associated with each of the following instruments.
(a) metric ruler
centimeter (cm)
(c) graduated cylinder milliliter (mL)
(b)
balance
(d)
thermometer
gram (g)
d e g r ee Celsius (°C)
4. Select the measurement that is consistent with the uncertainty of each instrument.
(a) METRIC RULER A: 5 cm, 5.0 cm, 5.00 cm
_ 5 .0 cm _
(b) METRIC RULER B: 5 cm, 5.0 cm, 5.00 cm
_ 5 .00 cm _
(c) decigram balance: 5.0 g, 5.00 g, 5.000 g
_ 5 .0 g
(d) centigram balance: 5.0 g, 5.00 g, 5.000 g
_ 5 .00 g _
(e) milligram balance: 5.0 g, 5.00 g, 5.000 g
_ 5 .000 g _
(f) graduated cylinder: 5 mL, 5.0 mL, 5.00 mL
_ 5 .0 mL _
(g) Celsius thermometer: 5 °C, 5.0 °C, 5.00 °C
_ 5 .0 °C
_
_
5. State the uncertainty (for example, ± 0.5 cm) in each of the following measurements.
(a) 25.00 cm
± 0.05 cm
(b)
25.000 g
± 0.001 g _
(c) 25.0 mL
± 0.5 mL
(d)
25.0 °C
± 0.5 °C _
19
6. State the number of significant digits in each of the following measurements.
(a) 5.00 cm
____3 _____
(b)
0.50 cm
____2 _____
(c) 0.500 g
____3 _____
(d)
0.005 g
____1 _____
(e) 50.0 mL
____3 _____
(f)
5.5 mL
____2 _____
(g) 50.5 °C
____3 _____
(h)
–0.5 °C
____1 _____
7. Perform the indicated math operation and round off the answer to the proper significant digits.
(a)
+
50.511 g
10.25 g
(b)
60.761 g rounds off to 60.76 g
97.5 g
– 95.826 g
1.674 g rounds off to 1.7 g
8. Perform the indicated math operation and round off the answer to the proper significant digits.
(a)
(5.15 cm) (2.25 cm) (1.0 cm)
= 11.5875 rounds off to 12 cm 2
(b)
15.15 cm3
12.0 cm2
= 1.2625 rounds off to 1.26 cm
9. Explain why you round off the numbers in a calculator display after addition, subtraction,
multiplication, or division of measurements.
Since some of the numbers in a calculator display may be nonsignificant digits,
the answer in the display must be rounded off.
10. (optional) A platinum cylinder has a mass of 1.000 kg, a diameter of 3.90 cm, and a height of
3.90 cm. What is the volume of the cylinder in grams per cubic centimeter? The volume of a
cylinder equals πd 2 h/4, where π is 3.14, d is the diameter, and h is the height.
πd 2 h
4
volume of the cylinder =
=
=
20
(3.14)(3.90 cm) 2 (3.90 cm)
4
46.6 cm 3