Le document traite de la mesure et de l'analyse dimensionnelle en chimie, définissant des concepts clés tels que la précision, l'exactitude et les types de mensurations. Il décrit également les unités du système international et fournit des méthodes de calcul et de conversion d'unités. En outre, il aborde l'importance de l'incertitude des mesures et l'utilisation de l'analyse dimensionnelle pour résoudre des problèmes.

1. Topic 1: Measurement
and Dimensional Analysis
Prepared by:
Antonette C. Albina

2. Objectives:
• define measurement and dimensional analysis
• determine the different methods of measurement
• describe the properties and units of length,
mass, volume, density, temperature, and time
• differentiate accuracy and precision
• distinguish exact and uncertain numbers
• correctly represent uncertainty in quantities using
significant figures
• apply proper rounding rules to computed
quantities
• perform basic unit calculations and conversions
in the metric and other unit systems

3. CHEMISTRY IS
EVERYWHERE!!
1
3
4
5
6
2
7
8
9
10

5. Are the lines parallel?

6. What is measurement?
☺A measurement is a quantity
that has both a number and a
unit.
☻Measurements are fundamental to
the experimental sciences. For that
reason, it is important to be able to
make measurements and to decide
whether a measurement is correct.

7. What is measurement?
• Chemistry is about observation! Therefore, all lab
experiments involve data collection. There are two
types of data we can collect in any lab: qualitative and
quantitative. What is the difference between them?
Qualitative:
Descriptive, non-numerical data
(ex) color, phase, texture
Quantitative:
Numbers with units
**We need both types of measurements in chemistry.

8. HOW WE MEASURE
 We measure quantities
using a suitable unit and
measuring instrument.
 For e.g. to measure 1
liter of milk we can use a
measuring jug.

9. Methods of Measurement
• Direct method
• Indirect method
• Comparative method
• Coincidence method
• Contact method
• Deflection method
• Complementary method

10. Direct method
• Measurements are directly obtained
– Ex:Vernier Caliper, Scales

11. Indirect method
• Obtained by measuring other quantities
which are functionally related to the
required value.
– Ex: Weight=Length xBreadth xHeight x
Density

12. Comparative Method
• It’s compared with other known
value
– Ex:Comparators

13. Coincidence method
•Measurements coincide with certain
lines and signals
Fundamental method
•Measuring a quantity directly in related
with the definition of that quantity
Contact method
•Sensor/Measuring tip touch the surface
area

14. Complementary method
• The value of quantity to be measured
is combined with known value of the
same quantity
– Ex:Volume determination by liquid
displacement

15. Deflection method
• The value to be measured is directly
indicated by a deflection of pointer
– Ex: Pressure Measurement

16. The International System of Units
In the signs shown here, the distances are
listed as numbers with no units
attached.
Without the units, it is
impossible to
communicate the
measurement to others.
When you make a
measurement, you must
assign the correct units to
the numerical value.

17.  All measurements depend on units
that serve as reference standards. The
standards of measurement used in
science are those of the metric
system.
 The International System of Units
(abbreviated SI, after the French name,
Le Système International d’Unités) is
a revised version of the metric
system.

18. UNITS OF MEASUREMENT
BASIC UNITS IN METRIC
SYSTEM
Mass
Length
Volume
Time
Temperature
Energy
Amount of
substance
Kilogram
Meter
Liter
Second
Kelvin
joule
Mole
Second

19. Which five SI base units do chemists commonly use?
The five SI baseunits commonly usedby
chemists are the meter, the kilogram, the
kelvin, the second, and themole.

20. What metric units are
commonly used to measure
length, volume, mass,
temperature and energy?

21. In SI, the basic unit of length, or linear measure, is
the meter (m). For very large or and very small
lengths, it may be more convenient to use a unit
of length that has a prefix.
Units of Length

22. Common metric units of length
include the centimeter, meter,
and kilometer.

23.  The SI unit of volume is the amount of
space occupied by a cube that is 1 m along
each edge. This volume is the cubic meter
(m)3. A more convenient unit of volume for
everyday use is the liter, a non-SI unit.
 A liter (L) is the volume of a cube that is 10
centimeters (10 cm) along each edge (10
cm  10 cm  10 cm = 1000 cm3 = 1 L).
Units of Volume

24. Common metric units of volume
include the liter, milliliter, cubic
centimeter, and microliter.

25. The volume of 20 drops of liquid
from a medicine dropper is
approximately 1 mL.

26. A sugar cube has a volume of 1
cm3. 1 mL is the same as 1
cm3.

27. A gallon of milk has about twice
the volume of a 2-L bottle of
soda.

28. Units of Mass
 The mass of an object is measured
in comparison to a standard mass
of 1 kilogram (kg), which is the
basic SI unit of mass.
 A gram (g) is 1/1000 of a kilogram;
the mass of 1 cm3 of water at 4°C is
1 g.

29. Common metric units of mass include
kilogram, gram, milligram, and
microgram.

30.  Weight is a force that measures the
pull on a given mass by gravity.
 The astronaut shown on the surface
of the moon weighs one sixth of
what he weighs on Earth.

31.  Temperature is a measure
of how hot or cold an
object is.
 Thermometers are used to
measure temperature.
Units of Temperature

32. Scientists commonly
use two equivalent
units of temperature,
the degree Celsius and
the Kelvin.

33. ▪ On the Celsius scale, the freezing
point of water is 0°C and the boiling
point is 100°C.
▪ On the Kelvin scale, the freezing point
of water is 273.15 kelvins (K), and the
boiling point is 373.15 K.
▪ The zero point on the Kelvin scale, 0
K, or
absolute zero, is equal to 273.15 °C.

36. Units of Energy
 Energy is the capacity to do
work or to produce heat.
 The joule and the calorie are
common units of energy.

37.  Thejoule (J)is the SIunit of energy.
 One calorie (cal) is the quantity of heat
that raisesthe temperature of 1g of pure
water by 1°C.

38. This house is equipped with solar
panels. The solar panels convert the
radiant energy from the sun into
electrical energy that can be used to
heat water and power appliances.

39. What is a GOOD measurement?
• Most data is collected at STP. Why do you think STP is
important when trying to obtain data?
• Any good data that is collected needs to be both
precise and accurate. What is the difference between
precision and accuracy?
Accuracy:
is a measure of how close a measurement comes
to the actual or true value of whatever is measured
Precision:
is a measure of how close a series of
measurements are to one another, irrespective of the
actual value

40. To evaluate the accuracy of a measurement,
the measured value must be compared to the
correct value.
To evaluate the precision of a measurement,
you must compare the values of two or more
repeated measurements.
How to evaluate Accuracy
and Precision?

41. Three
targets with
three
arrows each
to shoot.
Can you hit the bull's-eye?
Label the following targets as precise,
accurate, neither or both.
Both
accurate
and
precise
Precise
but not
accurate
Neither
accurate
nor
precise
How do
they
compare?
Can you define accuracy vs. precision?

42. Accuracy and Precision
Good Accuracy,
Good Precision
Poor Accuracy,
Good Precision
Poor Accuracy,
Poor Precision
The closeness of a dart to the bull’s-eye corresponds
to the degree of accuracy. The closeness of several
darts to one another corresponds to the degree of
precision.

44. Example: Accuracy
• Who is more accurate when measuring a
book that has a true length of 17.0 cm?
Susan:
17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm
Amy:
15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

45. Example: Precision
Who is more precise when measuring the same
17.0 cm book?
Susan:
17.0 cm, 16.0 cm, 18.0 cm, 15.0 cm
Amy:
15.5 cm, 15.0 cm, 15.2 cm, 15.3 cm

47. Measurement Error

48. Error
• Measured values are never absolutely accurate, they always
have error. There is a certain amount of error that is allowable.
What determines the allowable error?
The measuring tool
For example, a balance that reads to the nearest 0.001 g is more
accurate than one that reads to the nearest 0.01 g.
Ex) A graduated cylinder that measures to the nearest hundredths
place contains exactly 32.70 mL of liquid. One of your
classmates reads the volume in the graduated cylinder to be
32.20 mL. Is this amount of error acceptable?
What if another classmate reads the volume of the liquid to be 33.2
mL? Is this an acceptable amount of error?
Why?

49. Percent Error
% error = measured value – accepted value x 100
accepted value
** % error can be either positive or negative. Positive
error means that your value was larger than the real
value and negative means your value was smaller.
• There is a difference between the accepted value,
which is the correct value for the measurement
based on reliable references, and the
experimental value, the value measured in the
lab.
• The difference between the experimental value
and the accepted value is called the error.

50. 1.Subtract one value from another. The order
does not matter if you are dropping the sign
(taking the absolute value. Subtract the
theoretical value from the experimental value if
you are keeping negative signs. This value is your
"error."
2.Divide the error by the exact or ideal value (not
your experimental or measured value). This will
yield a decimal number.
3.Convert the decimal number into a percentage
by multiplying it by 100.
4.Add a percent or % symbol to report your
percent error value
Percent Error Calculation Steps

51. Percent Error Example Calculation
In a lab, you are given a block of aluminum.
You measure the dimensions of the block
and its displacement in a container of a
known volume of water. You calculate
the density of the block of aluminum to be
2.68 g/cm3. You look up the density of a
block of aluminum at room temperature and
find it to be 2.70 g/cm3. Calculate the
percent error of your measurement.

52. Step by Step Solution
1.Subtract one value from the other:2.68 -
2.70 = -0.02
2.Depending on what you need, you may
discard any negative sign (take the
absolute value): 0.02This is the error.
3.Divide the error by the true
value:0.02/2.70 = 0.0074074
4.Multiply this value by 100% to obtain the
percent error:
0.0074074 x 100% = 0.74% (expressed
using 2 significant figures).

53. You are given a cube of pure
copper. You measure the sides of
the cube to find the volume and
weigh it to find its mass. When you
calculate the density using your
measurements, you get 8.78
grams/cm3. Copper’s accepted
density is 8.96 g/cm3. What is your
percent error?

54. Importance Of Uncertainty of
Measurement in Chemistry

55. What is Uncertainty?
It is a parameter, associated with the result of
a measurement that defines the range of the
values that could reasonably be attributed to
the measured quantity.
When uncertainty is evaluated and reported in
a specified way it indicates the level of
confidence that the value actually lies within
the range defined by the uncertainty interval.

56. Why is Uncertainty
important?

57. Causes of Uncertainty
In general, in clinical laboratory sciences the
most relevant elements that can contribute to
uncertainty for a given system of
measurement are:
Incomplete definition of the particular quantity under
measurement,
Unrepresentative sampling,
Withdrawal conditions,
Effects of additives,
Storage conditions,
Day-to-day (or between-run) imprecision,
Systematic error,
Lack of specificity,
Values assigned to calibrators

58. UNCERTAINTY IN
MEASUREMENT
 Measurement of any
property is made using
an instrument which
always has some
limitations.
 This weighing balance
cannot measure any
quantity smaller than
0.1 mg.

59. UNCERTAINTY IN MEASUREMENT
Burette is used to
measure volume of
liquid. In a 50 ml burette
distance between two
lines measure 0.1 ml.
Any quantity smaller than
0.1 ml cannot be
measured on this burette
with accuracy.

60. UNCERTAINTY IN MEASUREMENT
In case of burette if the
meniscus of liquid stays
between two lines,
accurate measurement
cannot be made.
Link on how to solve uncertainties:
https://www.youtube.com/watch?v=B7dKWE-0FZY

61. SIGNIFICANT FIGURES
 To show and understand
uncertainty in measurement the
results of any measurement are
expressed mathematically up to
a certain number of decimal
digits. These decimal digits
are called significant figure.
 Depending on the accuracy
required, the number of decimal
digits varies.
0.1
0.01
0.001
.0001
Etc.

62. CONVERSION OF UNITS
62
There adifferent types
of units re in use
throughout the world.
One type of units can
be converted to
another type which is
equivalent to the
previous one.
Kilometers to miles
Meter to yard
Centimeters to inches
Kg and g to pound
Liter to gallons
ml to liquid ounce
Centigrade to
fahrenheight

63. 63
 Conversion factor is
a mathematical
figure which
converts a quantity
in certain
measurement
system to units of
another
measurement
system.
1 kg = 2.2005 lb
Hence to convert kg
to pound, the number
of kg’s must be
multiplied by 2.2005
for example:
2 kg is = (2 x 2.005
= 4.014 lb)
CONVERSION OF UNITS

64. What happens when a measurement is
multiplied by a conversion factor?
Conversion Factors

65. – If you think about any number of everyday
situations, you will realize that a quantity can
usually be expressed in several different
ways.
– For example:
• 1 dollar = 4 quarters = 10 dimes = 20
nickels = 100 pennies
– These are all expressions, or measurements,
of the same amount of money.
Conversion Factors

66. – The same thing is true of scientific quantities.
– For example:
• 1 meter = 10 decimeters = 100
centimeters = 1000 millimeters
– These are different ways to express the same
length.
Conversion Factors

67. – Whenever two measurements are equivalent,
a ratio of the two measurements will equal 1,
or unity.
– For example, you can divide both sides of the
equation 1 m = 100 cm by 1 m or by 100 cm.
Conversion Factors
1 m
1 m
= 100 cm
1 m
= 1 or 1 m
100 cm
= 100 cm
100 cm
= 1

68. – The ratios 100 cm/1 m and 1 m/100 cm are
examples of conversion factors.
– A conversion factor is a ratio of
equivalent measurements.
Conversion Factors
conversion factors
1 m
1 m
= 100 cm
1 m
= 1 or 1 m
100 cm
= 100 cm
100 cm
= 1

69. – The measurement in the numerator (on the
top) is equivalent to the measurement in the
denominator (on the bottom).
– The conversion factors shown below are read
“one hundred centimeters per meter” and
“one meter per hundred centimeters.”
Conversion Factors
conversion factors
1 m
1 m
= 100 cm
1 m
= 1 or 1 m
100 cm
= 100 cm
100 cm
= 1

70. • The figure above illustrates another way to look
at the relationships in a conversion factor.
– The smaller number is part of the
measurement with the larger unit.
– The larger number is part of the measurement
with the smaller unit.
Conversion Factors
1 meter 100 centimeters
Larger unit
Smaller unit
100
1 m
cm
Smaller number
Larger number

71. When a measurement is multiplied by a
conversion factor, the numerical value is
generally changed, but the actual size of
the quantity measured remains the same.
• For example, even though the numbers in
the measurements 1 g and 10 dg
(decigrams) differ, both measurements
represent the same mass.
Conversion Factors

72. – In addition, conversion factors within a system
of measurement are defined quantities or
exact quantities.
• Therefore, they have an unlimited number
of significant figures and do not affect the
rounding of a calculated answer.
Conversion Factors

73. – Here are some additional examples of pairs of
conversion factors written from equivalent
measurements.
– The relationship between grams and kilograms
is 1000 g = 1 kg.
• The conversion factors are
Conversion Factors
1000 g
1 kg
and 1 kg
1000 g

74. • The figure at right
shows a scale that can
be used to measure
mass in grams or
kilograms.
– If you read the scale in
terms of grams, you can
convert the mass to
kilograms by multiplying
by the conversion factor
1 kg/1000 g.
Conversion Factors

75. • The relationship between nanometers
and meters is given by the equation 109
nm = 1 m.
– The possible conversion factors are
Conversion Factors
109 nm
1 m
and
1 m
109 nm

76. – Common volumetric units used in chemistry
include the liter and the microliter.
– The relationship 1 L = 106μL yields the
following conversion factors:
Conversion Factors
1 L
106 μL
and
1 L
106 μL

77. What is the relationship between
the two components of a
conversion factor?

78. What is the relationship between
the two components of a
conversion factor?
The two components of a conversion
factor are equivalent measurements
with different units. They are two ways
of expressing the same quantity.

79. What kinds of problems can you solve
using dimensional analysis?
Dimensional Analysis

80. – Many problems in chemistry are conveniently
solved using dimensional analysis, rather
than algebra.
– Dimensional analysis is a way to analyze
and solve problems using the units, or
dimensions, of the measurements.
• Sample Problem below explains dimensional
analysis by using it to solve an everyday situation.
Dimensional Analysis

81. Sample Problem
Using Dimensional Analysis
How many seconds are in a workday that
lasts exactly eight hours?

82. Analyze List the knowns and the unknown.
To convert time in hours to time in seconds,
you’ll need two conversion factors. First you
must convert hours to minutes: h  min. Then
you must convert minutes to seconds: min  s.
Identify the proper conversion factors based on
the relationships 1 h = 60 min and 1 min = 60 s.
KNOWNS UNKNOWN
time worked = 8 h seconds worked = ? s
1 hour = 60 min
1 minute = 60 s
1

83. Calculate Solve for the unknown.
The first conversion factor is based on 1 h =
60 min. The unit hours must be in the
denominator so that the known unit will
cancel.
2
60 min
1 h

84. Calculate Solve for the unknown.
The second conversion factor is based on 1
min = 60 s. The unit minutes must be in the
denominator so that the desired units
(seconds) will be in your answer.
2
60 s
1 min

85. Calculate Solve for the unknown.
Multiply the time worked by the conversion
factors.
60 s
1 min
60 min
1 h
8 h x x = 28,000 s = 2.8800 x 104 s
2

86. Evaluate Does the result make sense?
The answer has the desired unit (s). Since the
second is a small unit of time, you should
expect a large number of seconds in 8 hours.
The answer is exact since the given
measurement and each of the conversion
factors is exact.
3

87. Using Dimensional Analysis
The directions for an experiment ask
each student to measure 1.84 g of
copper (Cu) wire. The only copper wire
available is a spool with a mass of 50.0
g. How many students can do the
experiment before the copper runs
out?
Sample Problem

88. Analyze List the knowns and the unknown.
From the known mass of copper, use the
appropriate conversion factor to calculate the
number of students who can do the
experiment. The desired conversion is mass of
copper  number of students.
KNOWNS
mass of copper available = 50.0 g Cu
Each student needs 1.84 grams of
copper.
UNKNOWN
number of students = ?
1

89. Calculate Solve for the unknown.
The experiment calls for 1.84 grams of
copper per student. Based on this
relationship, you can write two conversion
factors.
2
and
1.84 g Cu
1 student
1.84 g Cu
1 student

90. Calculate Solve for the unknown.
Because the desired unit for the answer is
students, use the second conversion factor.
Multiply the mass of copper by the
conversion factor.
Note that because students
cannot be fractional, the answer is
rounded down to a whole number.
50.0 g Cu x
1.84 g Cu
1 student
= 27.174 students = 27 students
2

91. Evaluate Does the result make sense?
The unit of the answer (students) is the one
desired. You can make an approximate
calculation using the following conversion
factor.
Multiplying the above conversion factor by 50
g Cu gives the approximate answer of 25
students, which is close to the calculated
answer.
3
1 student
2 g Cu

92. Using Density as a Conversion
Factor
What is the volume of a pure
silver coin that has a mass of
14 g? The density of silver (Ag)
is 10.5 g/cm3.

93. Analyze List the knowns and the unknown.
You need to convert the mass of the coin into
a corresponding volume. The density gives
you the following relationship between volume
and mass: 1 cm3 Ag = 10.5 g Ag. Multiply the
given mass by the proper conversion factor to
yield an answer in cm3.
KNOWNS
mass = 14 g
density of silver = 10.5 g/cm3
UNKNOWN
volume of a coin = ? cm3
1

94. Calculate Solve for the unknown.
Use the relationship 1 cm3 Ag = 10.5 g Ag to
write the correct conversion factor.
2
1 cm3 Ag
10.5 g Ag

95. Calculate Solve for the unknown.
Multiply the mass of the coin by the
conversion factor.
2
Sample Problem 3.12
14 g Ag x = 1.3 cm3 Ag
1 cm3 Ag
10.5 g Ag

96. Evaluate Does the result make sense?
Because a mass of 10.5 g of silver has a
volume of 1 cm3, it makes sense that 14.0
g of silver should have a volume slightly
larger than 1 cm3. The answer has two
significant figures because the given mass
has two significant figures.
3

97. – In chemistry, as in everyday life, you often
need to express a measurement in a unit
different from the one given or measured
initially.
Dimensional analysis is a powerful tool
for solving conversion problems in
which a measurement with one unit is
changed to an equivalent measurement
with another unit.
Dimensional Analysis
Simple Unit Conversions

98. What kind of problems can you
solve using dimensional analysis?

99. What kind of problems can you
solve using dimensional analysis?
Problems that require the conversion
of a measurement from one unit to
another can be solved using
dimensional analysis.

100. When a measurement is multiplied by a
conversion factor, the numerical value is
generally changed, but the actual size of the
quantity measured remains the same.
Dimensional analysis is a powerful tool for
solving conversion problems in which a
measurement with one unit is changed to an
equivalent measurement with another unit.
Key Concepts

101. – conversion factor: a ratio of equivalent
measurements used to convert a
quantity from one unit to another
– dimensional analysis: a technique of
problem-solving that uses the units that
are part of a measurement to help solve
the problem

102. Significant Figures
• Significant Figure:
Any number in a measurement that is known for
sure plus one estimated number.
7 cm
7.6 cm
7.59 cm
measurement # sig figs

103. Counting sig figs
• Non-zero numbers are always significant.
The rules always apply to zeros.
– All zeros that are actually measured are
significant, while zeros that represent place
holders or rounding are not significant.
Therefore zeros to the left of any # or to the right
of a number without a decimal point are not
significant, while zeros in between other #’s or
after numbers with decimal points are significant.
• The rule you need to remember is this:
Count from the first non-zero number to the
last non-zero number and if there is a
decimal anywhere in the #, the zeroes after
the number counts.

104. Counting sig figs
• Exact # Rule: if the number is an exact number,
like a number of people or conversion factors (1
hour = 60 min), there is an infinite number of sig
figs (in other words, the number of sig figs in a
calculation depend on the other measurements).
(Ex) 0.0007010
(Ex) 7010
(Ex) 7010.
http://science.widener.edu/svb/tutorial/sigfigures.html
4
3
4

105. Why is measurement
important?

106. References
https://www.keyence.com/ss/products/measure/measurement_librar
y/basic/measurement/
https://www.brainkart.com/article/Methods-of-Measurements_5808/
https://en.wikipedia.org/wiki/SI_base_unit
https://manoa.hawaii.edu/exploringourfluidearth/physical/world-
ocean/map-distortion/practices-science-precision-vs-accuracy
https://courses.lumenlearning.com/boundless-
statistics/chapter/measurement-error/
https://www.isobudgets.com/estimate-uncertainty-in-measurement-
for-chemistry-laboratories/
https://courses.lumenlearning.com/trident-boundless-
chemistry/chapter/dimensional-analysis/