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Chapter 2 - Measurement
Mass and Weight
Measurement
Sig. Figs. And Rounding
Scientific Notation
Sig. Figs. in Calculations
Metric system
Measurement – Length, Mass,
Volume, and Temperature
8. Density
9. Problem Solving
1.
2.
3.
4.
5.
6.
7.
1
Mass and Weight
 Mass: The amount of matter in that body

Measured on a balance with a comparison
with known masses
 Weight: The measure of the earth’s
gravitational attraction for that object

Measured on a scale, which measures force
against a spring – Varies with location of the
object
 Matter: Anything that has mass and occupies
space.
2
Nature of Measurement
 Experiments are performed.
 Numerical values or data are obtained from
these measurements.
3
Nature of Measurement
 Measurement - quantitative observation
consisting of 2 parts


Part 1 - number
Part 2 - scale (unit)
 Examples:
 20 grams
 6.63   Joule seconds
4
Nature of Measurement
numerical value
70.0 kilograms = 154 pounds
unit
5
Precision and Accuracy

Accuracy refers to the
agreement of a particular value
with the true value.

Precision refers to the
degree of agreement among
several elements of the same
quantity.
6
Types of Error

Random Error (Indeterminate
Error) - measurement has an
equal probability of being high or
low.

Systematic Error (Determinate
Error) - Occurs in the same
direction each time (high or low),
often resulting from poor
technique.
7
Measurement and
Significant Figures
 Numbers obtained from a measurement are
never exact values.
 Degree of uncertainty


Due to limitations of instrument
Skill of the individual
 Recorded value should indicate uncertainty

Maximum precision


Contain all known digits
Plus one digit that is estimated
 These digits are know as Significant Figures
8
Uncertainty in Measurement

A digit that must be
estimated is called
uncertain. A
measurement always
has some degree of
uncertainty.
9
Measurement and
Significant Figures
Between 60 and
70 mm
Estimate next
digit, 4
Measurement 64
mm
Between 64 and
65 mm
Estimate next
digit, 2
Measurement
64.2 mm
Between 64.2 and
64.3 mm
Estimate next
digit, 5
Measurement
10
64.25 mm
Measurement and
Significant Figures
11
The
temperature
Temperature
is
oC is expressed
21.2
estimated
to be
oC. The last 2 is
to
3 significant
21.2
figures.
uncertain.
12
The
temperature
Temperature
is
oC is expressed
22.0
estimated
to be
to
3 osignificant
22.0
C. The last 0 is
figures.
uncertain.
13
The
temperature
Temperature
is
oC isto
22.11
expressed
estimated
be
oC. The last 1
to
4 significant
22.11
figures.
is uncertain.
14
Rules for Counting Significant Figures - Zero
 1.
 2.



 3.
Nonzero integers
Zeros
 leading zeros
 captive zeros
 trailing zeros
Exact numbers
15
Rules for Counting Significant Figures
- Details

Nonzero integers always count as
significant figures.
3456 has
4 sig figs.
16
Rules for Counting Significant Figures
- Details
 Zeros


Leading zeros do not count as

significant figures.
 0.0486 has
 3 sig figs.
17
Rules for Counting Significant Figures
- Details
 Zeros

 Captive zeros always count as

significant figures.
 16.07 has
 4 sig figs.
18
Rules for Counting Significant Figures
- Details
 Zeros
 
Trailing zeros are significant only

if the number contains a
decimal point.
 9.300 has
 4 sig figs.
19
Significant Figures
All nonzero numbers are significant.
3 Significant
Figures
461
20
Significant Figures
A zero is significant when it is between nonzero
digits.
3 Significant
Figures
401
21
Significant Figures
A zero is significant when it is between nonzero
digits.
5 Significant
Figures
93 . 006
22
Significant Figures
A zero is significant when it is between nonzero
digits.
3 Significant
Figures
9 . 03
23
Significant Figures
A zero is significant at the end of a number that
includes a decimal point.
5 Significant
Figures
55 . 000
24
Significant Figures
A zero is significant at the end of a number that
includes a decimal point.
5 Significant
Figures
2 . 1930
25
Significant Figures
A zero is not significant when it is before the first
nonzero digit.
1 Significant
Figure
0 . 006
26
Significant Figures
A zero is not significant when it is before the first
nonzero digit.
3 Significant
Figures
0 . 709
27
Significant Figures
A zero is not significant when it is at the end of a
number without a decimal point.
1 Significant
Figure
50000
28
Significant Figures
A zero is not significant when it is at the end of a
number without a decimal point.
4 Significant
Figures
68710
29
Rules for Counting Significant Figures
- Details

Exact numbers have an infinite
number of significant figures.
1 inch = 2.54 cm, exactly
30
Exact Numbers
 Exact numbers have an infinite number of
significant figures.
 Exact numbers occur in simple counting
operations
12345
• Defined numbers are exact.
12 inches
100
centimeters
= 1 foot
= 1 meter
31
Rounding Off Numbers
 Often when calculations are performed extra
digits are present in the results.
 It is necessary to drop these extra digits so as
to express the answer to the correct number
of significant figures.
 When digits are dropped the value of the last
digit retained is determined by a process
known as rounding off numbers.
32
Rounding off Numbers
 Rule 1. The first digit after those to be
retained is 4 or less, all other digits are
dropped.

34.642 = 34.64
 Rule 2. The first digit after those to be
retained is 5 or more, all other digits are
dropped and the last digit is increased by
one.

34.6426 = 34.643
33
Rounding Off Numbers
Rule 1. When the first digit after those you want to
retain is 4 or less, that digit and all others to its right are
dropped. The last digit retained is not changed.
4 or less
80.873
34
Rounding Off Numbers
Rule 1. When the first digit after those you want to
retain is 4 or less, that digit and all others to its right are
dropped. The last digit retained is not changed.
4 or less
1.875377
35
Rounding Off Numbers
Rule 2. When the first digit after those you want to
retain is 5 or greater, that digit and all others to its right
are dropped. The last digit retained is increased by 1.
drop
5 or
these
greater
figures
increase by 1
6
5.459672
36
Scientific Notation
 Why? A convenient way of writing very small
or very big numbers.

Earth age is 4,500,000,000 years



Estimated value to the nearest 0.1 billion years
Thus can be written as 4.5 x109 years.
Radius of hydrogen 0.000,000,000,037 meters

Written 3.7 x 10-11 meters
37
Scientific Notation
 Write a number as a power of 10
 Move the decimal point in the original number so that
it is located after the first nonzero digit.
 Follow the new number by a multiplication sign and
10 with an exponent (power).
 The exponent is equal to the number of places that
the decimal point was shifted.
38
Write 6419 in scientific notation.
decimal after
first nonzero
digit
power of 10
1
2
3
6.419
641.9x10
64.19x10
6419.
6419
x 10
39
Write 0.000654 in scientific notation.
decimal after
first nonzero
digit
6.54 x
0.000654
0.00654
0.0654
0.654
power of 10
-4
-2
-1
-3
10
40
Rules for Significant Figures in
Mathematical Operations
The results of a calculation
cannot be more precise than
the least precise measurement.
41
Rules for Significant Figures in
Mathematical Operations

Multiplication and Division: # sig figs
in the result equals the number in the
least precise measurement used in the
calculation.
6.38  2.0 =
12.76  13 (2 sig figs)
42
2.3 has two significant
figures.
(190.6)(2.3) = 438.38
190.6 has four
significant figures.
Answer given
by calculator.
The answer should have two significant
figures because 2.3 is the number with
the fewest significant figures.
Round off this
digit to four.
Drop these three
digits.
438.38
The correct answer is 440 or 4.4 x 102
43
Rules for Significant Figures in
Mathematical Operations

Addition and Subtraction: # sig figs in the
result equals the number of decimal places in
the least precise measurement.
6.8 + 11.934 =
18.743  18.7 (3 sig figs)
11.934 – 10.8 =
1.134  1.1 (2 sig figs)
44
Add 125.17, 129 and 52.2
Least precise number.
Answer given
by calculator.
125.17
129.
52.2
306.37
Round off to the
Correct answer.
nearest unit.
306.37
45
1.039 - 1.020
Calculate
1.039
Answer given
by calculator.
1.039 - 1.020
= 0.018286814
1.039
Two
1.039 - 1.020 = 0.019
0.019
= 0.018286814
1.039
significant
figures.
0.018286814
0.018
286814
The answer should have two significant
Drop these
Correct
answer.
figures because 0.019 is the number
6 digits.
with the fewest significant figures.
46
Practice
12.62 + 1.5 + 0.25 = 14.37 = 14.4
8
3
4
1.08
x
10
(2.25 x 10 ) (4.80 x 10 ) =
(452)(6.2)
 195.97 = 2.0 x 102
14.3
0.4278
 0.0007177852 = 7.18 x 10-4
59.6
10.4 + 3.75(1.5 x 10-4) =10.4005625 = 10.4
47
International System
(le Système International)
Based on metric system and
units derived from metric system.
48
International System – SI – Standard
Units
Quantity
Length
Mass
Temperature
Time
Amount of
Substance
Current
Luminous
Name of unit
Meter
Kilogram
Kelvin
Second
Abbreviation
m
kg
K
s
mole
ampere
candela
mol
A
cd
49
The Fundamental SI Units
50
Problem Solving
 Many chemical principles can be illustrated
mathematically


Usually can be solved by many methods.
Dimensional analysis offers
1.
2.
3.
4.
A systematic and orderly approach
Gives a clear understanding of the principles
Helps you to organize and evaluate data
Identifies error!!! Since unwanted units are
retained if problem setup is incorrect
51
Problem Solving
 Basic steps in problem solving
1. Read the problem carefully. Determine what
is to solved for, and write it down.
2. Tabulate the data given in the problem with
proper units.
3. Determine which principles are involved and
which unit relationships are needed to solve
the problem
4. Set up in a neat, organized, and logical
fashion, then check to see that unwanted
units cancel
5. Do the math – Check Sig Figs
6. Check the answer – is it reasonalble?
52
Conversion factors
 List on Back cover of book and throughout text
 Use of conversion factors
 unit1 x conversion factor = unit2
1000mm
1m 
 1000mm
m
Use conversion factors to change from one unit to other
Ex. How many seconds in a day
24hr 60 min 60s
1day 


 86400s
day
hr
min
Do as many examples in the book as possible – Exercises 19-56
53
How many millimeters are there in 2.5 meters?
The
conversion
factor
must
unit1 x conversion factor = unit2
accomplish two things:
m x conversion factor = mm
 It must cancel
meters.
 It must introduce
millimeters
54
The conversion factor takes a fractional
form.
mm
mx
= mm
m
55
The conversion factor is
derived from the equality.
1 m = 1000 mm
Divide both sides by 1000 mm
1m
1000 mm
conversion
=
 1
factor
1000m 1000 mm
Divide both sides by 1 m
1 m 1000 mm
conversion
=
 1
factor
1m
1m
56
How many millimeters are there in 2.5 meters?
Use the conversion factor with millimeters in the
numerator and meters in the denominator.
1000 mm
= 2500 mm
2.5 m x
3
1m
2.5 x 10 mm
57
Convert 16.0 inches to centimeters.
Use this
conversio
n factor
2.54 cm
1 in
2.54 cm
16.0 in x
= 40.6 cm
1 in
58
Convert 16.0 inches to centimeters.
59
Convert 3.7 x 103 cm to micrometers.
Centimeters can be converted to micrometers
by writing down conversion factors in
succession.
cm  m  meters
1m
10 μm
7
3.7 x 10 cm x
x
= 3.7 x 10 μm
1m
100 cm
6
3
60
Convert 45 decigrams to grams.
1 g = 10 dg
1g
45 dg x
= 4.5 g
10 dg
62
An atom of hydrogen weighs 1.674 x 10-24 g. How
many ounces does the atom weigh?
Grams can be converted to ounces using a linear
expression by writing down conversion factors
in succession.
1 lb
16 oz
-26
x

5.90
x
10
oz
x
1.674 x 10 g
454 g
1 lb
-24
64
Convert 4.61 x 102 microliters to milliliters.
Microliters can be converted to milliliters using
a linear expression by writing down conversion
factors in succession.
L  L  mL
1L
1000 mL
-1
4.61x10 μL x 6
x
= 4.61 x 10 mL
10 μL
1L
2
66
Heat
 A form of energy that is associated with the
motion of small particles of matter.
 Heat refers to the quantity of this energy
associated with the system.
 The system is the entity that is being heated
or cooled.
67
Temperature
 A measure of the intensity of heat.
 It does not depend on the size of the system.
 Heat always flows from a region of higher
temperature to a region of lower temperature.
68
Temperature Measurement
 The SI unit of temperature is the Kelvin.
 There are three temperature scales: Kelvin,
Celsius and Fahrenheit.
 In
the laboratory temperature is commonly
measured with a thermometer.
69
Temperature
C
Kelvin scale = K
Fahrenheit scale = F
Celsius scale =
70
To convert between the scales use the
following relationships.
o
K = C + 273.15
o
o
o
F = 1.8 x C + 32
o
F
32
o
o
o
o
= = 1.8 x C
F C- 32
1.8
71
Temperature
72
180 Farenheit Degrees
= 100 Celcius degrees
180
=1.8
100
73
Temperature - Conversion
74
It is not uncommon for temperatures in the Canadian plains
to reach –60oF and below during the winter. What is this
temperature in oC and K?
o
o
o
F - 32
C=
1.8
- 60. - 32
C=
1.8
o
= -51 C
75
It is not uncommon for temperatures in the Canadian planes
to reach –60oF and below during the winter. What is this
temperature in oC and K?
o
K = C + 273.15
o
K = -51 C + 273.15 = 222 K
76
Density
 Density is the mass of substance per unit
volume of the substance:
mass
g
g
d


3
volume mL cm
77
Density of Gases
Mass
is usually
The density
of gases is
expressed
expressed in
in grams
grams per
and
liter.volume in mL
or cm3.
g
ddd=== 3
mL
cm
L
78
Density
Important to note that density varies
with temperature.
Because volume changes with
temperature
d H2O = 1.0000 g/ml at 4oC
d H2O = 0.9718 g/ml at 80oC
79
Density varies with temperature
d
d
4oC
H 2O
o
80 C
H 2O
1.0000 g
g
=
= 1.0000
1.0000 mL
mL
1.0000 g
g
=
= 0.97182
1.0290 mL
mL
80
81
82
A 13.5 mL sample of an unknown liquid has a mass
of 12.4 g. What is the density of the liquid?
M 12.4g
 0.919 g/mL
D 
V 13.5mL
83
A graduated cylinder is filled to the 35.0 mL mark with water. A
copper nugget weighing 98.1 grams is immersed into the cylinder and
the water level rises to the 46.0 mL. What is the volume of the
copper nugget? What is the density of copper?
Vcopper nugget = Vfinal - Vinitial = 46.0mL - 35.0mL = 11.0mL
M
98.1g
D

 8.92 g/mL
V 11.0 mL
46.0 mL
35.0 mL
98.1 g
84
The density of ether is 0.714 g/mL. What is the
mass of 25.0 milliliters of ether?
Method 1
(a) Solve the density equation for mass.
mass
d=
volume
mass = density x volume
(b) Substitute the data and calculate.
0.714 g
25.0 mL x
= 17.9 g
mL
85
The density of ether is 0.714 g/mL. What is the
mass of 25.0 milliliters of ether?
Method 2 Dimensional Analysis. Use density as a
conversion factor. Convert:
mL → g
g
The conversion of units is mL x
=g
mL
0.714 g
25.0 ml x
= 17.9 g
mL
86
The density of oxygen at 0oC is 1.429 g/L. What is the
volume of 32.00 grams of oxygen at this temperature?
Method 1
(a) Solve the density equation for volume.
mass
d=
volume
mass
volume =
density
(b) Substitute the data and calculate.
87
The density of oxygen at 0oC is 1.429 g/L.
What is the volume of 32.00 grams of oxygen
at this temperature?
Method 2 Dimensional
Analysis. Use density as
a conversion factor.
Convert:
The conversion of units is
g→L
L
gx =L
g
88
Specific Gravity
The ratio of the density of a substance with the
density of another substance – usually water at
4oC. (unitless)
89
Chapter 2 concepts
 Mass vs. Weight
 Metric units of mass, length, and volume
 Metric prefixes: Deci, Centi, Milli, Micro, Nano, Kilo,






and Mega
Scientific notation
Significant Figures
Dimensional analysis
Conversion – Length, Volume, Mass, Temeperature
Heat vs. Temperature
Density – Mass - Volume
90