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1
Chapter 1
Chemistry: The Central Science
Introduction and Some Basic
Concepts
General Chemistry 2020 – 2021
16
2
 Everything in this universe is made out of approximately
100 different kinds of atoms.
 Sand (Silicon, Oxygen)
 Table Salt (Sodium, Chloride)
 Water (Oxygen, Hydrogen)
 They are as letters in an alphabet.
Chapter1
Why Chemistry?
3
Why Chemistry?
4
 Chemical reactions are very common in this life
and are important for our survival on the Earth.
 They also cause many problems for humanity!
 Can you think of “good” and “bad” chemical
reactions?
Why Chemistry?
5
Scientific Method
 The scientific method is the way used
by scientists to understand the universe
and its changes.
 The more creative you’re at solving
problems, the more effective you will be
in your career and your personal life.
 Chemistry helps to develop
solving problems capabilities.
6
 Steps of scientific methods:
 Observation.
• Can be qualitative or quantitative.
 Prediction (Hypothesis).
• Trying to explain the observation.
 Experiment.
• Performed to test the validity of the hypothesis.
• Experiments always produce new information.
Scientific Method
 To understand the universe and its
changes.
7
Scientific Method
 A set of valid hypotheses is
assembled into a theory (model).
 This theory is confirmed, modified
or may be discarded as more
observations are recorded. Thus,
it is a continuous process.
8
Theory vs. Law
 Theory changes over time as more
observations from experiments are recorded.
 Some observations are found to apply to
many different systems.
 Law (what happens)
A summary of observed behaviors applied to
different systems.
 Law of conservation of mass.
 Law of conservation of energy.
 Theory (why it happens)
An attempt to explain these observations.
9
Scientific Method
Chapter 1 Section 1
10
Classification of Matter
 Matter (‫)المادة‬ is anything occupying the space
and having a mass.
 Matter anything that has mass and volume (or
occupies space)
 Matter can be:
 A substance is a form of matter that has a
defined composition and unique properties.
 A mixture is a combination of two or more
substances that retain their distinct identities.
11
Classification of Matter
States of matter:
 Solid: rigid, has fixed volume and shape.
 Liquid: has definite volume but not fixed shape.
 Gas: has no fixed volume or shape. and is compressible.
12
Classification of Matter
Chapter 1 Section 2
• Wood
• Sand
• Rocks
• Gasoline
• Juices and tea
• Air (N2, O2, H2,
CO2, etc.)
• H2O
• NaCl
• H2SO4
• C (carbon)
• Hg (mercury)
• H or H2
(hydrogen)
13
Separation (Physical) Methods
 Based on the physical properties of the substances
(boiling point, adsorption, solubility, etc.)
 Separation methods discussed in the text:
 Distillation.
 Filtration.
 Chromatography.
Chapter 1 Section 2
14
Atoms, Elements and Compounds
Chemical changes (decomposition of compounds or recombining elements),
such as electrolysis, heating, and photolysis.
Compounds (
‫المركبات‬
) are substances with
constant composition that can be broken
down into elements by chemical processes.
Compound – substance made of 2 or more
types of atoms that are chemically bonded.
Elements (
‫العناصر‬
) are substances that can’t
be decomposed into simpler substances by
physical or chemical means
Element – pure substance made of only
one type of atom.
Atom(‫)الذرة‬- smallest unit of an element
that keeps the properties of element.
15
Molecule and Mixture
 Molecule(‫)الجزيء‬: type of compound in which the bonds are covalent
bonds.
Mixture (‫)الخليط‬
•In chemistry, a mixture is a material made up of two or more different
substances which are mixed.
A mixture differs from a compound in that( ‫في‬ ‫المركب‬ ‫عن‬ ‫الخليط‬ ‫)يختلف‬
(
1
) mixed in any proportion (‫نسبة‬ ‫باي‬ ‫)يخلط‬
(
2
.) the components of which can be separated ) ‫اهلصف‬
( by simple mechanical
means.
• Separating the Components of a Mixture: techniques to separate the
components of mixtures (Size, density, solubility, electrical charge
16
Classification of Matter
 Classify the following as mixtures, elements,
compounds, etc.
Aluminum foil:
substance, element
Table salt:
substance, compound
Milk:
mixture, homogeneous
Sea water:
mixture, homogeneous
Copper wire:
substance, element
17
The Properties of Matter
 Quantitative: expressed using numbers.
 Qualitative: expressed using properties.
 Physical properties: can be observed and measured
without changing the substance.
 Examples: color, melting point, states of matter.
 Physical changes: the identity of the substance stays
the same and only its state changes.
 Examples: changes of state (melting, freezing).
18
The Properties of Matter
 Chemical properties: must be determined by the
chemical changes that are observed.
 Examples: flammability, acidity, corrosiveness, reactivity.
 Chemical changes: after a chemical change, the
original substance no longer exists
 Examples: combustion, digestion, corrosion.
19
The Properties of Matter
20
The Properties of Matter
 Extensive
property: depends
on the amount of
matter.
 Examples: mass,
length.
 Intensive
property: does not
depend on the
amount of matter.
 Examples: density,
temperature, color.
Mass of water 100.0 g 10.0 g
Volume of water 0.100 L 0.010 L
Temperature of water 25 °C 25 °C
Density of water 1.00 g/mL 1.00 g/mL
21
The Properties of Matter
22
Scientific Measurement
Number Unit
(1) Metric Units
International System (SI Units)
(2) English Units
Used in Science
There are two major systems of measurements:
 Making observations can be done quantitatively or qualitatively.
 A quantitative observation is called a measurement. It must
include two important pieces of information:
23
Units of Measurement
Number Unit
10 kilometers
1 gram
5 kelvin
20 miles
1 pound
60 Fahrenheit
(1) Metric
Units
International
System (SI
Units)
(2) English
Units
Used in
Science
There are two
major systems of
measurements:
24
The Fundamental SI Units
All other units of measurement can be derived from the above
seven fundamental SI units .
25
Using Prefixes in the SI System
 The distance between Sanaa and
Ibb is 90,000 meters.
 90×103 meters.
 90 kilo-meters (km)
 The capacity of this computer is
80,000,000,000 bites.
 80×109 bites
 80 giga-bites (GB)
26
Table of Prefixes in the SI System
Must be memorized!
27
Scientific Notation
 0.0001 kg
 1×10-4 kg
 0.1 g
 1 with 35 zeros kg
 1×1035 kg
 Mass vs. Weight
How much does that pin weigh?
How much does the earth weigh?
Scientific Notation
28
Scientific Notations
 123.1 = 1.231× 102 = 1.231 × 100
 0.00013 = 1.3 × 10-4 = 1.3 / 10000
= 0.13 × 10-3
 Avogadro’s Number*:
602,214,000,000,000,000,000,000
*The number of atoms contained in 12 g of carbon and is equal to 1 mole.
6.022 × 1023
Scientific notation is a very convenient way to express the number of atoms
in chemistry problems.
29
Temperature
 Three systems are used to measure temperatures:
 Celsius scale (°C)
 Kelvin scale (K)
 Fahrenheit (°F)
 You have to be able to convert from one scale to
another.
30
The Three Major Temperature Scales
Fahrenheit (F) Celsius (oC) Kelvin (K)
31
Celsius Scale vs. Kelvin Scale
 Temperature scales for °C
and K are identical, but
their zeros are different.
TK = TC + 273.15
TC = TK – 273.15
32
Fahrenheit Scale vs. Celsius Scale
 Both unit temperature
size and zero locations
are different.
Since:
180°F = 100°C => 9°F =
5°C
and:
32°F = 0°C
Then to convert from °F to °C:
[Tf (°F) – 32 (°F)] = Tc
(°C)
5°C
9°F
33
Fahrenheit Scale vs. Celsius Scale
[ Tc (a) – Tc (b) ] °C = (5°C/9°F) [ Tf (a) – Tf (b) ] °F
When Tc (b) = - 40°C, then Tf (b) = -40°F
giving that:
[ Tc (a) – (-40) ] °C = (5°C/9°F) [ Tf (a) – (-40) ] °F
Thus:
or
F
9
C
5
40
40





f
c
T
T
C
5
F
9
40
40





c
f
T
T
34
Volume
 Volume is not an SI unit, but it is
extremely important in chemical
measurements.
 Volume = 1m × 1m × 1m = 1m3
 1m = 10dm
(1m)3 = (10dm)3
1m3 = 1000dm3
 1dm3 = 1L
1L = 1000mL = 1000cm3
1mL = 1cm3
 (milli)Liter milli = 10-3
(centi)Meter centi = 10-2
35
Measurement of Volume
Common types of laboratory equipment used to measure liquid
volume.
36
Density
 It is the mass of substance
per unit volume. volume
mass
Density 
Substance Physical State Density (g/cm3)
Oxygen Gas 0.00133
Hydrogen Gas 0.000084
Ethanol Liquid 0.789
Water Liquid 0.998
Aluminum Solid 1.47
Iron Solid 7.87
Mercury Liquid 13.6
37
Uncertainty in Measurement
 A measurement always has
some degree of uncertainty.
Chapter 1 Section 5
20.16 ml
20.17 ml
20.15 ml
20.18 ml
20.16 ml
certain
digit
uncertain digit
(must be estimated)
• Uncertainty is
± 0.01 ml.
• Certain and
uncertain digits are
known as significant
figures.
38
 Now you should be able to tell how many
digits you need to include in your reading
(measurement).
 20 ml
20.1 ml
20.16 ml
20.160 ml
20.1600 ml
Uncertainty in Measurement
Chapter 1 Section 5
Which one??
These meaningful digits are the significant figures
39
Uncertainty in Measurement
Different equipments have different
uncertainties in their measurements.
Chapter 1 Section 5
2.5 ± 0.1 cm
2.46 ± 0.01 cm
These meaningful
digits are the
significant figures
Uncertainty
40
Significant Figures (‫المعنوية‬ ‫)األرقام‬
 In many cases, important physical quantities are obtained
from measured values.
Volume = l w h
Density = mass / volume
 Calculations need to be done on the basis of Significant
Figure (S.F.) Rules
 Rules for counting S.F.
 Rules of mathematical operations on S.F.
 Implication of the word “Significant”. It is to have the
correct degree of uncertainty in the resultant physical
quantities.
Mathematical
operations
41
Rules for Counting Significant Figures
1- Nonzero integers are always counted as
S.F.
Example: Give the number of S.F. for the following:
34
236
17296.1
12.1×102 Exponential (Scientific) notation
Chapter 1 Section 5
42
Rules for Counting Significant Figures
2- Zeros (leading zeros, captive zeros, and
trailing zeros)
a) Leading zeros are not counted as S.F.
Example: Give the number of S.F. for the following:
00121.1
0.0025
Chapter 1 Section 5
43
Rules for Counting Significant Figures
b) Captive zeros are always counted as S.F.
Example: Give the number of S.F. for the following:
1.008
701.1 ×10-4
3.000000008
0.0901
Chapter 1 Section 5
44
Rules for Counting Significant Figures
c) Trailing zeros are counted as S.F. only if the
number contains a decimal point.
Example: Give the number of S.F. for the following:
1.000
320.00 ×10-1
100 (can’t tell!) may be 1, 2 or 3.
100.
100.0
Chapter 1 Section 5
45
Rules for Counting Significant Figures
3- Exact numbers are assumed to have an
infinite number of S.F.
Examples:
3 Apples is 3.00000000 (zeros are all the way to ∞)
2 in 2πr (the circumference of a cycle).
1 km = 1000 m
1 in = 2.54 cm
Chapter 1 Section 5
Mathematical
relationships
Definitions
46
Exercise
 How many significant figures are there in the
following numbers?
Chapter 1 Section 5
3004
5.
10
10
120
0 
.
0
250.
m
cm3
kg
47
Mathematical Operations
 Multiplication or division
4.56 × 1.4 = 6.38 6.4
Chapter 1 Section 5
From
calculator
before
correction
Number
of S.F. 3 2 2 S.F. (After
correction)
 Addition and Subtraction
12.11
+ 18.0
+ 1.013 31.1
31.123
before
correction
3 S.F. (After
correction)
48
Rule for Rounding Numbers (‫االرقام‬ ‫تقريب‬ ‫)قواعد‬
 6.38
 The digit to be removed
If ≥ 5, then round up, i.e. the 3 becomes 4.
 6.4
If < 5, then the digit stays unchanged.
 6.34 becomes 6.3
49
Exercises
 Perform the following mathematical operation and
express the result to the correct number of significant
figures:
Chapter 1 Section 5
01
1
273
0821
0
102
0
.
.
. 

Rounding off should be carried out for the final answer
and NOT to the intermediate answers. However, you must
keep track of the significant figures in the intermediate
steps.
50
Precision and Accuracy
Chapter 1 Section 5
Random error Systematic error
Precise but not
accurate
“reproducible”
Neither precise
nor accurate
Accurate and
precise
Poor technique Good technique but
needs calibration
Good technique
51
Precision and Accuracy
 Accuracy: Agreement of a particular value
(measurement) with the true value.
 Precision: Agreement among several
values (measurements), not necessarily
agreeing with the true value.
Chapter 1 Section 5
52
Precision and Accuracy
Chapter 1 Section 5
Student A Student B Student C
0.335 g 0.357 g 0.369 g
0.331 g 0.375 g 0.373 g
0.333 g 0.338 g 0.371 g
Average:
0.333 g 0.357 g 0.371 g
 True mass was 0.370 grams
Three students are asked to determine the
mass of an aspirin tablet.
53
Precision and Accuracy
Chapter 1 Section 5
Three students are asked to determine the
mass of an aspirin tablet.
True mass was 0.370 grams
54
Conversion Factors
 Used to convert from one unit to another.
Chapter 1 Section 6
Example 1:
How many centimeters in
25.5 inches (in)?


in
1
cm
2.54
in
25.5 64.8 cm
Example 2:
How many inches in 25.5
centimeters?


cm
2.54
in
1
cm
25.5 10.0 in
55
Dimensional Analysis – Tracking Units
1L = 1000 ml
1 ml = 0.001 L
= 1× 10-3 L
Chapter 1 Section 6
Example 3:
How many ml are in
1.63 L?
Which direction you choose?
1.63 L × =
1.63 L × =
1 L
1000 ml
?
1 L
1000 ml
L2
ml
0.00163
1.63×103 ml
56
 How many centimeters are in 0.25 megameters?
0.25 megameters × = 0.25×106 m
0.25×106 m × = 0.25×108 cm
= 2.5×107 cm
= 25.×106 cm
Solving Problems Using Dimensional
Analysis
Chapter 1 Section 6
megameters
1
m
1×106
1 meters
cm
100
57
 The Food and Drug Administration (FDA) recommends
that dietary sodium intake be no more than 2400 mg
per day.
What is this mass in pounds (lb), if 1 lb = 453.6 g?
Solving Problems Using Dimensional
Analysis
Chapter 1 Section 6
lb
10
5.3
g
453.6
lb
1
mg
1000
g
1
mg
2400 3





58
Exercise
 Perform the following mathematical operation and
express the result to the correct number of significant
figures:
4326
.
0
705
.
80
623
.
0
470
.
0
1
.
3
526
.
2


Rounding off should be carried out for the final answer
and NOT to the intermediate answers. However, you must
keep track of the significant figures in the intermediate
steps.
59
Exercise
Methodology to solve such problems:
• Start with the quantity given in the question.
• Use possible conversion factors to convert the unit of the
given quantity in the question to the desired/needed unit.
60
61

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CH1.pdf

  • 1. 1 Chapter 1 Chemistry: The Central Science Introduction and Some Basic Concepts General Chemistry 2020 – 2021 16
  • 2. 2  Everything in this universe is made out of approximately 100 different kinds of atoms.  Sand (Silicon, Oxygen)  Table Salt (Sodium, Chloride)  Water (Oxygen, Hydrogen)  They are as letters in an alphabet. Chapter1 Why Chemistry?
  • 4. 4  Chemical reactions are very common in this life and are important for our survival on the Earth.  They also cause many problems for humanity!  Can you think of “good” and “bad” chemical reactions? Why Chemistry?
  • 5. 5 Scientific Method  The scientific method is the way used by scientists to understand the universe and its changes.  The more creative you’re at solving problems, the more effective you will be in your career and your personal life.  Chemistry helps to develop solving problems capabilities.
  • 6. 6  Steps of scientific methods:  Observation. • Can be qualitative or quantitative.  Prediction (Hypothesis). • Trying to explain the observation.  Experiment. • Performed to test the validity of the hypothesis. • Experiments always produce new information. Scientific Method  To understand the universe and its changes.
  • 7. 7 Scientific Method  A set of valid hypotheses is assembled into a theory (model).  This theory is confirmed, modified or may be discarded as more observations are recorded. Thus, it is a continuous process.
  • 8. 8 Theory vs. Law  Theory changes over time as more observations from experiments are recorded.  Some observations are found to apply to many different systems.  Law (what happens) A summary of observed behaviors applied to different systems.  Law of conservation of mass.  Law of conservation of energy.  Theory (why it happens) An attempt to explain these observations.
  • 10. 10 Classification of Matter  Matter (‫)المادة‬ is anything occupying the space and having a mass.  Matter anything that has mass and volume (or occupies space)  Matter can be:  A substance is a form of matter that has a defined composition and unique properties.  A mixture is a combination of two or more substances that retain their distinct identities.
  • 11. 11 Classification of Matter States of matter:  Solid: rigid, has fixed volume and shape.  Liquid: has definite volume but not fixed shape.  Gas: has no fixed volume or shape. and is compressible.
  • 12. 12 Classification of Matter Chapter 1 Section 2 • Wood • Sand • Rocks • Gasoline • Juices and tea • Air (N2, O2, H2, CO2, etc.) • H2O • NaCl • H2SO4 • C (carbon) • Hg (mercury) • H or H2 (hydrogen)
  • 13. 13 Separation (Physical) Methods  Based on the physical properties of the substances (boiling point, adsorption, solubility, etc.)  Separation methods discussed in the text:  Distillation.  Filtration.  Chromatography. Chapter 1 Section 2
  • 14. 14 Atoms, Elements and Compounds Chemical changes (decomposition of compounds or recombining elements), such as electrolysis, heating, and photolysis. Compounds ( ‫المركبات‬ ) are substances with constant composition that can be broken down into elements by chemical processes. Compound – substance made of 2 or more types of atoms that are chemically bonded. Elements ( ‫العناصر‬ ) are substances that can’t be decomposed into simpler substances by physical or chemical means Element – pure substance made of only one type of atom. Atom(‫)الذرة‬- smallest unit of an element that keeps the properties of element.
  • 15. 15 Molecule and Mixture  Molecule(‫)الجزيء‬: type of compound in which the bonds are covalent bonds. Mixture (‫)الخليط‬ •In chemistry, a mixture is a material made up of two or more different substances which are mixed. A mixture differs from a compound in that( ‫في‬ ‫المركب‬ ‫عن‬ ‫الخليط‬ ‫)يختلف‬ ( 1 ) mixed in any proportion (‫نسبة‬ ‫باي‬ ‫)يخلط‬ ( 2 .) the components of which can be separated ) ‫اهلصف‬ ( by simple mechanical means. • Separating the Components of a Mixture: techniques to separate the components of mixtures (Size, density, solubility, electrical charge
  • 16. 16 Classification of Matter  Classify the following as mixtures, elements, compounds, etc. Aluminum foil: substance, element Table salt: substance, compound Milk: mixture, homogeneous Sea water: mixture, homogeneous Copper wire: substance, element
  • 17. 17 The Properties of Matter  Quantitative: expressed using numbers.  Qualitative: expressed using properties.  Physical properties: can be observed and measured without changing the substance.  Examples: color, melting point, states of matter.  Physical changes: the identity of the substance stays the same and only its state changes.  Examples: changes of state (melting, freezing).
  • 18. 18 The Properties of Matter  Chemical properties: must be determined by the chemical changes that are observed.  Examples: flammability, acidity, corrosiveness, reactivity.  Chemical changes: after a chemical change, the original substance no longer exists  Examples: combustion, digestion, corrosion.
  • 20. 20 The Properties of Matter  Extensive property: depends on the amount of matter.  Examples: mass, length.  Intensive property: does not depend on the amount of matter.  Examples: density, temperature, color. Mass of water 100.0 g 10.0 g Volume of water 0.100 L 0.010 L Temperature of water 25 °C 25 °C Density of water 1.00 g/mL 1.00 g/mL
  • 22. 22 Scientific Measurement Number Unit (1) Metric Units International System (SI Units) (2) English Units Used in Science There are two major systems of measurements:  Making observations can be done quantitatively or qualitatively.  A quantitative observation is called a measurement. It must include two important pieces of information:
  • 23. 23 Units of Measurement Number Unit 10 kilometers 1 gram 5 kelvin 20 miles 1 pound 60 Fahrenheit (1) Metric Units International System (SI Units) (2) English Units Used in Science There are two major systems of measurements:
  • 24. 24 The Fundamental SI Units All other units of measurement can be derived from the above seven fundamental SI units .
  • 25. 25 Using Prefixes in the SI System  The distance between Sanaa and Ibb is 90,000 meters.  90×103 meters.  90 kilo-meters (km)  The capacity of this computer is 80,000,000,000 bites.  80×109 bites  80 giga-bites (GB)
  • 26. 26 Table of Prefixes in the SI System Must be memorized!
  • 27. 27 Scientific Notation  0.0001 kg  1×10-4 kg  0.1 g  1 with 35 zeros kg  1×1035 kg  Mass vs. Weight How much does that pin weigh? How much does the earth weigh? Scientific Notation
  • 28. 28 Scientific Notations  123.1 = 1.231× 102 = 1.231 × 100  0.00013 = 1.3 × 10-4 = 1.3 / 10000 = 0.13 × 10-3  Avogadro’s Number*: 602,214,000,000,000,000,000,000 *The number of atoms contained in 12 g of carbon and is equal to 1 mole. 6.022 × 1023 Scientific notation is a very convenient way to express the number of atoms in chemistry problems.
  • 29. 29 Temperature  Three systems are used to measure temperatures:  Celsius scale (°C)  Kelvin scale (K)  Fahrenheit (°F)  You have to be able to convert from one scale to another.
  • 30. 30 The Three Major Temperature Scales Fahrenheit (F) Celsius (oC) Kelvin (K)
  • 31. 31 Celsius Scale vs. Kelvin Scale  Temperature scales for °C and K are identical, but their zeros are different. TK = TC + 273.15 TC = TK – 273.15
  • 32. 32 Fahrenheit Scale vs. Celsius Scale  Both unit temperature size and zero locations are different. Since: 180°F = 100°C => 9°F = 5°C and: 32°F = 0°C Then to convert from °F to °C: [Tf (°F) – 32 (°F)] = Tc (°C) 5°C 9°F
  • 33. 33 Fahrenheit Scale vs. Celsius Scale [ Tc (a) – Tc (b) ] °C = (5°C/9°F) [ Tf (a) – Tf (b) ] °F When Tc (b) = - 40°C, then Tf (b) = -40°F giving that: [ Tc (a) – (-40) ] °C = (5°C/9°F) [ Tf (a) – (-40) ] °F Thus: or F 9 C 5 40 40      f c T T C 5 F 9 40 40      c f T T
  • 34. 34 Volume  Volume is not an SI unit, but it is extremely important in chemical measurements.  Volume = 1m × 1m × 1m = 1m3  1m = 10dm (1m)3 = (10dm)3 1m3 = 1000dm3  1dm3 = 1L 1L = 1000mL = 1000cm3 1mL = 1cm3  (milli)Liter milli = 10-3 (centi)Meter centi = 10-2
  • 35. 35 Measurement of Volume Common types of laboratory equipment used to measure liquid volume.
  • 36. 36 Density  It is the mass of substance per unit volume. volume mass Density  Substance Physical State Density (g/cm3) Oxygen Gas 0.00133 Hydrogen Gas 0.000084 Ethanol Liquid 0.789 Water Liquid 0.998 Aluminum Solid 1.47 Iron Solid 7.87 Mercury Liquid 13.6
  • 37. 37 Uncertainty in Measurement  A measurement always has some degree of uncertainty. Chapter 1 Section 5 20.16 ml 20.17 ml 20.15 ml 20.18 ml 20.16 ml certain digit uncertain digit (must be estimated) • Uncertainty is ± 0.01 ml. • Certain and uncertain digits are known as significant figures.
  • 38. 38  Now you should be able to tell how many digits you need to include in your reading (measurement).  20 ml 20.1 ml 20.16 ml 20.160 ml 20.1600 ml Uncertainty in Measurement Chapter 1 Section 5 Which one?? These meaningful digits are the significant figures
  • 39. 39 Uncertainty in Measurement Different equipments have different uncertainties in their measurements. Chapter 1 Section 5 2.5 ± 0.1 cm 2.46 ± 0.01 cm These meaningful digits are the significant figures Uncertainty
  • 40. 40 Significant Figures (‫المعنوية‬ ‫)األرقام‬  In many cases, important physical quantities are obtained from measured values. Volume = l w h Density = mass / volume  Calculations need to be done on the basis of Significant Figure (S.F.) Rules  Rules for counting S.F.  Rules of mathematical operations on S.F.  Implication of the word “Significant”. It is to have the correct degree of uncertainty in the resultant physical quantities. Mathematical operations
  • 41. 41 Rules for Counting Significant Figures 1- Nonzero integers are always counted as S.F. Example: Give the number of S.F. for the following: 34 236 17296.1 12.1×102 Exponential (Scientific) notation Chapter 1 Section 5
  • 42. 42 Rules for Counting Significant Figures 2- Zeros (leading zeros, captive zeros, and trailing zeros) a) Leading zeros are not counted as S.F. Example: Give the number of S.F. for the following: 00121.1 0.0025 Chapter 1 Section 5
  • 43. 43 Rules for Counting Significant Figures b) Captive zeros are always counted as S.F. Example: Give the number of S.F. for the following: 1.008 701.1 ×10-4 3.000000008 0.0901 Chapter 1 Section 5
  • 44. 44 Rules for Counting Significant Figures c) Trailing zeros are counted as S.F. only if the number contains a decimal point. Example: Give the number of S.F. for the following: 1.000 320.00 ×10-1 100 (can’t tell!) may be 1, 2 or 3. 100. 100.0 Chapter 1 Section 5
  • 45. 45 Rules for Counting Significant Figures 3- Exact numbers are assumed to have an infinite number of S.F. Examples: 3 Apples is 3.00000000 (zeros are all the way to ∞) 2 in 2πr (the circumference of a cycle). 1 km = 1000 m 1 in = 2.54 cm Chapter 1 Section 5 Mathematical relationships Definitions
  • 46. 46 Exercise  How many significant figures are there in the following numbers? Chapter 1 Section 5 3004 5. 10 10 120 0  . 0 250. m cm3 kg
  • 47. 47 Mathematical Operations  Multiplication or division 4.56 × 1.4 = 6.38 6.4 Chapter 1 Section 5 From calculator before correction Number of S.F. 3 2 2 S.F. (After correction)  Addition and Subtraction 12.11 + 18.0 + 1.013 31.1 31.123 before correction 3 S.F. (After correction)
  • 48. 48 Rule for Rounding Numbers (‫االرقام‬ ‫تقريب‬ ‫)قواعد‬  6.38  The digit to be removed If ≥ 5, then round up, i.e. the 3 becomes 4.  6.4 If < 5, then the digit stays unchanged.  6.34 becomes 6.3
  • 49. 49 Exercises  Perform the following mathematical operation and express the result to the correct number of significant figures: Chapter 1 Section 5 01 1 273 0821 0 102 0 . . .   Rounding off should be carried out for the final answer and NOT to the intermediate answers. However, you must keep track of the significant figures in the intermediate steps.
  • 50. 50 Precision and Accuracy Chapter 1 Section 5 Random error Systematic error Precise but not accurate “reproducible” Neither precise nor accurate Accurate and precise Poor technique Good technique but needs calibration Good technique
  • 51. 51 Precision and Accuracy  Accuracy: Agreement of a particular value (measurement) with the true value.  Precision: Agreement among several values (measurements), not necessarily agreeing with the true value. Chapter 1 Section 5
  • 52. 52 Precision and Accuracy Chapter 1 Section 5 Student A Student B Student C 0.335 g 0.357 g 0.369 g 0.331 g 0.375 g 0.373 g 0.333 g 0.338 g 0.371 g Average: 0.333 g 0.357 g 0.371 g  True mass was 0.370 grams Three students are asked to determine the mass of an aspirin tablet.
  • 53. 53 Precision and Accuracy Chapter 1 Section 5 Three students are asked to determine the mass of an aspirin tablet. True mass was 0.370 grams
  • 54. 54 Conversion Factors  Used to convert from one unit to another. Chapter 1 Section 6 Example 1: How many centimeters in 25.5 inches (in)?   in 1 cm 2.54 in 25.5 64.8 cm Example 2: How many inches in 25.5 centimeters?   cm 2.54 in 1 cm 25.5 10.0 in
  • 55. 55 Dimensional Analysis – Tracking Units 1L = 1000 ml 1 ml = 0.001 L = 1× 10-3 L Chapter 1 Section 6 Example 3: How many ml are in 1.63 L? Which direction you choose? 1.63 L × = 1.63 L × = 1 L 1000 ml ? 1 L 1000 ml L2 ml 0.00163 1.63×103 ml
  • 56. 56  How many centimeters are in 0.25 megameters? 0.25 megameters × = 0.25×106 m 0.25×106 m × = 0.25×108 cm = 2.5×107 cm = 25.×106 cm Solving Problems Using Dimensional Analysis Chapter 1 Section 6 megameters 1 m 1×106 1 meters cm 100
  • 57. 57  The Food and Drug Administration (FDA) recommends that dietary sodium intake be no more than 2400 mg per day. What is this mass in pounds (lb), if 1 lb = 453.6 g? Solving Problems Using Dimensional Analysis Chapter 1 Section 6 lb 10 5.3 g 453.6 lb 1 mg 1000 g 1 mg 2400 3     
  • 58. 58 Exercise  Perform the following mathematical operation and express the result to the correct number of significant figures: 4326 . 0 705 . 80 623 . 0 470 . 0 1 . 3 526 . 2   Rounding off should be carried out for the final answer and NOT to the intermediate answers. However, you must keep track of the significant figures in the intermediate steps.
  • 59. 59 Exercise Methodology to solve such problems: • Start with the quantity given in the question. • Use possible conversion factors to convert the unit of the given quantity in the question to the desired/needed unit.
  • 60. 60
  • 61. 61