In the metric and SI systems, one unit is used for each type of measurement:
Measurement Metric SI Length meter (m) meter (m) Volume liter (L) cubic meter (m3)
Mass gram (g) kilogram (kg) Time second (s) second (s) Temperature Celsius (°C) Kelvin (K)
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For each of the following, indicate whether the unit describes 1) length 2) mass or 3) volume. ____ A. A bag of tomatoes is 4.6 kg.
____ B. A person is 2.0 m tall.
____ C. A medication contains 0.50 g aspirin.
____ D. A bottle contains 1.5 L of water.
Learning Check
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For each of the following, indicate whether the unit describes 1) length 2) mass or 3) volume.
2 A. A bag of tomatoes is 4.6 kg.
1 B. A person is 2.0 m tall.
2 C. A medication contains 0.50 g aspirin.
3 D. A bottle contains 1.5 L of water.
Solution
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The Metric System (SI)
The metric system or SI (international system) is § A decimal system based on 10.
§ Used in most of the world.
§ Used everywhere by scientists.
THE USE OF PREFIXES • Prefixes are used to relate basic and derived units. • The common prefixes are given in the following table:
COMMONLY USED METRIC UNITS
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13
1 m = ________ cm 100 cm 2 Kg = _______ g 2000 g 3 L = ________ ml 3000 ml
Learning Check 1.2. Properties and Changes: Physical & Chemical • PHYSICAL PROPERTIES OF MATTER
• Physical properties can be observed or measured without attempting to change the composition of the matter being observed.
• Examples: color, shape and mass
• CHEMICAL PROPERTIES OF MATTER • Chemical properties can be observed or
measured only by attempting to change the matter into new substances.
• Examples: flammability and the ability to react (e.g. when vinegar and baking soda are mixed)
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Example: Physical Properties of Elements The physical properties of an element § Are observed or measured without changing its identity. § Include the following:
Shape Color Odor
Taste Density Melting point Boiling Point
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Some physical properties of copper are: Color Red-orange Luster Very shiny Melting point 1083°C Boiling point 2567°C Conduction of electricity Excellent Conduction of heat Excellent
Example: Physical Properties of Elements
PHYSICAL & CHEMICAL CHANGES • PHYSICAL CHANGES OF MATTER
• Physical changes take place without a change in composition.
• Examples: freezing, melting, or evaporation of a substance (e.g. water)
• CHEMICAL CHANGES OF MATTER • Chemical changes are always
accompanied by a change in composition.
• Examples: burning of paper and the fizzing of a mixture of vinegar and baking soda
1. Food digesting 2. Sodium reacting
with water 3. Methanol burning
in air 4. Liquid helium
boiling
Which of the following is a physical change? Learning Check:
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1.3. PARTICULATE MODEL OF MATTER
• All matter is made up of tiny particles called molecules and atoms.
• MOLECULES • A molecule is the smallest
particle of a pure substance that is capable of a stable independent existence.
• ATOMS • Atoms are the particles that
make up molecules. 20
Atoms § Are tiny particles of matter. § Of an element are similar
and different from other elements.
§ Of two or more different elements combine to form compounds.
§ Are rearranged to form new combinations in a chemical reaction.
MOLECULE CLASSIFICATION • Diatomic molecules contain two atoms.
• Triatomic molecules contain three atoms.
• Polyatomic molecules contain more than three atoms.
MOLECULE CLASSIFICATION (continued)
• HOMOATOMIC MOLECULES • The atoms contained in homoatomic molecules are of
the same kind.
• HETEROATOMIC MOLECULES • The atoms contained in heteroatomic molecules are of
two or more kinds.
homoatomic heteroatomic
MOLECULE CLASSIFICATION EXAMPLE
• Classify the molecules in these diagrams using the terms diatomic, triatomic, or polyatomic molecules.
• Solution: H2O2 is a polyatomic molecule, H2O is a triatomic molecule, and O2 is a diatomic molecule.
• Classify the molecules using the terms homoatomic or heteroatomic molecules.
• Solution: H2O2 and H2O are heteroatomic molecules and O2 is a homoatomic molecule.
1.4. CLASSIFICATION OF MATTER • Matter can be classified into several categories based on
chemical and physical properties.
• PURE SUBSTANCES • Pure substances have a constant composition and a fixed
set of other physical and chemical properties. • Example: pure water
(always contains the same proportions of hydrogen and oxygen and freezes at a specific temperature)
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CLASSIFICATION OF MATTER (continued)
• MIXTURES • Mixtures can vary in composition and properties. • Example: mixture of table sugar and water
(can have different proportions of sugar and water) • A glass of water could contain one, two, three, etc.
spoons of sugar. • Properties such as
sweetness would be different for the mixtures with different proportions.
HETEROGENEOUS MIXTURES • The properties of a sample of a heterogeneous mixture
depends on the location from which the sample was taken.
• A pizza pie is a heterogeneous mixture. A piece of crust has different properties than a piece of pepperoni taken from the same pie.
HOMOGENEOUS MIXTURES • Homogeneous mixtures are also called solutions. The
properties of a sample of a homogeneous mixture are the same regardless of where the sample was obtained from the mixture.
• Samples taken from any part of a mixture made up of one spoon of sugar mixed with a glass of water will have the same properties, such as the same taste.
ELEMENTS • Elements are pure substances that are made up of
homoatomic molecules or individual atoms of the same kind.
• Examples: oxygen gas made up of homoatomic molecules and copper metal made up of individual copper atoms
COMPOUNDS • Compounds are pure substances that are made up of
heteroatomic molecules or individual atoms (ions) of two or more different kinds.
• Examples: pure water made up of heteroatomic molecules and table salt made up of sodium atoms (ions) and chlorine atoms (ions)
MATTER CLASSIFICATION SUMMARY
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MATTER CLASSIFICATION EXAMPLE • Classify H2, F2, and HF using the classification scheme from
the previous slide.
• Solution: • H2, F2, and HF are all pure substances because they
have a constant composition and a fixed set of physical and chemical properties.
• H2 and F2 are elements because they are pure substances composed of homoatomic molecules.
• HF is a compound because it is a pure substance composed of heteroatomic molecules.
TEMPERATURE SCALES • The three most
commonly-used temperature scales are the Fahrenheit, Celsius and Kelvin scales.
• The Celsius and Kelvin scales are used in scientific work.
TEMPERATURE CONVERSIONS • Readings on one temperature scale can be converted to the
other scales by using mathematical equations. • Converting Fahrenheit to Celsius.
• Converting Celsius to Fahrenheit.
• Converting Kelvin to Celsius.
• Converting Celsius to Kelvin.
( )32F95C != !!
( ) 32C59F += !!
273KC !=!
273CK +=!
TEMPERATURE CONVERSION PRACTICE
• Covert 22°C and 54°C to Fahrenheit and Kelvin.
( ) F72F6.7132C2259F !!!! !=+=
K 295273C22K =+= !
( ) F129F2.12932C5459F !!!! !=+=
K 327273C54K =+= !
1.7. SCIENTIFIC NOTATION • Scientific notation provides a convenient way to express
very large or very small numbers. • Numbers written in scientific notation consist of a product of
two parts in the form M x 10n, where M is a number between 1 and 10 (but not equal to 10) and n is a positive or negative whole number.
• The number M is written with the decimal in the standard position.
1.7.SCIENTIFIC NOTATION (continued) • STANDARD DECIMAL POSITION
• The standard position for a decimal is to the right of the first nonzero digit in the number M.
• SIGNIFICANCE OF THE EXPONENT n • A positive n value indicates the number of places to the
right of the standard position that the original decimal position is located.
• A negative n value indicates the number of places to the left of the standard position that the original decimal position is located.
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Learning Check
Select the correct scientific notation for each. A. 0.000 008
1) 8 x 106 2) 8 x 10-6 3) 0.8 x 10-5 B. 72 000
1) 7.2 x 104 2) 72 x 103 3) 7.2 x 10-4
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Solution
Select the correct scientific notation for each. A. 0.000 008
2) 8 x 10-6 B. 72 000
1) 7.2 x 104
1.7. SCIENTIFIC NOTATION MULTIPLICATION
• Multiply the M values (a and b) of each number to give a product represented by M'.
• Add together the n values (y and z) of each number to give a sum represented by n'.
• Write the final product as M' x 10n'. • Move decimal in M' to the standard position and adjust n' as
necessary.
( )( ) ( )( )zyzy 10ba10b10a +!=!!
( )( ) ( )( ))2()8(-28 104.03.0104.0103.0 !+"=""
7
6
102.11012!=
!=
1.7. SCIENTIFIC NOTATION DIVISION • Divide the M values (a and b) of each number to give a
quotient represented by M'. • Subtract the denominator (bottom) n value (z) from the
numerator (top) n value (y) to give a difference represented by n'.
• Write the final quotient as M' x 10n'. • Move decimal in M' to the standard position and adjust n' as
necessary.
( )( ) ( )zyz
y
10ba
10b10a -!
"
#$%
&=
'
'
9
10
105.71075.0
!=
!=
( )( ) ( )(-2)(8)
2-
8
100.40.3
104.0103.0 -=
!
!
1.8. SIGNIFICANT FIGURES • Significant figures are the numbers in a measurement that represent the
certainty of the measurement, plus one number representing an estimate.
• COUNTING ZEROS AS SIGNIFICANT FIGURES • Leading zeros are never significant figures. • Buried zeros are always
significant figures. • Trailing zeros are generally
significant figures with decimal. • Trailing zeros are not
significant figures without decimal.
1.8. SIGNIFICANT FIGURES (continued) • The answer obtained by multiplication or division must contain
the same number of significant figures (SF) as the quantity with the fewest number of significant figures used in the calculation.
( ) ( ) SF 2 SF 2SF 4194625.19 5.4 325.4
=!
"=!
( ) ( ) SF 2 SF 2SF 496.0169.0 5.4 325.4
=÷
!=÷
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1.8. SIGNIFICANT FIGURES (continued) • The answer obtained by addition or subtraction must contain
the same number of places to the right of the decimal (prd) as the quantity in the calculation with the fewest number of places to the right of the decimal.
( ) ( ) prd 1 prd 1prd 38.10825.10 5.5 325.5
=+
!=+
( ) ( ) prd 1 prd 1prd 32.0175.0 5.5 325.5
=!
!"!=!
ROUNDING RULES FOR NUMBERS • If the first of the nonsignificant figures to be dropped from an
answer is 5 or greater, all the nonsignificant figures are dropped and the last remaining significant figure is increased by one.
• If the first of the nonsignificant figures to be dropped from an answer is less than 5, all nonsignificant figures are dropped and the last remaining significant figure is left unchanged.
Round 10.825 to 1place to the right of the decimal. ⇒10.8
Round －0.175 to 1 place to the right of the decimal. ⇒ −0.2
EXACT NUMBERS • Exact numbers are numbers that have no uncertainty (they
do not affect significant figures). • A number used as part of a defined relationship between
quantities is an exact number (e.g. 100 cm = 1 m). • A counting number obtained by counting individual objects
is an exact number (e.g. 1 dozen eggs = 12 eggs). • A reduced simple fraction is an exact number (e.g. 5/9 in
equation to convert ºF to ºC).
1.9. USING UNITS IN CALCULATIONS • The factor-unit method for solving numerical problems is a
four-step systematic approach to problem solving.
• Step 1: Write down the known or given quantity. Include both the numerical value and units of the quantity.
• Step 2: Leave some working space and set the known quantity equal to the units of the unknown quantity.
• Step 3: Multiply the known quantity by one or more factors, such that the units of the factor cancel the units of the known quantity and generate the units of the unknown quantity.
• Step 4: After you generate the desired units of the unknown quantity, do the necessary arithmetic to produce the final numerical answer.
SOURCES OF FACTORS • The factors used in the factor-unit method are fractions
derived from fixed relationships between quantities. These relationships can be definitions or experimentally measured quantities.
• An example of a definition that provides factors is the relationship between meters and centimeters: 1m = 100cm. This relationship yields two factors: and
m 1cm 100
cm 100m 1
FACTOR UNIT METHOD EXAMPLES • A length of rope is measured to be 1834 cm. How many meters is
this?
• Solution: Write down the known quantity (1834 cm). Set the known quantity equal to the units of the unknown quantity (meters). Use the relationship between cm and m to write a factor (100 cm = 1 m), such that the units of the factor cancel the units of the known quantity (cm) and generate the units of the unknown quantity (m). Do the arithmetic to produce the final numerical answer.
m 34.18cm 100m 1cm 1834
m cm 1834
=!"
#$%
&
=
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1.10. PERCENTAGE • The word percentage means per one hundred. It is the
number of items in a group of 100 such items.
• PERCENTAGE CALCULATIONS • Percentages are calculated using the equation:
• In this equation, part represents the number of specific items included in the total number of items.
100wholepart
% !=
EXAMPLE PERCENTAGE CALCULATION
• A student counts the money she has left until pay day and finds she has $36.48. Before payday, she has to pay an outstanding bill of $15.67. What percentage of her money must be used to pay the bill?
• Solution: Her total amount of money is $36.48, and the part is what she has to pay or $15.67. The percentage of her total is calculated as follows:
%96.4210048.3667.15
100wholepart
% =!=!=
1.11. DENSITY • Density is the ratio of the mass of a sample of matter divided
by the volume of the same sample. or
volumemass
density =
vmd =
DENSITY CALCULATION EXAMPLE • A 20.00 mL sample of liquid is put into an empty beaker that
had a mass of 31.447 g. The beaker and contained liquid were weighed and had a mass of 55.891 g. Calculate the density of the liquid in g/mL.
• Solution: The mass of the liquid is the difference between the mass of the beaker with contained liquid, and the mass of the empty beaker or 55.891g -31.447 g = 24.444 g. The density of the liquid is calculated as follows:
mLg222.1
mL 20.00g 444.24
vmd ===
Accuracy and Precision
The accuracy of a measurement signifies how close it comes to the true (or accepted) value- that is, how nearly correct it is.
A !A AA ± !A 11 in. ± 0.2.
3.0ºC 37.0ºC34.0ºC 40.0ºC 3.0ºC
A !A
% unc =!AA !100%.
Precision
refers to the agreement among repeated measurements-that is, the “spread” of the measurements or how close they are together. The more precise a group of measurements, the closer together they are.
A !A AA ± !A 11 in. ± 0.2.
3.0ºC 37.0ºC34.0ºC 40.0ºC 3.0ºC
A !A
% unc =!AA !100%.
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a science that studies the composition and properties of matter, and the changes that matter undergoes.
