Spencer L. SeagerMichael R. Slabaugh

www.cengage.com/chemistry/seager

Jennifer P. Harris

Chapter 1:Matter, Measurements,

and Calculations

LEARNING OBJECTIVES/ASSESSMENT 

When you have completed your study of this chapter, you should be able to:  1. Explain what matter is.  (Section 1.1; Exercise 1.2) 

 2. Explain differences between the terms physical and chemical  as applied to:      a.  Properties of matter (Section 1.2; Exercises 1.10 b & c)     b.  Changes in matter (Section 1.2; Exercises 1.8 a & b) 

 3. Describe matter in terms of the accepted scientific model.   (Section 1.3; Exercise 1.12) 

 4. On the basis of observation or information given to you, classify  matter into the correct category of each of the following pairs: 

    a.  Heterogeneous or homogeneous (Section 1.4; Exercise 1.22)     b.  Solution or pure substance (Section 1.4; Exercise 1.24)     c.  Element or compound (Section 1.4; Exercise 1.18)  

5. Recognize the use of measurement units in everyday activities.   (Section 1.5; Exercise 1.28) 

 6. Recognize units of the metric system, and convert measurements done  using the metric system into related units.  (Section 1.6; Exercises 1.30 and 1.40) 

 7. Express numbers using scientific notation, and do calculations with  numbers expressed in scientific notation.  (Section 1.7; Exercises 1.48 and 1.60) 

 8. Express the results of measurements and calculations using the  correct number of significant figures.   (Section 1.8; Exercises 1.64 and 1.66) 

  9. Use the factor‐unit method to solve numerical problems.   (Section 1.9; Exercise 1.82) 

 10. Do calculations involving percentages.  (Section 1.10; Exercise 1.92) 

 11. Do calculations involving densities.  (Section 1.11; Exercise 1.98)  

Topics covered in Chapter OneAll sections of Chapter One will be covered.

Example exercises include:1.7 – 1.171.22 – 1.251.29 – 1.381.46 – 1.751.77 – 1.801.87 – 1.99

MATTER & MASS• Matter is anything that has mass and occupies space.

• Mass is a measurement of the amount of matter in an object.

• Mass is independent of the location of an object.• An object on the earth has the same mass as the same

object on the moon.

WEIGHT• Weight is a measurement of the gravitational force acting

on an object.• Weight depends on the location of an object.• An object weighing 1.0 lb on earth weighs about 0.17 lb

on the moon.

PHYSICAL & CHEMICAL PROPERTIES• PHYSICAL PROPERTIES OF MATTER

• Physical properties can be observed or measured without attempting to change the composition of the matter being observed.

• Examples: physical state (duh), 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)

PHYSICAL & CHEMICAL CHANGES• PHYSICAL CHANGES OF MATTER

• Physical changes take place without a change in composition.

• Examples: changes of state, like freezing, melting, or evaporation of a substance (e.g. water)

• CHEMICAL CHANGES OF MATTER• Chemical changes are always

accompanied by a change in composition. Most color changes.

• Examples: burning of paper and the fizzing of a mixture of vinegar and baking soda

Physical or Chemical Properties?1. Color of gold2. Tendency of silver to tarnish3. Flammability of gasoline4. Boiling point of alcohol5. Smell of perfume6. Different properties of ozone• Has the formula of O3

• Bluish color• A gas a room temperature• Decomposes on exposure to sunlight

Physical or Chemical Changes?1. Sugar dissolves in hot water2. Copper metal turns green over time with exposure to air3. Compressed liquid propane evaporates when the valve is

opened on the container4. Sugar burns in a pot when heated to a high temperature

PARTICULATE MODEL OF MATTER• All matter is made up of tiny

particles called molecules and atoms.

• MOLECULES• A molecule (or atom, depending

on the substance) 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.

MOLECULE CLASSIFICATION• Diatomic molecules contain two atoms.

• Triatomic molecules contain three atoms.

• Polyatomic molecules contain many 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.

• Classify the molecules using the terms homoatomic or heteroatomic molecules.

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)

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

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.

Matter Classification1. Coffee2. Apple juice3. Gold4. Table salt5. Methane (CH4)

6. Urine7. Clean air8. Pure water9. Nitrogen gas10. Concrete11. Bronze (composed of tin and copper)12. water and gasoline mixed together

MEASUREMENTS & UNITS• Measurements consist of two

parts, a number and a unit or label such as feet, pounds, or gallons.

• Measurement units are agreed upon by those making and using the measurements.

• Measurements are made using measuring devices (e.g. rulers, balances, graduated cylinders, etc.). (Name other common measuring devices)

METRIC SYSTEM• The metric system is a decimal system in which larger and

smaller units are related by factors of 10.

• TYPES OF METRIC SYSTEM UNITS• Basic or defined units [e.g. 1 meter (1 m)] are used to

calculate derived units [e.g. 1 square meter (1 m2)].• Which of the above are basic units?

THE USE OF PREFIXES• Prefixes are used to relate basic and derived units.• The common prefixes are given in the following table:

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

COMMONLY USED METRIC UNITS

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.

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.

Convert to scientific notation1. 1,0002. 0.13. 104. 15. 1,016,2006. 0.03107. 0.0000009203Convert to regular numbers1. 1.034 X 100

2. 9.02 X 101

3. 2.003 X 10-5

4. 6.023 X 107

More conversionsPut final answer into scientific notation.1.12.5 mm into km2.3.650 X 108 ng into g3.125 uL into mL

Make these changes in exponential numbers1.670 X 10-8 = ? X 10-11 2.0.0475 X 106 = ? X 105 3.1.25 X 10-3 = ? X 102

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

102.1

1012

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.

zy

z

y

10ba

10b10a -

9

10

105.7

1075.0

(-2)(8)

2-

8

100.40.3

104.0103.0 -

SCI NOTATION ADD/SUBTRACT• Change the exponential values of numbers involved to be the

same for all numbers.• Add or subtract (a and b values) in the usual way, the

exponential value doesn’t change• Write the answer as M' x 10n'.• Move decimal in M' to the standard position and adjust n' as

necessary.

1.25 X 105 + 4.62 X 104 = 1.25 X 105 + 0.462 X 105 = 1.712 X 105 or 1.71 X 105

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.

SIGNIFICANT FIGURES (continued)Using the apparatus supplied at each station, determine the measurement with the correct number of significant figures.

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

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).

EXACT NUMBERSSome exact numbers are defined.

2.54 cm = 1 in (exact numbers)

1 mL = 1 cm3

Calculate the followingReport answers to the correct number of significant figures and round as appropriate.1.89.3 X 77.0 X 0.08 =2.(7.890 X 1012) / (6.7 X 104) =3.67.8 X 9.8 / 100.04 =4.89.6 + 98.33 – 4.674 =5.0.004 + 0.09879 =6.(2.45 X 108) + (1.225 X 10-3) =7.(568.99 – 232.1) X 5.3 =

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

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:

%96.4210048.3667.15100

wholepart%

DENSITY• Density is the ratio of the mass of a sample of matter divided

by the volume of the same sample.

or

volumemassdensity

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

Perform the following calculationsReport the final answer using the correct number of significant figures and rounding as appropriate.1.convert 22.55 in. into cm.2.1760 yds into m. Use 36 in/yd. 3.-40oC into K.4.-40oC into 0F5.A possible gold tooth crown has a volume of 1.07 mL and a mass of 20.6 g. Calculate the density. Is it pure gold?6.How many minutes does it take to run 10.0 km at a pace of 7.5 mi/hr? 7.How many mL are in 2.0 gallons? Use 4 qts/gal, 2 pints/qt, 16 oz = 1 pint and 29.57 mL = 1 oz. 8.60.0 g of a solution contains 3.7 g of salt. What is the % concentration of NaCl?