Chapter 1Chapter 1Matter,Measurement, Matter,Measurement,

and Problem and Problem SolvingSolving

Classification of MatterClassification of Matter

matter is anything that has mass and occupies space we can classify matter based on whether it’s solid,

liquid, or gas

State Shape Volume Compress Flow

Solid Fixed Fixed No No

Liquid Indef. Fixed No Yes

Gas Indef. Indef. Yes Yes

• Fixed = keeps shape when placed in a container • Indefinite = takes the shape of the container

SolidsSolids the particles in a solid are

packed close together and are fixed in position◦ though they may vibrate

incompressible the inability of the particles

to move around results in solids retaining their shape and volume when placed in a new container, and prevents the particles from flowing

Crystalline vs. Amorphous Crystalline vs. Amorphous solidssolids

some solids have their particles arranged in an orderly geometric pattern – we call these crystalline solids◦ salt and diamonds

some solids have their particles randomly distributed without any long-range pattern – we call these amorphous solids◦ plastic◦ glass◦ charcoal

LiquidsLiquids

the particles in a liquid are closely packed, but they have some ability to move around

Incompressible take the shape of their container

and to flow however, they don’t have

enough freedom to escape and expand to fill the container

GasesGases in the gas state, the

particles have complete freedom from each other

the particles are constantly flying around, bumping into each other and the container

Compressible

because there is a lot of empty space, the particles can be squeezed closer together – therefore gases are compressible

because the particles are not held in close contact and are moving freely, gases expand to fill and take the shape of their container, and will flow

Classification of MatterClassification of Matterby Compositionby Composition

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1) made of one type of particle

2) all samples show the same intensive properties

1) made of multiple types of particles

2) samples may show different intensive properties

Classification of Pure Classification of Pure SubstancesSubstances

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1) made of one type of atom (some elements found as multi-atom molecules in nature)

2) combine together to make compounds

1) made of one type of molecule, or array of ions

2) molecules contain 2 or more different kinds of atoms

Classification of MixturesClassification of Mixtures

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1) made of multiple substances, but appears to be one substance

2) all portions of a sample have the same composition and properties

1) made of multiple substances, whose presence can be seen

2) portions of a sample have different composition and properties

Separation of MixturesSeparation of Mixtures separate mixtures based on different physical

properties of the components◦ Physical change

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Centrifugation &Decanting

Density

EvaporationVolatility

ChromatographyAdherence to a Surface

FiltrationState of Matter (solid/liquid/gas)

DistillationBoiling Point

TechniqueDifferent Physical Property

Changes in MatterChanges in Matter changes that alter the

state or appearance of the matter without altering the composition are called physical changes

state changes◦ boiling / condensing◦ melting / freezing◦ subliming

Dissolving of Sugar

C12H22O11(s)

C12H22O11(aq)

Physical change vs. Physical change vs. Chemical changeChemical change changes that alter the

composition of the matter are called chemical changes◦ during the chemical

change, the atoms that are present rearrange into new molecules, but all of the original atoms are still present

rusting processes that release

lots of energy burning

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C3H8(g) + 5 O2(g) → 3 CO2(g) + 4 H2O(l)

Burning propane gas

EnergyEnergy changes in matter, both physical and chemical, result

in the matter either gaining or releasing energy energy is the capacity to do work work is the action of a force applied across a distance

◦ a force is a push or a pull on an object◦ electrostatic force is the push or pull on objects that

have an electrical charge

EnergyEnergykinetic energy is energy of motion

motion of the atoms, molecules, and subatomic particlespotential energy is energy that is stored in the matter

due to the composition of the matter and its position in the universe

chemical potential energy arises from electrostatic forces between atoms, molecules, and subatomic particles

Law of Conservation of Energyenergy is neither created nor destroyed. It is converted from one form to another

Spontaneous ProcessesSpontaneous Processes

processes in nature tend to occur on their own when the result is material(s) with lower total potential energy

◦ processes that result in materials with higher total potential energy can occur, but generally will not happen without input of energy from an outside source

when a process results in materials with less potential energy at the end than there was at the beginning, the difference in energy is released into the environment

TemperatureTemperature measure of the average amount of kinetic energy

◦ higher temperature = larger average kinetic energy

heat flows from the matter that has high thermal energy into matter that has low thermal energy◦ until they reach the same temperature◦ heat is exchanged through molecular collisions

between the two materials

Temperature ScalesTemperature Scales

Fahrenheit Scale, °F◦ used in the U.S.

Celsius Scale, °C◦ used in all other

countries Kelvin Scale, K

◦ absolute scale no negative numbers

◦ directly proportional to average amount of kinetic energy

◦ 0 K = absolute zero

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Fahrenheit vs. CelsiusFahrenheit vs. Celsius a Celsius degree is 1.8 times larger than a Fahrenheit

degree the standard used for 0° on the Fahrenheit scale is a

lower temperature than the standard used for 0° on the Celsius scale

the size of a “degree” on the Kelvin scale is the same as on the Celsius scale◦ so 1 kelvin is 1.8 times larger than 1°F

the 0 standard on the Kelvin scale is a much lower temperature than on the Celsius scale

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TF = 1.8 TC + 32

TC = (TF – 32)

1.8

K = °C + 273.15

ExampleExample

The melting point of gallium is 85.6oF. What is this temperature on ◦ Celsius scale

◦ Kelvin scale

The Standard UnitsThe Standard Units

Scientists have agreed on a set of international standard units for comparing all our measurements called the SI units◦ Système International = International System

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Quantity Unit Symbol

length meter m

mass kilogram kg

time second s

temperature kelvin K

Common Prefix Multipliers in the Common Prefix Multipliers in the SI SystemSI System

Prefix SymbolDecimal

EquivalentPower of 10

mega- M 1,000,000 Base x 106

kilo- k 1,000 Base x 103

deci- d 0.1 Base x 10-1

centi- c 0.01 Base x 10-2

milli- m 0.001 Base x 10-3

micro- or mc 0.000 001 Base x 10-6

nano- n 0.000 000 001 Base x 10-9

pico p 0.000 000 000 001 Base x 10-12

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All units in the SI system are related to the standard unit by a power of 10The power of 10 is indicated by a prefix multiplierThe prefix multipliers are always the same, regardless of the standard unitReport measurements with a unit that is close to the size of the quantity being measured

Common Units and Their Common Units and Their EquivalentsEquivalents

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Volume

1 liter (L) = 1000 milliliters (mL)

1 liter (L) = 1000 cubic centimeters (cm3)

1 liter (L) = 1.057 quarts (qt)

1 U.S. gallon (gal) = 3.785 liters (L)

Mass

1 kilogram (km) = 2.205 pounds (lb)

1 pound (lb) = 453.59 grams (g)

1 ounce (oz) = 28.35 grams (g)

Length

1 kilometer (km) = 0.6214 mile (mi)

1 meter (m) = 39.37 inches (in.)

1 meter (m) = 1.094 yards (yd)

1 foot (ft) = 30.48 centimeters (cm)

1 inch (in.) = 2.54 centimeters (cm) exactly

VolumeVolume Derived unit◦ any length unit cubed

Measure of the amount of space occupied

SI unit = cubic meter (m3)

Commonly measure solid volume in cubic centimeters (cm3)

Commonly measure liquid or gas volume in milliliters (mL)

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Mass & VolumeMass & Volume two main physical properties of matter mass and volume are extensive properties

◦ the value depends on the quantity of matter◦ extensive properties cannot be used to identify what

type of matter something is Large iceberg and small ice cube

even though mass and volume are individual properties, for a given type of matter they are related to each other!

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Volume vs. Mass of Brass y = 8.38x

0

20

40

60

80

100

120

140

160

0.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 16.0 18.0Volume, cm3

Mas

s, g

DensityDensity◦ Ratio of mass:volume is

an intensive property value independent of

the quantity of matter Solids = g/cm3

◦ 1 cm3 = 1 mL Liquids = g/mL Gases = g/L Volume of a solid can be

determined by water displacement – Archimedes Principle

Density : solids > liquids >>> gases◦ except ice is less dense

than liquid water!

For equal volumes, denser object has larger mass

For equal masses, denser object has smaller volume

Heating an object generally causes it to expand, therefore the density changes with temperature

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Volume

MassDensity

A MeasurementA Measurement the unit tells you what standard you are comparing

your object to the number tells you

1. what multiple of the standard the object measures2. the uncertainty in the measurement

scientific measurements are reported so that every digit written is certain, except the last one which is estimated

If the length is reported as 3.26 cm,

• the digits 3 and 2 are certain (known).

• the final digit, 6, is estimated (uncertain).

• all three digits (2, 7, and 6) are significant, including the estimated digit.

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Known & Estimated DigitsKnown & Estimated Digits

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E.g

l8. . . . l . . . . l9. . . . l . . . . l10. . cm

What is the length of the line?

1) 9.2 cm

2) 9.13 cm

3) 9.19 cm

For the following volume readings, what would be measured values?

Uncertainty in Measured Uncertainty in Measured NumbersNumbers

accuracy is an indication of how close a measurement comes to the actual value of the quantity

precision is an indication of how reproducible a measurement is

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Accuracy, Precision, and Accuracy, Precision, and Significant FiguresSignificant Figures

Significant figures: The number of meaningful digits in a measured or calculated quantity. They come from uncertainty in any measurement.

Generally the last digit in a reported measurement is uncertain (estimated).

Exact numbers and relationships (7 days in a week, 30 students in a class, etc.) effectively have an infinite number of significant figures.

ExamplesExamplesClassify each of the following as (1) exact or (2)

measurednumbers.

A.__Gold melts at 1064 °C.

B.__1 yard = 3 feet

C.__The diameter of a red blood cell is 6 x 10-4 cm.

D.__There are 6 hats on the shelf.

E.__A can of soda contains 355 mL of soda.

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Accuracy, Precision, and Significant Accuracy, Precision, and Significant FiguresFiguresRules for counting significant figures (left-to-right):

1. Zeros in the middle of a number are like any other digit; they are always significant.

◦ 4.803 cm 4 sf

2. Rules for counting significant figures (left-to-right):◦ Zero at the beginning of a number are not significant

(placeholders).

0.00661 g 3 sf or 6.61 x 10-3 g3. Zeros at the end of a number and after the decimal point are

always significant.55.220 K 5 sf

4. Zeros at the end of a number without a written decimal point are ambiguous and should be avoided by using scientific notation

if 150 has 2 sig. figs. then 1.5 x 102

but if 150 has 3 sig. figs. then 1.50 x 102

Rounding NumbersRounding NumbersIf the first digit you remove is 4 or less, it and all following

digits are dropped from the number 5.664 425 = 5.664 (4 s.f)

If the digit you remove is 5 or greater, the last digit of the number is increases by 1 5.664 525 = 5.665 (4 s.f)

Sometimes, a calculator displays a small whole number. To give an answer with the correct number of significant figures, significant zeros may need to be written after the calculator result.

E.g 8.00 ÷ 2.00 = 4 4.00

3 s.f 3 s.f calculator 2 zeros are needed

result to give 3 s.f

Significant figures in Significant figures in calculationcalculation

When multiplying or dividing

• the final answer must have the same number of significant figures as the measurement with the fewest significant figures.

Example:

110.5 x 0.048 = 5.304 = 5.3 (rounded)

4 SF 2 SF calculator 2 SF

When adding or subtracting

• the final answer must have the same number of decimal places as the measurement with the fewest decimal places.

25.2 one decimal place

+ 1.34 two decimal places

26.54 calculated answer

26.5 final answer with one decimal place

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Both Multiplication/Division and Both Multiplication/Division and Addition/Subtraction with Significant Addition/Subtraction with Significant FiguresFigures

when doing different kinds of operations with measurements with significant figures, do whatever is in parentheses first, evaluate the significant figures in the intermediate answer, then do the remaining steps

3.489 × (5.67 – 2.3) =

2 dp 1 dp

3.489 × 3.37 = 12

4 sf 1 dp & 2 sf 2 sf

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Metric EqualitiesMetric Equalities

An equalitystates the same measurement in two different units.can be written using the relationships between two

metric units.

Example: 1 meter is the same as 100 cm and 1000 mm.

1 m = 100 cm10-2 m= 1cm1 m = 1000 mm10-3m = 1 mm

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Conversion FactorsConversion FactorsA conversion factor is

• obtained from an equality.

• E.g Metric – U.S system

Equality: 1 in. = 2.54 cm

• written as a fraction (ratio) with a numerator and denominator.

• inverted to give two conversion factors for every equality.

1 in. = 1 = 2.54 cm 2.54 cm 1 in.

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Arrange conversion factors so given unit cancelsArrange conversion factor so given unit is on the bottom of the conversion factor

unit desiredunitgiven

unit desiredunitgiven

Using Two or More Factors Using Two or More Factors

• Often, two or more conversion factors are required to obtain the unit needed for the answer.

Unit 1 Unit 2 Unit 3

• Additional conversion factors are placed in the setup problem to cancel each preceding unit.

Given unit x factor 1 x factor 2 = needed unitUnit 1 x Unit 2 x Unit 3 = Unit 3

Unit 1 Unit 2

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ExampleExample If a ski pole is 3.0 feet in length, how long is the ski pole

in mm?

Convert 288.0 cm to yard

Convert 9255 cm3 to gallons

1.8 Density1.8 DensityDensity

• compares the mass of an object to its volume.

• is the mass of a substance divided by its volume.

Density ExpressionDensity = mass = g or g = g/cm3 volume mL cm3

Note: 1 mL = 1 cm3

Can we use density as a conversion factor to calculate mass or volume?

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ExamplesExamples What is the density (g/cm3) of 48.0 g of a

metal if the level of water in a graduated cylinder rises from 25.0 mL to 33.0 mL after the metal is added?

A drop of gasoline has a mass of 22.0 mg and a density of 0.754 g/cm3. What is its volume in Liters?

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object

33.0 mL 25.0 mL