Chapter 1Chapter 1

Introduction: Some Basic ConceptsIntroduction: Some Basic Concepts

Welcome to the World Welcome to the World of of

ChemistryChemistry

ChemistryChemistryThe study of matter – its nature, its structure The study of matter – its nature, its structure

(how it is related to its atoms and (how it is related to its atoms and molecules), properties, transformations, molecules), properties, transformations,

and its interactions with energyand its interactions with energy

GoldGold MercuryMercury

MatterMatterAnything that has mass Anything that has mass

and occupies spaceand occupies space

Mass vs WeightMass vs Weight

weight = force = mgweight = force = mg

g: gravitational accelerationg: gravitational acceleration Mass is a measurement of the Mass is a measurement of the

quantity of matter in a body or quantity of matter in a body or samplesample

Weight is the magnitude of Earth’s Weight is the magnitude of Earth’s attraction to such a body or sampleattraction to such a body or sample

Physical States (Phases)Physical States (Phases)Example of bromine, BrExample of bromine, Br22, a halogen, a halogen

SolidSolid definite shape and volumedefinite shape and volume made of particles (atoms, molecules, or made of particles (atoms, molecules, or

ions) held close together and rigidly in ions) held close together and rigidly in placeplace

reasonably well understood.reasonably well understood.

Example:Example:

GraphiteGraphite — layer — layer structure of carbon structure of carbon atoms reflects atoms reflects physical properties.physical properties.

LiquidLiquid

definite volume but definite volume but indefinite shapeindefinite shape

made of particles made of particles (atoms, molecules, or (atoms, molecules, or ions) held close together ions) held close together but allowed to move but allowed to move relative to each other relative to each other

fluid and may not fill a fluid and may not fill a container completely container completely

not well understoodnot well understood

GasGas indefinite volume and indefinite volume and

indefinite shapeindefinite shape the same shape and the same shape and

volume as their container volume as their container made of particles (atoms or made of particles (atoms or

molecules) separated from molecules) separated from each other by large each other by large distances and that move distances and that move very fastvery fast

fluidfluid good theoretical good theoretical

understandingunderstanding

Physical PropertyPhysical Property characteristic of matter characteristic of matter

that can be observed that can be observed without changing the without changing the basic identity of the basic identity of the mattermatter

characteristics that are characteristics that are directly observabledirectly observable

eg. state, size, mass, eg. state, size, mass, V, color, odor, melting V, color, odor, melting point (Tpoint (Tmm), boiling point ), boiling point

(T(Tbb), density, ), density,

solubility...solubility...

Chemical PropertyChemical Property

characteristic of matter that requires characteristic of matter that requires change in identity of the matter for change in identity of the matter for observation (a chemical reaction) observation (a chemical reaction)

characteristic that describes the characteristic that describes the behavior of matterbehavior of matter

eg. flammability, corrosiveness, eg. flammability, corrosiveness, bleaching power, explosiveness, ...bleaching power, explosiveness, ...

Scientific MethodScientific Method

Observation HypothesisObservation Hypothesis

**

Law Law ** Theory Theory

* experiment and then modify* experiment and then modify

*

Tro: Chemistry: A Molecular Approach

12

Scientific MethodScientific Method

Careful noting and recording of natural phenomena

Procedure designed to test an idea

Tentative explanation of a single or small number of observations

General explanation of natural phenomena

Generally observed occurrence in nature

Tro: Chemistry: A Molecular Approach, 2/e

Tro: Chemistry: A Molecular Approach

13

Relationships Between Pieces of Relationships Between Pieces of the Scientific Methodthe Scientific Method

Tro: Chemistry: A Molecular Approach, 2/e

HypothesisHypothesis – a tentative interpretation or – a tentative interpretation or explanation for an observationexplanation for an observation– falsifiable – confirmed or refuted by other falsifiable – confirmed or refuted by other

observationsobservations– tested by experiments – validated or tested by experiments – validated or

invalidatedinvalidated when similar observations are consistently when similar observations are consistently

made, it can lead to a made, it can lead to a Scientific LawScientific Law– a statement of a behavior that is always a statement of a behavior that is always

observedobserved– summarizes past observations and summarizes past observations and

predicts future onespredicts future ones– Law of Conservation of MassLaw of Conservation of Mass

A A theory theory is a unifying principle that explains is a unifying principle that explains a body of facts and the laws based on them. a body of facts and the laws based on them. It is capable of suggesting new hypotheses.It is capable of suggesting new hypotheses.

Classification of MatterClassification of Matter

MixtureMixture

A combination of pure substances in A combination of pure substances in which the components retain their which the components retain their identities (no reaction)identities (no reaction)

Can be separated into simpler Can be separated into simpler mixtures and/or pure substances bymixtures and/or pure substances by

Physical Separation MethodsPhysical Separation Methods mechanical: eg. sand and iron filingsmechanical: eg. sand and iron filings filtration: eg. sand and waterfiltration: eg. sand and water extraction: eg. washing clothes, decaffeinating extraction: eg. washing clothes, decaffeinating

coffeecoffee distillationdistillation chromatographychromatography

DistillationDistillation Simple - for separation of volatile component Simple - for separation of volatile component

from non-volatile component(s)from non-volatile component(s)

DistillationDistillation

Fractional - for separation of multiple Fractional - for separation of multiple volatile components from each other. volatile components from each other. Employed in many chemistry labs, Employed in many chemistry labs, labs, and in crude oil refining.labs, and in crude oil refining.

ChromatographyChromatography Mixture placed in mobile phase (gas or Mixture placed in mobile phase (gas or

liquid). Mobile phase flows over and liquid). Mobile phase flows over and through stationary phase (solid or liquid). through stationary phase (solid or liquid). Mixture components separate based on Mixture components separate based on relative affinity for mobile and stationary relative affinity for mobile and stationary phases.phases.

Heterogeneous MixtureHeterogeneous Mixture inconsistent composition inconsistent composition atoms or molecules mixed not uniformlyatoms or molecules mixed not uniformly contains regions within the sample with contains regions within the sample with

different characteristicsdifferent characteristics eg. pizza, carpet, beach sand, ...eg. pizza, carpet, beach sand, ...

Homogeneous MixtureHomogeneous Mixture solutionsolution consistent composition throughout consistent composition throughout atoms or molecules mixed uniformlyatoms or molecules mixed uniformly eg. air in a room, glass of tap watereg. air in a room, glass of tap water

CompoundCompound

can be broken down to 2 or more can be broken down to 2 or more elements by chemical meanselements by chemical means

constant compositionconstant composition eg. water, Heg. water, H22O, by mass H:O = 1:8O, by mass H:O = 1:8

hydrogen peroxide, Hhydrogen peroxide, H22OO22, H:O = 1:16, H:O = 1:16 elements combined lose individual elements combined lose individual

identitiesidentities more than 20 million compounds are more than 20 million compounds are

now knownnow known

ElementsElements basic substances of basic substances of

which all matter is which all matter is composedcomposed

pure substances that pure substances that cannot be decomposed cannot be decomposed by by ordinaryordinary means to means to other substances.other substances.

made up of atomsmade up of atoms ~ 117 known at this time~ 117 known at this time given name and chemical given name and chemical

symbolsymbolAluminum Bromine

Element SymbolsElement Symbols 1, 2 or 3 letters: 1, 2 or 3 letters: first letter first letter alwaysalways capitalized capitalized usually first letter(s) of nameusually first letter(s) of name

H hydrogenH hydrogen C carbonC carbon

O oxygen O oxygen N nitrogenN nitrogen

Na sodium Cl chlorine Mg magnesiumNa sodium Cl chlorine Mg magnesium

Al aluminumAl aluminum PP phosphorus phosphorus KK potassium potassium

PoPo polonium polonium

learn Latin names where appropriate, learn Latin names where appropriate, antimony - Sb - stibiumantimony - Sb - stibium

gold - Au - aurumgold - Au - aurum

tungsten - W – wolframtungsten - W – wolfram

sodium – Na – natriumsodium – Na – natrium

potassium – K - kaliumpotassium – K - kalium elements from 104 to 111 are named elements from 104 to 111 are named

after scientists; 112-118 have 3 letter after scientists; 112-118 have 3 letter symbols based on Latin name for symbols based on Latin name for numbernumber

112 Uub ununbium112 Uub ununbium

113 Uut ununtrium113 Uut ununtrium

114 Uuq ununquadium114 Uuq ununquadium

115 Uup ununpentium115 Uup ununpentium

116 Uuh ununhexium116 Uuh ununhexium

Homework:Homework: learn the names of learn the names of

first 36 elements in the periodic tablefirst 36 elements in the periodic table

Periodic TablePeriodic Table

a listing of the elements arranged a listing of the elements arranged according to their atomic numbers, according to their atomic numbers, chemical and physical propertieschemical and physical properties

VERY useful and importantVERY useful and important

Physical ChangePhysical Change

transformation of matter from one transformation of matter from one state to another that does not involve state to another that does not involve change in the identity of the matterchange in the identity of the matter

examples: boiling, subliming, examples: boiling, subliming, melting, dissolving (forming a melting, dissolving (forming a solution), ...solution), ...

Chemical ChangeChemical Change transformation of matter from one state to another transformation of matter from one state to another

that involves changing the identity of the matterthat involves changing the identity of the matter examples: rusting (of iron), burning (combustion), examples: rusting (of iron), burning (combustion),

digesting, formation of a precipitate, gas forming, digesting, formation of a precipitate, gas forming, acid-base neutralization, displacing reactions...acid-base neutralization, displacing reactions...

Intensive PropertyIntensive Property

independent of amount of matterindependent of amount of matter eg. density, temperature, eg. density, temperature,

concentration of a solution, specific concentration of a solution, specific heat capacity...heat capacity...

Extensive PropertyExtensive Property

depends on amount of matterdepends on amount of matter eg. mass, volume, pressure, internal eg. mass, volume, pressure, internal

energy, enthalpy, ...energy, enthalpy, ...

DensityDensity mass (g) mass (g)mass (g) mass (g) Density = Density = = = volume (cmvolume (cm33) volume (mL)) volume (mL)

density of Hdensity of H22O is 1.00 g/cmO is 1.00 g/cm3 3 (pure water at ~ 4 °C)(pure water at ~ 4 °C) 1cm1cm33 = 1mL = 1mL

Mercury Platinum

Aluminum

liquidliquid13.6 g/cm13.6 g/cm33 21.5 g/cm21.5 g/cm33

2.7 g/cm2.7 g/cm33

They sink in waterThey sink in water

Know and Own and Practice Know and Own and Practice WellWell

Metric SystemMetric System SI UnitsSI Units Unit ConversionsUnit Conversions Learn a Conversion Factor Between Learn a Conversion Factor Between

English and Metric forEnglish and Metric for

– length, mass, volume, pressurelength, mass, volume, pressure

SI UnitsSI Units

Système International d’UnitésSystème International d’Unités A different base unit is used for each quantity.A different base unit is used for each quantity.

PrefixesPrefixes

A A prefixprefix

in front of a unit increases or decreases the size of in front of a unit increases or decreases the size of that unit. that unit.

makes units larger or smaller than the initial unit by makes units larger or smaller than the initial unit by one or more factors of 10. one or more factors of 10.

indicates a numerical value.indicates a numerical value.

prefixprefix = value = value

11 kilokilometermeter = = 10001000 meters meters

1 1 kilokilogramgram = = 1000 1000 gramsgrams

Metric and SI PrefixesMetric and SI Prefixes

Learning CheckLearning CheckIndicate the unit that matches the description.Indicate the unit that matches the description.

1. A mass that is 1000 times greater than 1 1. A mass that is 1000 times greater than 1 gram.gram. 1) kilogram1) kilogram 2) milligram 3) megagram2) milligram 3) megagram

2. A length that is 1/100 of 1 meter.2. A length that is 1/100 of 1 meter. 1) decimeter1) decimeter 2) centimeter 3) millimeter2) centimeter 3) millimeter

3. A unit of time that is 1/1000 of a second.3. A unit of time that is 1/1000 of a second. 1) nanosecond 1) nanosecond 2) microsecond 2) microsecond

3) millisecond3) millisecond

Learning CheckLearning CheckSelect the unit you would use to measure Select the unit you would use to measure

A. your height.A. your height. 1) millimeters1) millimeters 2) meters2) meters 3) kilometers 3) kilometers

B. your mass. B. your mass. 1) milligrams1) milligrams 2) grams2) grams 3) kilograms 3) kilograms

C. the distance between two cities.C. the distance between two cities. 1) millimeters1) millimeters 2) meters2) meters 3) kilometers 3) kilometers

D. the width of an artery.D. the width of an artery. 1) millimeters1) millimeters 2) meters2) meters 3) kilometers 3) kilometers

VolumeVolume 1 m = 10 dm1 m = 10 dm

(1m)(1m)33 = (10 dm) = (10 dm)33

1m1m33 = 1000 dm = 1000 dm33 = 1000 L = 1000 L

1 dm = 10 cm 1 dm = 10 cm

(1dm) (1dm)33 = (10 cm) = (10 cm)33

1dm1dm33 = 1000 cm = 1000 cm33 = 1000mL = 1000mL

EqualitiesEqualitiesEqualitiesEqualities

• use two different units to describe the same use two different units to describe the same measured amount. measured amount.

• are written for relationships between units of the are written for relationships between units of the metric system, U.S. units, or between metric and metric system, U.S. units, or between metric and U.S. units. U.S. units.

For example,For example, 1 in = 2.54 cm1 in = 2.54 cm

1 m = 1 m = 1000 mm 1 ft = 12 in1000 mm 1 ft = 12 in

1 lb = 16 oz1 lb = 16 oz 1 mile = 5280 ft 1 mile = 5280 ft

2.205 lb = 1 kg2.205 lb = 1 kg 1 lb = 454 g 1 lb = 454 g

1 L = 1.057 qt1 L = 1.057 qt 1 gal = 4 qt 1 gal = 4 qt

1 hour = 60 min1 hour = 60 min 1 cm 1 cm33 = 1 cc = 1 = 1 cc = 1 mLmL

Conversion FactorsConversion FactorsA A conversion factorconversion factor

• is a fraction obtained from an equality.is a fraction obtained from an equality.

EqualityEquality: : 1 in. = 2.54 cm1 in. = 2.54 cm

• is written as a ratio with a numerator and is written as a ratio with a numerator and denominator.denominator.

• can be inverted to give two conversion factors can be inverted to give two conversion factors for every equality.for every equality.

1 in.1 in. andand 2.54 cm 2.54 cm 2.54 cm2.54 cm 1 in. 1 in.

Learning CheckLearning Check

Write conversion factors for each pair of units.Write conversion factors for each pair of units.

A. liters and mL Equality: 1 L = 1000 mLA. liters and mL Equality: 1 L = 1000 mL

B. hours and minutes Equality: 1 hr = 60 minB. hours and minutes Equality: 1 hr = 60 min

C. meters and kilometers C. meters and kilometers Equality: 1 km = 1000 mEquality: 1 km = 1000 m D. micrograms and grams D. micrograms and grams Equality: 1 µg = 10Equality: 1 µg = 10-6-6 g g

Conversion Factors in a ProblemConversion Factors in a ProblemA A conversion factorconversion factor • may be obtained from information in a word may be obtained from information in a word

problem.problem.• is written is written for that problem onlyfor that problem only..

Example 1: Example 1: The price of The price of one pound (1 lb)one pound (1 lb) of red peppers is of red peppers is

$2.39.$2.39.1 lb red peppers1 lb red peppers and and $2.39$2.39 $2.39$2.39 1 lb red peppers 1 lb red peppers

Example 2:Example 2: The cost of The cost of one gallon (1 gal)one gallon (1 gal) of gas is of gas is $3.95.$3.95.

1 gallon of gas1 gallon of gas and and $3.95$3.95 $3.95$3.95 1 gallon of gas 1 gallon of gas

Percent as a Conversion FactorPercent as a Conversion FactorA A percent factorpercent factor

• gives the ratio of the parts to the whole.gives the ratio of the parts to the whole. %% = = Parts Parts x 100 x 100

WholeWhole• uses the same unit to express the percent.uses the same unit to express the percent.• uses the value 100 and a unit for the whole.uses the value 100 and a unit for the whole.• can be written as two factors. can be written as two factors.

Example:Example: A food contains 30% (by mass) fat. A food contains 30% (by mass) fat.

30 g fat 30 g fat and and 100 g food100 g food100 g food100 g food 30 g fat 30 g fat

Density as a conversion factorDensity as a conversion factor

Density of a mineral oil = 0.875 g/mLDensity of a mineral oil = 0.875 g/mL

0.875 g oil 0.875 g oil and and 1 mL1 mL

1 mL1 mL 0.875 g oil 0.875 g oil

Learning CheckLearning Check

Write the equality and conversion factors forWrite the equality and conversion factors for

each of the following.each of the following.

A. square meters and square centimetersA. square meters and square centimeters

B. jewelry that contains 18% (by mass) goldB. jewelry that contains 18% (by mass) gold

C. One gallon of gas is $4.00C. One gallon of gas is $4.00

Solving: Solving: Given and Needed UnitsGiven and Needed UnitsTo solve a problemTo solve a problem• Identify the Identify the givengiven unitunit• Identify the Identify the neededneeded unit. unit.

ExampleExample: :

A person has a height of 2.0 meters. A person has a height of 2.0 meters. What is that height in inches?What is that height in inches?

The The given unitgiven unit is the initial unit of is the initial unit of height. height.

given unit = meters (m)given unit = meters (m)

The The needed unitneeded unit is the unit for the is the unit for the answer.answer.

needed unit = inches (in.)needed unit = inches (in.)

Problem Setup: Problem Setup: Dimensional AnalysisDimensional Analysis

• Write the given and needed units.Write the given and needed units.• Write a unit plan to convert the given unit Write a unit plan to convert the given unit

to the needed unit.to the needed unit.• Write equalities and conversion factors that Write equalities and conversion factors that

connect the units.connect the units.• Use conversion factors to cancel the given Use conversion factors to cancel the given

unit and provide the needed unit.unit and provide the needed unit.

Unit 1 x Unit 1 x Unit 2Unit 2 = Unit 2 = Unit 2 Unit 1Unit 1

Given Given x x Conversion = NeededConversion = Needed unit unit factor factor unit unit

Setting up a ProblemSetting up a Problem

How many minutes are 2.5 hours?How many minutes are 2.5 hours?

Given unitGiven unit = 2.5 hr= 2.5 hr

Needed unitNeeded unit == minmin

Unit PlanUnit Plan == hr → minhr → min

Setup problem to cancel hours (hr). Setup problem to cancel hours (hr).

Given Conversion NeededGiven Conversion Neededunitunit factor factor unit unit

2.5 hr x 2.5 hr x 60 min 60 min = 150 min = 150 min ((2 SF2 SF))

1 hr1 hr

Learning CheckLearning Check

A rattlesnake is 2.44 m long. How manyA rattlesnake is 2.44 m long. How many

centimeters long is the snake?centimeters long is the snake?

1) 1) 2440 cm2440 cm

2)2) 0.0244 cm0.0244 cm

3)3) 24.4 cm24.4 cm

4) 244 cm4) 244 cm

Using Two or More FactorsUsing Two or More Factors• Often, two or more conversion factors are Often, two or more conversion factors are

required to obtain the unit needed for the answer.required to obtain the unit needed for the answer.

Unit 1 Unit 1 →→ Unit 2 Unit 2 →→ Unit 3Unit 3

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

Given unit Given unit x x factor 1 factor 1 xx factor 2 factor 2 = needed = needed unitunit

Unit 1 Unit 1 x x Unit 2Unit 2 x x Unit 3Unit 3 = Unit 3= Unit 3 Unit 1Unit 1 Unit 2 Unit 2

Example: Problem SolvingExample: Problem Solving

How many minutes are in 1.4 days?How many minutes are in 1.4 days?

Given unit:Given unit: 1.4 days 1.4 days

Factor 1 Factor 2Factor 1 Factor 2

Plan:Plan: days → hr → min days → hr → min

Set up problem:Set up problem:

1.4 days x 1.4 days x 24 hr24 hr x x 60 min60 min = 2.0 x 10 = 2.0 x 103 3 minmin

1day 1 hr1day 1 hr

2 SF Exact2 SF Exact Exact = Exact = 2 SF2 SF

Learning CheckLearning CheckA bucket contains 4.65 L of water. How manyA bucket contains 4.65 L of water. How manygallons of water is that?gallons of water is that?

Unit plan:Unit plan: L → qt → L → qt → gallon gallon

Equalities:Equalities: 1.06 qt = 1 L 1 gal = 4 qt 1.06 qt = 1 L 1 gal = 4 qt

Set up Problem:Set up Problem:

4.65 L x 4.65 L x 1.06 qt 1.06 qt x x 1 gal1 gal = 1.23 gal = 1.23 gal

1 L 4 qt 1 L 4 qt

3 SF Exact Exact 3 SF

Learning CheckLearning CheckIf a ski pole is 3.0 feet in length, how long is the ski If a ski pole is 3.0 feet in length, how long is the ski pole in mm? pole in mm? Solution:Solution:

3.0 ft x 3.0 ft x 12 in 12 in x x 2.54 cm2.54 cm x x 10 mm10 mm = = 1 ft 1 in. 1 cm1 ft 1 in. 1 cm

Calculator answer: Calculator answer: 914.4 mm 914.4 mm Needed answer:Needed answer: 910 mm (2 SF rounded) 910 mm (2 SF rounded)

Check factor setup:Check factor setup: Units cancel properlyUnits cancel properlyCheck needed unit:Check needed unit: mm mm

Learning CheckLearning CheckIf your pace on a treadmill is 65 meters per minute,If your pace on a treadmill is 65 meters per minute,how many minutes will it take for you to walk ahow many minutes will it take for you to walk adistance of 7500 feet?distance of 7500 feet?

Solution:Solution:Given:Given: 7500 ft 7500 ft 65 m/min65 m/min Needed: minNeeded: minPlan:Plan: ft → in. → cm → m → min ft → in. → cm → m → minEqualities:Equalities: 1 ft = 12 in. 1 in. = 2.54 cm 1 m = 100 cm 1 ft = 12 in. 1 in. = 2.54 cm 1 m = 100 cm

1 min = 65 m (walking pace)1 min = 65 m (walking pace)Set Up Problem:Set Up Problem:

7500 ft x 7500 ft x 12 in.12 in. x x 2.54 cm2.54 cm x x 1m 1m x x 1 min1 min 1 ft1 ft 1 in. 1 in. 100 cm 65 m 100 cm 65 m

= 35 min = 35 min final answer (2 SF)final answer (2 SF)

(# 11): Ethylene glycol, C(# 11): Ethylene glycol, C22HH66OO22, is an ingredient of , is an ingredient of

automobile antifreeze. Its density is 1.11 g/cmautomobile antifreeze. Its density is 1.11 g/cm33 at 20 °C. at 20 °C. If you need exactly 500. mL of this liquid, what mass of If you need exactly 500. mL of this liquid, what mass of the compound, in grams, is required?the compound, in grams, is required?

Needed: m(g) Given: d(g/cmNeeded: m(g) Given: d(g/cm33) and V(mL)) and V(mL)

1 cm1 cm33 = 1 mL = 1 mL

1.11 g1.11 g500. mL 500. mL ────────── = 555 g = 555 g 1 mL 1 mL 3 SF3 SF

(# 13): A chemist needs 2.00 g of a liquid compound (# 13): A chemist needs 2.00 g of a liquid compound with a density of 0.718 g/cmwith a density of 0.718 g/cm33. What volume of the . What volume of the compound is required?compound is required?

Needed: V(cmNeeded: V(cm33) Given: d(g/cm) Given: d(g/cm33) and m(g)) and m(g)

1 cm1 cm33

2.00 g 2.00 g ──────────── = 2.78 cm = 2.78 cm33

0.718 g 0.718 g 3 SF3 SF

(# 15): A sample of 37.5 g of unknown metal is placed in a (# 15): A sample of 37.5 g of unknown metal is placed in a graduated cylinder containing water. The levels of the graduated cylinder containing water. The levels of the water before and after adding the sample are 7.0 and 20.5 water before and after adding the sample are 7.0 and 20.5 mL respectively. Which metal in the following list is most mL respectively. Which metal in the following list is most likely the sample?likely the sample?

Metal d(g/mL) Metal d(g/mL)Metal d(g/mL) Metal d(g/mL)

MgMg 1.741.74 Al Al 2.702.70

FeFe 7.877.87 Cu Cu 8.968.96

AgAg 10.510.5 Pb Pb 11.311.3

The volume of sample = volume of waterThe volume of sample = volume of water

displaced in cylinder = 20.5 – 7.0 = 13.5 mLdisplaced in cylinder = 20.5 – 7.0 = 13.5 mL

one dec. placeone dec. place

BeforeBefore

After After placing the placing the

piece of piece of metalmetal

(# 15):(# 15):

Needed: d(g/cmNeeded: d(g/cm33) Given: V(mL) and m(g)) Given: V(mL) and m(g)

m 37.5 gm 37.5 g

d = d = ──── = = ──────────── = 2.78 g/mL = 2.78 g/mL V 13.5 mLV 13.5 mL 3 SF3 SF

From the list, the metal is Al.From the list, the metal is Al.

AccuracyAccuracy: nearness of the : nearness of the measurement to accepted measurement to accepted value of the quantity.value of the quantity.

PrecisionPrecision: reproducibility; : reproducibility; how well several how well several determinations of the same determinations of the same quantity agree.quantity agree.

Consider a sample that was analyzed for Consider a sample that was analyzed for

lead content and was lead content and was known to contain 49.3 known to contain 49.3 ppmppm

lead. lead. Two analysesTwo analyses

Analysis AAnalysis A Analysis B Analysis B diff. fromdiff. from

Trial Trial ppm Pb Trial ppm Pb ppm Pb Trial ppm Pb averageaverage

11 38.938.9 1 48.9 4.6 1 48.9 4.6

22 23.223.2 2 59.8 6.3 2 59.8 6.3

33 55.955.9 3 54.5 1.0 3 54.5 1.0

44 80.180.1 4 49.0 4.5 4 49.0 4.5

5 46.95 46.9 5 55.3 1.8 5 55.3 1.8

average = 49.0 ppm Pbaverage = 49.0 ppm Pb 53.5 ppm 53.5 ppm

average diff. 15.5 ppm 3.6 ppmaverage diff. 15.5 ppm 3.6 ppm

More accurate More preciseMore accurate More precise

NumbersNumbers

magnitude, valuemagnitude, value direction: sign (+ or −)direction: sign (+ or −) type of measurement: unitstype of measurement: units precision of original measurement: precision of original measurement:

significant figuressignificant figures

Measured NumbersMeasured Numbers

A measuring tool A measuring tool

is used to determine is used to determine a quantity such as a quantity such as height or the mass height or the mass of an object.of an object.

• provides numbers provides numbers for a measurement for a measurement called called measured measured numbersnumbers..

~4.56 mL~4.56 mL

Reading a Meter StickReading a Meter Stick

. l. l22. . . . l . . . . l. . . . l . . . . l33 . . . . l . . . . l . . . . l . . . . l44. . . . cmcm

• The markings on the meter stick at the end The markings on the meter stick at the end of the orange line are read asof the orange line are read as

the first digit the first digit 2 2

plus the second digit plus the second digit 2.7 2.7 • The last digit is obtained by The last digit is obtained by estimatingestimating.. • The end of the line might beThe end of the line might be estimated estimated

between 2.7–2.8 as half-way (0.5) or a little between 2.7–2.8 as half-way (0.5) or a little more (0.6), which gives a reported length more (0.6), which gives a reported length of 2.7of 2.755 cm or 2.7 cm or 2.766 cm. cm.

Known & Estimated DigitsKnown & Estimated Digits

In the length reported as 2.76 cm, In the length reported as 2.76 cm,

• The digits 2 and 7 are The digits 2 and 7 are certain certain ((knownknown).).

• The final digit 6 was The final digit 6 was estimated estimated ((uncertainuncertain).).

• All three digits (2.76) are All three digits (2.76) are significant including the significant including the estimated estimated digit.digit.

Significant Figures in Significant Figures in Measured NumbersMeasured Numbers

Significant figuresSignificant figures

• obtained from a measurement obtained from a measurement include all of the known digits include all of the known digits plusplus the estimated digit. the estimated digit.

• reported in a measurement reported in a measurement depend on the measuring tool.depend on the measuring tool.

Significant FiguresSignificant Figures

Examples of Counting SFExamples of Counting SF

143.22143.22 143.0143.0 300592300592 0.00209300.0020930 100.0100.0 100.100. 100100

Exact numbersExact numbers have an have an unlimited number of significant unlimited number of significant figures figures

A number whose value is A number whose value is known with complete certainty known with complete certainty is is exactexact– from counting individual from counting individual

objectsobjects– from definitionsfrom definitions1 cm is exactly equal to 0.01 m1 cm is exactly equal to 0.01 m– from integer values in from integer values in

equationsequationsin the equation for the radius in the equation for the radius

of a circle, the 2 is exactof a circle, the 2 is exact

SF in CalculationsSF in Calculations

Addition and/or SubtractionAddition and/or Subtraction

perform operationperform operation

round answer to same number of round answer to same number of digits after decimal digits after decimal as number in as number in calculation with the fewestcalculation with the fewest

ExampleExample

132.09 + 35.94376 – 0.0173 =132.09 + 35.94376 – 0.0173 =

132.132.0909 + 35.94376 – 0.0173 = + 35.94376 – 0.0173 =

168.01646168.01646

must have 2 digits after decimalmust have 2 digits after decimal

168.168.0202

Multiplication and/or Multiplication and/or DivisionDivision

perform operation(s)perform operation(s)

round answer to same number of round answer to same number of significant figures as number in the significant figures as number in the calculation with the fewestcalculation with the fewest

ExampleExample

(26.894)(0.0837)/13 = (26.894)(0.0837)/13 =

(26.894)(0.0837)(26.894)(0.0837) = 0.1731560 = 0.1731560

1313

must have 2 SFmust have 2 SF

0.0.1717

Log and/or AntilogLog and/or Antilog

number of number of digitsdigits in mantissa of log = in mantissa of log =

number of number of significant figures significant figures in antilogin antilog

ExampleExample

log (14.8003) = log (14.8003) =

log (log (14.800314.8003) = 1.17027051857) = 1.17027051857 antilogantilog

1.1.170271170271 mantissamantissa

RoundingRounding

if first digit to be eliminated is if first digit to be eliminated is ≥≥ 5, 5, round preceding digit up oneround preceding digit up one

if first digit to be eliminated is <5, if first digit to be eliminated is <5, truncatetruncate

ExamplesExamples

Round each of the following to Round each of the following to 4 SF4 SF 10.0270010.02700 10.0310.03 10.0249510.02495 10.0210.02 10.0250210.02502 10.0310.03

10.0250010.02500 10.0310.03 10.0150010.01500 10.0210.02 10.0250000000000000000000000110.02500000000000000000000001 10.0310.03

ExponentialsExponentialsScientific notation: Scientific notation: very large or very small very large or very small

numbers are expressed in the followingnumbers are expressed in the following

general form:general form:

exponent term, n = exponent term, n = ± integer± integer

NN x x 1010nn

digit term, between digit term, between ±± 1 and 9.9999… 1 and 9.9999…

(coefficient)(coefficient)

eg −12,760,000 = −1.276 x 10eg −12,760,000 = −1.276 x 1077

0.000012760 = 1.2760 x 100.000012760 = 1.2760 x 10-5-5

Write the following in scientific notation:Write the following in scientific notation:

22,400 = 22,400 = 2.24 x 102.24 x 1044

22,400. = 22,400. = 2.2400 x 102.2400 x 1044

892 x 10892 x 1055 = = 8.92 x 108.92 x 1077

-0.00198 x 10-0.00198 x 10-10-10 = = -1.98 x 10-1.98 x 10-13-13

127.60 x 10127.60 x 10-5-5 = = 1.2760 x 101.2760 x 10-3-3

Write in fixed notation:Write in fixed notation:

5.720 x 105.720 x 10-2-2 = = 0.057200.05720

-1.982 x 10-1.982 x 1044 = = -19,820-19,820

Exponentials in calculationsExponentials in calculations5.750 x 105.750 x 1033 + 7.25 x 10 + 7.25 x 1022 = =

1.75 x 101.75 x 10-3-3 x 6.45 x 10 x 6.45 x 1022

57.50 x 1057.50 x 1022 + 7.25 x 10 + 7.25 x 1022 = =

1.75 x 101.75 x 10-3-3 x 6.45 x 10 x 6.45 x 1022

64.75 x 1064.75 x 102 2 = =

1.75 x 101.75 x 10-3-3 x 6.45 x 10 x 6.45 x 1022

64.75 64.75 x x 10 102 2 = = 5.74 x 105.74 x 1033

1.75 x 6.45 101.75 x 6.45 10-3-3 x 10 x 1022 3 SF3 SF

(0.000345 – 0.0001273) x 6.730x10(0.000345 – 0.0001273) x 6.730x1033 == 154.00 154.00

6 dec places (we keep the 6 dec places (we keep the 777,7, though) though) 0.0002170.00021777 x 6.730x10 x 6.730x103 3 = = 154.00154.00 2.172.1777 has 3 SF onlyhas 3 SF only

2.172.1777x10x1044 x 6.730x10 x 6.730x103 3 = 0.00951= 0.0095133 = 9.51x10 = 9.51x103 3

1.5400 x 101.5400 x 102 2 3 SF3 SF

TemperatureTemperatureTemperature Temperature

• is a measure of how hot or is a measure of how hot or cold an object is compared cold an object is compared to another object.to another object.

• indicates that heat flows indicates that heat flows from the object with a from the object with a higher temperature to the higher temperature to the object with a lower object with a lower temperature. temperature.

• is measured using a is measured using a thermometer.thermometer.

Temperature ScalesTemperature Scales

Temperature Temperature ScalesScales

are Fahrenheit, Celsius, and Kelvin.

have reference points for the boiling and freezing points of water.

Temperature ScalesTemperature Scales Fahrenheit (°F )Fahrenheit (°F )

Celcius or Centigrade (°C ) Kelvin (K)Celcius or Centigrade (°C ) Kelvin (K)

99 °F = °F = ──── °C +32 = 1.8 °C + 32 °C +32 = 1.8 °C + 32 55

5 (°F - 32)5 (°F - 32) °C = °C = (°F -32) = (°F -32) = 9 1.89 1.8

K = °C + 273 273.15 (exact) K = °C + 273 273.15 (exact)

ΔΔT(T(K) = K) = ΔΔT(T(°C) variation of temperature°C) variation of temperature

Learning checkLearning checka. The normal temperature of a chickadee isa. The normal temperature of a chickadee is105.8°F. What is that temperature on the105.8°F. What is that temperature on theCelsius scale? Celsius scale? 1) 73.8°C 2) 58.8°C 1) 73.8°C 2) 58.8°C 3) 41.0°C3) 41.0°C

b. A pepperoni pizza is baked at 235°C. Whatb. A pepperoni pizza is baked at 235°C. Whattemperature is needed on the temperature is needed on the FahrenheitFahrenheit scale? scale? 1) 267°F1) 267°F 2) 508°F 2) 508°F 3) 455°F3) 455°F

c. Convert 204.3 K into °C.c. Convert 204.3 K into °C.

Other elements to Other elements to rememberremember

Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, ZnSc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn Ru, Rh, Pd, Ag, CdRu, Rh, Pd, Ag, Cd Pt, Au, HgPt, Au, Hg