MatterAnd

Measurement

Unit 1Introduction:

Matter and Measurement

Dr. Jorge L. AlonsoMiami-Dade College –

Kendall CampusMiami, FL

CHM 1045: General Chemistry and Qualitative Analysis

Textbook References:

•Module #1

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Scientific Method:A systematic approach to solving problems.

Observation: the detection of a phenomenon by our sensory organs or their extensions (instruments).

Scientist study CAUSE EFFECT Relationships

Which factors affect the behavior of gasses?

Experiment: carefully designed hypothesis testing; done by controlling all the variables except your suspected CAUSE (independent variable, x) which is manipulated in order to observe its EFFECT (dependent variable, y).

Hypothesis: initial or tentative explanation of the causes of a phenomenon.

η,P, V, & T{GasVariables}

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Law: concise verbal or mathematical summary for a variety of observations and experiences.

Experiment: carefully designed hypothesis testing; done by controlling all the variables except your suspected CAUSE (independent variable, x) which is manipulated in order to observe its EFFECT (dependent variable, y).

Also,P ↑ V ↓ = k

V 1P

V = kP

ORDependent Variable

Independent Variable

Theory: a comprehensive explanation for natural phenomena that has withstood repeated analysis and experimentation.

Boyle’s Law

Kinetic Molecular Theory

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What is the universe composed of?

Matter: Anything that has mass and takes up space.

Energy: the ability to perform an activity (work).

•Chemicals•Substances•Things

• Kinetic (motion & heat)• Electromagnetism (light, electricity & chemical bonds)• Nuclear• Gravity

Chemistry

Physics

{Matter with Energy}

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Describing Matter: Physically and Chemically

(1) Physical Properties (3) Chemical Properties

(2) Physical Change (4) Chemical Change

Chemistry: The study of matter and the changes it undergoes.

(reactions & equations)

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Let’s get Physical!

Physical Changes:Changes in the physical properties of matter.

Changes of: state (s l g), density, temperature, shape,

volume, etc.

Physical Properties: The physical characteristics (appearance) of matter.

State or phase (s,l,g), color, mass, volume, density, melting & boiling points, solubility, etc

H2O (s) H2O (l) H2O (g)

HH22OO (g) (g)

Physical changes occur without changes in the composition of matter.

2 H2O (s) 2 H2 (g) + O2 (g)

Physical change:

Chemical change:

HH22OO (l) (l)

HH22OO (s) (s)

MatterAnd

MeasurementPhase Changes = Changes of State

(fusion)

Heat Energy & Phase (State) Changes

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Kinetic Energy & States of Matter

{KineticMolecularTheory: PhaseChange}

c. pt. (condensation point)

m. pt (melting point)

f. pt. (freezing point)

b. pt. (boiling point)

For H2O: m.pt. = f.pt = 0OC b.pt. = c.pt = 100OC

For Methanol: m.pt. = f.pt = -98OC b.pt. = c.pt = 65OC

Density (mass per unit volume)

Heat = Kinetic Energy Temperature

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Heating Curve: Energy & Phase Changes

Heat of Vaporization

For H2O: m.pt. = f.pt = 0OC b.pt. = c.pt = 100OC

For Methanol: m.pt. = f.pt = -98OC b.pt. = c.pt = 65OC

Heat of Fusion

Heating water vapor

Heating solid ice

Heating liquidwater

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Let’s get Chemical!

Chemical Properties:Can only be observed when a substance reacts and is changed into another substance.

Does it react? With which substance does it react? Flammability? Corrosiveness?, etc.

What happens when you add Na to water? K?

{Na & K in H2O}

Chemical Changes: The changes that occur in the process of producing new substances. Combustion, oxidation, decomposition, etc.

Is this chemical or physical change?

Chemical change is always accompanied by physical change!

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Describing Chemical Change

Chemical Reaction: the actual phenomenon that occurs when chemicals change in composition.

Chemical Equation: a symbolic representation of a chemical reaction. Based on the Atomic Theory.

Quiz Question:Write the balanced chemical equations for the reactions of (1) Sodium (Na) + Water (HOH) (2) Potassium (K) + Water

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2 Na + 2 HOH 2 NaOH + H2

2 K + 2 HOH 2 KOH + H2

Chemical Reactions and Equations

(Hint: single displacement or replacement reaction)

+ -+

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Matter and the Atomic Theory

• Atoms are the building blocks of all matter.• Elements are made of the same kind of atom.• Compounds are made of two or more different kinds of atoms.• Mixtures are composed of different elements/compounds

together.

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Classification of Matter

Elements

Compounds

Heterogeneous

HomogeneousPhysical

Separation

Chemical

Decomposition

Physical

Separation

Mixtures

Pure

Substances

Mixtures (Heterogeneous)

Solutions (Homogeneous)

Cu(NO3)2

Cu(NO3)2 (s)

Cu(NO3)2 (aq)

*

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• methods of physically separating (purifying) substances from mixtures and solutions into pure substances.

1. Filtration – by solubility vs. insolubility

2. Metal Smelting & Refining - by differences in melting point (ability to form a liquid)

3. Distillation –by differences in boiling points (ability to form a gas)

4. Chromatography – by differences in degree of solubility

Separatory Techniques

• based on differences in physical properties of the substances present in the mixture/solution.

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(1) Filtration: Separates insoluble solid substances from liquids and solutions.

Mixture:K2Cr2O7(s)

+NaNO3(s)

NaNO3(aq)

K2Cr2O7(s)

+ H2O

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(2) Metal Smelting & Refining

The sweat furnace operates at a temp at which one metal is selectively melted from a component, leaving the metal with the higher melting point, usually a ferrous metal as a recoverable solid.

These techniques are used to differentially melt mixtures of metals (alloys) by means of their different melting points (ability to form a liquid when heated).

Example: mixture of Cu + Zn, heated to 500°C

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(3) Distillation: Separates homogeneous mixture on the basis of differences in boiling points (ability to form a gas).

Substance b.pt.

Ethyl Alcohol 77oC

Water 100oC

Sodium Chloride 1413oC

Alcohol +

Solution:

*

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Distillation of Hydrocarbons: Petroleum Refinery Towers

compounds composed of molecules arranged in a long chain of carbon atoms with hydrogen atoms attached to the carbon chain.

Name (b.pt. C) # C Structural Formula

Methane (-162) 1 CH4

Ethane (-89) 2 CH3CH3

Propane (-42) 3 CH3CH2CH3

Butane (-0.5) 4 CH3CH2CH2CH3

Pentane (36) 5 CH3CH2CH2CH2CH3

Hexane (69) 6

CH3CH2CH2CH2CH2CH3

Heptane (98) 7

CH3CH2CH2CH2CH2CH2CH3

Octane (126) 8

CH3CH2CH2CH2CH2CH2CH2CH3

Nonane (151) 9 CH3 CH2

CH2CH2CH2CH2CH2CH2CH3

Decane (174) 10

CH3CH2CH2CH2CH2CH2CH2CH2CH2CH3

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120 C

200 C

250 C

300 C

0 C

Distillation of Hydrocarbons: Petroleum Refinery Towers

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• Mixtures can be separated by differences in the physical properties of the substances they are composed of.

• Pure substances cannot be separated by physical methods.

Separation by differences in ability to form a gas (boiling points)

Physical

Separation

Mixture / Solution or Pure Substance?

HH22O vaporO vapor

Cu(NOCu(NO33))2(s)2(s)

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Separation by differential solubility, filtration and evaporation

Mixture: CdS (yellow, insoluble substance), Cu(NO3)2 (blue soluble substance), H2O(clear liquid).

HH22O vaporO vapor

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(4) Chromatography: Separates substances on the basis of their differences in their solubility in a

specific solvent.

{Paper Chromatography}Solvent: 50: 50

Water: Alcohol

Substance to be separated (black ink)

Filter paper

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Classification of Matter

Elements

Compounds

Heterogeneous

HomogeneousPhysical

Separation

Chemical

Decomposition

Physical

Separation

Mixtures

Pure

Substances

Mixtures (Heterogeneous)

Solutions (Homogeneous)

Cu(NO3)2

Cu(NO3)2 (s)

Cu(NO3)2 (aq)

*

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Chemical Decomposition of Pure Substances

• Cannot be separated by physical means.

• Composed of one substance only, which can be either an element or a compound.

• Compounds can be broken down by chemical means, elements cannot. Examples of pure substances:

Gold (Au), Oxygen (O2), Water (H20), Methanol (CH3OH), Table salt (NaCl)

Each has its specific physical properties (m. pt., density, etc.)

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Compoundscan be broken down into more elemental particles

(elements) by chemical decomposition reactions.

Electrolysis of Water:

{Electrolysis}2 H2O (l) → 2 H2 (g) + O2 (g)

elect.

MatterAnd

MeasurementNaCl is electrolyzed in a Downs cell.– Gaseous Cl2 allowed to disperse

– Molten Na siphoned off

How do we get pure Sodium?

2 NaCl (l) → 2 Na (l) + Cl2 (g)

elect

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Elementscannot be broken down into more elemental particles

by ordinary chemical means.

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Classification of Matter

Mixture

Solution

Element Compound

Heterogeneous

Homogeneous

Physical

Separation

Chemical

Decomposition

Physical

Separation

{mixture vs. compound}

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Units of

Measurement

length (m)mass (g, kg)

volume (mL, L)temperature (oC, oK)

time (s)

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SI Prefixes

Prefix Symbol Meaning Multiplier(numerical)

Multiplier(exponential)

yotta Y septillion 1,000,000,000,000,000,000,000,000 1024

zetta Z sextillion 1,000,000,000,000,000,000,000 1021

exa E quintillion 1,000,000,000,000,000,000 1018

peta P quadrillion 1,000,000,000,000,000 1015

tera T trillion 1000,000,000,000 1012

giga G billion 1,000,000,000 109

mega M million 1,000,000 106

kilo k thousand 1,000 103

hecto h hundred 100 102

deka da ten 10 101

UNIT ONE 1 1

100

deci d tenth 0.1 10-1

centi c hundredth 0.01 10-2

milli m thousandth 0.001 10-3

micro millionth 0.000 001 10-6

nano billionth 0.000 000 001 10-9

pico trillionth 0.000 000 000 001 10-12

femto quadrillionth 0.000 000 000 000 001 10-15

atto quintillionth 0.000 000 000 000 000 001 10-18

zepto z () sextillionth 0.000 000 000 000 000 000 001 10-21

yocto y septillionth 0.000 000 000 000 000 000 000 001 10-24

Metric System

cm

m

1

0.01

When using dimensional

analysis for metric problems: always

consider the larger unit as having a value of 1, then the smaller unit would contain a

large multiple of that unit.

Example: 1 m compared to cm.

cm

m

100

1

X 1000

X 1000

X 10

X 10

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Atoms

Tenth of a nanometer (10 -9 m)

Nuclei of atoms

Hundredth of a picometer (10 -12 m)

Protons & Neutrons

Fentometer (10-15 m)

Quarks & electrons

Attometer (10-18 m)

Atomic Dimensions

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SI Prefixes

Prefix Symbol Meaning Multiplier(numerical)

Multiplier(exponential)

yotta Y septillion 1,000,000,000,000,000,000,000,000 1024

zetta Z sextillion 1,000,000,000,000,000,000,000 1021

exa E quintillion 1,000,000,000,000,000,000 1018

peta P quadrillion 1,000,000,000,000,000 1015

tera T trillion 1000,000,000,000 1012

giga G billion 1,000,000,000 109

mega M million 1,000,000 106

kilo k thousand 1,000 103

hecto h hundred 100 102

deka da ten 10 101

UNIT ONE 1 100

deci d tenth 0.1 10-1

centi c hundredth 0.01 10-2

milli m thousandth 0.001 10-3

micro millionth 0.000 001 10-6

nano billionth 0.000 000 001 10-9

pico trillionth 0.000 000 000 001 10-12

femto quadrillionth 0.000 000 000 000 001 10-15

atto quintillionth 0.000 000 000 000 000 001 10-18

zepto z () sextillionth 0.000 000 000 000 000 000 001 10-21

yocto y septillionth 0.000 000 000 000 000 000 000 001 10-24

Metric Conversions

m

cm

1

100

Always convert PREFIXES to UNITS (not PREFIXES to other PREFIXES)

Example: Mm compared to pm.

Example: cm compared to m.

μm10

m 16

pm

m

10

112

m

Mm

000,000,1

1

meter, liter, gram

Factors, ratios, equivalences.

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Metric Conversion Problems• How many pm are there in 0.0023 cm?

cm

m

100

1

• Change 60. mph to km/s. {Hint: 1 mi. = 1.6 km}

cmpm 0023.0?

hrmi

skm .60?

m

pm

1

1012

pm701 x 3.2

mi

km

1

6.1

min60

1hr

s 60

min 1s

km 027.0

• How many m3 of water are there in 25 ft3 ?

33

ft 25 m ?

ft 1

in 12

in 1

cm 2.54

cm 100

m 1 3m 0.71

LENGTH

km

hm

dam

METER (m)

dm

cm

mm

2.54 cm = 1 in.

1 mile = 5,280 ft.

1 yd = 36 in.

3 ft. = 1 yard

12 in. = 1 ft.

333

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A liter is a cube 1 dm3 = 10 cm long on each side.

Volume: Liter (L) and the milliliter (mL)

A milliliter (mL) is a cube 1 cm long on each side.

1 L = dm3 = (10 cm)3 = (10 X 10 X 10) cm3 = 1000 cm3

= 1000 mL or 1mL = 1/1000 L

10 cm 10 cm

10 cm

mL

cccm

1

11 3

Cubic centimeter

= milliliter

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Temperature: measure of the average kinetic energy (motion caused by heat) of the particles in a sample.

K = C + 273.15 C = (F − 32) 1.8

F = 1.8(C) + 32

{K.E ∝ Temp}

As KE increases molecules vibrate more and their volume expands (Temp).

*

T = change in temp

373-273100

100 - 0 100

212- 32180

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Measured vs Exact Numbers

• Measured Numbers: (1) Accuracy & Precision (2) Uncertainty (3) Significant figures &

rounding-off

• Exact Numbers: from formulas, definitions & counting

3

r 4 V

3

1 mile = 5,280 ft

1 km = 1,000 m

For sphere

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Measured Numbers: Accuracy versus Precision

• Accuracy refers to the proximity of a measurement to the true value of a quantity.

• Precision refers to the proximity of several measurements to each other.

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Measured vs. Exact Numbers

Measured numbers are obtained when a measuring instrument (ruler, balance, thermometer) is used to determine a physical property of a substance. +0.1

+0.01

The number of significant figures these measurements contain depend on the accuracy of the instrument being used.

13.7

7.63

uncertainty

uncertainty

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Uncertainty in MeasurementsDifferent instruments have different degrees of accuracy, uncertainty is + 1 of estimated digit.

+0.01uncertainty

89.5 mL

2.65 mL

+0.1

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METRIC METRIC-ENGLISH ENGLISH CONVERSIONS

LENGTH

km

hm

dam

METER (m)

dm

cm

mm

2.54 cm = 1 in.

1 mile = 5,280 ft.

1 yd = 36 in.

3 ft. = 1 yard

12 in. = 1 ft.

Measured vs. Exact Numbers

Exact Numbers Exact Numbers

Measured Numbers

(1 in is exact, the 2.54 cm is measured)

How many km are there in a Marathon (26 miles)?

mikm 26?

mile

ft

1

280,5

ft

in

1

12

in

cm

1

54.2

cm

m

100

1

m

km

1000

1 km 842944.41km 8.41

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Significant Figures• Significant figures refers to digits that were

accurately measured by an instrument.

Example: 220g, 220. g, 220.5g, 220.50g, 220.507g.

(all numbers above are measures of the same object, what is the difference?)

accuracy

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Rules for determining the number of Significant Figures

1. All nonzero digits (NZD) are always significant.

2. Zeroes between NZD are always significant. Ex: 103

3. Zeroes to the left of NZD are never significant. Ex: 0.0103

4. Zeroes to the right of NZD are significant if a decimal point is written anywhere in the number. Ex. 0.01030

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Rounding-off

• Round-off your calculated numbers, to the correct number of significant figures, so we do not overstate the accuracy of our answers.

Example: 23g + 23.632g = 46.632

You cannot add an inaccurate measurement to a accurate measurement and get and accurate answer.

= 47g

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Significant Figures in Addition & Subtraction

• When addition or subtraction is performed, answers are rounded to the least significant decimal place.

Example: add the following numbers

34

231.678

0.00354

265.68154

266

*

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Significant Figures in Multiplication & Division

• Answers are rounded to the number of digits that corresponds to the least number of significant figures in any of the numbers used in the calculation.

Example: (29.2 – 20.0) (1.79 x 105)1.39

Calculator answer = 1.1847482 x 106

*

(29.2 – 20.0) = 9.2

Correct answer = 1.2 x 106

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Uncertainty in Measurements

• Piece of Black Paper – with rulers beside the edges: Determine the Area of Black Paper!

Area = Length x Width

Let’s look more accurately !

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Uncertainty in Measurements• Piece of Paper – Side A enlarged

– How long is the paper to the best of your ability to measure it?

When using an instrument your last digit recorded should be a significant digit estimated between the two smallest measurement lines of your instrument. Your precision would be + 1 of that digit.

13.6 cm

+ 0.1 cm

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Uncertainty in Measurements• Piece of Paper Side B – enlarged

– How wide is the paper to the best of your ability to measure it?

When using an instrument your last digit recorded should be a significant digit estimated between the two smallest measurement lines of your instrument. Your precision would be + 1 of that digit.

7.63 cm

+ 0.01 cm

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Area of Paper

Area = 13.6 cm x 7.63 cm = 103.768 cm2 is the calculator answer.

104 cm2

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A Physical property of a substance, defined as:

• Amount of matter (# atoms) per unit volume = compactness.

• the mass divided by the volume.

Density:

g 13.5

mL 1or

mL 1

g 13.5 :ratioa as used be can 13.5g/mL DHg

D =mV

= Mass (g)

Volume (mL)

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Density and Temperature

Density: the mass of a substance divided by its volume.

As the temperature increases the volume increases due to the greater kinetic energy of the atoms or molecules. The mass is not affected.

Temperature: a measure of the amount of kinetic energy (motion) an object possesses.

)mL(volume)g(massD

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Density of water at various temperatures

°C °F D in g/cm³

0.0 32.0 0.9998425

4.0 39.2 1.0000000

15.0 59.0 0.9991026

20.0 68.0 0.9982071

25.0 77.0 0.9970479

37.0 98.6 0.9933316

50.0 122.0 0.9880400

100.0 212.0 0.9583665

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Density Problems

mL 12 ?g

kg 34 mL ?

mL 1

g 7.86

For a Fe metal object whose density is 7.86 g/mL.

(a) What is the mass (g) of a piece of this metal if it displaces 12. mL of water in a graduated cylinder?

(b) What is the volume in mL of 34 kg of this same metal?

g 94

kg 1

g 1,000

g 7.86

mL 1mL 4300

*

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Density Problems

mLg 11.7

mkg ? 3

The density of Hg is 11.7 g/mL. What is it in kg/m3?

g 0001

kg 1

m 1

cm 001 3kg/m 11,700 3

*

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Density of various substances

{DBr MW}

Density is directly proportional to the Molecular Weight of a substance.