Edward Wen, PhD

Matters and Measurement

Chemistry is about Everyday experience

• Why Cookies tastes different from Cookie Dough?

• Why Baking Powder or Baking Soda?

• Why using Aluminum Foil, not Paper Towel?

• What if the Temperature is set too high?

Photo credit: itsnicethat.com

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Chapter Outline

• Classification of matters

• Measurement, Metric system (SI)

• Scientific Notation

• Significant figures

• Conversion factor

• Density

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4

In Your Room• Everything you can see,

touch, smell or taste in your room is made of matter.

• Chemists study the differences in matter and how that relates to the structure of matter.

5

What is Matter?

• Matter: anything that occupies space and has mass

• Matter is actually composed of a lot of tiny little pieces: Atoms and Molecules

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Atoms and Molecules

• Atoms: the tiny particles that make up all matter. Helium gas (for blimp) is made up of Helium atoms.

• Molecules: In most substances, the atoms are joined together in units. Liquid water is made up of water molecules (2 Hydrogen atoms + 1 Oxygen atoms)

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Physical States of Matters

• Matter can be classified as solid, liquid or gas based on what properties it exhibits

State Shape Volume Compress Flow

Solid Fixed Fixed No No

Liquid Indef. Fixed No Yes

Gas Indef. Indef. Yes Yes

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Why different States of a Matter? Structure Determines Properties

• the atoms or molecules have different structures in solids, liquid and gases

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Solids

• Particles in a solid: packed close together and are fixed in positionthough they may vibrate

Incompressibleretaining their shape and

volumeUnable to flow

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Liquids

• Particles are closely packed, but they have some ability to move around

Incompressible

Able to flow, yet not to escape and expand to fill the container (not “antigravity”)

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Gases• The particles have complete freedom from

each other (not sticky to each other)• The particles are constantly flying around,

bumping into each other and the container• There is a lot of empty space between the

particles (low density) Compressible Able to flow and Fill space (“antigravity”)

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Classifying Matter:

Sugar, Copper, Coke, Gasoline/Water

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Classification of Matter

Pure Substance

•Constant Composition

•Homogeneous

Mixture

•Variable Composition

•Matter

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Pure substance

Matter that is composed of only one kind of piece.

Solid: Salt, Sugar, Dry ice, Copper, Diamond

Liquid: Propane, distilled water (or Deionized water, DI water)

Gas: Helium gas (GOODYEAR blimp)

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Classifying Pure Substances: Elements and Compounds

Elements: Substances which can not be broken down into simpler substances by chemical reactions. (A,B)

Compounds: Most substances are chemical combinations of elements. (C)•Examples: Pure sugar, pure water

can be broken down into elementsProperties of the compound not

related to the properties of the elements that compose it

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Elements• Example: Diamond (pure carbon), helium gas.• 116 known, 91 are found in nature

others are man-made

• Abundance = percentage found in natureHydrogen: most abundant in the universe Oxygen: most abundant element (by mass) on earth and

in the human bodySilicon: abundant on earth surface

• every sample of an element is made up of lots of identical atoms

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Compounds

• Composed of elements in fixed percentageswater is 89% O & 11% H

• billions of known compounds• Organic (sugar, glycerol) or inorganic (table salt)• same elements can form more than one different

compoundwater and hydrogen peroxide contain just

hydrogen and oxygencarbohydrates all contain just C, H & O (sugar,

starch, glucose)

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Mixture

Matter that is composed of different kinds of pieces. Different samples may have the same pieces in different percentages. (D)

Examples:Solid: Flour, Brass (Copper and

Zinc), RockLiquid: Salt water, soda, GasolineGas: air

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Classification of Mixtures• Homogeneous = composition is uniform

throughout appears to be one thingevery piece of a sample has identical

properties, though another sample with the same components may have different properties

solutions (homogeneous mixtures): Air; Tap water

• Heterogeneous = matter that is non-uniform throughout contains regions with different

properties than other regions: gasoline mixed with water; Italian salad dressing

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What is a Measurement?

• Quantitative observation• comparison to an agreed upon standard

Every measurement has a number and a unit:• 77 Fahrenheit: Room temperature• 7.5 pounds: Average newborn body weight in the US:• 55 ± 0.5 grams: amount of sugar in one can of Coca

Cola

UNIT: 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 (±)

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Some Standard Units in the Metric System

Quantity Measured

Name of Unit

Abbreviation

Mass gram g

Length meter m

Volume liter L

Time seconds s

Temperature Kelvin K

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Related Units in the SI System

All units in the SI system are related to the standard unit by a power of 10 (exactly!)

• 1 kg = 103 g • 1 km = 103 m• 1 m = 102 cm

• The power of 10 is indicated by a prefix• The prefixes are always the same, regardless of

the standard unit

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Prefixes Used to Modify Standard Unit• kilo = 1000 times base unit = 103

1 kg = 1000 g = 103 g

• deci = 0.1 times the base unit = 10-1

1 dL = 0.1 L = 10-1 L; 1 L = 10 dL

• centi = 0.01 times the base unit = 10-2

1 cm = 0.01 m = 10-2 m; 1 m = 100 cm

• milli = 0.001 times the base unit = 10-3

1 mg = 0.001 g = 10-3 g; 1 g = 1000 mg

• micro = 10-6 times the base unit1 m = 10-6 m; 106 m = 1 m

• nano = 10-9 times the base unit1 nL = 10-9L; 109 nL = 1 L

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Common Prefixes in the SI System

Prefix SymbolDecimal

EquivalentPower of 10

mega- M 1,000,000 Base 106

kilo- k 1,000 Base 103

deci- d 0.1 Base 10-1

centi- c 0.01 Base 10-2

milli- m 0.001 Base 10-3

micro- or mc 0.000 001 Base 10-6

nano- n 0.000 000 001 Base 10-9

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Standard Unit vs. PrefixesUsing meter as example:

1 km = 1000 m = 103 m

1 g = 10 dm

= 100 cm = 102 cm

= 1000 mm = 103 mm

= 1,000,000 m = 106 m

= 1,000,000,000 nm = 109 nm

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Length• Two-dimensional distance an object covers

• SI unit: METER (abbreviation as m)About 3½ inches longer than a yard

1 m = 10-7 the distance from the North Pole to the Equator

• Commonly use centimeters (cm)1 m = 100 cm = 1.094 yard1 cm = 0.01 m = 10 mm1 inch = 2.54 cm (exactly)

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Mass• Amount of matter present in an object

• SI unit: kilogram (kg)about 2 lbs. 3 oz.

• Commonly measure mass in grams (g) or milligrams (mg)1 kg = 2.2046 pounds (1 lbs. = 0.45359)1 g = 1000 mg = 103 mg1 g = 0.001 kg = 10-3 kg

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Volume• Amount of three-dimensional space occupied• SI unit = cubic meter (m3)

• Commonly measure solid volume in cubic centimeters (cm3)1 m3 = 106 cm3 1 cm3 = 10-6 m3 = 0.000001 m3

• Commonly measure liquid or gas volume in milliliters (mL)1 gallon (gal) = 3.78 L = 3.78 103 mL1 L = 1 dm3 = 1000 mL = 103 mL 1 mL = 1 cm3 = 1 cc (cubic centimeter)

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Common Everyday Units and Their EXACT Conversions

11 cm

1 inch (in) = 2.54 cm

1 mile = 5280 feet (ft)

1 foot = 12 in

1 yard = 3 ft

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Common Units and Their Equivalents

Volume

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 (g)

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Units• Always write every number with its

associated unit

• Always include units in your calculationsyou can do the same kind of operations on units

as you can with numbers• cm × cm = cm2

• cm + cm = cm

• cm ÷ cm = 1

using units as a guide to problem solving

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Conversion Factor

• Relationships to Convert one unit of measurement to another: US dollar Canadian dollar, dollar cent

• Conversion Factors: Relationships between two unitsBoth parts of the conversion factor have the same

number of significant figures

• Conversion factors generated from equivalence statementse.g. 1 inch = 2.54 cm can give or

in1

cm54.2cm54.2

in1

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How to Use Conversion Factor

• Arrange conversion factors so starting unit cancelsArrange conversion factor so starting unit is on the

bottom of the conversion factor

unit 1unit 2unit 1

unit 2x =

Conversion Factor

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We have been using the Conversion Factor ALL THE TIME!

• How are we converting #cents into #dollars? Why?From 1 dollar = 100 cents

45,000 cents dollar

cents450 dollarsx =

Conversion Factor

1 dollar 100 cents

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Given: 325 mg

Find: ? g

Conv. Fact. 1 mg = 10-3 g Soln. Map: mg g

Convert 325 mg to grams

0.325 g

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Practice: How to set up Conversion?

• To convert 5.00 inches to cm, from 1 in = 2.54 cm (exact), which one of the two conversion factors should be used?

orcm 2.54

in 1

in 1

cm 2.54

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Practice: Conversion among Units

• 500 mg = ? g

• 3.78 L = ? mL

• 1.2 nm = ? m

* 8.0 in = ? m

mg

gmg

?

?500

L

mLL

?

?78.3

nm

mnm

?

?2.1

cm

m

in

cmin

?

?

?

?0.8

37

g5.0

mL3780

nm9102.1

m203.0

Scientific Notation

Very Large vs. Very Small numbers:

•The sun’s diameter is 1,392,000,000 m;

•An atom’s diameter is 0.000 000 000 3 m

Scientific Notation: 1.392 x 109 m & 3 x 10-10 m

the sun’sdiameter is

1,392,000,000 m

an atom’s average diameter is0.000 000 000 3 m

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Scientific Notation (SN)

Power of 10 (Math language):

• 10 x 10 = 100 100 = 102 (2nd power of 10)

• 10 x 10 x 10 = 1,000 1,000 = 103 (3rd power of 10)

each Decimal Place in our number system represents a different power of 10

• 24 = 2.4 x 101 = 2.4 x 10

• 1,000,000,000 (1 billion) = 109

• 0.0000000001 (1/10 billionth ) = 10-10

Easily comparable by looking at the power of 10

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Exponents 10Y

• when the exponent on 10 (Y) is positive, the number is that many powers of 10 larger sun’s diameter = 1.392 x

109 m = 1,392,000,000 m

• when Y is negative, the number is that many powers of 10 smalleravg. atom’s diameter =

3 x 10-10 m = 0.0000000003 m

1.23 x 10-8

decimal part exponent part

exponent

1.23 x 105 > 4.56 x 102

4.56 x 10-2 > 7.89 x 10-5

7.89 x 1010 > 1.23 x 1010

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Writing Numbers in SN

Big numbers:

12,340,000

Small numbers:

0.0000234

1.234 x 107

2.34 x 10-5

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Writing a Number in Standard Form

1.234 x 10-6

• since exponent is -6, move the decimal point to the left 6 placesif you run out of digits, add zeros

000 001.234

If the exponent > 1, add trailing zeros:

1.234 x 1010

1.2340000000

0.000 001 234

12,340,000,000

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Scientific calculators

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Inputting Scientific Notation into a Calculator

• input decimal part of the number if negative press +/- key

• (–) on some

• press EXP keyEE on some (maybe 2nd

function)

• input exponent on 10press +/- key to change

exponent to negative

-1.23 x 10-3

-1.23 -03

Press +/-

Input 1.23 1.23

Press EXP -1.23 00

Input 3 -1.23 03

-1.23 Press +/-

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Significant Figures (Sig. Fig.)

Definition: The non-place-holding digits in a reported measurementsome zero’s in a written number are

only there to help you locate the decimal point

What is Sig. Fig. for? the range of values to expect for repeated

measurementsthe more significant figures there are in

a measurement, the smaller the range of values is

12.3 cmhas 3 sig. figs. and its range is12.2 to 12.4 cm

0.1230 cmhas 4 sig. figs. and its range is

0.1229 to 0.1231 cm

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Counting Significant Figures1. All non-zero digits are significant

1.5 : 2 Sig. Fig.s

2. Interior zeros are significant 1.05 : 3 Sig. Fig.s

3. Trailing zeros after a decimal point are significant 1.050 : 4 Sig. Fig.s. Leading zeros are NOT

significant 0.001050 : 4 Sig. Fig.s Place-holding zero’s

= SN : 1.050 x 10-3

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Counting Significant Figures (Contd)4. Exact numbers has infinite () number of significant

figures:example: 1 pound = 16 ounces 1 kilogram = 1,000 grams = 1,000,000 milligrams 1 water molecule contains 2 hydrogen atoms

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

Example: 150. has 3 sig. fig 150 is ambiguous number 1.50 x 102 has 3 sig. fig.

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Example–Counting Sig. Fig. in a Number

How many significant figures are in each of the following numbers?

0.00351.080

272.97 × 105

1 m = 1000 mm

2 Sig. Fig. – leading zeros not sig. 4 Sig. Figs – trailing & interior zeros

sig. 2 sig. Figs, all digits sig. 3 Sig. Figs – only decimal parts count

sig. both 1 and 1000 are exact numbers.

unlimited sig. figs.

Practice: How many Significant figures vs.

Decimal places?

• 2.2 cm

• 2.50 cm

2 sig. Figs; 1 decimal place

3 sig. Figs; 2 decimal places

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Sig. Fig. in Multiplication/Division; Rounding vs. Zeroing

• When multiplying or dividing measurements with Sig. Fig., the result has the same number of significant figures as the measurement with the fewest number of significant figures

Rounding • 5.02 × 89,665 × 0.10 = 45.0118

• 5.892 ÷ 6.10 = 0.96590

3 SF 5 SF 2 SF 2 SF

4 SF 3 SF 3 SF

= 45

= 0.966

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Sig. Fig. in Multiplication/Division: Scientific notation

• Occasionally, scientific notation is needed to present results with proper significant figures.

5.89 × 6,103 = 35946.67 = 3.59 × 104

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Example: Determine the Correct Number of Sig. Fig.

1. 1.01 × 0.12 × 53.51 ÷ 96 = 0.067556

2. 56.55 × 0.920 ÷ 34.684 = 1.5

3 SF 2 SF 4 SF 2 SF result should have 2 Sig. Fig.

4 SF. 3 SF. 6 SF. result should have 3 Sig. Fig.

= 0.068

= 1.50

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Sig. Fig. in Addition/Subtraction

• when adding or subtracting measurements with significant figures, the result has the same number of decimal places as the measurement with the fewest number of decimal places

5.74 + 0.823 + 2.651 = 9.214

4.865 - 3.965 = 0.9

2 dp 3 dp 3 dp 2 dp

3 dp 3 dp 3 dp

= 9.21

= 0.900

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Example: Determine the Correct Number of Significant Figures

1. 0.987 + 125.1 – 1.22 = 124.867

2. 0.764 – 3.449 – 5.315 = -8

3 dp 1 dp 2 dp result should have 1 dp

3 dp 3 dp 3 dp result should have 3 dp

= 124.9

= -8.000

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Sig. Fig. in Combined Calculations

• Do and/or , then + and/or -3.489 – 5 .67 × 2.3 3 dp 3 Sig. Fig. 2 Sig. Fig.

= 3.489 – 13 = -9.511 = -10

3 dp 0 dp 0 dp (2 sig. fig.) • Parentheses (): Do calculation in () first, then the rest

3.489 × (5.67 – 2.3) 2 dp 1 dp

= 3.489 × 3.4 = 11.8628 = 124 Sig. Fig. 2 Sig. Fig. 2 Sig. Fig.

Practice: Calculation with Proper Significant Figures

a. 12.99 + 2.09 x 1.921 =

b. 2.00 x 3.5 - 1.000 =

75.3

46.1254.2 c.

8.8)7.60025.0( d.

12.99 + 4.01 = 17.00

7.0 – 1.000 = 6.0

15.00/3.75 = 4.00

6.7 8.8 = 5956

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How to solve Unit Conversion Problems

1) Write down Given Amount and Unit2) Write down what you want to Find and Unit3) Write down needed Conversion Factors or

Equations4) Design a Solution Map for the Problem

order Conversions to cancel previous units or

arrange Equation so Find amount is isolated. Example: from Equation A = b c to solve for b

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Solution Map for Unit Conversion

5) Check the Answer to see if its Reasonable correct size and unit

22

/9.157.7

00.15

5.21.3

46.1254.2cmg

cm

g

cmcm

gg

4) Apply the Steps in the Solution Map check that units cancel properly multiply terms across the top and divide

by each bottom term

Example:

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Example: Unit Conversion

60

Given: 7.8 km

Find: ? mi

Conv. Fact. 1 mi = 5280 ft

1 foot = 12 in 1 in = 2.54 cm (exact)

Soln. Map: km mi

Alternative Route:Convert 7.8 km to miles

km m cm in ft mi

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• Apply the Solution Map:

Given: 7.8 km

Find: ? mi

Conv. Fact. 1 mi = 5280 ft

1 foot = 12 in 1 in = 2.54 cm (exact)

Soln. Map: km mi

Alternative Route:Convert 7.8 km to miles

mi ft 5280

mi 1

in 12

ft 1

cm 2.54

in 1

1m

cm 100

km 1

m 1000km 7.8

= 4.84692 mi

= 4.8 mi

• Sig. Figs. & Round:

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Temperature

• Temperature is a measure of the average kinetic energy of the molecules in a sample

• Not all molecules have in a sample the same amount of kinetic energy

• a higher temperature means a larger average kinetic energy

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Fahrenheit Temperature Scale

Two reference points:

• Freezing point of concentrated saltwater (0°F)

• Average body temperature (100°F)more accurate measure now set average body

temperature at 98.6°F

• Room temperature is about 75°F

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Celsius Temperature Scale

Two reference points:

• Freezing point of distilled water (0°C)

• Boiling point of distilled water (100°C)more reproducible standardsmost commonly used in science

• Room temperature is about 25°C

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Fahrenheit 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

1.8

32-F C

32C1.8 F

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The Kelvin Temperature Scale

• both the Celsius and Fahrenheit scales have “-” numbers

• Kelvin scale is an absolute scale, meaning it measures the actual temperature of an object

• 0 K is called Absolute Zero: all molecular motion would stop, theoretically the lowest temperature in the universe0 K = -273°C = -459°FAbsolute Zero is a theoretical value

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Kelvin vs. Celsius• the size of a “degree” on the Kelvin scale is the

same as on the Celsius scalethough technically, call the divisions on the

Kelvin as kelvins, not degreesthat makes 1 K 1.8 times larger than 1°F

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

273C K

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Extremes of TemperatureOn the Earth, • Lowest temperature recorded: -89.2°C (-128.6 °F,

184 K)• Highest air temperature recorded: ~60°C (140 F)

In science lab,• the highest temperature: 4 x 1012 K (?)• the lowest temperature: ~10-10 K (?)

Conversion BetweenFahrenheit and Kelvin

Temperature Scales

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• Fahrenheit to Celsius:

= 40 °C (keep 2 significant figures)

Celsius to Kelvin:

= 313 K

Information

Given: 104 F

Find: ? °C, ? K

Eq’ns:

Convert 104°F into Celsius and Kelvin

C 273K F 23C1.8

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Mass & Volume

Mass & Volume: • two main characteristics of matter• even though mass and volume are individual

properties - for a given type of matter they are related to each other!

Density (ratio of mass vs. volume): for a certain matter, its density is one of the characteristic to distinguish from one another

V olum e

M assDensity

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Unit for density• Solids = g/cm3

1 cm3 = 1 mL• Liquids = g/mL: Density of water = 1.00 g/mL• Gases = g/L: Density of Air ~ 1.3 g/L

Volume of a solid can be determined by water displacement

• Density : solids > liquids >>> gasesexcept ice and dry wood are less dense than

liquid water!

V olum e

M assDensity

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Density of Common Matters

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Density

• Temperature affects the density: Heating objects causes objects to expand, densityThe Lava Lamp: heating/cooling

• In a heterogeneous mixture, the denser object sinksWhy do hot air balloons rise?The “Gold Rush”: Extracting gold

particle from sandDensity of gasoline changes over the

day!

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Density and Volume

Styrofoam vs. Quarter:

Both of these items have a mass of 23 grams, but they have very different volumes; therefore, their densities are different as well.

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Density and Buoyancy

• Average density of human body = 1.0 g/cm3

• Average density of sea water = 1.03 g/mL• Density of mercury, liquid metal, = 13.6 g/mL• Density of copper penny = 8.9 g/cm3

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Density of Body and Body Fat

Density of fat tissue < Density of Muscle/Bones

Estimate the mass percentage of body fat:

Average body fat%:

Female 28%, Male 22%

%100142.4)/(

57.4fat%Body

3

cmgDensity

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Using Density in Calculations

VolumeMass

Density

DensityMass

Volume

V olu m e D en sity M a ss

Solution Maps:

m, V D

m, D V

V, D m

• Both sides multiplied by Volume

• Both sides divided by Density

DM

V

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A man gives a woman an engagement ring and tells her that it is made of platinum (Pt). Critical thinking : test to determine the ring’s density before giving him an answer about marriage. Data: She places the ring on a balance and finds it has a mass of 5.84 grams. She then finds that the ring displaces 0.556 cm3 of water.

Density Pt = 21.4 g/cm3

Application of Density

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Test resultsGiven: Mass = 5.84 grams

Volume = 0.556 cm3

Density Pt = 21.4 g/cm3

Find: Density in grams/cm3

33 cmg 10.5

cm 0.556

g 5.84

DV

m

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Density as a Conversion Factor

• Between mass and volume!!Density H2O = 1 g/mL

• 1 g H2O 1 mL H2O

Density lead = 11.3 g/cm3

• 11.3 g lead 1 cm3 lead

• How much does 4.0 cm3 of Lead weigh?

=4.0 cm3 Pb 11.3 g Pb 1 cm3 Pb

45 g Pbx

g 1.00

mL 1

mL 1

g 1.00 or

g 11.3

mL 1

mL 1

g 11.3 or

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Measurement and Problem SolvingDensity as a Conversion Factor

• The gasoline in an automobile gas tank has a mass of 60.0 kg and a density of 0.752 g/cm3. What is the volume?

• Given: 60.0 kg

• Find: Volume in L

• Conversion Factors: 0.752 grams/cm3

1000 grams = 1 kg

83

Measurement and Problem SolvingDensity as a Conversion Factor

• kg g cm3

343

cm107.98 g 0.752

cm 1

kg 1

g 1000kg 60.0

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Example:A 55.9 kg person displaces 57.2 L of water when submerged in a water tank. What is the density of the person in g/cm3?

Volume = 57.2 L = 5.72 x 104 cm3

Information:

Given: m = 5.59 x 104 g

Find: density, g/cm3

Solution Map: m,VD

Equation:V

m D

34

4

cm 10 x 72.5

g 10 x 59.5

V

m D

= 0.977 g/cm3

Practice: Calculation involving Density

1. The density of air at room temperature and sea level is 1.29 g/L. Calculate the mass of air in a 5.0-gal bottle (1 gal = 3.78 L).

2. A driver filled 15.60 kg of gasoline into his car. If the density of gasoline is 0.788 g/mL, what is the volume of gasoline in liters?

KEY: 24 g (2SF)

KEY: 19.8 L (3SF)

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About Challenging Problems

1.99+: Proper dosage of a drug is 3.5 mg/kg of body weight. Calculate the milligrams of this drug for a 138-lb individual? (1 lb = 454 g).

1.103: 100. mg ibuprofen/5 mL Motrin. Calculate the grams of ibuprofen in 1.5 teaspoons of Motrin. (1 teaspoon = 5.0 mL)

KEY: 2.2×102 mg (2SF)

KEY: 0.15 g (2SF)

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