CHEM 101

PPts from week of1/25/20121/27/2012

Significant FiguresSignificant Figures

Significant Digits

• Any non-zero digit• A zero between two nonzero digits • Zeroes to the right of a nonzero digit and to

the right of the decimal point

461

All nonzero numbers are significant.

Significant Figures

461

All nonzero numbers are significant.

Significant Figures

461

All nonzero numbers are significant.

Significant Figures

461

3 Significant Figures

All nonzero numbers are significant.

Significant Figures

A zero is significant when it is between nonzero digits.

5 Significant Figures

600.39

Significant Figures

3 Significant Figures

30.9

A zero is significant when it is between nonzero digits.

Significant Figures

A zero is significant at the end of a number that includes a decimal point.

5 Significant Figures

000.55

Significant Figures

A zero is significant at the end of a number that includes a decimal point.

5 Significant Figures

0391.2

Significant Figures

Non-Significant Digits

• Zeroes to the left of the leftmost nonzero digit• Zeroes to the left of an implied decimal point

– 567 has an implied decimal point– 450 has an implied decimal point we do not know

if the zero is significant therefore it is non-significant

A zero is not significant when it is before the first nonzero digit.

1 Significant Figure

600.0

Significant Figures

A zero is not significant when it is before the first nonzero digit.

3 Significant Figures

907.0

Significant Figures

A zero is not significant when it is at the end of a number without a decimal point.

1 Significant Figure

00005

Significant Figures

A zero is not significant when it is at the end of a number without a decimal point.

4 Significant Figures

01786

Significant Figures

12 inches = 1 foot100 centimeters = 1 meter

• Exact numbers have an infinite number of significant figures.

• Exact numbers occur in simple counting operations

Exact Numbers

• Defined numbers are exact.

12345

Rounding Off NumbersRounding Off Numbers

• Often when calculations are performed on a calculator extra digits are present in the results.

• It is necessary to drop these extra digits so as to express the answer to the correct number of significant figures.

• When digits are dropped, the value of the last digit retained is determined by a process known as rounding off numbers.

80.873

Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed.

4 or less

Rules for Rounding Off

1.875377

Rule 1. When the first digit after those you want to retain is 4 or less, that digit and all others to its right are dropped. The last digit retained is not changed.

4 or less

Rounding Off Numbers

5 or greater

5.459672

Rule 2. When the first digit after those you want to retain is 5 or greater, that digit and all others to its right are dropped. The last digit retained is increased by 1.

drop these figuresincrease by 1

6

Rounding Off Numbers

Significant Figures in Calculations

Significant Figures in Calculations

The results of a calculation based on measurements cannot be more precise than the least precise measurement.

It is important to remember that:

Multiplication or DivisionMultiplication or Division

• In multiplication or division, the answer must contain the same number of significant figures as in the measurement that has the least number of significant figures.

(190.6)(2.3) = 438.38

438.38

Answer given by calculator.

2.3 has two significant figures.

190.6 has four significant figures.

The answer should have two significant figures because 2.3 is the number with the fewest significant figures.

Drop these three digits.Round off this digit to

four.

The correct answer is 440 or 4.4 x 102

Addition or SubtractionAddition or Subtraction

The results of an addition or a subtraction must be expressed to the same precision as the least precise measurement.

The result must be rounded to the same number of decimal places as the value with the fewest decimal places.

1.039 - 1.020Calculate

1.0391.039 - 1.020

= 0.0182868141.039

Answer given by calculator.

1.039 - 1.020 = 0.019

0.019 = 0.018286814

1.039

The answer should have two significant figures because 0.019 is the number with the fewest significant figures.

2 80.018 6814

Two significant figures.

Drop these 6 digits.

0.018286814

Correct answer.

Units of Measurement

• Recall that the unit part of a measurement tells us the scale or standard used to represent the results of a measurement

• The two most widely used systems of measurement are the English System and the Metric System

Measurement of mass, length and volume

• In the United States, we use a fairly awkward system of measurement for most things - the English system

• Scientists use the metric or SI system of units for the measurement of physical quantities

• This system uses standard units based on very precisely known properties of matter and light

• Metric Prefixes are used to change the size of the fundamental or standard units.

The Metric SystemThe Metric System

The Metric or International System (SI, Systeme International)

• Is a decimal system of units.

• It is built around standard units.

• It uses prefixes representing powers of 10 to express quantities that are larger or smaller than the standard units.

International System’s Standard Units of Measurement

Quantity Name of Unit Abbreviation

Length meter m

Mass kilogram kg Temperature Kelvin K

Time second sAmount of substance mole mol

Electric Current ampere A

Luminous Intensity candela cd

Because these fundamental units are not always convenient size, the SI System uses metric prefixes to change the size of the unit

Common Prefixes and Numerical Values for SI Units Power of 10

Prefix Symbol Numerical Value Equivalent

giga G 1,000,000,000 109

mega M 1,000,000 106

kilo k 1,000 103

hecto h 100 102

deca da 10 101

— — 1 100

Prefixes and Numerical Values for SI Units

deci d 0.1 10-1

centi c 0.01 10-2

milli m 0.001 10-3

micro 0.000001 10-6

nano n 0.000000001 10-9

pico p 0.000000000001 10-12

femto f 0.00000000000001 10-15

Power of 10Prefix Symbol Numerical Value Equivalent

Measurement of LengthMeasurement of Length

The standard unit of length in the SI system is the meter. 1 meter is the distance that light travels in a vacuum during of a second.

1299,792,458

The Meter

• 1 meter = 39.37 inches

• 1 meter is a little longer than a yard

Metric Units of Length Exponential

Unit Abbreviation Metric Equivalent Equivalent

kilometer km 1,000 m 103 m

meter m 1 m 100 m

decimeter dm 0.1 m 10-1 m

centimeter cm 0.01 m 10-2 m

millimeter mm 0.001 m 10-3 m

micrometer m 0.000001 m 10-6 m

nanometer nm 0.000000001 m 10-9 m

angstrom Å 0.0000000001 m 10-10 m

Converting Between Units

Converting Between Units

• The standard method to convert between two different units is the factor-label or dimensional analysis method

• Dimensional analysis converts a measurement in one unit to another by the use of a conversion factor

• Conversion factors are developed from relationships between two units

Dimensional Analysis

• Dimensional analysis converts one unit to another by using conversion factors.

• The conversion factor must accomplish two things: 1. It must cancel unit1 2. It must introduce unit2

unit1 x conversion factor = unit2

Conversion factors

• Unit factors - factors that relate a quantity in a certain unit to one of another unit e.g. 103 m = 1 km

• The conversion factor is created by dividing both sides by the same quantity

103 m = 1 = 1 km103 m 103m or

103 m = 1 km = 1 1km 1 km Each unit factor gives 2 possible conversion

factors.

Dimensional analysis

• Multiplying a quantity in one unit by an appropriate conversion factor converts the number into the new unit

• Note that conversion factors are exact relationships• Exact relationships have unlimited precision, so they can be

ignored for the purposes of deciding the number of significant digits in a calculation

km1068.4m10

km1m468.0 4

3

Some Problems

• How many millimeters are there in 2.5 meters?

The conversion factor must accomplish two things:

m x conversion factor = mm

It must cancel meters.

It must introduce millimeters

The conversion factor takes a

fractional form.

mmm x = mm

m

conversion factor

conversion factor

The conversion factor is derived from the equality. 1 m = 1000 mm

Divide both sides by 1000 mm

Divide both sides by 1 m

1 m 1000 mm = 1

1 m 1 m

1 m 1000 mm = 1

1000m 1000 mm

Use the conversion factor with millimeters in the numerator and meters in the denominator.

1000 mmx

1 m2.5 m = 2500 mm

32.5 x 10 mm

How many millimeters are there in 2.5 meters?

1000 mm

1 m

How many millimeters are there in 2.5 meters?

Use the conversion factor with millimeters in the numerator and meters in the denominator.

1000 mm

1 m

2.5 m 1000 mmx

1 m= 2500 mm

32.5 x 10 mm

16.0 in2.54 cm

x 1 in

= 40.6 cm

2.54 cm1 in

Use this conversion factor

Convert 16.0 inches to centimeters.

Centimeters can be converted to micrometers by a series of two conversion factors.

cm m meters

33.7 x 10 cm1 m

x 100 cm

1 = 3.7 x 10 m

610 μmx

1 m7 = 3.7 x 10 μm13.7 x 10 m

Convert 3.7 x 103 cm to micrometers.

Convert 3.7 x 103 cm to micrometers.

33.7 x 10 cm1 m

x 100 cm

610 μmx

1 m7 = 3.7 x 10 μm

Centimeters can be converted to micrometers by writing down conversion factors in succession.

cm m meters

MeasuringMass and Volume

MeasuringMass and Volume

MassMass

The standard unit of mass in the SI system is the kilogram. 1 kilogram is equal to the mass of a platinum-iridium cylinder kept in a vault at Sevres, France.

1 kg = 2.205 pounds

Metric Units of mass Exponential

Unit Abbreviation Gram Equivalent Equivalent

kilogram kg 1,000 g 103 g

gram g 1 g 100 g

decigram dg 0.1 g 10-1 g

centigram cg 0.01 g 10-2 g

milligram mg 0.001 g 10-3 g

microgram g 0.000001 g 10-6 g

Convert 45 decigrams to grams.

45 dg1 g

x 10 dg

= 4.5 g

1 g = 10 dg

An atom of hydrogen weighs 1.674 x 10-24 g. How many ounces does the atom weigh?

1 lbx

454 g-241.674 x 10 g -27 3.69 x 10 lb

16 ozx

1 lb-26 5.90 x 10 oz-273.69 x 10 lb

1 lb = 454 g

16 oz = 1 lb

Grams can be converted to ounces using a series of two conversion factors.

An atom of hydrogen weighs 1.674 x 10-24 g. How many ounces does the atom weigh?

-241.674 x 10 g1 lb

x454 g

16 ozx

1 lb-26 5.90 x 10 oz

Grams can be converted to ounces using a single linear expression by writing down conversion factors in succession.

VolumeVolume

Volume

• The amount of 3-dimensional space occupied by a substance

• Fundamental unit of volume in the SI System for volume is based on the volume of a cube measuring

1m x 1m x 1m = (1m)3 = 1m3 = one cubic meter

The liter (L) and milliliter (mL) are the standard units of volume used in most

chemical laboratories.• 1m3 is split into 1000 smaller

cubes ….each has a volume of 1dm3

• 1dm3 = 1L (liter)

• A cube with a volume of 1dm3 can be split into 1000 smaller cubes each with a volume of 1cm3 = 1mL

(milliliter)

1L = 1000mL

Convert 4.61 x 102 microliters to milliliters.

Microliters can be converted to milliliters using a series of two conversion factors.

L L mL

6

1 Lx

10 μL24.61x10 μL -4 4.61x10 L

-1 = 4.61 x 10 mL-44.61x10 L1000 mL

x1 L

Microliters can be converted to milliliters using a linear expression by writing down conversion factors in succession.

L L mL

24.61x10 μL 6

1 Lx

10 μL1000 mL

x1 L

-1= 4.61 x 10 mL

Convert 4.61 x 102 microliters to milliliters.

An extensive property of a material depends upon how much matter is is being considered.

An intensive property of a material does not depend upon how much matter is is being considered.

• mass

• length

• volume

• density

• temperature

• color

Extensive and Intensive Properties

Measurement of Temperature

Measurement of Temperature

Heat

• A form of energy that is associated with the motion of small particles of matter.

• Heat refers to the quantity of this energy associated with the system.

• The system is the entity that is being heated or cooled.

Temperature

• A measure of the intensity of heat.• It does not depend on the size of the system.• Heat always flows from a region of higher

temperature to a region of lower temperature.

Temperature Measurement

• The SI unit of temperature is the Kelvin.

• There are three temperature scales: Kelvin, Celsius and Fahrenheit.

• In the laboratory, temperature is commonly measured with a thermometer.

3 Temperature Scales1. Celsius Scale – used in Europe and in physical and life sciences• Unit is oC• Freezing point of H2O is 0oC• Boiling point of H2O is 100oC

2. Fahrenheit Scale – used in US and Britain• Unit is oF • Freezing point of H2O is 32oF• Boiling point of H2O is 212oF

3. Absolute or Kelvin Scale Unit is K• Freezing point of H2O is 273K• Boiling point of H2O is 373K

Temperature Scales

• The size of each temperature unit (each degree) is the same for the Celsius and Kelvin Scale

- the difference between the freezing point and boiling point of H2O is 100 units on both scales

• The Fahrenheit degree is smaller than the C or K degree

- On the F scale there are 180 F degrees between the boiling point and freezing point of H2O compared to 100 in the Celsius and Kelvin scales

• The zero points are different on all 3 scales

Converting Between Scales

• Conversions Between K and C Scales• simple because the size of the units is the same toC + 273 = tK

Convert 70oC to K:70 + 273 = tK

tK = 343K

Convert 77K to oC:toC = 77 -273

toC = -196 oC

Conversions Between F and C Scales

• Requires 2 adjustments1. Adjustment for different size of unit2. Adjustment for different zero points

• To convert Co to Fo: toF = 1.80(toC) + 32

Factor 1.8 is due to the fact that there are: 100C divisions/180F divisions = 1C division/ 1.8 F divisions or 1.8F div./1C div

• To convert Fo to Co: Subtract 32 from the F temperature (so both scales start at the same point) then multiply by the proper conversion unit toC = (toF – 32) (1oC/1.8oF)

o o oF - 32 = 1.8 x C

To convert between the scales, use the following relationships:

o o oF = 1.8 x C + 32

oK = C + 273.15

oo F - 32C =

1.8

It is not uncommon for temperatures in the Canadian plains to reach –60oF and below during the winter.

What is this temperature in oC and K?

oo F - 32C =

1.8

o o60. - 32C = = -51 C

1.8

DensityDensity

Density is the ratio of the mass of a substance to the volume occupied by that substance.

massd =

volume

Mass is usually expressed in grams and volume in mL or cm3.

gd =

mL3

gd =

cm

The density of gases is expressed in grams per liter.

gd =

L

Density varies with temperature

o

2

4 CH O

1.0000 g gd = = 1.0000

1.0000 mL mL

o

2

80 CH O

1.0000 g gd = = 0.97182

1.0290 mL mL

ExamplesExamples

A 13.5 mL sample of an unknown liquid

has a mass of 12.4 g. What is the density of the liquid?

MD

V 0.919 g/mL12.4g

13.5mL

46.0 mL

98.1 g

A graduated cylinder is filled to the 35.0 mL mark with water. A copper nugget weighing 98.1 grams is immersed into the cylinder and the water level rises to the 46.0 mL. What is the volume of the copper nugget? What is the density of copper?

35.0 mL

copper nugget final initialV = V -V = 46.0mL - 35.0mL = 11.0mL

g/mL8.92mL11.0g98.1

VM

D

The density of ether is 0.714 g/mL. What is the mass of 25.0 milliliters of ether?

Method 1 (a) Solve the density equation for mass.

massd =

volume

(b) Substitute the data and calculate.

mass = density x volume

0.714 g25.0 mL x = 17.9 g

mL

The density of ether is 0.714 g/mL. What is the mass of 25.0 milliliters of ether?

Method 2 Dimensional Analysis. Use density as a conversion factor. Convert:

0.714 g25.0 ml x = 17.9 g

mL

mL → g

gmL x = g

mLThe conversion of units is

The density of oxygen at 0oC is 1.429 g/L. What is the volume of 32.00 grams of oxygen at this temperature?

Method 1 (a) Solve the density equation for volume.

massd =

volume

(b) Substitute the data and calculate.

massvolume =

density

2

2

32.00 g Ovolume = = 22.40 L

1.429 g O /L

The density of oxygen at 0oC is 1.429 g/L. What is the volume of 32.00 grams of oxygen at this temperature?

Method 2 Dimensional Analysis. Use density as a conversion factor. Convert:

2 22

1 L32.00 g O x = 22.40 L O

1.429 g O

g → L

Lg x = L

gThe conversion of units is

Solving Problems

1. Read the problem carefully. Determine what is known and what is to be solved for and write it down.

– It is important to label all factors and units with the proper labels.

2. Determine which principles are involved and which unit relationships are needed to solve the problem.

– You may need to refer to tables for needed data.3. Set up the problem in a neat, organized and

logical fashion.– Make sure unwanted units cancel. – Use sample problems in the text as guides for

setting up the problem.

Basic Steps

4. Proceed with the necessary mathematical operations.

– Make certain that your answer contains the proper number of significant figures.

5. Check the answer to make sure it is reasonable.

Basic Steps

Chapter 2

Atoms, Molecules and IonsPart 1

In studying the materials of theEarth (and other parts of the Universe) scientists have found that all matter can be broken down chemically into about 118 different elements It is quite amazing that millions of known substances are composed of so few fundamental elements ….a phenomena not unlike the hundreds of thousands of known words composed from only 26 letters of the alphabet

Compounds

Are made by combining atoms of the various elements…..

just as words are constructed from the 26 letters of the alphabet

and you had to learn the letters of the alphabet before you learned to read and write

You now must learn the names and symbols of the Chemical Elements before you can read and write chemistry!

The Elements There are presently 118 known elements 88 occur naturally the remainder were made in the lab and decompose

spontaneously into others by radioactive decay the elements vary tremendously in abundance -only 10 constitute over 99% of the Earth’s crust -about 93% of the mass of our bodies is composed of only 3 elements: C, H, and O -the list of elements found in living matter differs greatly from that of the earth’s

crust

*** Elements are fundamental to understanding Chemistry

How Chemists use the word Element

Element

-single atom of that element

-sample of the element large

enough to weigh on a balance

-some elementsthat contain

molecules ratherthan individual

atoms

Single Atoms of an Element – microscopic form of an element

Sample of an Element Large Enough to Weigh on a Balance – Contains many, many atoms of the element and are the macroscopic form of an element

Some Elements that Contain Molecules Rather than Individual Atoms – macroscopic form of elements like oxygen, hydrogen Nitrogen, chlorine, bromine and iodine exist as O2 , H2 , N2 , Cl2 , Br2,F2 and I2

Names for Elements The names of chemical elements come from a variety of

sources - they are often derived from Greek, Latin or German words

that describe some property of the element

ie. Gold- originally called aurum (Latin for “shinning dawn”) Lead- called plumbum (heavy) Names of Cl2(chlorine) and I2(iodine) come from Greek words describing their colors Bromine- derived from a Greek word for “stench”

Some elements are named for the place they were discovered: Francium, Germanium, Californium and Americium

Element Symbols

Element symbols are abbreviations for element names.

Consist of the first letter or first two letters of the elements name The first letter is always capitalized! The second letter (if present) is never capitalized.

Element Symbols

• Fluorine – F• Oxygen – O• Neon – Ne• Silicon – Si

Some have two letters which are not the first and second letters in the name

• Zinc – Zn• Chlorine – Cl• Cadmium – Cd• Platinum - Pt

More Element Symbols

Some other elements are based on the Latin or Greek name.

• Gold (aurum) - Au• Lead (plumbum)- Pb• Sodium (natrium) - Na• Iron (ferrum) - Fe

• All 118 elements and their symbols are found in the inside front cover of your text….as well as in the Periodic Table

• We will look at the Periodic Table in detail in chapters to come

Atomic Theory As scientists of the 18th Century studied the nature

of materials, several things became clear:1. Most natural materials are mixtures of pure substances2. Pure substances are either elements or combinations of elements

called compounds3. A given compound always contains the same proportions by mass of its

elementsie. H2O always contains 8g of oxygen for every 1g of hydrogen and CO2 always contains 2.7g of oxygen for every 1g of carbon - this is known as the Law of Constant Composition - this law says that a given compound has the same composition regardless of where it comes from

John Dalton

• An English scientist and teacher• He knew of these observations and offered an

explanation for them• His explanation is known as:

DALTON’S ATOMIC THEORYThe main ideas of his theory include:

1. Elements are made of tiny particles called atoms.2. All atoms of a given element are identical. Atoms of a given

element are different from those of any other element.3. Atoms of one element can combine with atoms of other

elements to form compounds. A given compound always has the same relative number and types of atoms

4. Atoms are indivisible in chemical processes. ** Atoms are not created or destroyed in chemical reactions.

A chemical reaction simply changes the way atoms are grouped together.

* Dalton’s Theory offered simple explainations for some basic laws of chemistry such as:

The Law of Conservation of Mass Mass is neither created or destroyed. If atoms are conserved in a reaction then mass must also be

conservedThe Law of Constant Composition Tells us that a cmpd regardless of its origin or method of

preparation always contains the same elements in the same proportions by weight

Law of Multiple Proportions When 2 elements combine to form more than 1 cmpd the

masses of one element which combines with a fixed mass of the other elelment are in a ratio of small whole numbers such as 2:1