The Mole as a Quantity

Previous lectures

• Dimensional Analysis

• Scientific Notation

The Mole as a Quantity

LHSE Presents The Mole

The Mole as a Quantity

• Counting: Larger Units

– Conversion Factors – Unit Factors

– Practice problems

• The Mole; Introduction

• The Mole; Conversion Factor

• Quiz

Counting: Larger Units

o 12 eggs o 24 soda cans o 500 sheets of paper

When common items are dealt with in large numbers they are NOT counted individually

• Appropriate size terms (counting units) are used

= 1 dozen eggs

= 1 case of cans

= 1 ream of paper

5 reams is easier to understand than 2500

• Collection terms allows for the use of smaller numbers

Conversion Factor: Units

desired units

Conversion factors

desired units current units

current units x current units

1 x = desired units

Conversion factors are a tool for changing units of a measured /given value into different units

WITHOUT CHANGING THE VALUE!

current units

Conversion Factor: Intro

12 eggs 1 dozen ⁼ 1

o 12 eggs o 24 soda cans o 500 sheets of paper

= 1 dozen eggs

= 1 case of cans

= 1 ream of paper

24 cans

1 case ⁼ 1 500 papers 1 ream ⁼ 1

1 dozen

12 eggs ⁼ 1 1 case

24 cans ⁼ 1 1 ream

500 papers ⁼ 1

Unit factor: a fraction that has the same value in the numerator as in the denominator and is therefore equal to ONE

= 12 eggs 1 dozen

Begin with an equality

Divide both sides by the one of the sides

1 dozen = 12 eggs

Solve

1

Unit factor: a fraction that has the same value in the numerator as in the denominator and is therefore equal to ONE

12 eggs 1 dozen ⁼ 1

1 dozen 12 eggs 1 dozen 1 dozen

= 12 eggs 1 dozen

Begin with an equality

Divide both sides by the one of the sides

1 dozen = 12 eggs

Solve

1

=

Unit factor: a fraction that has the same value in the numerator as in the denominator and is therefore equal to ONE

12 eggs 1 dozen ⁼ 1

12 eggs 12 eggs 1 dozen 12 eggs

1 dozen 12 eggs

Conversion Factor: Examples

desired units current units

current units x = desired units

60 cans

=

24 cans

= 1 case 1 case 24 cans

x 2.5

Conversion Factor: Examples

desired units current units

current units x = desired units

60 cans ^{1 case}

=

24 cans

x 2.5

78 donuts ^{1 dozen}

=

12 donuts

x 6.5

12 donuts

= 1 dozen

Conversion Factor: Examples

desired units current units

current units x = desired units

60 cans x _{24 cans} ^{1 case}

=

78 donuts _{12 donuts} ^{1 dozen}

=

5.5 reams 500 papers

=

1 ream

x ²⁷⁵⁰

500 papers = 1 ream

x

Counting Atoms and Compounds

Particles on the atomic scale are so small that

It takes about 1 x 10

water molecule to fill a shoot glass

As there is a need for dozens, cases and

The MOLE is the counting unit for chemistry

The Mole

The mole is a number (a counting unit):

• dozen = 12

• case = 24

• ream = 500

• mole = 602,200,000,000,000,000,000,000

6.022 X 10²³ (in scientific notation)

6.022 X 10²³ is called Avogadro's number after the Italian scientist Amedeo Avogadro

The symbol N_a is used for 6.022 X 10²³

How Big is 6.022 X 10

?

• 6.022 X 10²³ seconds is 14 quintillion years.

• A mole of pennies would be a stack that made 3.5 round trips to the moon

• There are about N_a ml of water in the pacific ocean

• 1.66 moles of the molecule H₂O?

1 x 10²⁴ water molecule

The mole is a good counting unit for:

• Electrons, protons and neutrons

• Atoms, ions, molecule and compounds

The Mole: In a Compound

The molecular formula or the formula unit gives the ratio of atoms/ions in the compound.

1 mole of compound will therefore have that ratio of moles of atoms/ions

1 mole of the compound BaCl₂: 1 mole Ba²⁺ and 2 mole Cl^-

1 mole of the ion CO₃^-2: 1 moles C and 3 moles O 1 mole of the molecule C₆H₁₂O₆:

6 moles C, 12 moles H, and 6 moles O

= 6.022 X 10²³ 1 mole

Begin with an equality

Divide both sides by the one of the sides

1 mole = 6.022 X 10²³

Solve

1

The mole can be made into a unit factor:

– a fraction with the same value in the numerator as in the denominator

1 mole 6.022 X 10²³

1 mole 1 mole

Conversion Factor: Mole

= 6.022 X 10²³ 1 mole

Begin with an equality

Divide both sides by the one of the sides

1 mole = 6.022 X 10²³

Solve ₌

1

The mole can be made into a unit factor:

– a fraction with the same value in the numerator as in the denominator

6.022 X 10²³

1 mole 6.022 X 10²³

6.022 X 10²³

Conversion Factor: Mole

6.022 X 10²³

1 mole

=

1

1 mole 6.022 X 10²³

Conversion Factor: Mole

6.022 X 10²³

1 mole

= 6.022 X 10²³ 1 mole

= 6.022 X 10²³ 1 mole

atoms

atoms atoms

atoms

1 mole atoms = 6.022 X 10²³ atoms

=

1

1 mole 6.022 X 10²³

Conversion Factor: Mole

6.022 X 10²³

1 mole

= 6.022 X 10²³ 1 mole

= 6.022 X 10²³ ions 1 mole ions

ions

ions ions

ions

=

1

1 mole 6.022 X 10²³

Conversion Factor: Mole

6.022 X 10²³

1 mole

= 6.022 X 10²³ 1 mole

= 6.022 X 10²³ molecules 1 mole molecules

molecules

molecules molecules

molecules

=

1

1 mole 6.022 X 10²³

Conversion Factor: Mole

6.022 X 10²³

1 mole

= 6.022 X 10²³ 1 mole

= 6.022 X 10²³ atoms 1 mole atoms

atoms

atoms atoms

atoms

10²⁴ atoms x = mole atoms 1.66

1 mole 6.022 X 10²³

atoms atoms

Conversion Factor: Mole

=

1

1 mole 6.022 X 10²³

6.022 X 10²³

1 mole

= 6.022 X 10²³ 1 mole

= 6.022 X 10²³ atoms 1 mole atoms

atoms

atoms atoms

atoms

1.66 mole atoms = atoms x ^{6.022 X 10 23 1024}

1 mole atoms atoms

QUIZ: CF; Mole

= 6.022 X 10²³ 1 mole

1 mole

1

6.022 X 10²³

6.022 X 10²³

1 mole

1. Calculate the number of moles that contain 3.5 x 10²⁴ molecules of H₂O.

=

x ^{1 mole} _5.8

6.022 X 10²³ molecules

molecules mole H₂O 3.5 x 10²⁴ molecules H₂O

QUIZ: CF; Mole

= 6.022 X 10²³ 1 mole

1 mole

1

6.022 X 10²³

6.022 X 10²³

1 mole

=

x ^{6.022 X 1023 protons} _{1.73 x 10}²³

1 mole protons protons 2.88 mole protons

QUIZ: CF; Mole

= 6.022 X 10²³ 1 mole

1 mole

1

6.022 X 10²³

6.022 X 10²³

1 mole

3. How many moles of ‘particles’ are 2.0 x 10²² particles?

=

x 1 mole 0.033

6.022 X 10²³ particles

particles mole particles 2.0 x 10²² particles

Recap

When common items are dealt with in large numbers they are NOT counted individually

• Appropriate size terms (counting units) are used The mole is a number (a counting unit):

• mole = 602,200,000,000,000,000,000,000 6.022 X 10²³ (in scientific notation)

• The mole is only used atomic scale particles

• Sub-atomic particles, atoms, ions and compounds For 1 mole of a compound, the molecular formula/formula unit gives the ratio of moles of the atoms/ions

Conversion factors are a tool for changing units of a measured /given value into different units

• Unit factor: a fraction that has the same value in the numerator as in the denominator and is equal to ONE

desired units current units

current units x = desired units

Make mole

conversions a tool!