11

Unit E: The MoleUnit E: The Mole

6.02 X 6.02 X 10102323

22

Learning Objectives

• Identify Avogadro’s Number

• Distinguish between counting numbers and mass/volume numbers

• Calculate the number of particles in a mole

• Calculate the number of moles in a quantity

33

STOICHIOMETRYSTOICHIOMETRYSTOICHIOMETRYSTOICHIOMETRY- the study of the the study of the

quantitative aspects quantitative aspects of chemical of chemical reactions.reactions.

- Stoich = elementStoich = element- Metry = study of Metry = study of

(think: geo(think: geometrymetry))

44Avogadro's Number (the Avogadro's Number (the Mole)Mole)

• A counting unit• Similar to a dozen, except instead of 12,

it’s 602 billion trillion 602,000,000,000,000,000,000,000

• 6.02 X 1023 (in scientific notation)• This number is named in honor of

Amedeo _________ (1776 – 1856)Amedeo _________ (1776 – 1856), who studied quantities of gases and discovered that no matter what the gas was, there were the same number of molecules present in a given volume

55

Just How Big is a Mole?Just How Big is a Mole?

• Enough soft drink cans to cover the surface of the earth to a depth of over 200 miles.

• If you had Avogadro's number of unpopped popcorn kernels, and spread them across the United States of America, the country would be covered in popcorn to a depth of over 9 miles.

• If we were able to count atoms at the rate of 10 million per second, it would take about 2 billion years to count the atoms in one mole.

• In other words: a LOT.

66

Everybody Has AvogadroEverybody Has Avogadro’’s s Number!Number!

But Where Did it Come From?But Where Did it Come From?• It was NOT just picked!

It was MEASURED.• One of the better

methods of measuring this number was the Millikan Oil Drop Experiment

• Since then we have found even better ways of measuring using x-ray technology

77

Suppose we invented a new collection unit called a rapp. One rapp contains 8 objects.

1. How many paper clips in 1 rapp?

a) 1 b) 4 c) 8

2. How many oranges in 2.0 rapp?

a) 4 b) 8 c) 16

3. How many rapps contain 40 gummy bears?

a) 5 b) 10 c) 20

Try it yourself…Try it yourself…

88

The MoleThe Mole• 1 dozen cookies = 12 cookies• 1 mole of cookies = 6.02 X 1023 cookies

• 1 dozen cars = 12 cars• 1 mole of cars = 6.02 X 1023 cars

• 1 dozen Al atoms = 12 Al atoms• 1 mole of Al atoms = 6.02 X 1023 atoms

Note that the NUMBER is always the same, but the MASS is very different! (a mole of cars will probably weigh more than a mole of cookies!)

Mole is abbreviated mol (gee, that’s a lot quicker to write, huh?)

99

= 6.02 x 1023 C atoms

= 6.02 x 1023 H2O molecules

= 6.02 x 1023 NaCl “molecules”(technically, ionic compounds are ratios not

molecules so they are called formula units)

6.02 x 1023 Na+ ions and

6.02 x 1023 Cl– ions

A Mole of ParticlesA Mole of Particles Contains 6.02 x 1023 particles

1 mole C

1 mole H2O

1 mole NaCl

1010

6.02 x 1023 particles

1 mole

or

1 mole

6.02 x 1023 particles

Note that a particle could be an atom OR a molecule!

AvogadroAvogadro’’s Number as s Number as Conversion FactorConversion Factor

1111

1. Number of atoms in 0.500 mole of Ala) 500 Al atoms

b) 6.02 x 1023 Al atomsc) 3.01 x 1023 Al atoms

2.Number of moles of S in 1.8 x 1024 S atomsa) 1.0 mole S atomsb) 3.0 mole S atomsc) 1.1 x 1048 mole S atoms

Learning CheckLearning Check

1212

Part 2: Molar Mass

• Describe what molar mass is

• Distinguish between gram molecular mass and gram formula mass

• Find the molar mass of elements and compounds

1313

Molar MassMolar Mass

• The mass (in grams) of 6.02 x 1023 particles (1

mole) of a substance

• Equal to the average atomic mass (mass

number) on the periodic table

1 mole of C atoms = 12.0 g

1 mole of Mg atoms = 24.3 g

1 mole of Cu atoms = 63.5 g

1414

The Unit

• We express molar mass using the unit g/mol(grams per mole)

• Similar to density (g/mL)

1515

Formula/Atomic/Molecular Mass

• Gram atomic mass (gam) is the mass of 1 mole of atoms

• Gram Molecular Mass (gmm) is the mass of 1 mole of molecules (covalent only!)

• Gram Formula Mass (gfm) is the mass of 1 mole of ionic compounds

These are all examples of the same thing: molar mass!

1616

Other Names Related to Molar MassOther Names Related to Molar Mass

• Molecular Mass/Molecular Weight: If you have a single

molecule, mass is measured in amu’s instead of grams. But,

the molecular mass/weight is the same numerical value as 1

mole of molecules. Only the units are different. (This is the

beauty of Avogadro’s Number!)

• Formula Mass/Formula Weight: Same goes for

compounds. But again, the numerical value is the same.

Only the units are different.

• THE POINT: You may hear all of these terms which mean the SAME NUMBER… just different units

1717

Find the molar mass

(usually we round to the tenths place)

Learning Check!Learning Check!

A.1 mole of Br atomsB.1 mole of Sn atoms

= 79.9 g/mole

= 118.7 g/mole

1818

Mass in grams of 1 mole equal numerically to the sum of the atomic masses

1 mole of CaCl2 = 111.1 g/mol

1 mole Ca x 40.1 g/mol

+ 2 moles Cl x 35.5 g/mol = 111.1 g/mol CaCl2

1 mole of N2O4 = 92.0 g/mol

Molar Mass of Molecules and Molar Mass of Molecules and CompoundsCompounds

1919

A. Molar Mass of K2O = ? Grams/mole

B. Molar Mass of antacid Al(OH)3 = ? Grams/mole

Learning Check!Learning Check!

94. 2 g/mol

78.0 g/mol

2020

Prozac, C17H18F3NO, is a widely used

antidepressant that inhibits the uptake

of serotonin by the brain. Find its molar

mass.

ChallengeChallenge

2121

molar mass

Grams Moles

Calculations with Molar MassCalculations with Molar Mass

• Moles to Grams/Grams to Moles• Particles to Grams/Grams to Particles• Volume

2222

Aluminum is often used for the structure of light-weight bicycle frames. How many grams of Al are in 3.00 moles of Al?

3.00 moles Al ? g Al

Converting Moles and GramsConverting Moles and Grams

2323

1. Molar mass of Al 1 mole Al = 27.0 g Al

2. Conversion factors for Al

27.0g Al or 1 mol Al

1 mol Al 27.0 g Al

3. Setup 3.00 moles Al x 27.0 g Al

1 mole Al

Answer = 81.0 g Al

2424

After leaving his bike out all night, Mr.

Pinson collected a 36g sample of Iron

(II) Oxide from his wheel. How many

moles of rust were formed?

Learning Check!Learning Check!

2525

The artificial sweetener aspartame

(Nutra-Sweet) formula C14H18N2O5 is

used to sweeten diet foods, coffee and

soft drinks. How many moles of

aspartame are present in 225 g of

aspartame?

Challenge!Challenge!

2626

Atoms/Molecules and GramsAtoms/Molecules and Grams

• Since 6.02 X 1023 particles = 1 mole AND1 mole = molar mass (grams)….

• You can convert atoms/molecules to moles and then moles to grams! (Two step process)

2727

…But!!

• You can’t go directly from atoms to grams!!!! You MUST go thru MOLES.

• That’s like asking 2 dozen cookies weigh how many ounces if 1 cookie weighs 4 oz? You have to convert to dozen first!

2828

molar mass Avogadro’s number Grams Moles particles

Everything must go through Moles!!!

CalculationsCalculations

2929

Atoms/Molecules and GramsAtoms/Molecules and Grams

How many atoms of Cu are present in 35.4 g of Cu?

35.4 g Cu 1 mol Cu 6.02 X 1023 atoms Cu 63.5 g Cu 1 mol Cu

= 3.4 X 1023 atoms Cu

3030

Learning Check!Learning Check!

How many atoms of K are present in 78.4 g of K?

3131

Learning Check!Learning Check!

What is the mass (in grams) of 1.20 X 1024 molecules of glucose (C6H12O6)?

3232

Learning Check!Learning Check!

How many atoms of O are present in 78.1 g of oxygen?

78.1 g O2 1 mol O2 6.02 X 1023 molecules O2 2 atoms O 32.0 g O2 1 mol O2 1 molecule O2

3333

Volume of a Mole

• Through experimentation, scientists have discovered that 1 mole of any gas will occupy the same volume: 22.4 L

• They will still have different molar masses, however, and so their densities will be different

3434

Example

• How much space will 2.5 moles of N2 gas occupy?

2.5 moles x 22.4 L = mole

56 L

3535

Example 2

• How many moles are in 34.5 L of methane gas?

34.5 L x 1 mole = 22.4 L

1.54 Moles CH3

3636

Try it yourself

1. 1.34 moles ozone = ? L

2. 13 L of mustard gas = ? Moles

3. 230 L of Helium gas = ? Moles

4. 5.6 moles Nitrogen gas = ? L

3737

What is the percent carbon in C5H8NO4 (the

glutamic acid used to make MSG

monosodium glutamate), a compound used

to flavor foods and tenderize meats?

a) 8.22 %C

b) 24.3 %C

c) 41.1 %C

Percent CompositionPercent Composition

3838

Chemical Formulas of Chemical Formulas of CompoundsCompounds

• Formulas give the relative numbers of atoms or Formulas give the relative numbers of atoms or moles of each element in a formula unit - always moles of each element in a formula unit - always a whole number ratio (the law of definite a whole number ratio (the law of definite proportions).proportions).

NONO22 2 atoms of O for every 1 atom of N 2 atoms of O for every 1 atom of N

1 mole of NO1 mole of NO22 : 2 moles of O atoms to : 2 moles of O atoms to

every 1 mole of N atomsevery 1 mole of N atoms

• If we know or can determine the relative number If we know or can determine the relative number of moles of each element in a compound, we can of moles of each element in a compound, we can determine a formula for the compound.determine a formula for the compound.

3939

Types of Formulas

• Empirical

• Molecular (true)

4040

Empirical FormulaEmpirical Formula

• The formula of a compound The formula of a compound that expresses the that expresses the smallest smallest whole number ratiowhole number ratio of the of the atoms present.atoms present.

• Ionic formula are always Ionic formula are always empirical formulasempirical formulas

4141

Molecular Formula (true formula)

• The formula that states the The formula that states the actualactual number of each kind of number of each kind of atom found in atom found in one moleculeone molecule of the compound.of the compound.

4242

Examples

Empirical Formula

Molecular Formula

CH C2H2

CH2O C6H12O6

NaCl NaClCH4N C2H8N2

4343To obtain an To obtain an Empirical Empirical FormulaFormula

1.1. Convert % to grams, if necessaryConvert % to grams, if necessary

2.2. Calculate the number of Calculate the number of molesmoles of of each each element.element.

3.3. Divide each by the smallest number of Divide each by the smallest number of moles to obtain the moles to obtain the simplest whole simplest whole number ratio.number ratio.

4.4. If whole numbers are not obtainedIf whole numbers are not obtained** in step in step 3), multiply through by the smallest 3), multiply through by the smallest number that will give all whole numbersnumber that will give all whole numbers

** Be careful! Do not round off numbers prematurelyBe careful! Do not round off numbers prematurely

4444A sample of a brown gas, a major air A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N pollutant, is found to contain 2.34 g N and 5.34g O. Determine a formula for and 5.34g O. Determine a formula for this substance.this substance.

1. Convert grams to moles

2.34g N x 1 mole N = 0.167 14g mol

5.34g O x 1 mole O = 0.333 mol16g

4545A sample of a brown gas, a major air A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N pollutant, is found to contain 2.34 g N and 5.34g O. Determine a formula for and 5.34g O. Determine a formula for this substance.this substance.

2. Divide by smallest mol number

0.167 mol N

0.333 mol O___________ 0.167

___________ 0.167

= About 1 = About 2

4646A sample of a brown gas, a major air A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N pollutant, is found to contain 2.34 g N and 5.34g O. Determine a formula for and 5.34g O. Determine a formula for this substance.this substance.

3. Assign ratio numbers to formula

1 mole N for every 2 moles O =

NO2

Note: This is an empirical formula, NOT a molecular formula! The compound is not necessarily Nitrogen Dioxide!

4747

Empirical Formula Song

1. % to Grams

2. Grams to Moles

3. Divide by the Smallest

4. Multiply to Whole!

4848

Empirical Formula from % Empirical Formula from % CompositionComposition

A substance has the following composition by mass: 60.80 % Na ; 28.60 % B ; 10.60 % H What is the empirical formula of the substance?

• Consider a sample size of 100 gramsThis will contain 60.8g of Na, 28.60 grams of B

and 10.60 grams H

Note: Because % Composition is a constant, you could use ANY sample size to find empirical formula…but 100g is the easiest

4949

1. Convert grams to moles

60.8g Na x 1 mole Na = 2.65 mol 23g

28.60g B x 1 mole B = 2.65 mol 10.8g

10.60g H x 1 mole H = 10.6 mol 1g

5050

2. Divide by smallest mole

2.65 mol Na 2.65 mol B 10.60 mol H__________ 2.65

__________ 2.65

__________ 2.65

=1 = 1 = 4

Ratio = 1:1:4

5151

3. Assign ratio to elements in formula

1:1:4 = NaBH4

5252

Practice: Empirical Formula

1. 94.1% O, 5.9% H

2. 79.8% C, 20.2% H

3. 67.6% Hg, 10.8% S, 21.6% O

4. 27.59% C, 1.15% H, 16.09% N, 55.17% O

OHCH3

HgSO4

C2HNO3

5353

Multiply to Whole

• You cannot round anything more than .1

• 1.3 = 1.3, NOT 1!

• To convert to whole numbers, multiply the whole problem by 2, 3, or 4

• 1.5 x 2 = 3 1.25 x 4 = 5

• 1.3 x 3 = 3.999 (4)

5454

Example w/ Multiply to Whole

A sample contains 70% iron, 30% oxygen. What is its empirical formula?

1. % to grams70% = 70g Fe30% = 30g O

2. Grams to moles 70g x 1mole = 1.25 55.8g

30g x 1 mole = 1.875 16g

3. Divide by the Smallest

____1.25

____1.25

= 1

= 1.5

5555

FeO1.5

4. Multiply to Whole

( )2

= Fe2O3

5656Calculation of the Molecular FormulaCalculation of the Molecular Formula

A compound has an empirical formula A compound has an empirical formula of NOof NO22. The colourless liquid, used in . The colourless liquid, used in

rocket engines has a molar mass of rocket engines has a molar mass of 92.0 g/mole. What is the 92.0 g/mole. What is the molecular molecular formula formula of this substance?of this substance?

5757

1. Find molar mass of Empirical Formula (efm)

Element# of

AtomsMass per

AtomTotal Mass

N 1 14 14

O 2 16 32

= 46g

5858

2. Divide molar mass of compound by empirical formula

mass

92g

46g= 2

5959

3. Multiply the answer by the formula subscripts

• NO2 x 2 = N2O4

=The compound is Dinitrogen Tetroxide

6060

Practice: Molecular Formula

1. Ethylene glycol (CH3O), used in antifreeze, with a molar mass of 62g/mol

2. P-dichlorobenzene (C3H2Cl), makes up mothballs with molar mass of 147g/mol

C2H6O2

C6H4Cl2