11

The MoleThe Mole

6.02 X 6.02 X 10102323

22

The MoleThe 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

33• Just as a dozen eggs equals 12 eggs, a mole = 602,000,000,000,000,000,000,000– It is equal to that number no matter what

kind of particles you’re talking about– It could be represent marbles, pencils, or

bikes– usually deals with atoms and molecules

• The word “mole” was introduced about 1896 by Wilhelm Oswald, who derived the term from the latin word moles meaning a “heap” or “pile.”

• The mole, whose abbreviation is “mol”, is the SI base unit for measuring amount of a pure substance.

• Just as a dozen eggs equals 12 eggs, a mole = 602,000,000,000,000,000,000,000– It is equal to that number no matter what

kind of particles you’re talking about– It could be represent marbles, pencils, or

bikes– usually deals with atoms and molecules

• The word “mole” was introduced about 1896 by Wilhelm Oswald, who derived the term from the latin word moles meaning a “heap” or “pile.”

• The mole, whose abbreviation is “mol”, is the SI base unit for measuring amount of a pure substance.

44• The mole, as a unit, is only used to count very small items– Represents a # of items, so, we can know

exactly how many items are in 1 mole• The experimentally determined number a

mole is called, Avogadro’s Number.– Or 6.02x1023

• The term representative particle refers to the species present in a substance– Usually atoms– Molecules– Or formula units (ions)

• The mole, as a unit, is only used to count very small items– Represents a # of items, so, we can know

exactly how many items are in 1 mole• The experimentally determined number a

mole is called, Avogadro’s Number.– Or 6.02x1023

• The term representative particle refers to the species present in a substance– Usually atoms– Molecules– Or formula units (ions)

55How Do We Use The Mole?How Do We Use The Mole?• We’d never use the mole to describe

macroscopic or real world objects. – 1 mole (6.02x1023) of watermelon seeds

would be found inside a watermelon the size of the moon.

– 1 mole (6.02x1023) of donut holes would cover the earth and would be 5 miles deep.

• Since the mole is such a huge number of items, it is only used to describe the amount of things that are very, very small.– 1 mole (6.02x1023) of water molecules would

barely fill a shot glass

• We’d never use the mole to describe macroscopic or real world objects. – 1 mole (6.02x1023) of watermelon seeds

would be found inside a watermelon the size of the moon.

– 1 mole (6.02x1023) of donut holes would cover the earth and would be 5 miles deep.

• Since the mole is such a huge number of items, it is only used to describe the amount of things that are very, very small.– 1 mole (6.02x1023) of water molecules would

barely fill a shot glass

66

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.

77

Everybody Has Avogadro’s Everybody Has Avogadro’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

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!

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, ionics are compounds 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!

Avogadro’s Number as Avogadro’s Number as Conversion FactorConversion Factor

1111

If you have a 35.67g piece of Chromium metal on your car, how many atoms of Chromium are

in this piece of metal?

If you have a 35.67g piece of Chromium metal on your car, how many atoms of Chromium are

in this piece of metal?

• You are given mass and asked for number of particles

• Let’s get some strategy

• You are given mass and asked for number of particles

• Let’s get some strategy

Using the mole in calculations #7Using the mole in calculations #7

1212

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

1313

• Do you know how to measure out 3 moles of sugar or salt or water?– The mole is a counting unit, so we would have

to count out 6.02x1023 particles of each substance. (no thank you)

• There are 2 ways we can use to measure out a number of moles of a substance.– Measure it in grams (a mass)– Or measure it in liters (a volume)

• Do you know how to measure out 3 moles of sugar or salt or water?– The mole is a counting unit, so we would have

to count out 6.02x1023 particles of each substance. (no thank you)

• There are 2 ways we can use to measure out a number of moles of a substance.– Measure it in grams (a mass)– Or measure it in liters (a volume)

How we measure moles…How we measure moles…

1414

• One of the units we can use to measure out a particular amount of moles is to weigh it out in grams?– The only problem with this method is that 1

mol of books will weigh more than 1 mol of pencils, since each book is heavier.

– What if 1 mol of pencils weighs 500Gtons and 1 mol of books weighs 1x106Gtons.

• How much would 3.0 mols of pencils and 3 mols of books weigh? – 500 Gtons * 3 mols = 1500 Gtons pencils– 1x106 Gtons * 3 mols = 3x106 Gtons

• One of the units we can use to measure out a particular amount of moles is to weigh it out in grams?– The only problem with this method is that 1

mol of books will weigh more than 1 mol of pencils, since each book is heavier.

– What if 1 mol of pencils weighs 500Gtons and 1 mol of books weighs 1x106Gtons.

• How much would 3.0 mols of pencils and 3 mols of books weigh? – 500 Gtons * 3 mols = 1500 Gtons pencils– 1x106 Gtons * 3 mols = 3x106 Gtons

Using mass to measure moles…Using mass to measure moles…

1515Using mass to measure moles…Using mass to measure moles…• To be able to measure out 1 mol of a

substance we would need access to the known mass in grams of 1 mol of any substance in question– We would need a data table that provided

all of these masses since every substance involved would have its own mass.

• Remember, we don’t use the mole to count anything but atoms, molecules, etc.– So we need a table that provides the mass 1

mole would weigh for every combination of atoms known to man.

• To be able to measure out 1 mol of a substance we would need access to the known mass in grams of 1 mol of any substance in question– We would need a data table that provided

all of these masses since every substance involved would have its own mass.

• Remember, we don’t use the mole to count anything but atoms, molecules, etc.– So we need a table that provides the mass 1

mole would weigh for every combination of atoms known to man.

1616

• The Mass of 1 mole (in grams)

• Equal to the numerical value of the average

atomic mass (get from 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

Molar MassMolar Mass

1717

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

1818

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

1919

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

2020

A. Molar Mass of K2O = ? Grams/mole

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

Learning Check!Learning Check!

2121

molar mass

Grams Moles

Calculations with Molar MassCalculations with Molar Mass

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 mole of any gas at STP has volume 22.4L

STP: STANDARD TEMPERATURE AND PRESSURE

= 0C and 101.3 KPa

molar volume

Volume Moles

Calculations with Molar Calculations with Molar VolumeVolume

2424

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

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?

Learning Check!Learning Check!

2626

Atoms/Molecules and GramsAtoms/Molecules and Grams

• Since 6.02 X 1023 particles = 1 mole AND

1 mole = molar mass (grams)• You can convert atoms/molecules to

moles and then moles to grams! (Two step process)

• 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!

2727

If you have a 35.67g piece of Chromium metal on your car, how many atoms of Chromium are

in this piece of metal?

If you have a 35.67g piece of Chromium metal on your car, how many atoms of Chromium are

in this piece of metal?

• You are given mass and asked for number of particles

• Let’s get some strategy

• You are given mass and asked for number of particles

• Let’s get some strategy

Using the mole in calculations #7Using the mole in calculations #7

2828

We are given a We are given a massmass

We are given a We are given a massmass

2929

molar mass Avogadro’s number

Grams Moles particles

Everything must go through Moles!!!

CalculationsCalculations

3030

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

3131

Learning Check!Learning Check!

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

3232

Learning Check!Learning Check!

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

3333

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

3434

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

3535

Chemical Formulas of Chemical Formulas of CompoundsCompounds

(HONORS only)(HONORS only)

• 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.

3636Types of FormulasTypes of Formulas(HONORS only)(HONORS only)

• Empirical FormulaEmpirical Formula

The formula of a compound that The formula of a compound that expresses the expresses the smallest whole number smallest whole number ratioratio of the atoms present. of the atoms present.

Ionic formula are always empirical formulaIonic formula are always empirical formula

• Molecular FormulaMolecular Formula

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

3737To obtain an To obtain an Empirical Empirical Formula Formula (HONORS only)(HONORS only)

1.1. Determine the mass in grams of each Determine the mass in grams of each element present, if necessary.element present, 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 moles Divide each by the smallest number of moles to obtain the to obtain the simplest whole number ratio.simplest whole 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 number 3), multiply through by the smallest number that will give all whole numbersthat will give all whole numbers

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

3838A sample of a brown gas, a major air pollutant, is A sample of a brown gas, a major air pollutant, is found to contain 2.34 g N and 5.34g O. Determine a found to contain 2.34 g N and 5.34g O. Determine a formula for this substance.formula for this substance.

require require molemole ratios so convert grams to moles ratios so convert grams to moles

moles of N = moles of N = 2.34g of N 2.34g of N = 0.167 moles of N= 0.167 moles of N

14.01 g/mole14.01 g/mole

moles of O = moles of O = 5.34 g5.34 g = 0.334 moles of O = 0.334 moles of O

16.00 g/mole16.00 g/mole

Formula:Formula:

0.334 0.167ON 0.167 0.334 2

0.167 0.167

N O NO

(HONORS only)(HONORS only)

3939Calculation of the Molecular FormulaCalculation of the Molecular Formula(HONORS only)(HONORS only)

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?

4040

Empirical Formula from % Empirical Formula from % CompositionComposition (HONORS only)(HONORS only)

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 28.60 grams of B and 10.60

grams HDetermine the number of moles of eachDetermine the simplest whole number ratio