Mole Conversion

Unit One: The Mole

Molar mass, percent composition,
empirical and molecular formulas

Atomic Mass

� A single atom has a very small mass.

● on the order of 10-23 grams per atom

● 1 atom has a mass of about

0.000 000 000 000 000 000 000 01g

� Because this mass is so small, we use a unit called

amu to describe the mass of a single atom.

● 1 atom of carbon has a mass of 12.011 amu

● 1 atom of hydrogen has a mass of 1.00794 amu

● 1 atom of gold has a mass of 196.967 amu

Formula Mass

� Formula Mass – the mass, in amu, of one

formula unit of a compound.

� To calculate the formula mass of a

compound;

● Count and record the number of each atom

in the formula.

● Multiply the number of atoms by the mass of

that atom from the periodic table.

● Add these products together.

Formula Mass

Calculate the formula mass of CaCl2

Ca

1 x 40.08 = 40.08

Cl 2 x 35.45= + 70.90

110.98 amu

One fomula unit of CaCl2 has a
mass of 110.98 amu.
Ca

Cl

Cl

Formula Mass

� Calculate the formula mass of iron (III)

nitrate. Fe(NO3)3

Fe 1 x 55.85 = 55.85
N 3 x 14.01 = 42.03
O 9 x 16.00 = 144.00

241.88 amu

The Mole

� The mass of a single atom is too small

a quantity for use in lab.

� We need to come up with a way to

take atomic masses from the periodic
table and turn them into a mass that is
useable in lab.

� In 1811, Amedeo Avogadro

determined the number of atoms in
one mole of a substance.

The Mole

� The mole establishes a relationship

between the atomic mass unit (on periodic
table) and the gram (used in lab).

� Mole (mol) - The amount of a pure

substance that contains 6.02 x 10²³ particles
of that substance.

� The mole is used to describe a huge

amount of any extremely small particle. A
mole of gold, a mole of salt and a mole of
water each contain 6.02 x 10²³ individual
units.

The Mole

� One mole of

oxygen, one mole
of salt and one
mole of water.

� Each sample

contains one mole,
6.02 x 1023,
particles.

The Mole

� There are 6.02 x 10²³ carbon atoms in

12 grams, one mole, of carbon.

� There are 6.02 x 10²³ gold atoms in

197 grams, one mole, of gold.

� There are 6.02 x 10²³ formula units of

calcium chloride in 110.98 grams, one
mole, of CaCl2.

How big is one mole?

� One mole of popcorn kernels would cover

the United States to a depth of nine miles.

� One mole of soft drink cans would cover the

Earth to a depth of 200 miles.

� There are approximately one mole of cups

of water in the Pacific Ocean.

� If you inherited a mole of pennies, you could

give one million dollars away to every
person on Earth every day and would die
long before you ran out of money!

� One mole of pennies, equally divided

between every human on the planet, would
make each of us a trillionaire!

So, how do we use the mole
in Chemistry?

� We use the mole to convert between the

mass, volume and number of particles in
a substance.

� We can make conversions from:

● Moles to particles and particles to moles.

● Moles to grams and grams to moles.

● Moles to volume of a gas and volume of

a gas to moles.

● Any combination of the above categories!

Molar Mass

� A molar mass is calculated the same way

that you calculated formula mass.

� The only difference is the unit that will be

placed on the final answer because you
are calculating the mass of one mole of a
substance.

� If the formula mass of CaCl2 is 110.98

amu, then the molar mass of CaCl2 is
110.98 grams.

Match

Match the following molar masses with their compounds

• 158.03 g/mol

• 386.11 g/mol

• 342.14 g/mol

• 149.12 g/mol

• 142.01 g/mol

KMnO₄

Zn₃(PO₄)₂

Al₂(SO₄)₃

(NH₄)₃PO₄

Na₂SO₄

• KMnO₄

• Zn₃(PO₄)₂

• Al₂(SO₄)₃

• (NH₄)₃PO₄

• Na₂SO₄

Formula vs. Molecular Mass

Molar Conversions

Mole

Particles
Mass

Volume

6.02 x 1023

Avogadro’s
Number

Molar Mass

(calculate)

22.4 L

Molar Volume

Converting from Moles to
Particles.

� How many formula units of Sodium Chloride

are there in 2.50 moles of Sodium Chloride
(NaCl)?

2.50 mol NaCl x 6.02 x 10²³units NaCl= 1.51 x 1024

1 mole NaCl

Converting from Moles to
Particles

� How many atoms of gold are there in 4.25 moles of

Au?

4.25 mol Au x 6.02 x 10²³ atoms = 2.56x10²⁴atoms

1 mole Au

Converting from Particles to
Moles.

� How many moles of gold are there in 1.5 x 1024

atoms of gold?

1.5 x 10²⁴ atoms Au x 1 mole = 2.5 moles Au

6.02 x 1023 atoms

Converting from Particles to
Moles

� How many moles of calcium chloride are

there in 3.6 x 1024 formula units of CaCl2?

3.6 x 1024 units x 1 mole CaCl2 = 6.0 mol CaCl2

6.02 x 1023 units

Multiple Choice

Determine the number of moles in 2.73 x 10²⁶ particles of NH₄?

• 907 mol NH₄

• 707 mol NH₄

• 453.5 mol NH₄

• 534.5 mol NH₄

Multiple Choice

Determine the number of moles in 5.46 x 10²⁶ particles of CuCl₂?

• 907 mol CuCl₂

• 707 mol CuCl₂

• 453.5 mol CuCl₂

• 534.5 mol CuCl₂

Multiple Choice

Determine the number of molecules in 5.47 mol of Ca₃P₂?

• 3.29 x 10²⁴ molecules of Ca₃P₂

• 6.37 x 10²⁴ molecules of Ca₃P₂

• 4.53 x 10²⁴ molecules Ca₃P₂

• 5.34 x 10²⁴ molecules Ca₃P₂

Multiple Choice

Determine the number of molecules in 10.94 mol of AlPO₄?

• 6.58 x 10²⁴ molecules of AlPO₄

• 6.37 x 10²⁴ molecules of AlPO₄

• 4.53 x 10²⁴ molecules AlPO₄

• 5.34 x 10²⁴ molecules AlPO₄

Converting from Mass to
Moles

� How many moles of gold are there in 25.0 grams of

gold?

25.0 g Au x 1 mole Au = 0.127 mol Au

196.97 g Au

Converting from Mass to
Moles

� How many moles of calcium chloride are there

in 75.5 grams of CaCl2?

75.5 g CaCl2 x 1 mole CaCl2 = 0.680mol CaCl2

110.98 g CaCl2

Converting from Moles to
Mass

� How many grams of Carbon are there in 4.2

moles of Carbon?

4.2 mole C x 12.01 g C = 50. g C

1 mole C

Converting from Moles to
Mass

� How many grams of water are there in 2.75

moles of water?

The molar mass of water is:
16.00 + 1.01 + 1.01 = 18.02 g/mol

2.75 moles H2O x 18.02 g H2O = 49.6 g H2O

1 mole H2O

Multiple Choice

Determine the number of moles of 50.0 grams of NaCl

• 0.428 mol NaCl

• 0.754 mol NaCl

• 0.836 mol NaCl

• .92 mol NaCl

Multiple Choice

Determine the mass of 75.0 g of potassium permanganate(KMnO₄)

• 0.475 g KMnO₄

• 0.633 g KMnO₄

• 0.575 g KMnO₄

• 0.775 g KMnO₄

Multiple Choice

How many grams are in 2.5 moles NH₃?

• 45.6 g NH₃

• 52.6 g NH₃

• 72.6 g NH₃

• 42.6 g NH₃

Multiple Choice

How many moles are contained in 200. g C₃H₈?

• 2.27 moles C₃H₈

• 4.54 moles C₃H₈

• 3.27 moles C₃H₈

• 2.72 moles C₃H₈

Volume of Gases

� One mole of gas (6.02 x 1023 particles

of gas) occupies a volume of 22.4
liters at standard temperature and
pressure.

� This is true if the gas is monatomic

like Helium (He), diatomic like Oxygen
(O2) or a compound like Carbon
dioxide (CO2).

Converting from Volume to
Moles of a gas

� How many moles of oxygen are there in

10.0L of oxygen?

10.0L O2 x 1 mole O2 = 0.446 mole O2

22.4 L O2

Converting from Volume to
Moles of a gas

� How many moles of Carbon dioxide (CO2)

are there in 2.50 L of CO2 gas?

2.50 L CO2 x 1 mole CO2 = 0.112 mole CO2

22.4 L CO2

Converting from Moles to
Volume of a gas

� How many liters of Helium are there in 3.6

moles of Helium?

3.6 moles He x 22.4 L He = 81 L He

1 mole He

Converting from Moles to
Volume of a gas

� What volume will 8.24 moles of CO2 occupy?

8.24 mol CO2 x 22.4 L CO2 = 185 L CO2

1 mole CO2

Multiple Choice

Determine how many liters of O₂ are moles 5.0 moles of O₂.

• 112 L O₂

• 56 L O₂

• 136 L O₂

• 92 L O₂

Multi-Step Conversions

� If you need to convert from:

● Mass to particles or particles to mass,

● Mass to volume or volume to mass,

● Volume to particles or particles to volume,
then you need to perform a 2-step conversion.

� Notice the mole is not present in the starting or

ending quantities. You will ALWAYS use the mole
when converting between these units!

Multi-Step Conversions

Mole

Particles
Mass

Volume

6.02 x 1023

Avogadro’s
Number

Molar Mass

22.4 L

Molar Volume

Multi-Step Conversions

� How many formula units of calcium chloride are

there in 10.0 grams of CaCl2?

10.0 g CaCl2 x 1 mole CaCl2 x 6.02 x 1023 units =

110.98 g CaCl2 1 mole CaCl2

5.42 x 1022 formula units of CaCl2

Multi-Step Conversions

� What volume would 2.25 grams of hydrogen gas

(H2) occupy at standard temperature and
pressure?

2.25 g H2 x 1 mole H2 x 22.4 L = 25.0 L H2

2.02 g H2 1 mole

Multi-Step Conversions

� How many atoms of Argon gas are there in a

typical light bulb (0.20 liters) at standard
temperature and pressure?

0.20 L Ar x 1 mole x 6.02 x 1023 atoms = 5.4 x 1021

22.4 L 1 mole

atoms Ar

Percent Composition

� The Percent Composition – the percent

by mass of each element in a compound.

� To calculate %Comp:

mass of element x 100 = % by mass

mass of compound

Percent Composition

� Determine the percent by mass of each element in

calcium chloride (CaCl2).

Ca1 x 40.08 = 40.08

40.08 x 100 = 36.11% Ca

110.98

Cl 2 x 35.45 = 70.90

70.90 x 100 = 63.89% Cl

110.98

40.08 + 70.90 =110.98

(molar mass)

Percent Composition

� Calculate the percent by mass of each element in

Calcium sulfate, CaSO4.

Ca 1 x 40.08 = 40.08

40.08 x 100 = 29.44% Ca

136.15

S 1 x 32.07 = 32.07

32.07 x 100 = 23.55% S

136.15

O 4 x 16.00 = 64.00

64.00 x 100 = 47.01% O

136.15

40.08 + 32.07 + 64.00 = 136.15

molar mass

Percent Composition

� You can determine the %Comp of a substance

experimentally.

● Measure the mass of a sample

● Decompose the sample (usually by heating) to

separate the component substances.

● Measure the mass of the substance that

remains.

● Calculate %Comp as before

Empirical Formula

� Empirical Formula – the smallest whole

number mole ratio of elements in a
compound.

� The empirical formula for a class of

molecules is often the same for each
sample.

● Examples: C5H10O5 = CH2O

C6H12O6 = CH2O
C11H22O11 = CH2O

Calculating Empirical
Formula

1)
Assume you are working with a 100.0g sample
so the mass of each element will be the same
as the percent of that element (for simplicity).

2)
Convert each mass in grams to moles using the
molar mass of the element.

3)
Find the whole number ratio of these calculated
amounts by dividing each mole value by the
smallest number of moles calculated.

4)
Round to whole numbers and use the ratio to
determine the empirical formula.

Calculating Empirical
Formula

� A compound was found to contain

29.6% Calcium, 23.7% Sulfur and
46.8% Oxygen. What is the empirical
formula for the compound?

� If you had a 100 gram sample, you

would have 29.6g Ca, 23.7g S and
46.8g O.

Calculating Empirical
Formula

Ca29.6g x 1 mole = 0.739 mol Ca

40.08g

S 23.7g x 1 mole = 0.739 mole S

32.07g

O 46.8 x 1 mole = 2.93 mole O
16.00g

0.739 = 1 0.739 = 1 2.93 = 3.96
0.739 0.739 0.739

Round to the nearest whole numbers, 1 : 1 : 4
Therefore the empirical formula is CaSO4

Molecular Formulas

� Molecular Formula – the actual

number of atoms of each element in
one molecule of a compound.

� The ratio of molecular mass to

empirical mass is the same as the
ratio of molecular formula to empirical
formula.

Calculating Molecular
Formula

� Example:
Molecular formula

Molecular Mass

C6H12O6
180.18

Empirical formula

Empirical Mass

CH2O

30.03

Ratio C6H12O6 = 6

Ratio 180.18 = 6

CH2O

30.03

Calculating Molecular
Formula

� Ribose has a molar mass of 150g/mol

and a chemical composition of
40.0%C, 6.67% hydrogen and 53.3%
oxygen. What is the molecular
formula for ribose?

● Begin by calculating the empirical

formula for Ribose.

Calculating the Molecular
Formula for Ribose

40.0g x 1 mole = 3.33 mole C

12.01g

6.67g x 1 mole = 6.60 mole H

1.01g

53.3g x 1 mole = 3.33 mole O

16.00g

3.33 = 1

6.60 = 1.98

3.33 = 1

3.33

3.33

3.33

Empirical Formula for Ribose

CH2O

Calculating Molecular
Formula

� Once you know the empirical formula, you

can calculate the molecular formula.

� Covalent bonds can form in many different

ratios.

� Use the empirical formula and the ratio of

molar mass to empirical formula mass to
determine the molecular formula.

Calculating the Molecular
Formula for Ribose

� The molecular mass of Ribose is 150 g/mol

� The empirical mass of Ribose is 30 g/mol
(CH2O = 12.01 + (2 x 1.01) + 16.00 = 30.03 g/mol)

150 = 5

Therefore, the Molecular

30

formula is 5 times the

Empirical Formula

C5H10O5

The Formula of a Hydrate

� Hydrate – a compound that has a

specific number of water molecules
bound to its atoms.

� Examples:

CaCl2. 2H2O
FePO4. 4H2O
MgSO4. 7H2O

Determining the Formula for
a Hydrate

� To determine the formula of a hydrate, the sample

must be heated to remove all of the water.

� The mass of the anhydrous sample is subtracted

from the mass of the hydrated sample to
determine the mass of water removed.

� The mass of the anhydrous sample and the mass

of the water are used to determine the empirical
formula and molecular formula as before.

Determining the Molecular
Formula of a Hydrate

� Cobalt (II) chloride is a hydrated salt.

� If 11.75g of this hydrate is heated, 9.25g

of anhydrous cobalt chloride remains.
What is the formula for this hydrate?

11.75g hydrated salt

📫

9.25g anhydrous salt
2.50g water

Determining the Molecular
Formula of a Hydrate

9.25g CoCl2 x 1 mole = 0.0712 mol CoCl2

129.83g
2.50g H2O x 1 mole = 0.139 mol H2O

18.02g

0.0712 = 1

0.139 = 1.95

0.0712

0.0712

1:2 ratio Therefore the formula for the hydrate is

CoCl2. 2H2O