The Mole
Chapter 11 – Chemistry L1
LSM High School
Section 11.1: Measuring Matter
Objectives:
 Describe how a mole is used in chemistry
 Relate a mole to common counting units
 Covert moles to number of representative particles and number of
representative particles to moles.
How do Chemists measure
how much of a substance?
Chemists can measure mass or volume or
they can count pieces.
 Chemists can measure mass in grams.


Chemists can measure volume in liters.
No, not that kind of mole!!!

Chemists can count pieces in MOLES.
What are MOLES?

Moles are defined as the number of carbon
atoms in exactly 12 grams of the carbon-12
isotope.
1 mole of _____ = 6.02 x 1023 particles
 Mole: unit = “mol”
 Avogadro’s number


dozen, baker’s dozen, pi
A Little History



Amedeo Avogadro was born
in 1776 in Turin, Italy.
He went on to study molecular
theory and helped other
scientists distinguish between
atoms and molecules.
Because of his
accomplishments in this field,
the variable that tells the
number of molecules in one
mole was named after him
What are Representative
Particles?
These particles are the smallest pieces of a
substance.
• The types of representative particles that
chemists generally work with are:

• atoms – the smallest particle of an element
• ions – atoms with positive or negative charges
• molecules – two or more covalently bonded atoms
• formula units – the simplest ratio of ions that make up
an ionic compound
Converting
Moles to Particles
and Particles to Moles
Using Avogadro’s Number as a Conversion Factor:
Practice Problem 1

How many atoms are in 2.50 mol of zinc?


Answer: 1.51 x 1024 atoms Zn
Practice Problem 2

How many molecules of CO2 are there in
4.56 moles of CO2 ?


Answer: 2.75 x 1024 molecules of CO2
 How many atoms is this?
Practice Problem 3

How many moles of water is 5.87 x 1022 molecules
of water?


ANSWER: 0.0975 moles of water
Practice Problem 4
Given 3.25 mol AgNO3, determine the
number of formula units.
 K:
UK:


ANSWER: 1.96 x 1024 formula units AgNO3
Section 11.2:
Mass and the Mole
Objectives:
• Relate the mass of an atom to the mass of a
mole of atoms.
• Calculate the number of moles in a given mass
of an element, and the mass of a given number
of moles of an element.
• Calculate the number of moles of an element
when given the number of atoms of an element.
• Calculate the number of atoms of an element
when given the number of moles of the element.
Let’s Look at the Periodic
Table!

Atomic Numbers - always increase across a row.




Atomic Mass - usually increase across a row
Why do they have decimal values?


The atomic number is the number of protons in an atom of that
element.
This number identifies it as an atom of a particular element.
The atomic mass (sometimes called average atomic mass) is the
weighted average of the masses of all the naturally occurring
isotopes of that element.
A relative scale: Uses isotope carbon-12 as the standard


Each atom of carbon-12 has a mass of exactly 12 amu (atomic
mass units)
Ex: One atom of hydrogen-1 has a mass of 1 amu, meaning 1 atom
of hydrogen-1 is one-twelfth the mass of one atom of carbon-12

The mass in grams of one mole of ANY pure
substance is its molar mass.


Same value as atomic mass - has units of g/mol
Occasionally referred to as:




12.01 grams of carbon has the same number of
particles as 1.01 grams of hydrogen and 55.85 grams
of iron.


Gram atomic mass (gam) – for atoms
Gram molecular mass (gmm) – for molecules
Gram formula mass (gfm) – for formula units (ionic compounds)
The molar mass is found in the periodic table!
Avogadro’s number tells us the number of particles.
Using Molar Mass as a
Conversion Factor:
# of grams
1 mol
or
1mol
# of grams
Practice Problems:
1.
What is the mass, in grams, of 2.34 moles
of carbon?
28.1 g carbon
2. How many moles of magnesium are in
4.61g of Mg?
0.190 mol Mg
Section 11.3:
Moles of Compounds
Objectives:
•
•
•
•
Recognize the mole relationships shown by a
chemical formula.
Calculate the molar mass of a compound.
Calculate the number of moles of a compound
from a given mass of the compound, and the
mass of a compound from a given number of
moles of the compound.
Determine the number of atoms or ions in a
mass of a compound.
Enough about atoms:
What about compounds?


The chemical formula for a compound tells us the types of
elements and the number of each element contained in one
unit of the compound.
Ammonia (NH3)


1 molecule contains:
 1 atom of nitrogen and 3 atoms of hydrogen
Baking soda (sodium hydrogen carbonate,
NaHCO3)

1 formula unit contains:
 1 atom of sodium, 1 atom of hydrogen, 1 atom of
carbon, and 3 atoms of oxygen
Example Problems:
1. Calculate the number of moles of hydrogen
found in 3.50 moles of NH3.
10.5 mol Hydrogen
2. Calculate the number of moles of carbon
found in 9.85 moles of C6H12O6 (sugar).
59.1 mol carbon
The Molar Mass of Compounds
Summary of Getting the Molar
Mass of Compounds:





The mass of a mole of a compound equals the sum of the
masses of every particle that makes up the compound.
Use the formula to tell you how many of each element that
is in the compound
Use the periodic table to get the masses of each element
Add them all up and you get the molar mass of the
compound in units of g/mol
(NH4)2SO4
Example Problems of
Molar Masses:

1) What is the molar mass of NH3?

17.04 g/mol
2) What is the molar mass of Sr(NO3)2?
211.64 g/mol
Example Problems of MoleMass Conversions:

1) How many moles is 4.56 g of CO2 ?
K:
UK:
0.104 moles CO2
 2) How many moles is 46.8 g of CH4?
K:
UK:
2.92 mol CH4

3) How many grams is 9.87 moles of H2O?
K:
UK:
178g H2O
 4) How many grams is 0.157 mol Fe2O3?
K:
UK:
25.0 g Fe2O3
Using Molar Volume as a
Conversion Factor:

Molar Volume:

Standard Temperature and Pressure is 0°C or 273 K and 101.3 kPa or 1 atm
22.4 L
1 mol
for any gas at STP, 1 mol = 22.4 L
or
1mol
22.4 L
Practice Problem:
What is the volume of 1.5 moles of nitrogen gas?
K:
UK:
34 L N2 (17 2-Liter bottles!)
REVIEW:

What types of particles are contained in
covalent compounds?

What types of particles are contained in ionic
compounds?
Multi-step Conversions

You must first convert to moles and then
convert to the desired unit either using molar
mass or Avogadro’s number or molar
volume.
Example Problems:
1. What is the volume of 45.6 g of water vapor
at STP?
K:
UK:
56.6 L H2O(g)
2. How many atoms are in 0.120 kg Ti?
K:
UK:
1.51 x 1024 atoms Ti
3. What is the mass, in grams, of 1.50 x 1015
atoms uranium?
K:
UK:
5.93 x 10-7 g U
4. What is the mass, in grams, of 1.50 x 1015
formula units of NaCl?
K:
UK:
1.46 x 10-7 g NaCl
More Example Problems…

1) How many ions if the compound is made of
Na+ and NO3- ions are there in 4.9 g of NaNO3?
11.4 – Empirical and
Molecular Formulas
Percent Composition

Every chemical compound has a definite
composition. What law is this referring to?
The composition of a compound is usually
stated as the percent by mass of each
element in the compound.
 The type of chemist whose job it is to identify
the elements & their percent by mass in a
compound is an analytical chemist.

The equation used to determine the percent
composition of an element in a compound is:
 total mass of element in compound 
% by mass of an element = 
 *100
molar mass of compound


Percent Composition
Example Problems:

1) Determine the percent by mass of each
element in calcium chloride (CaCl2).
K:
UK:
36.11% Ca and 63.89% Cl

2) What is the percent of oxygen in H3PO4?
K:
UK:
65.31% oxygen

3) Calculate the percent composition of a
compound that is 29.0 g of Ag with 4.30 g of S.
K:
UK:
87.1% Ag and 12.9% S

4) Which has the larger percent by mass of
sulfur, H2SO3 or H2S2O8?
K:
UK:
H2SO3  39.06% S
Empirical Formula
The information from the percent
composition can be used to determine the
formula for a compound.
 The empirical formula is the simplest
whole-number ratio of atoms of elements in
the compound. In many cases, the empirical
formula is the actual formula for the
compound.
 EX: H2O or H2SO4

Calculating Empirical Formulas

If percent composition is given:
1.
Assume that the total mass of the compound is 100.00 g.
(Percentages of each element equals the mass in grams.)
Convert grams to moles (using the molar mass of each
element).
Find the mole ratio by dividing everything by the smallest # of
moles.
If those numbers are whole numbers you have just found the
subscripts for the formula.
2.
3.
4.

If actual masses are given you can skip to step 3.
Example Problem:

What is the empirical formula for a compound that
contains 10.89% magnesium, 31.77% chlorine and
the rest is oxygen?
K:
UK:
MgCl2O8

Determine the empirical formula of a compound
containing 2.644g of gold and 0.476g of chlorine.
K:
UK:
AuCl

BUT…often in determining empirical
formulas, the calculated mole ratios are still
not whole numbers. In such cases all the
mole ratio values must be multiplied by the
smallest factor that will make them whole
numbers.
More Examples:
1. A blue solid is found to contain 36.84% nitrogen
and 63.16% oxygen. What is the empirical formula
for the solid?
K:
UK:
N2O3
2.
Propane is a hydrocarbon. It is composed of
81.68% carbon and 18.31% hydrogen. What is
the empirical formula?
K:
UK:
C3H8
Molecular Formula

For many compounds, the empirical formula is not
the true formula.


The molecular formula identifies the actual number
of elements in a molecule.


Examples: CH2 (empirical formula) vs. C2H4 (molecular
formula)
Sometimes the empirical and molecular formulas are the
same. Ex: Water H2O
To determine the molecular formula the molar
mass of the compound must be determined
through experimentation and compared with the
mass represented by the empirical formula.

Notice that the molecular formula for acetic
acid (C2H4O2) has exactly twice as many
atoms of each element as the empirical
formula (CH2O).

The molecular formula for a compound is
always a whole-number multiple of the
empirical formula.

In order to determine the molecular formula
for an unknown compound, you must know
the molar mass of the compound in addition
to its empirical formula.

Then you can compare the molar mass of
the compound with the molar mass
represented by the empirical formula.

This is done using the following equation:
given molar mass of compound
mass of empirical formula
You get a number to multiply the subscripts
of the empirical formula by to get the
molecular formula.
 Let’s do some practice problems.

Practice Problems:
1) Maleic acid is a compound that is used in the plastics
and textiles industries. The composition of maleic acid
is 41.39% carbon, 3.47% hydrogen, and 55.14%
oxygen. Its molar mass is 116.10 g/mol. Calculate the
molecular formula for maleic acid.
K:
UK:

Start by determining the empirical formula:

What is the mole ratio of the elements? 1C:1H:1O

So the empirical formula is: CHO
Next, calculate the molar mass represented
by the empirical formula. 29.02 g/mol
 As stated in the problem, the molar mass of
maleic acid is known to be 116.10 g/mol.
 To determine the molecular formula for
maleic acid, calculate the whole number
multiple to apply to its empirical formula.

116.10 g / mol
 4.001
29.02 g / mol



This calculation shows that the molar mass of
maleic acid is four times the molar mass of its
empirical formula CHO.
Therefore, the molecular formula must have four
times as many atoms of each element as the
empirical formula.
Thus, the molecular formula is C4H4O4
To Review:
=n
More Practice Problems:
2) Caffeine is 49.48% C, 5.15% H, 28.87% N and
16.49% O. It has a molar mass of 194 g/mol. What is
its molecular formula?
K:
UK:
3) A compound was found to contain 49.98 g carbon and 10.47 g
hydrogen. The molar mass of the compound is 58.12 g/mol.
Determine the molecular formula.
K:
UK:
C4H10
11.5 – The Formula
for a Hydrate
What is a hydrate?
A hydrate is a compound that has a specific
number of water molecules that are
“trapped” inside its crystal structure.
 Common ones are opal and cobalt chloride.

Images from wikipedia
What’s in a name?
To show the number of water molecules in a
formula unit of a hydrate chemists write the
formula with a dot and the number of water
molecules in it.
 Example: CaCl2 . 2H2O
 The name is calcium chloride dihydrate
 This means that for every one formula unit of
calcium chloride there are 2 water molecules
associated with it.

Counting the Water Molecules



Chemists use prefixes
to count how many
water molecules are
associated with a
hydrated compound.
Each prefix means a
certain number.
The root word hydrate
means water
Prefix
Molecules of H2O
mono-
1
di-
2
tri-
3
tetra-
4
penta-
5
hexa-
6
hepta-
7
octa-
8
nona-
9
deca-
10
Analyzing a Hydrate



To analyze a hydrate you must remove the water
of hydration.
Usually this is done by heating it so that the
remaining substance has no water. It is then
called an anhydrous substance.
You must find the number of moles of water
associated with one mole of the hydrate.
Hydrated cobalt chloride
anhydrous cobalt chloride
Example:
Suppose you have a sample of a hydrate of
copper(II) sulfate.
 The formula is CuSO4 . xH2O. You must
determine “x”. The “x” is the number of
moles of water associated with one mole of
CuSO4.
 We are going to heat a sample and figure it
out together.

What data should be
collected?
What calculations should be
done?
Let’s name the compound
Uses of hydrates


They can absorb water
into their structure so
they are used as
drying agents in the lab
or in stores.
Examples: Calcium
sulfate in the lab and
the silica packets that
sometimes come in
shoe boxes or purses