# CMC Chapter 10

```The Mole
Section 10.1 Measuring Matter
Section 10.2 Mass and the Mole
Section 10.3 Moles of Compounds
Section 10.4 Empirical and
Molecular Formulas
Section 10.5 Formulas of Hydrates
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Section 10.1 Measuring Matter
• Explain how a mole is
used to indirectly count
the number of particles of
matter.
molecule: two or more
atoms that covalently
bond together to form a
unit
• Relate the mole to a
common everyday
counting unit.
mole
• Convert between moles
and number of
representative particles.
Chemists use the mole to count atoms,
molecules, ions, and formula units.
Counting Particles
• Chemists need a convenient method for
accurately counting the number of atoms,
molecules, or formula units of a substance.
• The mole is the SI base unit used to measure
the amount of a substance.
• 1 mole is the amount of atoms in 12 g of pure
carbon-12, or 6.02  1023 atoms.
• The number is called Avogadro’s number.
Converting Between Moles and Particles
• Conversion factors must be used.
• Moles to particles
Number of molecules in 3.50 mol of sucrose
Converting Between Moles and Particles (cont.)
• Particles to moles
• Use the inverse of Avogadro’s number as the
conversion factor.
Section 10.1 Assessment
What does the mole measure?
A. mass of a substance
B. amount of a substance
C. volume of a gas
D
C
A
0%
B
D. density of a gas
A. A
B. B
C. C
0%
0%
0%
D. D
Section 10.1 Assessment
What is the conversion factor for
determining the number of moles of a
substance from a known number of
particles?
A
D. 1 mol  6.02  1023 particles
0%
D
C. 1 particle  6.02  1023
C
B.
A. A
B. B
C. C
0%
0%
0%
D. D
B
A.
Section 10.2 Mass and the Mole
• Relate the mass of an atom conversion factor: a
to the mass of a mole of
ratio of equivalent
atoms.
values used to express
the same quantity in
• Convert between number
different units
of moles and the mass of
an element.
• Convert between number
of moles and number of
atoms of an element.
molar mass
A mole always contains the same number
of particles; however, moles of different
substances have different masses.
The Mass of a Mole
• 1 mol of copper and 1 mol of carbon have
different masses.
• One copper atom has a different mass than 1
carbon atom.
The Mass of a Mole (cont.)
• Molar mass is the mass in grams of one
mole of any pure substance.
• The molar mass of any element is
numerically equivalent to its atomic mass and
has the units g/mol.
Using Molar Mass
• Moles to mass
3.00 moles of copper has a mass of 191 g.
Using Molar Mass (cont.)
• Convert mass to moles with the inverse
molar mass conversion factor.
• Convert moles to atoms with Avogadro’s
number as the conversion factor.
Using Molar Mass (cont.)
• This figure shows the steps to complete
conversions between mass and atoms.
Section 10.2 Assessment
The mass in grams of 1 mol of any pure
substance is:
A. molar mass
D
A
0%
C
D. 1 g/mol
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. atomic mass
Section 10.2 Assessment
Molar mass is used to convert what?
A. mass to moles
B. moles to mass
C. atomic weight
D
C
A
0%
B
D. particles
A. A
B. B
C. C
0%
0%
0%
D. D
Section 10.3 Moles of Compounds
• Recognize the mole relationships shown by a
chemical formula.
• Calculate the molar mass of a compound.
• Convert between the number of moles and mass of
a compound.
• Apply conversion factors to determine the number of
atoms or ions in a known mass of a compound.
representative particle: an atom, molecule, formula
unit, or ion
Section 10.3 Moles of Compounds
(cont.)
The molar mass of a compound can be
calculated from its chemical formula
and can be used to convert from mass
to moles of that compound.
Chemical Formulas and the Mole
• Chemical formulas indicate the numbers
and types of atoms contained in one unit of
the compound.
• One mole of CCl2F2 contains one mole of C
atoms, two moles of Cl atoms, and two moles
of F atoms.
The Molar Mass of Compounds
• The molar mass of a compound equals the
molar mass of each element, multiplied by
the moles of that element in the chemical
• The molar mass of a compound
demonstrates the law of conservation of
mass.
Converting Moles of a Compound to Mass
• For elements, the conversion factor is the
molar mass of the compound.
• The procedure is the same for compounds,
except that you must first calculate the molar
mass of the compound.
Converting the Mass of a Compound to Moles
• The conversion factor is the inverse of the
molar mass of the compound.
Converting the Mass of a Compound to
Number of Particles
• Convert mass to moles of compound with
the inverse of molar mass.
• Convert moles to particles with Avogadro’s
number.
Converting the Mass of a Compound to
Number of Particles (cont.)
• This figure summarizes the conversions
between mass, moles, and particles.
Section 10.3 Assessment
How many moles of OH— ions are in 2.50
moles of Ca(OH)2?
A. 2.00
B. 2.50
D
A
0%
C
D. 5.00
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 4.00
Section 10.3 Assessment
How many particles of Mg are in 10 moles
of MgBr2?
A. 6.02  1023
B. 6.02  1024
D
A
0%
C
D. 1.20  1025
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 1.20  1024
Section 10.4 Empirical and Molecular Formulas
• Explain what is meant by
the percent composition
of a compound.
• Determine the
empirical and molecular
formulas for a
compound from mass
percent and actual
mass data.
percent by mass: the
ratio of the mass of each
element to the total
mass of the compound
expressed as a percent
percent composition
empirical formula
molecular formula
A molecular formula of a compound is
a whole-number multiple of its
empirical formula.
Percent Composition
• The percent by mass of any element in a
compound can be found by dividing the
mass of the element by the mass of the
compound and multiplying by 100.
Percent Composition (cont.)
• The percent by mass of each element in a
compound is the percent composition of
a compound.
• Percent composition of a compound can also
be determined from its chemical formula.
Empirical Formula
• The empirical formula for a compound is
the smallest whole-number mole ratio of
the elements.
• You can calculate the empirical formula from
percent by mass by assuming you have
100.00 g of the compound. Then, convert the
mass of each element to moles.
• The empirical formula may or may not be the
same as the molecular formula.
Molecular formula of hydrogen peroxide = H2O2
Empirical formula of hydrogen peroxide = HO
Molecular Formula
• The molecular formula specifies the
actual number of atoms of each element in
one molecule or formula unit of the
substance.
• Molecular formula is always a whole-number
multiple of the empirical formula.
Molecular Formula (cont.)
Section 10.4 Assessment
What is the empirical formula for the
compound C6H12O6?
A. CHO
B. C2H3O2
D
A
0%
C
D. CH3O
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. CH2O
Section 10.4 Assessment
Which is the empirical formula for
hydrogen peroxide?
A. H2O2
B. H2O
D
A
0%
C
D. none of the above
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. HO
Section 10.5 Formulas of Hydrates
• Explain what a hydrate
is and relate the name of
the hydrate to its
composition.
• Determine the formula
of a hydrate from
laboratory data.
crystal lattice: a threedimensional geometric
arrangement of particles
hydrate
Hydrates are solid ionic compounds in
which water molecules are trapped.
Naming Hydrates
• A hydrate is a compound that has a
specific number of water molecules bound
to its atoms.
• The number of water molecules associated
with each formula unit of the compound is
written following a dot.
• Sodium carbonate decahydrate =
Na2CO3 • 10H2O
Naming Hydrates
(cont.)
Analyzing a Hydrate
• When heated, water molecules are
released from a hydrate leaving an
anhydrous compound.
• To determine the formula of a hydrate, find
the number of moles of water associated with
1 mole of hydrate.
Analyzing a Hydrate
(cont.)
• Weigh hydrate.
• Heat to drive off the water.
• Weigh the anhydrous compound.
• Subtract and convert the difference to moles.
• The ratio of moles of water to moles of
anhydrous compound is the coefficient for
water in the hydrate.
Use of Hydrates
• Anhydrous forms of hydrates are often
used to absorb water, particularly during
shipment of electronic and optical
equipment.
• In chemistry labs, anhydrous forms of
hydrates are used to remove moisture from
the air and keep other substances dry.
Section 10.5 Assessment
Heating a hydrate causes what to
happen?
A. Water is driven from the hydrate.
B. The hydrate melts.
D
A
0%
C
D. There is no change in the
hydrate.
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. The hydrate conducts
electricity.
Section 10.5 Assessment
A hydrate that has been heated and the
water driven off is called:
A. dehydrated compound
B. antihydrated compound
D
A
0%
C
D. hydrous compound
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. anhydrous compound
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Section 10.1 Measuring Matter
Key Concepts
• The mole is a unit used to count particles of matter
indirectly. One mole of a pure substance contains
Avogadro’s number of particles.
• Representative particles include atoms, ions,
molecules, formula units, electrons, and other similar
particles.
• One mole of carbon-12 atoms has a mass of exactly
12 g.
• Conversion factors written from Avogadro’s relationship
can be used to convert between moles and number of
representative particles.
Section 10.2 Mass and the Mole
Key Concepts
• The mass in grams of 1 mol of any pure substance is
called its molar mass.
• The molar mass of an element is numerically equal to
its atomic mass.
• The molar mass of any substance is the mass in grams
of Avogadro’s number of representative particles of the
substance.
• Molar mass is used to convert from moles to mass. The
inverse of molar mass is used to convert from mass to
moles.
Section 10.3 Moles of Compounds
Key Concepts
• Subscripts in a chemical formula indicate how many
moles of each element are present in 1 mol of the
compound.
• The molar mass of a compound is calculated from the
molar masses of all of the elements in the compound.
• Conversion factors based on a compound’s molar
mass are used to convert between moles and mass of
a compound.
Section 10.4 Empirical and
Molecular Formulas
Key Concepts
• The percent by mass of an element in a compound
gives the percentage of the compound’s total mass
due to that element.
• The subscripts in an empirical formula give the smallest
whole-number ratio of moles of elements in the
compound.
• The molecular formula gives the actual number of
atoms of each element in a molecule or formula unit of
a substance.
• The molecular formula is a whole-number
multiple of the empirical formula.
Section 10.5 Formulas of Hydrates
Key Concepts
• The formula of a hydrate consists of the formula of
the ionic compound and the number of water
molecules associated with one formula unit.
• The name of a hydrate consists of the compound name
and the word hydrate with a prefix indicating the
number of water molecules in 1 mol of the compound.
• Anhydrous compounds are formed when hydrates are
heated.
What does Avogadro’s number represent?
A. the number of atoms in 1 mol of
an element
B. the number of molecules in 1 mol of
a compound
D
C
B
A
A. A
C. the number of Na+ ions in 1 mol of
B. B
NaCl (aq)
C. C
D. all of the above
0%
0%
0%
0%
D. D
The molar mass of an element is
numerically equivalent to what?
A. 1 amu
B. 1 mole
D
A
0%
C
D. its atomic number
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. its atomic mass
How many moles of hydrogen atoms are
in one mole of H2O2?
A. 1
B. 2
D
A
0%
C
D. 0.5
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 3
What is the empirical formula of Al2Br3?
A. AlBr
B. AlBr3
D
A
0%
C
D. Al2Br3
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. Al2Br
What is an ionic solid with trapped water
molecules called?
A. aqueous solution
B. anhydrous compound
D
A
0%
C
D. solute
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. hydrate
Two substances have the same percent by
mass composition, but very different
properties. They must have the same ____.
A. density
A
0%
D
D. molar mass
C
C. molecular formula
A. A
B. B
C. C
0%
0%
0%
D. D
B
B. empirical formula
How many moles of Al are in 2.0 mol of
Al2Br3?
A. 2
B. 4
D
A
0%
C
D. 1
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 6
How many water molecules are
associated with 3.0 mol of CoCl2 • 6H2O?
A. 18
B. 1.1  1025
D
A
0%
C
D. 1.8  1024
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 3.6  1024
How many atoms of hydrogen are in
3.5 mol of H2S?
A. 7.0  1023
B. 2.1  1023
D
A
0%
C
D. 4.2  1024
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. 6.0  1023
Which is not the correct formula for an
ionic compound?
A. CO2
B. NaCl
D
A
0%
C
D. LiBr2
A. A
B. B
C. C
0%
0%
0%
D. D
B
C. Na2SO4
Click on an image to enlarge.
Figure 10.6 Molar Mass
Table 10.1 Formulas of Hydrates
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