Chapter 11—The Mole
Measuring Matter
a. Counting Particles
 Chemists need a convenient method for counting accurately the number of atoms,
molecules, or formula units in a sample of a substance.
 That’s why chemists created their own counting unit called the mole.
 The mole, commonly abbreviated mol, is the SI base unit used to measure the
amount of a substance.
 It is the number of atoms, in exactly 12 g of pure carbon-12.
 A representative particle is any kind of particle such as atoms, molecules, formula
units, electrons, or ions.
 Through years of experimentation, it has been established that a mole
of anything contains 602 billion trillion representative particles.
 The number 6.022 136 7 x 1023 is called Avogadro’s number in honor of the Italian
physicist and lawyer Amedeo Avogadro who, in 1811, determined the volume of
one mole of a gas.
 We will use Avogadro’s number rounded to three significant figures—6.02 x 1023.
 A mole of particles contains 6.02 x 1023 particles.
b. Converting Moles to Particles and Particles to Moles
Mass and the Mole
a. The Mass of a Mole
 The mass of 1 mole (in grams) is:
 equal to the average atomic mass (get from periodic table)
 1 g/mol = 1 amu
1 mole of C atoms
12.0 g
1 mole of Mg atoms
24.3 g
1 mole of Cu atoms
63.5 g
b. Using Molar Mass
 The mass in grams of one mole of any pure substance is called its molar mass.
Moles of Compounds
 A mole of a compound contains as many moles of each element as are indicated by the
subscripts in the formula for the compound.
 For example, a mole of ammonia (NH3) consists of one mole of nitrogen atoms and
three moles of hydrogen atoms.
 The molar mass equals the mass of one mole of nitrogen atoms plus the mass of three
moles of hydrogen atoms.
Chapter 11-The Mole
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Empirical and Molecular Formulas
a. Percent Composition
 Recall that every chemical compound has a definite composition—a
composition that is always the same wherever that compound is found.
 Percent composition is the percent by mass of each element in the compound.
 The percent of an element in a compound can be found in the following way.
1. Calculate the molar mass of compound
2. Calculate percent by mass of element
 Unit = %
 Report percents to 2 decimal places
 Always check to make sure percentages add up to 100%.
b. Empirical Formula
 You can use percent composition data to help identify an unknown compound by
determining its empirical formula.
 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
 For example, the simplest ratio of atoms of sodium to atoms of chlorine in
sodium chloride is 1 atom Na : 1 atom Cl.
 So, the empirical formula of sodium chloride is Na1Cl1, or NaCl, which is the true
formula for the compound.
c. Molecular Formula
 For many compounds, the empirical formula is not the true formula.
 A molecular formula tells the exact number of atoms of each element in a molecule
or formula unit of a compound.
 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 as shown in the following example problem.
Chapter 11-The Mole
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The Formula of a Hydrate
 A hydrate is a compound that has a specific number of water molecules bound to its atoms.
b. Naming Hydrates
 In the formula for a hydrate, the number of water molecules associated with each
formula unit of the compound is written following a dot
 Na2CO3 10H2O
 Name: sodium carbonate decahydrate
 The mass of water associated with a formula unit must be included in molar mass
c. Analyzing a Hydrate
 To analyze hydrates, you must drive off with water with heat.
 The resulting compound is called anhydrous (without water).
 To determine the formula for a hydrate you must find the number of moles of water
associated with one mole of the hydrate.
 The difference between the mass of the hydrate & the mass of the
anhydrous compound = the water in the hydrate
 Now you can calculate the ratio of moles of water to moles of
compound to determine the coefficient that precedes water
Chapter 11-The Mole
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Chapter 11—The Mole Measuring Matter Counting Particles