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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

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

mole

Avogadro’s number

• Relate the mole to a common everyday counting unit.
• Convert between moles and number of representative particles.

Chemists use the mole to count atoms, molecules, ions, and formula units.

Section 10-1

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.

Section 10-1

Converting Between Moles and Particles

• Conversion factors must be used.

• Moles to particles

Number of molecules in 3.50 mol of sucrose

Section 10-1

Converting Between Moles and Particles (cont.)

• Particles to moles

• Use the inverse of Avogadro’s number as the conversion factor.

Section 10-1

1. A
2. B
3. C
4. D

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. density of a gas

Section 10-1

1. A
2. B
3. C
4. D

Section 10.1 Assessment

End of Section 10-1

Section 10-2

Section 10.2 Mass and the Mole

• Relate the mass of an atom to the mass of a mole of atoms.

conversion factor: a ratio of equivalent values used to express the same quantity in different units

molar mass

• Convert between number of moles and the mass of an element.
• Convert between number of moles and number of atoms of an element.

A mole always contains the same number of particles; however, moles of different substances have different masses.

Section 10-2

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.

Section 10-2

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.

Section 10-2

Using Molar Mass

• Moles to mass

3.00 moles of copper has a mass of 191 g.

Section 10-2

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.

Section 10-2

Using Molar Mass (cont.)

• This figure shows the steps to complete conversions between mass and atoms.

Section 10-2

1. A
2. B
3. C
4. D

Section 10.2 Assessment

The mass in grams of 1 mol of any pure substance is:

A. molar mass

B. Avogadro’s number

C. atomic mass

D. 1 g/mol

Section 10-2

1. A
2. B
3. C
4. D

Section 10.2 Assessment

Molar mass is used to convert what?

A. mass to moles

B. moles to mass

C. atomic weight

D. particles

End of Section 10-2

Section 10-3

Section 10.3 Moles of Compounds

• Recognize the mole relationships shown by a chemical formula.

representative particle: an atom, molecule, formula unit, or ion

• 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.

Section 10-3

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.

Section 10-3

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.

Section 10-3

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 formula, added together.

• The molar mass of a compound demonstrates the law of conservation of mass.

Section 10-3

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.

Section 10-3

Converting the Mass of a Compound to Moles

• The conversion factor is the inverse of the molar mass of the compound.

Section 10-3

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.

Section 10-3

Converting the Mass of a Compound to Number of Particles (cont.)

• This figure summarizes the conversions between mass, moles, and particles.

Section 10-3

1. A
2. B
3. C
4. D

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

C. 4.00

D. 5.00

Section 10-3

1. A
2. B
3. C
4. D

Section 10.3 Assessment

How many particles of Mg are in 10 moles of MgBr₂?

A. 6.02  10²³

B. 6.02  10²⁴

C. 1.20  10²⁴

D. 1.20  10²⁵

End of Section 10-3

Section 10-4

Section 10.4 Empirical and Molecular Formulas

• Explain what is meant by the percent composition of a compound.

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

• Determine the empirical and molecular formulas for a compound from mass percent and actual mass data.

A molecular formula of a compound is a whole-number multiple of its empirical formula.

Section 10-4

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.

Section 10-4

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.

Section 10-4

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

Section 10-4

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.

Section 10-4

Molecular Formula (cont.)

Section 10-4

1. A
2. B
3. C
4. D

Section 10.4 Assessment

What is the empirical formula for the compound C₆H₁₂O₆?

A. CHO

B. C₂H₃O₂

C. CH₂O

D. CH₃O

Section 10-4

1. A
2. B
3. C
4. D

Section 10.4 Assessment

Which is the empirical formula for hydrogen peroxide?

A. H₂O₂

B. H₂O

C. HO

D. none of the above

End of Section 10-4

Section 10-5

Section 10.5 Formulas of Hydrates

• Explain what a hydrate is and relate the name of the hydrate to its composition.

crystal lattice: a three-dimensional geometric arrangement of particles

hydrate

• Determine the formula of a hydrate from laboratory data.

Hydrates are solid ionic compounds in which water molecules are trapped.

Section 10-5

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

Section 10-5

Naming Hydrates (cont.)

Section 10-5

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.

Section 10-5

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.

Section 10-5

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

1. A
2. B
3. C
4. D

Section 10.5 Assessment

Heating a hydrate causes what to happen?

A. Water is driven from the hydrate.

B. The hydrate melts.

C. The hydrate conducts � electricity.

D. There is no change in the � hydrate.

Section 10-5

1. A
2. B
3. C
4. D

Section 10.5 Assessment

A hydrate that has been heated and the water driven off is called:

A. dehydrated compound

B. antihydrated compound

C. anhydrous compound

D. hydrous compound

End of Section 10-5

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Study Guide

Chapter Assessment

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Study Guide 1

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.

Study Guide 2

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.

Study Guide 3

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.

Study Guide 4

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.

Study Guide 5

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.

Chapter Assessment 1

1. A
2. B
3. C
4. D

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

C. the number of Na⁺ ions in 1 mol of� NaCl (aq)

D. all of the above

Chapter Assessment 2

1. A
2. B
3. C
4. D

The molar mass of an element is numerically equivalent to what?

A. 1 amu

B. 1 mole

C. its atomic mass

D. its atomic number

Chapter Assessment 3

1. A
2. B
3. C
4. D

How many moles of hydrogen atoms are in one mole of H₂O₂?

A. 1

B. 2

C. 3

D. 0.5

Chapter Assessment 4

1. A
2. B
3. C
4. D

What is the empirical formula of Al₂Br₃?

A. AlBr

B. AlBr₃

C. Al₂Br

D. Al₂Br₃

Chapter Assessment 5

1. A
2. B
3. C
4. D

What is an ionic solid with trapped water molecules called?

A. aqueous solution

B. anhydrous compound

C. hydrate

D. solute

STP 1

1. A
2. B
3. C
4. D

Two substances have the same percent by mass composition, but very different properties. They must have the same ____.

A. density

B. empirical formula

C. molecular formula

D. molar mass

STP 2

1. A
2. B
3. C
4. D

How many moles of Al are in 2.0 mol of Al₂Br₃?

A. 2

B. 4

C. 6

D. 1

STP 3

1. A
2. B
3. C
4. D

How many water molecules are associated with 3.0 mol of CoCl₂ • 6H₂O?

A. 18

B. 1.1  10²⁵

C. 3.6  10²⁴

D. 1.8  10²⁴

STP 4

1. A
2. B
3. C
4. D

How many atoms of hydrogen are in �3.5 mol of H₂S?

A. 7.0  10²³

B. 2.1  10²³

C. 6.0  10²³

D. 4.2  10²⁴

STP 5

1. A
2. B
3. C
4. D

Which is not the correct formula for an ionic compound?

A. CO₂

B. NaCl

C. Na₂SO₄

D. LiBr₂

IB Menu

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IB 1

IB 2

IB 3

IB 4

IB 6

IB 7

CIM

Figure 10.6 Molar Mass

Table 10.1 Formulas of Hydrates

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