Chapter 7

Chapter Objectives

• Determine the molar mass of a compound from its formula.
• Convert between grams of a substance and moles using the molar mass as a conversion factor.
• Convert between mole and the number of particles using Avogadro’s number.
• Classify changes in matter as chemical or physical changes.
• Balance chemical equations.
• Classify chemical equations as combination, decomposition, single-displacement, double- displacement, or combustion.
• Describe the features of oxidation and reduction in an oxidation-reduction (redox) reaction.
• Using a given number of moles and a mole-mole conversion factor, calculate the corresponding number of moles for a reactant or product.
• Using a given mass of a substance in a chemical reaction and the appropriate mole factor and molar masses, calculate the mass of a reactant or product.

Readiness Key Math Skills

• Calculating a Percentage (1.4C)
• Solving Equations (1.4D)
• Writing Numbers in Scientific Notation (1.4F)

Readiness Core Chemistry Skills

• Counting Significant Figures (2.2)
• Using Significant Figures in Calculations (2.3)
• Writing Conversion Factors from Equalities (2.5)
• Using Conversion Factors (2.6)
• Using Energy Units (3.4)
• Writing Ionic Formulas (6.2)
• Naming Ionic Compounds (6.3)
• Writing the Names and Formulas for Molecular Compounds (6.5)

7.1 The Mole

• A counting term states a specific number of items.
• The terms dozen, case, gross, and ream are used to count the number of items present.

Learning Goal

• Use Avogadro’s number to determine the number of particles in a given number of moles.

Avogadro’s Number

• Small particles such as atoms, molecules, and ions are counted using the mole, a unit called Avogadro’s number that contains 6.02 × 10^{23} items.
• 1 mole = 6.02 × 10^{23} items
• Avogadro’s number 602 000 000 000 000 000 000 000 = 6.02 × 10^{23}
• Avogadro’s number is named for Amedeo Avogadro (1776–1856), an Italian physicist.

Mole of Atoms

• 1 mole of an element = 6.02 × 10^{23} atoms of that element
  • 1 mole of carbon= 6.02 × 10^{23} atoms of carbon
  • 1 mole of sodium= 6.02 × 10^{23} atoms of sodium

Core Chemistry Skill

• Converting Particles to Moles

Avogadro’s Number

• Avogadro’s number, 6.02 × 10^{23}, can be written as an equality and as two conversion factors.
• Equality: 1 mole = 6.02 × 10^{23} particles
• Conversion Factors:

Guide to Calculating Atoms or Molecules

Converting Moles to Molecules

• Avogadro’s number is used to convert moles of a substance to particles.

Example:

• How many CO2 molecules are in 0.50 mole of CO2?
• SOLUTION:
  • STEP 1 State the needed and given quantities.
    • ANALYZE
      • GIVEN: 0.50 mole of CO_2
      • NEED: molecules of CO_2
      • THE PROBLEM

Converting Moles to Molecules

• STEP 2 Write a plan to convert moles to atoms or molecules.
  • moles of CO2 molecules of CO2
• STEP 3 Use Avogadro’s number to write conversion factors.
  • 1 mole of CO2 = 6.02 × 10^{23} molecules of CO2
  • Avogadro’s number

Converting Moles to Molecules

• STEP 4 Set up the problem to calculate the number of particles.
  • 0.50 \,mole \,CO2 * \frac{6.02 × 10^{23} molecules \,CO2}{1\,mole \,CO2} = 3.0 × 10^{23} molecules \,CO2

Study Check

• What is the number of atoms in 2.0 mole of Al?
  • A. 2.0 Al atoms
  • B. 3.0 × 10^{23} Al atoms
  • C. 1.2 × 10^{24} Al atoms

Solution

• What is the number of atoms in 2.0 mole of Al?
  • STEP 1 State the needed and given quantities.
  • STEP 2 Write a plan to convert moles to atoms or molecules.
    • moles of Al atoms of Al
    • ANALYZE
      • GIVEN: 2.0 mole of Al
      • NEED: atoms of Al
      • THE PROBLEM
    • Avogadro’s number

Solution

• What is the number of atoms in 2.0 mole of Al?
  • STEP 3 Use Avogadro’s number to write conversion factors.
    • 1 mole \,Al = 6.02 × 10^{23} atoms of Al

Solution

• What is the number of atoms in 2.0 mole of Al?
  • STEP 4 Set up the problem to calculate the number of particles.
    • 2.0 \, mole \, Al * \frac{6.02 × 10^{23} atoms \,Al}{1 \,mole \,Al} = 1.2 × 10^{24}atoms \,Al
  • Answer is C.

Study Check

• What is the number of moles of S in 1.8 × 10^{24} atoms of S?
  • A. 1.0 mole of S atoms
  • B. 3.0 moles of S atoms
  • C. 1.1 × 10^{48} moles of S atoms

Solution

• What is the number of moles of S in 1.8 × 10^{24} atoms of S?
  • STEP 1 State the needed and given quantities.
  • STEP 2 Write a plan to convert moles to atoms or molecules.
    • atoms of S moles of S
    • ANALYZE
      • GIVEN: l.8 × 10^{24} atoms of S
      • NEED: moles of S
      • THE PROBLEM
    • Avogadro’s number

Solution

• What is the number of moles of S in 1.8 × 10^{24} atoms of S?
  • STEP 3 Use Avogadro’s number to write conversion factors.
    • 1 mole \,S = 6.02 × 10^{23} atoms of S

Solution

• What is the number of moles of S in 1.8 × 10^{24} atoms of S?
  • STEP 4 Set up the problem to calculate the number of particles.
    • 1.8 × 10^{24} atoms \,S * \frac{1 \,mole \,S}{6.02 × 10^{23} atoms \,S} = 3.0 \,moles \,S
  • Answer is B.

Moles of Elements in a Formula

Moles of Elements in a Formula

• The subscripts in a formula show
  • the relationship of atoms in the formula
  • the moles of each element in 1 mole of compound
• Aspirin C9H8O_4
• 1 molecule:
  • 9 atoms of C
  • 8 atoms of H
  • 4 atoms of O
• 1 mole:
  • 9 moles of C
  • 8 moles of H
  • 4 moles of O

Moles of Elements in a Formula

• Subscripts are used to write conversion factors for moles of each element in 1 mole of a compound.
• For 1 mole of aspirin, C9H8O_4, the possible conversion factors are as follows:
  • \frac{1 \,mole \,C9H8O4}{9 \,mole \,C}, \frac{9 \,mole \,C}{1 \,mole \,C9H8O4},
  • \frac{1 \,mole \,C9H8O4}{8 \,mole \,H}, \frac{8 \,mole \,H}{1 \,mole \,C9H8O4},
  • \frac{1 \,mole \,C9H8O4}{4 \,mole \,O}, \frac{4 \,mole \,O}{1 \,mole \,C9H8O4}

Guide to Calculating Moles of Elements in Compounds

Study Check

• How many atoms of O are in 0.150 mole of aspirin, C9H8O_4?

Solution

• How many atoms of O are in 0.150 mole of aspirin, C9H8O_4?
  • STEP 1 State the needed and given quantities.
  • STEP 2 Write a plan to convert moles to atoms.
    • moles of C9H8O_4 moles of O atoms of O
    • ANALYZE
      • GIVEN: l.50 mole of C9H8O_4
      • NEED: atoms of O
      • THE PROBLEM
    • Avogadro’s number
    • Subscript

Solution

• How many atoms of O are in 0.150 mole of aspirin, C9H8O_4?
  • STEP 3 Use Avogadro’s number to write conversion factors.
    • Subscript factor: 1 mole \,of \,C9H8O_4 = 4 \,moles \,of \,O
    • Avogadro’s number: 1 mole \,of \,O = 6.02 × 10^{23} atoms \,of \,O

Solution

• How many atoms of O are in 0.150 mole of aspirin, C9H8O_4?
  • STEP 4 Set up the problem to calculate the number of particles.
    • 0.150 \,mole \,C9H8O4 * \frac{4 \,mole \,O}{1 \,mole \,C9H8O4} * \frac{6.02 × 10^{23} atoms \,O}{1 \,mole \,O} = 3.61 × 10^{23} atoms of O

7.2 Molar Mass and Calculations

• The molar mass of an element is useful to convert moles of an element to grams, or grams to moles.
• For example, 1 mole of sodium has a mass of 22.99 grams.

Learning Goal

• Calculate the molar mass of a substance given its chemical formula; use molar mass to convert between grams and moles.

Molar Mass

• The molar mass is
  • the mass of 1 mole of an element
  • the atomic mass expressed in grams
    • 1 mole C = 12.01 g
    • 1 mole Li = 6.941 g

Core Chemistry Skill

• Calculating Molar Mass

Molar Mass from Periodic Table

• In this text, we round molar mass to the tenths (0.1 g) place or use at least three significant figures for calculations.

Guide to Calculating Molar Mass of a Compound

• To calculate the molar mass of a compound, we multiply the molar mass of each element by its subscript in the formula and add the results.

Calculating Molar Mass: Li2CO3

• Calculate the molar mass for lithium carbonate, Li2CO3, used to produce red color in fireworks.
• SOLUTION:
  • STEP 1 Obtain the molar mass of each element.
    • ANALYZE
      • GIVEN: formula, Li2CO3
      • NEED: molar mass, Li2CO3
      • THE PROBLEM

Calculating Molar Mass: Li2CO3

• Calculate the molar mass for lithium carbonate, Li2CO3, used to produce red color in fireworks.
  • STEP 2 Multiply each molar mass by the number of moles (subscript) in the formula.
    • 2 \,moles \,Li * \frac{6.941\, g \,Li}{1 \,mole \,Li} = 13.88 \,g \,Li
    • 1 \,mole \,C * \frac{12.01\, g \,C}{1 \,mole \,C} = 12.01 \,g \,C
    • 3 \,moles \,O * \frac{16.00\, g \,O}{1 \,mole \,O} = 48.00 \,g \,O

Calculating Molar Mass: Li2CO3

• Calculate the molar mass for lithium carbonate, Li2CO3, used to produce red color in fireworks.
  • STEP 3 Calculate the molar mass by adding the masses of the elements.
    • 2 moles Li = 13.88 g Li
    • 1 mole C = 12.01 g C
    • 3 moles O = + 48.00 g O
    • 1 mole Li2CO3 = 73.89 g

Study Check

• Calculate the molar mass of C2H6O.

Solution

• Calculate the molar mass of C2H6O.
  • STEP 1 Obtain the molar mass of each element.
    • ANALYZE
      • GIVEN: formula, C2H6O
      • NEED: molar mass, C2H6O
      • THE PROBLEM

Solution

• Calculate the molar mass of C2H6O.
  • STEP 2 Multiply each molar mass by the number of moles (subscripts) in the formula.
    • 2 \,moles \,C * \frac{12.01\, g \,C}{1 \,mole \,C} = 24.02 \,g \,C
    • 6 \,moles \,H * \frac{1.01\, g \,H}{1 \,mole \,H} = 6.06 \,g \,H
    • 1 \,mole \,O * \frac{16.00\, g \,O}{1 \,mole \,O} = 16.00 \,g \,O

Solution

• Calculate the molar mass of C2H6O.
  • STEP 3 Calculate the molar mass by adding the masses of the elements.
    • 2 moles C = 24.02 g C
    • 6 moles H = 6.06 g H
    • 1 mole O = + 16.00 g O
    • 1 mole C2H6O = 46.08 g

Calculations Using Molar Mass

• Molar mass conversion factors
  • are fractions (ratios) written from the molar mass
  • relate grams and moles of an element or compound
• For methane, CH_4, used in gas stoves and gas heaters,
  • 1 mole of CH4 = 16.05 g of CH4 (molar mass equality)
  • Conversion factors:
    • \frac{1 \,mole \,CH4}{16.05 \,g \,CH4}, and \frac{16.05 \,g \,CH4}{1 \,mole \,CH4}

Guide to Calculating Moles from Mass or Mass from Moles

Converting Mass to Moles of NaCl

• A box of table salt, NaCl, contains 737 g of NaCl. How many moles of NaCl are in the box?

Converting Mass to Moles of NaCl

• A box of table salt, NaCl, contains 737 g of NaCl. How many moles of NaCl are in the box?
  • STEP 1 State the given and needed quantities.
  • STEP 2 Write a plan to convert grams to moles.
    • grams of NaCl moles of NaCl
    • ANALYZE
      • GIVEN: 737 g NaCl
      • NEED: moles NaCl
      • THE PROBLEM
    • Molar Mass

Converting Mass to Moles of NaCl

• A box of table salt, NaCl, contains 737 g of NaCl. How many moles of NaCl are in the box?
  • STEP 3 Determine the molar mass and write conversion factors.
    • 1 mole \,NaCl = 58.5 \,g \,NaCl
    • \frac{1 \,mole \,NaCl}{58.5 \,g \,NaCl}, and \frac{58.5 \,g \,NaCl}{1 \,mole \,NaCl}

Converting Mass to Moles of NaCl

• A box of table salt, NaCl, contains 737 g of NaCl. How many moles of NaCl are in the box?
  • STEP 4 Set up the problem to convert grams to moles.
    • 737 \,g \,NaCl * \frac{1 \,mole \,NaCl}{58.5 \,g \,NaCl} = 12.6 \,moles \,NaCl

Study Check

• A sample of water has a mass of 59.8 grams. How many moles of water are in the sample?

Solution

• A sample of water has a mass of 59.8 grams. How many moles of water are in the sample?
  • STEP 1 State the given and needed quantities.
  • STEP 2 Write a plan to convert grams to moles.
    • grams of H2O moles of H2O
    • ANALYZE
      • GIVEN: 59.8 g H_2O
      • NEED: moles H_2O
      • THE PROBLEM
    • Molar Mass

Solution

• A sample of water has a mass of 59.8 grams. How many moles of water are in the sample?
  • STEP 3 Determine the molar mass and write conversion factors.
    • 1 mole \,H2O = 18.02 \,g \,H2O
    • \frac{1 \,mole \,H2O}{18.02 \,g \,H2O}, and \frac{18.02 \,g \,H2O}{1 \,mole \,H2O}

Solution

• A sample of water has a mass of 59.8 grams. How many moles of water are in the sample?
  • STEP 4 Set up the problem to convert grams to moles.
    • 59.8 \,g \,H2O * \frac{1 \,mole \,H2O}{18.02 \,g \,H2O} = 3.32 \,moles \,H2O

Map: Mass, Moles, and Particles

7.3 Equations for Chemical Reactions

• A chemical change occurs when a substance is converted into one or more new substances that have different formulas and different properties.

Learning Goal

• Write a balanced chemical equation from the formulas of the reactants and products for a reaction; determine the number of atoms in the reactants and products.

Chemical Changes

• A chemical change
  • occurs when a substance is converted into one or more substances with different formulas and different properties
  • may be observed by the formation of bubbles, a change in color, production of a solid, or heat that is produced or absorbed

Writing a Chemical Equation

Symbols Used in Chemical Equations

• To write a chemical equation,
  • an arrow separates reactants from the products
  • reactants are written on the left side of the arrow, products on the right side of the arrow
  • multiple reactants or products are separated by a plus (+) sign
  • the delta (Δ) sign indicates heat is used to start the reaction
    • reactant + reactant product + product
  • physical states of compounds are denoted in parentheses following the compound: solid (s), liquid (l), gas (g), and aqueous (aq) or dissolved in water

Symbols Used in Chemical Equations

Identifying a Balanced Equation

• In a balanced chemical equation,
  • no atoms are lost or gained
  • the number of atoms on the reactant side is equal to the number of atoms on the product side for each element

Core Chemistry Skill

• Balancing a Chemical Equation

Guide to Balancing a Chemical Equation

Balancing a Chemical Equation: Formation of Al2S3

*   STEP 1 Write an equation using the correct formulas of the reactants and products.
    *   Al(s) + S(s) \longrightarrow Al_2S_3(s)
*   STEP 2 Count the atoms of each element in the reactants and products.
    *   Al(s) + S(s)  Al_2S_3 (s)
        *   Reactants
            *   1 Al
            *   1 S
        *   Products
            *   2 Al
            *   3 S

Balancing a Chemical Equation: Formation of Al2S3

• STEP 3 Use coefficients to balance each element. Starting with the most complex formula, change coefficients to balance the equation.
  • 2Al(s) + 3S(s) \longrightarrow Al2S3(s)
• STEP 4 Check the final equation to confirm it is balanced. Make sure coefficients are the lowest ratio.
  • 2Al(s) + 3S(s) Al2S3(s)
    • Reactants
      • 2 Al
      • 3 S
    • Products
      • 2 Al
      • 3 S

Study Check

• State the number of atoms of each element on the reactant side and the product side for each of the following balanced equations.
  • A. P4(s) + 6Br2(l) \longrightarrow 4PBr_3(g)
  • B. 2Al(s) + Fe2O3(s) \longrightarrow 2Fe(s) + Al2O3(s)

Solution

• State the number of atoms of each element on the reactant side and the product side for each of the following balanced equations.
  • A. P4(s) + 6Br2(l) 4PBr_3(g)
    • Reactants
      • 4 P
      • 12 Br
    • Products
      • 4 P
      • 12 Br

Solution

• State the number of atoms of each element on the reactant side and the product side for each of the following balanced equations.
  • B. 2Al(s) + Fe2O3(s) 2Fe(s) + Al2O3(s)
    • Reactants
      • 2 Al
      • 2 Fe
      • 3 O
    • Products
      • 2 Al
      • 2 Fe
      • 3 O

Study Check

• Balance the chemical equation when solid Fe3O4 reacts with hydrogen gas to produce solid iron and water.

Solution

• Balance the chemical equation when solid Fe3O4 reacts with hydrogen gas to produce solid iron and water.
  • STEP 1 Write an equation using the correct formulas of the reactants and products.
    • Fe3O4(s) + H2(g) Fe(s) + H2O(l)

Solution

• Balance the chemical equation when solid Fe3O4 reacts with hydrogen gas to produce solid iron and water.
  • Fe3O4(s) + H2(g) Fe(s) + H2O(l)
  • STEP 2 Count the number of atoms of each element in the reactants and products.
    • Reactants
      • 3 Fe
      • 4 O
      • 2 H
    • Products
      • 1 Fe
      • 1 O
      • 2 H

Solution

• Balance the chemical equation when solid Fe3O4 reacts with hydrogen gas to produce solid iron and water.
  • Fe3O4(s) + 4H2(g) 3Fe(s) + 4H2O(l)
  • STEP 3 Use coefficients to balance each element.
    • Reactants
      • 3 Fe
      • 4 O
      • 8 H
    • Products
      • 3 Fe
      • 4 O
      • 8 H

Solution

• Balance the chemical equation when solid Fe3O4 reacts with hydrogen gas to produce solid iron and water.
  • Fe3O4(s) + 4H2(g) 3Fe(s) + 4H2O(l)
  • STEP 4 Check the final equation to confirm it is balanced.
    • Reactants
      • 3 Fe
      • 4 O
      • 8 H
    • Products
      • 3 Fe
      • 4 O
      • 8 H

Balancing with Polyatomic Ions

Balancing with Polyatomic Ions

• Balance the following chemical equation:
  • Na3PO4(aq) + MgCl2(aq) \longrightarrow Mg3(PO4)2(s) + NaCl(aq)
  • STEP 1 Write an equation using the correct formulas of the reactants and products.
    • Na3PO4(aq) + MgCl2(aq) Mg3(PO4)2(s) + NaCl(aq)
    • Unbalanced

Balancing with Polyatomic Ions

• STEP 2 Count the atoms of each element in the reactants and products. Balance the phosphate ion as a unit.
  • Na3PO4(aq) + MgCl2(aq) Mg3(PO4)2(s) + NaCl(aq)
    • Reactants
      • 3 Na
      • 1 PO_4
      • 1 Mg
      • 2 Cl
    • Products
      • 1 Na
      • 2 PO_4
      • 3 Mg
      • 1 Cl

Balancing with Polyatomic Ions

• STEP 3 Use coefficients to balance each element.
  • 2Na3PO4(aq) + 3MgCl2(aq) Mg3(PO4)2(s) + 6NaCl(aq)
    • Reactants
      • 6 Na
      • 2 PO_4
      • 3 Mg
      • 6 Cl
    • Products
      • 6 Na
      • 2 PO_4
      • 3 Mg
      • 6 Cl

Balancing with Polyatomic Ions

• STEP 4 Check the final equation to confirm it is balanced.
  • 2Na3PO4(aq) + 3MgCl2(aq) Mg3(PO4)2(s) + 6NaCl(aq)
    • Reactants
      • 6 Na
      • 2 PO_4
      • 3 Mg
      • 6 Cl
    • Products
      • 6 Na
      • 2 PO_4
      • 3 Mg
      • 6 Cl

Study Check

• Balance and list the coefficients from reactants to products.
  • A. _Fe2O_3(s) + __C(s) __Fe(s) + _CO2(g)
    • 1) 2, 3, 2, 3
    • 2) 2, 3, 4, 3
    • 3) 1, 1, 2, 3
  • B. __Al(s) + __FeO(s) __Fe(s) + _Al2O_3(s)
    • 1) 2, 3, 3, 1
    • 2) 2, 1, 1, 1
    • 3) 3, 3, 3, 1
  • C. __Al(s) + _H2SO_4(aq) _Al2(SO4)3(aq) + _H2(g)
    • 1) 3, 2, 1, 22) 2, 3, 1, 3
    • 2) 2, 3, 1, 3
    • 3) 2, 3, 2, 3

Solution

• A. 2) 2, 3, 4, 3
  • 2Fe2O3(s) + 3C(s) 4Fe(s) + 3CO_2(g)
• B. 1) 2, 3, 3, 1
  • 2Al(s) + 3FeO(s) 3Fe(s) + 1Al2O3(s)
• C. 2) 2, 3, 1, 3
  • 2Al(s) + 3H2SO4(aq) 1Al2(SO4)3(aq) + 3H2(g)

7.4 Types of Reactions

• In a combustion reaction, a candle burns using the oxygen in the air.

Learning Goal

• Identify a reaction as a combination, decomposition, single replacement, double replacement, or combustion.

Types of Reactions

• Chemical reactions can be classified as
  • combination reactions
  • decomposition reactions
  • single replacement reactions
  • double replacement reactions
  • combustion reactions

Core Chemistry Skill

• Classifying Types of Chemical Reactions

Combination Reactions

• In a combination reaction,
  • two or more elements form one product
  • simple compounds combine to form one product
    • 2Mg(s) + O_2(g) \longrightarrow 2MgO(s)
    • 2Na(s) + Cl_2(g) \longrightarrow 2NaCl(s)
    • SO3(g) + H2O(l) \longrightarrow H2SO4(aq)

Combination Reaction: MgO

Decomposition Reaction

• In a decomposition reaction, one substance splits into two or more simpler substances.
  • 2HgO(s) \longrightarrow 2Hg(l) + O_2(g)
  • 2KClO3(s) \longrightarrow 2KCl(s) + 3O2(g)

Decomposition Reaction: HgO

Single Replacement Reaction

• In a single replacement reaction, one element takes the place of a different element in another reacting compound.
  • Zn(s) + 2HCl(aq) \longrightarrow ZnCl2(aq) + H2(g)
  • $$Fe(s) + CuSO4(aq) \longrightarrow FeSO4(aq) + Cu(s