Chapter 3. Stoichiometry: Calculations with Chemical
Formulas and Equations
Media Resources
Figures and Tables in Transparency Pack: Section:
Figure 3.3 The Difference Between Changing 3.1 Chemical Equations
Subscripts and Changing Coefficients in
Chemical Equations
Figure 3.4 Methane Reacts with Oxygen in a 3.1 Chemical Equations
Bunsen Burner
Animations: Section:
Air Bags 3.2 Some Simple Patterns of Chemical Reactivity
Limiting Reagent 3.7 Limiting Reactants
Movies: Section:
Formation of Water 3.1 Chemical Equations
Sodium and Potassium in Water 3.1 Chemical Equations
Reactions with Oxygen 3.2 Some Simple Patterns of Chemical Reactivity
Nitrogen Triiodide 3.2 Some Simple Patterns of Chemical Reactivity
Formation of Aluminum Bromide 3.2 Some Simple Patterns of Chemical Reactivity
Activities: Section:
Stoichiometry: Calculations with Chemical Formulas and Equations
31
3-D Models: Section:
Water 3.5 Empirical Formulas from Analyses
Other Resources
Further Readings: Section:
More Chemistry in a Soda Bottle: A Conservation 3.1 Chemical Equations
of Mass Activity
Chemical Wastes and the Law of Conservation of 3.1 Chemical Equations
Matter
Gram Formula Weights and Fruit Salad 3.3 Formula Weights
Percentage Composition and Empirical Formula–A 3.3 Formula Weights
New View
Mole, Mole per Liter, and Molar. A Primer on SI 3.3 Formula Weights
and Related Units for Chemistry Students
Using Monetary Analogies to Teach Average 3.4 Avogadro’s Number and the Mole
Atomic Mass
Pictorial Analogies IV: Relative Atomic Weights 3.4 Avogadro’s Number and the Mole
Relative Atomic Mass and the Mole: A Concrete 3.4 Avogadro’s Number and the Mole
Analogy to Help Students These Abstract
Chapter 3
32
to Assess Conceptual Understanding
A Mole of M&M’s 3.4 Avogadro’s Number and the Mole
How to Visualize Avogadro’s Number 3.4 Avogadro’s Number and the Mole
Demonstrations of the Enormity of Avogadro’s 3.4 Avogadro’s Number and the Mole
A Recipe for Teaching Stoichiometry 3.6 Quantitative Information from Balanced
Equations
Pictorial Analogies XII: Stoichiometric 3.6 Quantitative Information from Balanced
Calculations Equations
Learning Stoichiometry with Hamburger Sandwiches 3.7 Limiting Reactants
Limiting and Excess Reagents, Theoretical Yield 3.7 Limiting Reactants
Limiting Reactant: An Alternative Analogy 3.7 Limiting Reactants
Limiting Reagent Problems Made Simple for 3.7 Limiting Reactants
Students
Coffee, Coins, and Limiting Reagents 3.7 Limiting Reactants
Electron Results and Reaction Yields 3.7 Limiting Reactants
Live Demonstrations: Section:
Measuring Avogadro’s Number on the Overhead 3.4 Avogadro’s Number and the Mole
Stoichiometry: Calculations with Chemical Formulas and Equations
33
Chapter 3. Stoichiometry: Calculations with Chemical
Formulas and Equations
Common Student Misconceptions
• Students confuse the subscripts in a chemical formula with the coefficients in front of the formula in a
balanced reaction equation.
• Students have difficulties grasping the meaning of a mole as a “collective”; a mole of a substance
contains a fixed number (6.022 1023) of “building blocks” (atoms for most elements, molecules for
Teaching Tips
• Students who have good high school backgrounds find this chapter quite easy. Others find this
chapter extremely difficult. Very few students have heard the term stoichiometry and can be
Lecture Outline
3.1 Chemical Equations
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• The quantitative nature of chemical formulas and reactions is called stoichiometry.
• Lavoisier observed that mass is conserved in a chemical reaction.
• This observation is known as the law of conservation of mass.
Chapter 3
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• Chemical equations give a description of a chemical reaction.
• There are two parts to any equation:
• reactants (written to the left of the arrow) and
• products (written to the right of the arrow):
• Note: in 2H2O there are four hydrogen atoms present (two for each water molecule).
Balancing Equations
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• Matter cannot be lost in any chemical reaction.
• Therefore, the products of a chemical reaction have to account for all the atoms present in the
reactants–we must balance the chemical equation.
• When balancing a chemical equation we adjust the stoichiometric coefficients in front of
chemical formulas.
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“Reading a Chemical Equation” Activity from Instructor’s Resource CD/DVD
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Figure 3.4 from Transparency Pack
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“Balancing Chemical Equations by Inspection” from Further Readings
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“The Fruit Basket Analogy” from Further Readings
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“A New Inspection Method for Balancing Redox Equations” from Further Readings
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“On Balancing Chemical Equations: Past and Present (A Critical Review and Annotated
Bibliography)” from Further Readings
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“Reading A Balanced Chemical Equation” Activity from Instructor’s Resource CD/DVD
Stoichiometry: Calculations with Chemical Formulas and Equations
35
Indicating the States of Reactants and Products
• The physical state of each reactant and product may be added to the equation:
CH4(g) + 2O2(g) → CO2(g) + 2H2O(g)
• Reaction conditions occasionally appear above or below the reaction arrow (e.g., “” is often used to
indicate the addition of heat).
FORWARD REFERENCES
• Stoichiometric coefficients will be used to determine molar ratios (stoichiometric factors) in
3.2 Some Simple Patterns of Chemical Reactivity
Combination and Decomposition Reactions
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• In combination reactions two or more substances react to form one product.
• Combination reactions have more reactants than products.
• Consider the reaction: 2Mg(s) + O2(g) → 2MgO(s)
metal and nitrogen gas.
Combustion Reactions
• Combustion reactions are rapid reactions that produce a flame.
• Most combustion reactions involve the reaction of O2(g) from air.
• Example: combustion of a hydrocarbon (propane) to produce carbon dioxide and water.
C3H8(g) + 5O2(g) → 3CO2(g) + 4H2O(l)
FORWARD REFERENCES
• Combustion reactions will be mentioned in Chapter 5 (as exothermic reactions involving fuels) and
further discussed in Chapter 24 (as oxidation of organic compounds).
Chapter 3
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3.3 Formula Weights
Formula and Molecular Weights
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• Formula weight (FW) is the sum of atomic weights for the atoms shown in the chemical formula.
• Example: FW (H2SO4)
• = 2AW(H) + AW(S) + 4AW(O)
Percentage Composition from Formulas
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• Percentage composition is obtained by dividing the mass contributed by each element (number of
atoms times AW) by the formula weight of the compound and multiplying by 100.
3.4 Avogadro’s Number and The Mole
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“Gram Formula Weights and Fruit Salad” from Further Readings
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“Percentage Composition and Empirical Formula—A New View” from Further Readings
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“Molecular Weight and Weight Percent” Activity from Instructor’s Resource CD/DVD
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“Mole, Mole per Liter, and Molar: A Primer on SI and Related Units for Chemistry Students” from
Further Readings
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“Developing an Intuitive Approach to Moles” from Further Readings
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“The Mole, the Periodic Table, and Quantum Numbers: An Introductory Trio” from Further Readings
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“The Size of a Mole” from Further Readings
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“What’s a Mole For?” from Further Readings
Stoichiometry: Calculations with Chemical Formulas and Equations
37
• The mole (abbreviated “mol”) is a convenient measure of chemical quantities.
• 1 mole of something = 6.0221421 1023 of that thing.
• This number is called Avogadro’s number.
• Thus, 1 mole of carbon atoms = 6.0221421 1023 carbon atoms.
• Experimentally, 1 mole of 12C has a mass of 12 g.
Molar Mass
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• The mass in grams of 1 mole of substance is said to be the molar mass of that substance. Molar mass
Interconverting Masses and Moles
• Look at units:
• Mass: g
Interconverting Masses and Numbers of Particles
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• Units:
• Number of particles: 6.022 1023 mol–1 (Avogadro’s number).
• Note: g/mol mol = g (i.e. molar mass moles = mass), and
• mol mol–1 = a number (i.e. moles Avogadro’s number = molecules).
• To convert between moles and molecules we use Avogadro’s number.
FORWARD REFERENCES
• It may be desirable to calculate molar masses with higher precision in later chapters.
40
“Moles, Pennies, and Nickels” from Further Readings
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“A Mole Mnemonic” from Further Readings
Chapter 3
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3.5 Empirical Formulas from Analyses
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• Recall that the empirical formula gives the relative number of atoms of each element in the molecule.
• Finding empirical formula from mass percent data:
• We start with the mass percent of elements (i.e. empirical data) and calculate a formula.
• Assume we start with 100 g of sample.
• Multiply each fraction by 100 to convert to a percent.
Molecular Formulas from Empirical Formulas
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• The empirical formula (relative ratio of elements in the molecule) may not be the molecular formula
(actual ratio of elements in the molecule).
• Example: ascorbic acid (vitamin C) has the empirical formula C3H4O3.
Combustion Analysis
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• Empirical formulas are routinely determined by combustion analysis.
• A sample containing C, H, and O is combusted in excess oxygen to produce CO2 and H2O.
• The amount of CO2 gives the amount of C originally present in the sample.
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“Water” 3–D Model from Instructor’s Resource CD/DVD
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“Hydrogen Peroxide” 3-D Model from Instructor’s Resource CD/DVD
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“Sucrose” 3-D Model from Instructor’s Resource CD/DVD
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“Oxygen” 3-D Model from Instructor’s Resource CD/DVD
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“Methane” 3-D Model from Instructor’s Resource CD/DVD
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“Carbon Dioxide” 3-D Model from Instructor’s Resource CD/DVD
Stoichiometry: Calculations with Chemical Formulas and Equations
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• The amount of H2O gives the amount of H originally present in the sample.
• Watch the stoichiometry: 1 mol H2O contains 2 mol H.
3.6 Quantitative Information from Balanced Equations
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• The coefficients in a balanced chemical equation give the relative numbers of molecules (or formula
units) involved in the reaction.
• The stoichiometric coefficients in the balanced equation may be interpreted as:
• the relative numbers of molecules or formula units involved in the reaction or
• the relative numbers of moles involved in the reaction.
• The molar quantities indicated by the coefficients in a balanced equation are called stoichiometrically
equivalent quantities.
FORWARD REFERENCES
• In Chapter 4 students will learn how to convert solution molarity and volume data into moles.
• In Chapter 10 students will learn how to use P, V and T information to find moles of gas.
• Stoichiometry of reactions will be further exploited when writing rate law expressions for elementary
steps (Chapter 14) as well as equilibrium constant and reaction quotient expressions (Chapters 15, 16,
17, 19, and 20).
• Acid-base titrations mentioned in Chapter 4, and further discussed in Chapter 17, are practical
applications of stoichiometry of acid-base neutralization reactions.
Chapter 3
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3.7 Limiting Reactants
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• It is not necessary to have all reactants present in stoichiometric amounts.
• Often, one or more reactants is present in excess.
• Therefore, at the end of reaction those reactants present in excess will still be in the reaction mixture.
• The one or more reactants which are completely consumed are called the limiting reactants.
Theoretical Yields
• The amount of product predicted from stoichiometry, taking into account limiting reactants, is called
the theoretical yield.
• This is often different from the actual yield – the amount of product actually obtained in the
reaction.
FORWARD REFERENCES
• Buffering action calculations in Chapter 17 (section 17.2) and pH calculations in acid-base titrations
(section 17.3) can be viewed as stoichiometric problems with a limiting reactant (added strong acid or
base).
Stoichiometry: Calculations with Chemical Formulas and Equations
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Further Readings:
1. Frederic L. Holmes, “Antoine Lavoisier and The Conservation of Matter,” Chemical and Engineering
News, September 12, 1994, 38–45.
7. Chunshi Guo, “A New Inspection Method for Balancing Redox Equations,” J. Chem. Educ., Vol. 74,
1997, 1365–1366.
8. Kenneth W. Watkins, “Lime,” J. Chem. Educ., Vol. 60, 1983, 60–63. An article on a some of the uses
of quicklime (CaO) and hydrated lime (Ca(OH)2).
9. Arthur M. Last and Michael J. Webb, “Using Monetary Analogies to Teach Average Atomic Mass,” J.
Chem. Educ., Vol. 70, 1993, 234–235.
10. John H. Fortman, “Pictorial Analogies IV: Relative Atomic Weights,” J. Chem. Educ., Vol. 70, 1993,
235–236.
11. Josefina Arce de Sanabia, “Relative Atomic Mass and the Mole: A Concrete Analogy to Help
Students Understand These Abstract Concepts,” J. Chem. Educ., Vol. 70, 1993, 233–234.
12. George L. Gilbert, “Percentage Composition and Empirical Formula–A New View,” J. Chem. Educ.,
Vol. 75, 1998, 851.
Chapter 3
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17. Sheryl Dominic, “What’s a Mole For?” J. Chem. Educ., Vol. 73, 1996, 309.
22. Henk van Lubeck, “How to Visualize Avogadro’s Number,” J. Chem. Educ., Vol. 66, 1989, 762.
23. Paul S. Poskozim, James W. Warrick, Permsook Tiempetpaisal and Joyce Albin Poskozim,
“Analogies for Avogadro’s Number,” J. Chem. Educ., Vol. 63, 1986, 125–126.
24. Damon Diemente, “Demonstrations of the Enormity of Avogadro’s Number,” J. Chem. Educ., Vol.
75, 1998, 1565–1566.
25. R. E. Ulte, “For Mole Problems, Call Avogadro: 602–1023”, J. Chem. Educ., Vol. 79, 2002, 1213.
30. Joel S. Thompson, “A Simple Rhyme for a Simple Formula,” J. Chem. Educ., Vol. 65, 1988, 704. An
easy way to remember the strategy for converting percentage composition to an empirical formula.
“Percent to mass, Mass to mol, Divide by small, Multiply ‘til whole”.
31. Christer Svensson, “How Many Digits Should we Use in Formula or Molar Mass Calculation”, J.
Chem. Educ., Vol. 81, 2004, 827–829.
32. John Olmsted III, “Amounts Tables as a Diagnostic Tool for Flawed Stoichiometric Reasoning,” J.
Chem. Educ., Vol. 76, 1999, 52–54.
33. Carla R. Krieger, “Stoogiometry: A Cognitive Approach to Teaching Stoichiometry,” J. Chem. Educ.,
Vol. 74, 1997, 306–309.
Stoichiometry: Calculations with Chemical Formulas and Equations
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40. Zoltan Toth, “Limiting Reactant: An Alternative Analogy,” J. Chem. Educ., Vol. 76, 1999, 934.
41. A. H. Kalantar, “Limiting Reagent Problems Made Simple for Students,” J. Chem. Educ., Vol. 62,
1985, 106.
42. Dennis McMinn, “Coffee, Coins, and Limiting Reagents,” J. Chem. Educ., Vol. 61, 1984, 591.
43. Romeu C. Rocha-Filho, “Electron Results and Reaction Yields,” J. Chem. Educ., Vol. 64, 1987, 248.
Live Demonstrations:
1. Sally Solomon and Chinhyu Hur, “Measuring Avogadro’s Number on the Overhead Projector,” J.
Chem. Educ., Vol. 70, 1993, 252–253. A monolayer of stearic acid on water is used to estimate
Avogadro’s number.
4. M. Dale Alexander and Wayne C. Woolsey, “Combustion of Hydrocarbons: A Stoichiometry
Demonstration,” J. Chem. Educ., Vol. 70, 1993, 327–328. The combustion of methane, propane, and
butane are compared in this simple demonstration of stoichiometry.
5. Crystal Wood and Bryan Breyfogle, “Interactive Demonstrations for Mole Ratios and Limiting
Reagents,” J. Chem. Educ., Vol. 83, 2006, 741–748.