382A Chapter 12

Stoichiometry Planning GuideStoichiomePlanning G12

Chemists use the mole to make sure that they measure the right amount of reacting material.

Lessons and Objectives Print Resources

For the Student For the Teacher

A-2, B-3 12.1 The Arithmetic of Equations p 384–38912.1.1 Describe how chemists use balanced

chemical equations.12.1.2 Describe the quantities you can use to

interpret a balanced chemical equation.12.1.3 Identify the quantities that are always

conserved in chemical reactions.

Reading and Study Workbook Lesson 12.1

Lesson Assessment 12.1 p 389

Teaching Resources, Lesson 12.1 Review

Teacher Demo, p 387: Interpreting a Chemical Equation

A-2, B-3 12.2 Chemical Calculations p 390–39812.2.1 Explain how mole ratios are used in

chemical calculations.12.2.2 Explain the general procedure for solving

a stoichiometric problem.

Reading and Study Workbook Lesson 12.2

Lesson Assessment 12.2 p 398

Small-Scale Lab: Analysis of Baking Soda, p 399

Teaching Resources, Lesson 12.2 Review

Teacher Demo, p 392: Interpreting a Chemical Equation

Class Activity, p 396: Stoichiometric Flash Cards

B-2, B-5 12.3 Limiting Reagent and Percent Yield p 400–408

12.3.1 Explain how the amount of product in a reaction is affected by an insufficient quantity of any of the reactants.

12.3.2 Explain what the percent yield of a reaction measures.

Reading and Study Workbook Lesson 12.3

Lesson Assessment 12.3 p 408

Quick Lab: Limiting Reagents, p 404

Teaching Resources, Lesson 12.3 Review

Teacher Demo, p 401: Limiting Factor

Class Activity, p 403: Molecular Models and Limiting Reagent

Class Activity, p 405: Actual Yield and Heat

Essential Questions1. How are balanced chemical equations used in

stoichiometric calculations?2. How can you calculate amounts of reactants

and products in a chemical reaction?

Study Guide p 409Math Tune-Up p 410STP p 417Reading and Study

Workbook Self-Check and Vocabulary Review Chapter 12

Chemists use the mole to make sure that they measure the right amount of reactingCh i t th l t k th t th

Introducing the BIGIDEA: THE MOLE; REACTIONS

Essential Questions1. How are balanced chemical equations used in

Study Guide p 409Math Tune-Up p 41

Assessing the BIGIDEA: THE MOLE; REACTIONS

NSES

Stoichiometry 382B

For the StudentSmall-Scale Lab, p 399

baking soda• 3 plastic cups• soda straw• balance• pipets of HCl, NaOH, and thymol blue• pH sensor (optional)•

Quick Lab, p 404graduated cylinder• balance• 3 250-mL Erlenmeyer flasks• 3 rubber balloons• 4.2 g magnesium ribbon• 300 mL 1.0• M hydrochloric acid

For the TeacherTeacher Demo, p 387

2.5–3.5-cm strip of • magnesium50 mL 1• M HCl100-mL beaker• baking soda•

Teacher Demo, p 3920.1• M KI0.1• M Pb(NO3)2250-mL beakers•

Class Activity, p 3968 index cards• 1 colored index card• paper punch• 2 brass paper • fasteners

Teacher Demo, p 40115 plastic bottles• 30 plastic caps to fit the • bottles6 containers to hold 5 • caps each

Teacher Demo, p 40320 metal paper clips • (symbol M)20 same-colored • vinyl-coated paper clips (symbol C)plastic sandwich bag•

Class Activity, p 4053 foam cups• a thermometer• 100 mL of 1.0• M HClapproximately 200 mL of • 1.0M NaOH

Online Student Edition Online Teacher’s Edition12.2 Virtual Chem Lab 28: Analysis of Baking Soda

L A B

VIRTUAL Analysis of Baking Soda

Online Student Edition

Additional Digital Resources

Digital Resources

Editable Worksheets PearsonChem.com

Lab 19: Quantitative Analysis

OV E R V I E

W

LESSON

V E WEE

N

12.1 Lesson Overview

T U T O R

CHEM

T

C M

Using a Balanced Equation as a Recipe

A R T

KINETIC

A T

K Balancing Chemical Equations

Lab 19: Quantitative AnalysisLab Practical 12-1: Stoichiometry

in a Reaction Small-Scale Lab Manual Lab 18:

Titration: Determining How Much Acid Is in a Solution

Small-Scale Lab Manual Lab 19: Titration: Measuring Molar Concentrations

Probeware Lab Manual Analysis of Baking Soda

Lab Practical 12-2: Limiting Reagent

OV E R V I E

W

LESSON

V E WEE

N

12.2 Lesson Overview

T U T O R

CHEM

T

C M

Calculating the Mass of a Product

Lab 20: Balanced Chemical Equations

OV E R V I E

W

LESSON

V E WEE

N

12.3 Lesson Overview

A R T

KINETIC

A T

K Limiting Reagents

T U T O R

CHEM

T

C M

Determining the Limiting Reagent in a Reaction

T U T O R

CHEM

T

C M

Calculating the Percent Yield of a Reaction

Exam View Assessment SuiteClassroom Resources Disc

(includes editable worksheets) • Lesson Reviews • Practice Problems • Interpret Graphs • Vocabulary Review • Chapter Quizzes and Tests • Lab Record Sheets

PR O B L E M

S

ONLINE

RO B L E MS

M

O E Chapter 12 Problem Set

T U T O R

MATH

Percents

T U T O R

MATH

Limiting Factors

F h S d

Materials List

A-2, B-3

National Science Education Standards 382

12Stoichiometry

INSIDE:12.1

12.2

12.3

I N

A C T I ON

CO

NCEPTS

A R T

KINETIC

A T

K

L A B

VIRTUAL

T U T O R

MATH

PRO BL E M

S

ONLINE

RORBL E M

SM

O E

T U T O R

CHEM

T

C M

Like a chemical equation, a recipe tells you the amount of each ingredient (your reactants) needed to make your product, in this case, bread.

382 Chapter 12

Focus on ELL

1 CONTENT AND LANGUAGE Present the chapter title by writing stoichiometry on the board and the phonetic spelling, toy kee AHM uh tree. Model pronunciation and have students repeat after you. Direct students’ attention to the photograph. Ask students what a recipe has to do with stoichiometry. Help students see that a recipe and stoichiometry both measure reactants and products and predict results.BEGINNING LOW Have students write the word stoichiometry on one side of a note card, and on the other side, have them copy the phonetic spelling of it. HIGH Have students determine the quantities of ingredients they would use to make a ham and cheese sandwich and write an equation.INTERMEDIATE: LOW/HIGH Paraphrase the Essential Questions. Summarize the CHEMystery story by writing the main idea of the story. ADVANCED: LOW/HIGH Develop a list of words that have the suffix -metry, which means “to measure.” Present the words to the class, along with their meanings.

CH

APTE

R 1

2What’s Online

T U T O R

CHEM

T

C M CHEM TUTOR Students access guided step-by-step tutorials for solving various stoichiometry problems. Students can practice key problem-solving skills in an online problem set.

T U T O R

MATH MATH HELP Identify the students that struggle with math by assigning an online math skills diagnostic test. These students can then improve and practice math skills using the MathXL tutorial system.

L A B

VIRTUAL VIRTUAL LAB Students go into a virtual lab

tour in which stoichiometry is studied in a simulated laboratory environment.

AR T

KINETIC

A T

K KINETIC ART Students watch animations of selected figures from the chapter followed by questions to check for understanding.

I N

A C T I ON

CO

NCEPTS CONCEPTS IN ACTION Students watch an overview of a key chapter concept using real-world contexts and concrete examples and analogies. Each activity includes an interactive animation followed by analysis questions.

1. How are balanced chemical equations used in stoichiometric calculations?

2. How can you calculate amounts of reactants and products in a chemical reaction?

BIGIDEAS

Cookie CrumblesFor the school bake sale, Jack wanted to make cookies to sell. He looked in cookbooks to find a good recipe. The recipe he chose called for specific amounts of butter, flour, sugar, eggs, vanilla, and baking soda. Jack wanted to make sure that his cookies were delicious and sweet. He didn’t think there was enough sugar in the recipe, so he added twice as much sugar as the recipe called for.

Jack mixed the ingredients, put balls of the dough on a cookie sheet, and placed them in the oven to bake. When the bake time was up, Jack was very disappointed in his cookies. Instead of sweet, delicious cookies, his cookies were brown, hard, and crumbly. What hap-pened? He checked the oven temperature and the amount of time that the cookies were in the oven. The time and temperature matched the directions in the recipe. Why didn’t Jack’s cookies turn out as he expected?

Connect to the BIGIDEA As you read about quantifying chemical reactions, think about what could have happened to Jack’s cookies.

YSTERY

NATIONAL SCIENCE EDUCATION STANDARDS

B-3

Stoichiometry 383

Understanding by DesignStudents are building toward measuring the efficiency of a chemical reaction by using the relationships of the mole and quantifying matter.

PERFORMANCE GOALS At the end of Chapter 12, students will be able to answer the essential questions by applying their knowledge of stoichiometry. Students will also be able to calculate and compare the theoretical yield and the actual yield of a chemical reaction.ESSENTIAL QUESTIONS Read the essential questions aloud. Ask What is conserved in a balanced chemical equation? (atoms, molecules, moles, mass, volume) Ask What information do you need to have before you can calculate the amount of a reactant or product? (the number of moles of the substance and the number of grams or liters of the substance in each mole)

BIGIDEA Use the chapter opener photo to help students connect with the

Big Idea of the relationship of balanced equations and stoichiometric equations. Invite students to share their experiences with recipes and ingredients, and the results. Ask How would you adjust the recipe to double it? Guide students to an understanding of the importance of maintaining the correct ratios of ingredients when adjusting a recipe.

CHEMYSTERY Have students read over the CHEMystery. Connect the

CHEMystery to the Big Idea by explaining that the amounts of reactants and products of a reaction can be predicted using a balanced chemical equation. Mole ratios of a balanced chemical equation can be used to relate the moles of reactant to the moles of product, and mass ratios can be used to relate the mass of reactant to the mass of product. Ask students to predict what happens to the cookies as a result of the additional sugar. As a hint, tell students that when they adjust a recipe, the ratios of the ingredients must be the same in order to achieve the desired product.

Introduce the ChapterIDENTIFY PRECONCEPTIONS Students often enter into the study of stoichiometry with preconceptions. Use the activity to show them that all reactants may not be used up during a reaction.Activity You’ll need to get a bowl and place in it 5 chocolate pieces, 8 graham crackers, and 9 marshmallows. Ask What’s the ratio of reactants if you need one chocolate piece, two graham crackers and two mini-marshmallows to make one s’more? (1:2:2 yields 1.) Have students predict the number of s’mores you will be able to make with your reactants. (Answers will vary.) Then, make as many s’mores as you can with the reactants that you have. Ask How many s’mores did I make? (four) Ask Did I use up all my reactants? (no) Ask What prevented me from being able to make more s’mores? (I ran out of graham crackers.)

CH

APTE

R 1

2

A-2, B-3

National Science Education Standards

CHEMISTRY YOU YOYY U&EMCH

F S 3W H 2P FSW3HP2

384

The Arithmetic of Equations12.1

Key Questions How do chemists use

balanced chemical equations?

In terms of what quantities can you interpret a balanced chemical equation?

Vocabulary

Q: How do you figure out how much starting material you need to make a fin-ished product? Whenever you make something, you need to have the ingredi-ents or the parts that make up the desired product. When making bikes, you need parts such as wheels, handlebars, pedals, and frames. If a factory needs to make 200 bikes, then the workers would need to calculate how many of each part they need to produce the 200 bikes. In this lesson, you will learn about how chemists determine how much of each reactant is needed to make a certain amount of product.

Using Equations How do chemists use balanced chemical equations?

One example of something that you might make is food. When you make cookies, for instance, you probably use a recipe. A cookie recipe tells you the precise amounts of ingredients to mix to make a certain number of cook-ies. If you need a larger number of cookies than the recipe provides for, you can double or triple the amounts of all the ingredients. In a way, a cookie rec-ipe provides the same kind of information that a balanced chemical equation provides. In a cookie recipe, you can think of the ingredients as the reactants and the cookies as the products.

Everyday Equations The making of tricycles, like bikes and cookies, is a job that requires quantitative information to create the final product. Let’s say you are in charge of manufacturing for the Travel Time Tricycle Company. The business plan for Travel Time requires the production of 640 custom-made tricycles each week. One of your responsibilities is to make sure there are enough parts available at the start of each workweek to make these tricy-cles. How can you determine the number of parts you need per week?

To simplify this discussion, assume that the major components of the tri-cycle are the frame (F), the seat (S), the wheels (W), the handlebars (H), and the pedals (P)—in other words, the reactants. The figure below illustrates how an equation can represent the manufacturing of a single tricycle.

384 Chapter 12 • Lesson 1

Key Objectives12.1.1 DESCRIBE how chemists use balanced

chemical equations.12.1.2 DESCRIBE the quantities you can use to

interpret a balanced chemical equation.12.1.3 IDENTIFY the quantities that are always

conserved in chemical reactions.

Additional Resources• Reading and Study Workbook, Lesson 12.1• Probeware Laboratory Manual, Lab 19• Teaching Resources, Lesson 12.1 Review

EngageCHEMISTRY YOU YYYYYOU&& Have students study the

photograph and read the text that opens the lesson. Ask How many wheels would be needed to make 200 bikes? (twice as many frames, or 400) AskHow did you calculate the number of frames? (multiplied the number needed for 200 bikes by two)

Activate Prior KnowledgeTell students that the word stoichiometry comes from the Greek words stoicheion, meaning “element,” and metron, meaning “measure.” Draw a two-column chart on the board, with Reactants on one side and Products on the other. Invite students to brainstorm a list of measurements that a chemist might use in relation to products and reactants, such as mass and moles. Ask students to compare the list to measurements studied in chemical reactions that relate to reactants and products.

Focus on ELL1 CONTENT AND LANGUAGE Begin the lesson by reviewing the meaning of the words interpret, balanced, conservation, and arithmetic. Review the key symbols used in chemical equations as well as the rules for writing and balancing a chemical equation.

2 FRONTLOAD THE LESSON Have students bring in their favorite recipes from their native countries, and guide students to understand how their recipes are similar to balanced chemical equations.

3 COMPREHENSIBLE INPUT Have students model Figure 12.2 using colored paper clips. Use one color to represent a nitrogen atom and one color to represent a hydrogen atom. Explain that 2 links of the same color represent either a nitrogen molecule or a hydrogen molecule.

LESSO

N 1

2.1

Additional Resources• Reading and Study Workbook, Lesson 12.1• Probeware Laboratory Manual, Lab 19• Teaching Resources, Lesson 12.1 Review

Sample Problem 12.1T U T O R

CHEM

T

C M

3 W

1 FSW3HP2 and

1 FSW3HP2

3 W

640 FSW3HP2 3 W

1 FSW3HP2

KNOWNS

number of tricycles 640 tricycles 640 FSW3HP2

F S 3W H 2P FSW3HP2

UNKNOWN

number of wheels W

Stoichiometry 385

Travel Time has decided to make 288 tricycles 1. each day. How many tricycle seats, wheels, and pedals are needed for each day?

Write an equation that 2. gives your own “recipe” for making a skateboard.

Using a Balanced Equation as a RecipeIn a five-day workweek, Travel Time is scheduled to make 640 tricycles. How many wheels should be in the plant on Monday morning to make these tricycles?

Analyze List the knowns and the unknown. Use the balanced equation to identify a conversion factor that will allow you to calculate the unknown. The conversion you need to make is from tricycles (FSW3HP2) to wheels (W).

Calculate Solve for the unknown.

Evaluate Does the result make sense? If three wheels are required for each tricycle and more than 600 tricycles are being made, then a num-ber of wheels in excess of 1800 is a logical answer. The unit of the known (FSW3HP2) cancels, and the answer has the correct unit (W).

The finished tricycle, your product, has a “formula” of FSW3HP2. The balanced equation for making a single tricycle is

F S 3W H 2P FSW3HP2

This balanced equation is a “recipe” to make a single tricycle: Making a tricy-cle requires assembling one frame, one seat, three wheels, one handlebar, and two pedals. Now look at Sample Problem 12.1. It shows you how to use the balanced equation to calculate the number of parts needed to manufacture a given number of tricycles.

Identify a conversion factor that relates wheels to tricycles. You can write two conversion factors relating wheels to tricycles.

The desired unit is W; so use the conversion factor on the left. Multiply the number of tricycles by the conversion factor.

When using conversion

factors, remember to

cancel like units when they

are in both the numerator

and denominator. This tells

you that you are using the

correct conversion factor.

1920 W

Stoichiometry 385

Answers 1. 288 seats, 864 wheels, 576 pedals2. Answers will vary but should include the correct

number of “parts” to make the product.

Foundations for Reading

BUILD VOCABULARY Have students use an analogy of ingredients and product of a recipe to explain their interpretation of stoichiometry.READING STRATEGY Have students construct tables similar to Figure 12.2 to help them understand the quantities involved with any balanced chemical equation they encounter in this chapter.

Explain

Using Equations START A CONVERSATION Direct students to look at the visual representation of a tricycle. Then write this statement on the board “A frame, a seat, wheels, a handlebar, and pedals are needed to assemble a complete tricycle.” Ask How can this statement be revised so that it more accurately describes the process of assembling a tricycle? (One frame, one seat, three wheels, one handlebar, and two pedals are needed to assemble a complete tricycle.)

MAKE A CONNECTION Write the equation on the board.

F + S + 3W + H + 2P → FSW3HP2

Point out that the balanced equation contains information that not only relates reactants to product but relates one reactant to another.

Ask Describe a method you can use to determine how many handlebars are needed to complete tricycles if you know how many pedals are available. (Set up and solve a proportion.)

Sample Practice Problems A. Set up and solve a proportion to find how many

handlebars are needed to complete tricycles if you know there are 24 pedals available. (12)

B. How many handlebars are needed to complete tricycles if 24 seats are available? (24)

C. How many handlebars are needed to complete tricycles if 24 wheels are available? (8)

Foundations for Math RATIOS AND PROPORTIONS Explain that a ratio represents the relationship between two quantities. For example, the ratio 1:3 can be used to represent the relationship 1 handlebar to 3 wheels in Sample Problem 12.1, or 1 molecule of nitrogen to 3 molecules of hydrogen in the balanced equation for ammonia. Explain that the ratio may not be a true representation if the equations are not balanced. Set two ratios equal to each other to show students how a proportion can be used to determine an unknown quantity. Solve the proportion by using cross products, and point out how the units cancel, leaving you with the desired unit of the quantity you were trying to find.

LESSO

N 1

2.1

386

Balanced Chemical Equations Nearly everything you use is manufac-tured from chemicals—soaps, shampoos and conditioners, CDs, cosmetics, medicines, and clothes. When manufacturing such items, the cost of making them cannot be greater than the price at which they are sold. Otherwise, the manufacturer will not make a profit. Therefore, the chemical processes used in manufacturing must be carried out economically. A situation like this is where balanced equations help.

A balanced chemical equation tells you what amounts of reactants to mix and what amount of a product to expect. Chemists use balanced chemi-cal equations as a basis to calculate how much reactant is needed or how much product will be formed in a reaction. When you know the quantity of one substance in a reaction, you can calculate the quantity of any other substance consumed or created in the reaction. Quantity usually means the amount of a substance expressed in grams or moles. However, quantity could just as well be in liters, tons, or molecules.

The calculation of quantities in chemical reactions is a subject of chem-istry called stoichiometry. Calculations using balanced equations are called stoichiometric calculations. For chemists, stoichiometry is a form of book-keeping. For example, accountants can track income, expenditures, and profits for a small business by tallying each in dollars and cents. Chemists can track reactants and products in a reaction by stoichiometry. It allows chemists to tally the amounts of reactants and products using ratios of moles or repre-sentative particles derived from chemical equations.

Chemical Equations In terms of what quantities can you interpret a balanced

chemical equation?In gardens such as the one shown in Figure 12.1, fertilizers are often used to improve the growth of flowers. Ammonia is widely used as a fertilizer. Ammonia is produced industrially by the reaction of nitrogen with hydrogen.

N2(g) 3H2(g) 2NH3(g)

The balanced chemical equation tells you the relative amounts of reac-tants and product in the reaction. However, your interpretation of the equa-tion depends on how you quantify the reactants and products. A balanced chemical equation can be interpreted in terms of different quan-tities, including numbers of atoms, molecules, or moles; mass; and volume. As you study stoichiometry, you will learn how to interpret a chemical equa-tion in terms of any of these quantities.

Number of Atoms At the atomic level, a balanced equation indicates the number and types of atoms that are rearranged to make the product or prod-ucts. Remember, both the number and types of atoms are not changed in a reaction. In the synthesis of ammonia, the reactants are composed of two atoms of nitrogen and six atoms of hydrogen. These eight atoms are recom-bined in the product.

2 atoms N 6 atoms H 2 atoms N and 6 atoms H 8 atoms 8 atoms

Q: How can you determine the amount of each reactant you need to make a product?

CHEMISTRY YOU YYYYY&

READING SUPPORTBuild Vocabulary: Word Origins Stoichiometry

stoikheioin,

metron,

What do you first need to know about a chemical reaction before doing stoichiometry calculations?

386 Chapter 12 • Lesson 1

LESSO

N 1

2.1

Explain

Chemical EquationsSTART A CONVERSATION Write the following two chemical reactions on the board:A. CuO(s) + NH3(aq) → Cu(s) + H2O(l ) + N2(g)B. 4NH3(g) + 5O2(g) → 4NO(g) + 6H2O(g)

Ask Which equation can be used in its current form to determine how much product is formed by the reactants? (equation A)

Ask If you used equation A. in its current form to make stoichiometric calculations, why would your answers not be accurate? (The equation is not balanced.)

Misconception AlertMake sure students understand that they cannot balance an equation by changing the subscripts in a formula. A change to the subscripts causes the chemical identity of the substance to change.

CHEMISTRY YOU YOYY U&& Use a balanced chemical equation.

Extend

Connect to ENVIRONMENTAL SCIENCE Tell students that Earth’s atmosphere contains 0.01 parts per million of ammonia, and small amounts of ammonia occur in volcanic gases. Most ammonia cycles through the living world without returning to the atmosphere. Ammonia plays a role in several stages of the nitrogen cycle. Nitrogen-fixing bacteria form nodules, or swellings, on the roots of plants in the legume family, such as beans and clover plants. These bacteria change atmospheric nitrogen into ammonia molecules or ammonium ions. Other bacteria break down the nitrogenous material in dead plants and animals into ammonia molecules. Certain soil bacteria oxidize these molecules into nitrate ions, the form readily absorbed by plant roots. When a plant dies, this cycle begins again.

Have students write and balance the equations involved in the stages of the nitrogen cycle that involve ammonia. Then have them identify the parts of the nitrogen cycle where these reactions take place.

Differentiated InstructionL1 LESS PROFICIENT READERS Have students create a two-column table with the following row headings: Number of Atoms, Number of Molecules, Moles, Mass, and Volume. Then have students complete their tables by writing an example of the formation of ammonia, N2(g) + 3H2(g) → 2NH3(g), and how the corresponding quantity is interpreted from the balanced equation.

ELL ENGLISH LANGUAGE LEARNERS Divide students into groups of five. Have each group draw or model the formation of ammonia, N2(g) + 3H2(g) → 2NH3(g). Then have each student in the group read one of the paragraphs in the Chemical Equations section. Students should use the model to explain the concept in their paragraph.

L3 ADVANCED STUDENTS Ask students to explain to the class the meaning of STP, the values of STP, the molar volume of any gas at STP, and how many particles it contains. (standard temperature and pressure; 0°C and 101.3 kPa; 22.4 L/mol; 22.4 L of any ideal gas at STP contains 6.02 × 1023 particles of that gas.)

Stoichiometry 387

Number of Molecules The balanced equation indicates that one molecule of nitrogen reacts with three molecules of hydrogen. Nitrogen and hydrogen will always react to form ammonia in a 1:3:2 ratio of molecules. If you could make 10 molecules of nitrogen react with 30 molecules of hydrogen, you would expect to get 20 molecules of ammonia. Of course, it is not practical to count such small numbers of molecules and allow them to react. You could, however, take Avogadro’s number of nitrogen molecules and make them react with three times Avogadro’s number of hydrogen molecules. This value would be the same 1:3 ratio of molecules of reactants. The reaction would form two times Avogadro’s number of ammonia molecules.

1 6.02 1023

molecules N23 6.02 1023

molecules H22 6.02 1023

molecules NH3

Moles You know that Avogrado’s number of representative particles is equal to one mole of a substance. Therefore, since a balanced chemical equation tells you the number of representative particles, it also tells you the number of moles. The coefficients of a balanced chemical equation indicate the rela-tive numbers of moles of reactants and products in a chemical reaction. These numbers are the most important pieces of information that a balanced chemi-cal equation provides. Using this information, you can calculate the amounts of reactants and products. In the synthesis of ammonia, one mole of nitrogen molecules reacts with three moles of hydrogen molecules to form two moles of ammonia molecules. As you can see from this reaction, the total number of moles of reactants does not equal the total number of moles of product.

1 mol N2 3 mol H2 2 mol NH3

Mass A balanced chemical equation obeys the law of conservation of mass. This law states that mass can be neither created nor destroyed in an ordinary chemical or physical process. As you recall, the number and type of atoms does not change in a chemical reaction. Therefore, the total mass of the atoms in the reaction does not change. Using the mole relationship, you can relate mass to the number of atoms in the chemical equation. The mass of 1 mol of N2 (28.0 g) plus the mass of 3 mol of H2 (6.0 g) equals the mass of 2 mol of NH3 (34.0 g). Although the number of moles of reactants does not equal the number of moles of product, the total number of grams of reactants does equal the total number of grams of product.

28.0 g N2 (3 2.0 g H2) (2 17.0 g NH3) 34.0 g 34.0 g

Volume If you assume standard temperature and pressure, the equation also tells you about the volumes of gases. Recall that 1 mol of any gas at STP occu-pies a volume of 22.4 L. The equation indicates that 22.4 L of N2 reacts with 67.2 L (3 22.4 L) of H2. This reaction forms 44.8 L (2 22.4 L) of NH3.

22.4 L N2 67.2 L H2 44.8 L NH3

Figure 12.1 Use of Ammonia Gardeners use ammonium salts as fertilizer. The nitrogen in these salts is essential to plant growth.

Stoichiometry 387

LESSO

N 1

2.1

Explore

Teacher DemoPURPOSE Students interpret a balanced equation of the reaction of magnesium and hydrochloric acid. MATERIALS 2.5–3.5-cm strip of magnesium, 50 mL 1M HCl(aq) in a 100-mL beaker, baking sodaSAFETY Wear safety glasses and an apron. Neutralize remaining HCl(aq) with baking soda before flushing down the drain.PROCEDURE Identify the two reactants as magnesium and hydrochloric acid. Have students observe the reaction as you carefully add the magnesium strip to the acid. Ask students to write a balanced chemical equation for the reaction of magnesium and hydrochloric acid. (Mg(s) + 2HCl(aq) → MgCl2(aq) + H2(g)) Have students interpret the equation in terms of particles, moles, and molar masses. EXPECTED OUTCOME Students should express the balanced equation at the particle level as one atom of magnesium reacts with two molecules of hydrogen chloride to produce one formula unit of magnesium chloride and one molecule of hydrogen gas. Similarly, one mole of magnesium reacts with two moles of hydrogen chloride to produce one mole of magnesium chloride and one mole of hydrogen gas. Finally, 24.31 g Mg + 72.92 g HCl produces 95.21 g MgCl2 + 2.02 g H2.

Check for UnderstandingThe Essential Question What is the purpose of balanced chemical equations in stoichiometric calculations?

Assess students’ knowledge of stoichiometry by asking them to interpret the following equation in terms of atoms, molecules, moles, mass, and/or volume.

2KClO3(s) → 2KCl(s) + 3O2(g)

Elicit oral responses from students to determine if they understand why chemical equations must be balanced.

Sample Problem 12.2

(2 mol 34.1 ) (3 mol 32.0 )g

mol

g

mol

(2 mol 64.1 ) (2 mol 18.0 )g

mol

g

mol

a. 2 molecules H2S 3 molecules O2 2 molecules SO2 2 molecules H2O

2 mol H2S 3 mol O2 2 mol SO2 2 mol H2O

b. 1 mol H2S 34.1 g H2S

1 mol O2 32.0 g O2

1 mol SO2 64.1 g SO2

1 mol H2O 18.0 g H2O

2 mol H2S 3 mol O2 2 mol SO2 2 mol H2O.

68.2 g H2S 96.0 g O2 128.2 g SO2 36.0 g H2O

164.2 g 164.2 g

Remember that atoms and molecules

are both representative particles. In this

equation, all the reactants and products

are molecules; so all the representative

particles are molecules.

388

Interpret the equation for the formation of 3. water from its elements in terms of numbers of molecules and moles, and volumes of gases at STP.

2H2(g) O2(g) 2H2O(g)

Balance the following equation:4.

C2H4(g) O2(g) CO2(g) H2O(g)

Interpret the balanced equation in terms of relative numbers of moles, volumes of gas at STP, and masses of reactants and products.

Interpreting a Balanced Chemical EquationHydrogen sulfide, which smells like rotten eggs, is found in volcanic gases. The balanced equation for the burning of hydrogen sulfide is

2H2S(g) 3O2(g) 2SO2(g) 2H2O(g)

Interpret this equation in terms ofnumbers of representative particles and moles.a. masses of reactants and products.b.

Analyze Identify the relevant concepts. The coefficients in the balanced equation give the relative number of represen-tative particles and moles of reactants and products. A balanced chemical equation obeys the law of conservation of mass.

Solve Apply concepts to this situation.

Use the coefficients in the balanced equation to identify the number of representative particles and moles.

Use the periodic table to calculate the molar mass of each reactant and product.

Multiply the number of moles of each reactant and product by its molar mass.

388 Chapter 12 • Lesson 1

LESSO

N 1

2.1

Explain CRITICAL THINKING Have students try to find a counterexample to the statement “The conservation of moles exists for every chemical reaction,” and have them try to find a counterexample to the statement “The conservation of mass exists for every chemical reaction” to prove that the law of conservation exists for mass but not for moles. (Answers may vary.)

Sample Practice ProblemsBalance the following equation:

C5H12(g) + O2(g) → CO2(g) + H2O(g)

Interpret the balanced equation in terms of relative number of moles, volumes of gas at STP, and masses of reactants and products. (1 mol C5H12(g) + 8 mol O2(g) → 5 mol CO2(g) + 6 mol H2O(g); 22.4 L C5H12(g) + 179 L O2(g) → 112 L CO2(g) + 134 L H2O(g); 328 g reactants → 328 g products)

Foundations for Math ORDER OF OPERATIONS Explain that students should always follow the order of operations to correctly determine the answer to a mathematical problem. Remind students of PEMDAS, a mnemonic commonly used to help students remember the order of operations:

Please Excuse My Dear Aunt Sally: Parentheses first, Exponents next, Multiplication and Division from left to right, Addition and Subtraction from left to right

In Sample Problem 12.2 part b, point out that to correctly determine the total mass of the reactants and the total mass of the products, multiplication is computed prior to addition.

Stoichiometry 389

LessonCheckPR O B L E M

S

ONLINE

RO B L E MS

M

O E

Lesso12.1Apply Concepts 9. Interpret the given equation in terms of relative numbers of representative particles, num-bers of moles, and masses of reactants and products.

2K(s) 2H2O(l) 2KOH(aq) H2(g)

Apply Concepts 10. Balance this equation:

C2H5OH(l) O2(g) CO2(g) H2O(g)

Show that the balanced equation obeys the law of con-servation of mass.

5. Explain How do chemists use bal-anced equations?

6. Identify Chemical reactions can be described in terms of what quantities?

Explain7. How is a balanced equation simi-lar to a recipe?

Identify8. What quantities are always con-served in chemical reactions?

Figure 12.2 summarizes the information derived from the balanced chemical equation for the formation of ammonia. As you can see, the mass of the reactants equals the mass of the products. In addition, the number of atoms of each type in the reactants equals the number of atoms of each type in the product. Mass and atoms are conserved in every chemical reaction. However, molecules, formula units, moles, and volumes are not necessarily conserved—although they may be. Consider, for example, the formation of hydrogen iodide.

H2(g) I2(g) 2HI(g)

In this reaction, molecules, moles, and volume are all conserved. But in the majority of chemical reactions, they are not.

N2(g) 3H2(g) 2NH3(g)

2 atoms N 6 atoms H 2 atoms N and 6 atoms H

1 molecule N2 3 molecules H2 2 molecules NH3

10 molecules N2 30 molecules H2 20 molecules NH3

1 6.02 1023

molecules N23 6.02 1023

molecules H22 6.02 1023

molecules NH3

1 mol N2 3 mol H2 2 mol NH3

28.0 g N2 3 2.0 g H2 2 17.0 g NH3

34.0 g reactants 34.0 g products

Assume STP

22.4L

22.4L

22.4L

22.4L

22.4L

22.4 L N2 67.2 L H2 44.8 L NH3

22.4L

Figure 12.2 Interpreting a Balanced Chemical EquationThe balanced chemical equation for the formation of ammonia can be interpreted in several ways.Predict How many molecules of NH3 could be made from 5 molecules of N2 and 15 molecules of H2?

See balancing chemical equations animated online. A R T

KINETIC

A TT

K

Stoichiometry 389

LESSO

N 1

2.1

5. as a basis to calculate how much reactant is needed or product is formed in a reaction

6. numbers of atoms, molecules, or moles; mass; and volumes

7. Both a balanced equation and a recipe give quantitative information about the starting and end materials.

8. mass and atoms

9. 2 atoms K + 2 molecules H2O → 2 formula units KOH + 1 molecule H2

2 mol K + 2 mol H2O → 2 mol KOH + 1 mol H2 78.2 g K + 36.0 g H2O →

112.2 g KOH + 2.0 g H2 10. C2H5OH + 3O2 → 2CO2 + 3H2O 46.0 g C2H5OH + 96.0 g O2 → 88.0 g CO2 + 54.0 g H2O 142.0 g reactants →

142.0 g products

AnswersFIGURE 12.2 10 molecules NH33. 2 molecules H2 + 1 molecule O2 → 2 molecules H2O 2 mol H2 + 1 mol O2 → 2 mol H2O 44.8 L H2 + 22.4 L O2 → 44.8 L H2O4. 1 mol C2H2 + 5 mol O2 →

4 mol CO2 + 2 mol H2O 44.8 L C2H2 + 112 L O2 →

89.6 L CO2 + 44.8 L H2O 212 g reactants → 212 g products

USE VISUALS Direct students to Figure 12.3. Remind students that the term STP represents “standard temperature and pressure.” Ask What are the values of STP? (0ºC and 101.3 kPa) Ask Why is the volume of a gas usually measured at STP? (because its volume varies with temperature and pressure) Ask What is the molar volume of any gas at STP? (22.4L/mol of any ideal gas at STP) How many particles does it contain? (22.4 L of any gas contains 6.02 x 1023 particles.)

Evaluate

Informal AssessmentDivide the class into three teams. Have Team 1 write five balanced chemical equations on separate note cards and place them in a box. Also have them create four note cards with one word per card: atoms, molecules, mass, moles. Have Team 2 draw an equation from the box, and have Team 3 randomly select one of the four cards. Team 3 tells Team 2 which quantitative relationship of their selected equation they have to determine within a one minute time period. Rotate teams after each round. Students can be assessed on participation, correctness of answers, and creativity of balanced equations.

ReteachConstruct a ”gizmo” from a large flask (F) fitted with a one-hole stopper (S) and glass tube (T). Show students the gizmo and write its balanced equation on the board as the following:

__F + __S + __T = __FST.

Explain that any counted quantity such as 2 dozen or 12 ten-packs could be used to fill any set of four blanks in the equation. However, a physical quantity such as 10 kg would not balance the equation. Have students explain why.

Lesson Check Answers