LESSON 12.2

Key Objectives 12.2.1 Explain how mole ratios are used in

chemical calculations. 12.2.2 Explain the general procedure for solving a stoichiometric problem.

12.2 Chemical Calculations CHEMISTRY

Additional Resources

Q: How do manufacturers know how to make enough of their desired product? Chemical plants produce ammonia by combining nitrogen with hydrogen. If too much ammonia is produced, then it might be wasted. But if too little is produced, then there might not be enough for all their customers. In this lesson, you will learn how to use a balanced chemical equation to calculate the amount of product formed in a chemical reaction.

• Reading and Study Workbook, Lesson 12.2 • Probeware Laboratory Manual, Lab 19 • Virtual Chemistry Labs, Analysis of Baking Soda • Core Teaching Resources, Lesson 12.2 Review

Key Questions How are mole ratios used in chemical calculations? What is the general procedure for solving a stoichiometric problem?

Engage

&

CHEMISTRY Y YO YOU U Have students study the photograph and read the text. Ask students what ammonia is used for. (Ammonia is used in cleaning products, in fertilizers, and in the manufacture of other chemicals.) Tell students to consider how stoichiometry might be used to calculate the amount of product as they read through the lesson.

YOU Y &YOU

Vocabulary t
NPMF
SBUJP

Writing and Using Mole Ratios How are mole ratios used in chemical calculations? As you learned in the previous lesson, a balanced chemical equation provides a great deal of quantitative information. It relates particles (atoms, molecules, formula units), moles of substances, and masses. A balanced chemical equation also is essential for all calculations involving amounts of reactants and products. For example, suppose you know the number of moles of one substance. The balanced chemical equation allows you to determine the number of moles of all other substances in the reaction. Look again at the balanced equation for the production of ammonia. N2(g) à 3H2(g)

2NH3(g)

The most important interpretation of this equation is that 1 mol of nitrogen reacts with 3 mol of hydrogen to form 2 mol of ammonia. Based on this interpretation, you can write ratios that relate moles of reactants to moles of product. A mole ratio is a conversion factor derived from the coefficients of In chemia balanced chemical equation interpreted in terms of moles. cal calculations, mole ratios are used to convert between a given number of moles of a reactant or product to moles of a different reactant or product. Three mole ratios derived from the balanced equation above are

Activate Prior Knowledge Engage students in a review of moles and molar mass. Ask What is a mole? (A mole is equivalent to 6.02 × 1023 particles of substance.) Ask How can you determine the number of moles of a substance in a chemical equation? (The number of moles is represented by the substance’s coefficient.) Ask What is molar mass? (Molar mass is the mass of one mole of a substance.)

1 mol N2 3 mol H2

2 mol NH3 1 mol N2

3 mol H2 2 mol NH3

Mole-Mole Calculations In the mole ratio below, W is the unknown, wanted, quantity and G is the given quantity. The values of a and b are the coefficients from the balanced equation. Thus, a general solution for a molemole problem, such as Sample Problem 12.3, is given by

b mol W xb x mol mol G ò

















ä







mol










W


a mol mol ol G a Given

National Science Education Standards

Mole ratio

Calculated

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A-2, B-3

Focus on ELL 1 CONTENT AND LANGUAGE Present academic vocabulary that appears in the lesson, such as instantaneously, conversion, and excess. Pair students and have them find these words in the lesson and use context clues to predict their meanings. Have students share their interpretations with the class. 2 FRONTLOAD THE LESSON Have students discuss their experience with ratios from

mathematics class. To check understanding, have students determine the ratio of males to females in the class and the ratio of each gender to total students. 3 COMPREHENSIBLE INPUT Explain Sample Problem 12.3 using a diagram. Write

each reactant using a different color. Continue to use the corresponding color throughout the calculation. Speak clearly and slowly, and use block arrows to show the steps of the process.

390

Chapter 12 • Lesson 2

Foundations for Reading Calculating Moles of a Product How many moles of NH3 are produced when 0.60 mol of nitrogen reacts with hydrogen?

— Analyze List the known and the unknown. The conversion mol NH3. According to the balanced equation, is mol N2 1 mol N2 combines with 3 mol H2 to produce 2 mol NH3. To determine the number of moles of NH3, the given quantity of N2 is multiplied by the form of the mole ratio from the balanced equation that allows the given unit to cancel. ˜ Calculate

KNOWN moles of nitrogen
ä
0.60 mol N2 UNKNOWN moles of ammonia
ä

mol NH3

Solve for the unknown.

Write the mole ratio that will allow you to convert from moles N2 to moles NH3.

2 mol NH3 1 mol N2

Multiply the given quantity of N2 by the mole ratio in order to find the moles of NH3.

2 mol NH3 0.60 mol N2

ò




















ä
1.2 mol NH3 1 mol N2

BUILD VOCABULARY Have students paraphrase the meaning of mole ratio using words or symbols. Guide students to use what they have already learned about balanced chemical equations from the previous lesson and about ratios from mathematics class to form their definitions. Have students read their definitions to the class. READING STRATEGY As students read the section about Mass-Mass Calculations, have them identify and list the main ideas presented by the text.

Explain Writing and Using Mole Ratios

™ Evaluate Does the result make sense? The ratio of 1.2 mol NH3 to 0.60 mol N2 is 2:1, as predicted by the balanced equation. 11. This equation shows the formation of aluminum oxide, which is found on the surface of aluminum objects exposed to the air. 4Al(s) à 3O2(g)

2Al2O3(s)

a. Write the six mole ratios that can be derived from this equation. b. How many moles of aluminum are needed to form 3.7 mol Al2O3?

Remember that the mole ratio must have N2 on the bottom so that the mol N2 in the mol ratio will cancel with mol N2 in the known. 12. According to the equation in Problem 11, a. How many moles of oxygen are required to react completely with 14.8 mol Al? b. How many moles of Al2O3 are formed when 0.78 mol O2 reacts with aluminum?

START A CONVERSATION Discuss with students what they know about the relationship of the total mass of the reactants and the total mass of the products in a chemical reaction. Ask Why do you think this relationship is important when trying to determine quantitative information about a chemical reaction? (Answers will vary.)

Be sure students understand the difference between moles and mole ratio. Point out to students that moles are always involved in stoichiometry problems. Mole ratios are used to convert from one substance in the balanced equation to another substance.

Sample Practice Problem Iron(III) oxide reacts with carbon monoxide to yield iron and carbon dioxide in the following reaction:

Mass-Mass Calculations No laboratory balance can measure substances directly in moles. Instead, the amount of a substance is usually determined by measuring its mass in grams. From the mass of a reactant or product, the mass of any other reactant or product in a given chemical equation can be calculated. The mole interpretation of a balanced equation is the basis for this conversion. If the given sample is measured in grams, then the mass can be converted to moles by using the molar mass. Then the mole ratio from the balanced equation can be used to calculate the number of moles of the unknown. If it is the mass of the unknown that needs to be determined, the number of moles of the unknown can be multiplied by the molar mass. As in mole-mole calculations, the unknown can be either a reactant or a product.

A.

Fe2O3(s) + 3CO(g) → 2Fe(s) + 3CO2(g) How many mole ratios can be derived from this equation? What are they? (12; A C FeD 2O3 B A3COB

B. Stoichiometry 391

,

A3COB A C FeD 2O3 B

,

A C FeD 2O3 B A2FeB

,

A2FeB A C FeD 2O3 B

,

How many moles of Fe are produced from 1.8 mol of Fe2O3? (3.6 mol)

Foundations for Math DIMENSIONAL ANALYSIS Remind students that to solve a problem by using dimensional analysis, they need to first find the conversion factor. A conversion factor is a ratio of equivalent measurements. Sample problem 12.3 asks students to find the moles of ammonia produced, so the answer needs to be in units of “moles of ammonia.” Remind students that they can multiply any quantity by anything equal to 1 without changing the value of the quantity.

Since the number of moles of nitrogen is given, the ratio of moles of nitrogen to moles of ammonia can be used as the conversion factor.

Answers 11. a. 4 mol Al

4 mol Al 3 mol O2 3 mol O2 4 mol Al 2 mol Al2O3

2 mol Al2O3 4 mol Al b. 7.4 mol 12. a. 11.1 mol b. 0.52 mol

3 mol O2 2 mol Al2O3

2 mol Al2O3 3 mol O2

Stoichiometry

391

LESSON 12.2

Sample Problem 12.3

LESSON 12.2

Explore Teacher Demo PURPOSE Students interpret a balanced equation in

terms of moles and mass. MATERIALS Prior to the demonstration, prepare 0.1M solutions of potassium iodide and lead(II) nitrate. Measure 50.0 mL of Pb(NO3)2 and 150 mL of KI into separate 250-mL beakers. SAFETY Wear safety glasses and an apron. PROCEDURE Tell students that you are going to mix 0.005 mole of lead(II) nitrate with excess potassium iodide. Have students observe as you combine both solutions in the 250-mL beaker. Have students write a balanced chemical equation for the observed reaction. [2KI(aq ) + Pb(NO3 )2(aq ) → 2KNO3(aq ) + PbI2(s )]

Steps for Solving a Mass-Mass Problem Mass-mass problems are solved in basically the same way as mole-mole problems. The steps for the mass-mass conversion of any given mass (G) to any wanted mass (W) are outlined below.

Figure 12.3 Ammonia in Space In this Hubble Space Telescope image, clouds of condensed ammonia are visible covering the surface of Saturn.

1. Change the mass of G to moles of G (mass G molar mass of G. mass G ñ

mol G) by using the

1 mol G â mol G molar mass G

2. Change the moles of G to moles of W (mol G mole ratio from the balanced equation. mol G ñ

Have students predict the number of moles of product produced. (0.005 mole PbI2 assuming the reaction was complete) Note that, in an actual reaction, the amounts of reactants often are not present in the mole ratios predicted by the coefficients in a balanced equation. Explain the importance of the mole ratios in an equation for calculating relative quantities. Ask What is the mass of lead(II) nitrate reacted and the mass of lead(II) iodide produced? (1.66 g Pb(NO3 )2 and 2.30 g PbI2)

mol W) by using the

b mol W â mol W a mol G

3. Change the moles of W to grams of W (mol W using the molar mass of W. mol W ñ

mass W) by

molar mass W â mass W 1 mol W

Figure 12.4 shows another way to represent the steps for doing mole-mass and mass-mole stoichiometric calculations. For a mole-mass problem, the first conversion (from mass to moles) is skipped. For a mass-mole problem, the last conversion (from moles to mass) is skipped. You can use parts of the three-step process shown in Figure 12.4 as they are appropriate to the problem you are solving.

EXPECTED OUTCOME A bright yellow precipitate

will form.

Misconception Alert Students sometimes try to do mass-mass conversions by incorrectly using the mole ratio as a mass ratio. That is, they use grams instead of moles as the units in the mole ratio and then skip the mass-mole conversion step. Stress that because the number of grams in one mole of a substance varies with its molar mass, a mass-mole conversion is a necessary intermediate step in mass-mass stoichiometric problems.

Figure 12.4 Mass-Mass Conversion Steps This general solution diagram indicates the steps necessary to solve a mass-mass stoichiometry problem: Convert mass to moles, use the mole ratio, and then convert moles to mass. Infer Is the given always a reactant?

mass 1 mol G ñ of G mass G Mass-mole conversion

aG

bW

(given quantity)

(wanted quantity)

mol G ñ

b mol W a mol G

Mole ratio from balanced equation

mol W ñ

mass W 1 mol W

mass of W

Mole-mass conversion

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Atmospheric Ammonia Ammonia is found in trace amounts in the atmospheres of three Jovian planets— Jupiter, Saturn, and Uranus. In Jupiter’s atmosphere, the clouds of ammonia consist of frozen ammonia droplets changing to liquid ammonia droplets nearer the planet’s surface. Because of colder temperatures, the ammonia clouds in the atmosphere of Saturn and Uranus consist of frozen ammonia droplets.

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Chapter 12 • Lesson 2

TU

TOR

Sample Problem 12.4

Explain

Calculating the Mass of a Product Ammonia (NH3) clouds are present around some planets, as in Figure 12.3. Calculate the number of grams of NH3 produced by the reaction of 5.40 g of hydrogen with an excess of nitrogen. The balanced equation is N2(g) à 3H2(g)

2NH3(g)

— Analyze List the knowns and the unknown. The mass of hydrogen will be used to find the mass of g NH3. The coefficients of the ammonia: g H2 balanced equation show that 3 mol H2 reacts with 1 mol N2 to produce 2 mol NH3. The following steps are necessary to determine the mass of ammonia: g H2

˜ Calculate

mol H2

mol NH3

g NH3

KNOWNS mass of hydrogen
ä
5.40 g H2 2 mol NH3/3 mol H2 (from balanced equation) 1 mol H2
ä
2.0 g H2 (molar mass) 1 mol NH3
ä
17.0 g NH3 (molar mass) UNKNOWN mass of ammonia
ä

g
NH3

Solve for the unknown.

Don’t forget to cancel the units at each step.

Start with the given quantity, and convert from mass to moles.

5.40 g H2 ò

1 mol H2 2.0 g H2

Then convert from moles of reactant to moles of product by using the correct mole ratio.

5.40 g H2 ò

1 mol H2 2 mol NH3 ò 3 mol H2 2.0 g H2

g H2 Finish by converting from moles to grams. Use the molar mass of NH3.

5.40 g H2 ò Given quantity

mol H2

mol NH3

Mole ratio

Guide students to understand that there are many types of reactions where reactants can combine or decompose to produce fewer or more moles of product. Explain that although the total mass of reactants and products is constant, the number of moles of particles can increase or decrease depending on the final grouping of atoms.

Sample Practice Problem Rust (Fe2O3) is produced when iron (Fe) reacts with oxygen (O2): 4Fe(s) + 3O2(g) → 2Fe2O3(s).

g NH3

1 mol H2 2 mol NH3 17.0 g NH3 ò ò ä
31 g NH3 3 mol H2 1 mol NH3 2.0 g H2 Change given unit to moles

START A CONVERSATION Take a quick vote in class to see who believes there is a “law of conservation of moles.” Discuss the reasons why students believe this law exists. Ask In the following reaction, 2H2O(l) → 2H2(g) + O2(g), is the number of moles of the products greater than, less than, or equal to the number of moles of the reactant? (greater than) Ask In the following reaction, 2Mg(s) + O2(g) → 2MgO(s), is the number of moles of product greater than, less than, or equal to the number of moles of the reactants? (less than)

How many grams of Fe2O3 are produced when 12.0 g of iron rusts? (17.2 g)

Change moles to grams

™ Evaluate Does the result make sense? Because there are three conversion factors involved in this solution, it is more difficult to estimate an answer. However, because the molar mass of NH3 is substantially greater than the molar mass of H2, the answer should have a larger mass than the given mass. The answer should have two significant figures. 13. Acetylene gas (C2H2) is produced by adding water to calcium carbide (CaC2). CaC2(s) à 2H2O(l)

C2H2(g) à Ca(OH)2(aq)

How many grams of acetylene are produced by adding water to 5.00 g CaC2?

14. Use the equation in Question 13 to determine how many moles of CaC2 are needed to react completely with 49.0 g H2O.

Stoichiometry 393

Foundations for Math SIGNIFICANT FIGURES The significant figures in a measurement are all the digits known with certainty plus one estimated digit.

The number of significant figures of a product or quotient should equal the least number of significant figures of any measurement in the calculation. For example, 5.5 cm × 2.24 cm = 12 cm2; notice that the product has 2 significant figures, the same as 5.5 cm. The number of decimal places of a sum or difference should equal the least number of decimal places in any of the measurements being added or subtracted. For example, 5.5 cm + 2.24 cm = 7.7 cm; notice that the sum has 2 significant figures, the same as 5.5 cm.

Answers FIGURE 12.4 No; the given could be a product. 13. 2.03 g C2H2 14. 1.36 mol CaC2

Stoichiometry

393

LESSON 12.2

CHEM

LESSON 12.2

Other Stoichiometric Calculations What is the general procedure for solving a stoichiometric problem?

Explain Other Stoichiometric Calculations START A CONVERSATION On the board, write equations for reactions in which the reactants are both gases or are a gas and a solid. Ask students how the reactants and products in each reaction would most likely be measured. Have students relate these measurements to the concept of a mole.

CHEMISTRY

CHEMISTRY

&YYOU

Q: How do you think air bag manufacturers know how to get the right amount of air in an inflated air bag?

Y YOU U & YO

Manufacturers use balanced chemical equations to calculate the amount of product formed from a given quantity of reactants.

Recall from Chapter 10 that the mole can be related to other quantities as well. For example, 1 mol â 6.02 ñ 1023 representative particles, and 1 mol of a gas â 22.4 L at STP. These two relationships provide four more conversion factors that you can use in stoichiometric calculations.

USE VISUALS Direct students to Figure 12.5, and

walk them through it carefully. Although it looks complicated, it’s really three steps: Take what you’re given, and find a way to change it to moles. Then use a mole ratio from the balanced equation to get moles of the second substance. Finally find a way to convert the moles into the units that you need for the final answer.

As you already know, you can obtain mole ratios from a balanced chemical equation. From the mole ratios, you can calculate any measurement unit that is related to the mole. The given quantity can be expressed in numbers of representative particles, units of mass, or volumes of gases at STP. The problems can include mass-volume, particle-mass, and volume-volume calculations. For example, you can use stoichiometry to relate volumes of reactants and In a typical stoichiometproducts in the reaction shown in Figure 12.5. ric problem, the given quantity is first converted to moles. Then, the mole ratio from the balanced equation is used to calculate the number of moles of the wanted substance. Finally, the moles are converted to any other unit of measurement related to the unit mole, as the problem requires. Thus far, you have learned how to use the relationship between moles and mass (1 mol â molar mass) in solving mass-mass, mass-mole, and mole-mass stoichiometric problems. The mole-mass relationship gives you two conversion factors. 1 mol molar mass and molar mass 1 mol

Figure 12.5 Solving Stoichiometric Problems With your knowledge of conversion factors and this problem-solving approach, you can solve a variety of stoichiometric problems. Identify What conversion factor is used to convert moles to representative particles?

1 mol 6.02 ñ 1023 particles

Figure 12.5 summarizes the steps for a typical stoichiometric problem. Notice that the units of the given quantity will not necessarily be the same as the units of the wanted quantity. For example, given the mass of G, you might be asked to calculate the volume of W at STP.

aG

bW

(wanted quantity)

Representative 1 mol G ñ particles of G 6.02 ñ1023

Volume of G 1 mol G ñ (liters) at STP 22.4 L G

6.02 ñ 1023 particles 1 mol

22.4 L 1 mol and 1 mol 22.4 L

(given quantity)

mass 1 mol G ñ of G mass G

and

mol G ñ

b mol W a mol G

mol W

Mole ratio from balanced equation

ñ

Representative 6.02 ñ1023 â particles of W 1 mol W

ñ

mass mass W â of W 1 mol W

ñ

Volume of W 22.4 L W â (liters) at STP 1 mol W

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Check for Understanding The Essential Question How do you calculate amounts of reactants and products in a chemical reaction? Assess students’ understanding of stoichiometry by showing students various equations for reactions in which the reactants are both gases or are a gas and a solid, such as 2Mg(s) + O2(g) → 2MgO(s). Have students create three note cards, one with the words mass-volume, one with the words particle-mass, and one with the words volume-volume. As you show students an equation, have them raise the card that names how they think the reactants and products in each reaction would most likely be measured. ADJUST INSTRUCTION If students are still having difficulty deciding which ratios to use, review Figures 12.4 and 12.5 with them.

394

Chapter 12 • Lesson 2

DRAW A DIAGRAM On the board or overhead

Calculating Molecules of a Product How many molecules of oxygen are produced when 29.2 g of water is decomposed by electrolysis according to this balanced equation? 2H2O(l) electricity 2H2(g) à O2(g) KNOWNS mass of water ä
29.2 g H2O 1 mol O2/2 mol H2O (from balanced equation) 1 mol H2O ä
18.0 g H2O (molar mass) 1 mol O2
ä
6.02 ò
1023 molecules O2

— Analyze

List the knowns and the unknown. The following calculations need to be performed: g H2O

mol H2O

mol O2

molecules O2

The appropriate mole ratio relating mol O2 to mol H2O from the balanced equation is 1 mole O2 Ž 2 mol H2O.

˜ Calculate

UNKNOWN molecules of oxygen
ä

moleciules O2

projector, draw a diagram showing the relationships that are useful for solving stoichiometry problems. One simple model reaction is A → B. Use doubleheaded arrows to connect these terms: Particles of A, Moles of A, Grams of A, Moles of B, Particles of B, and Grams of B. Above the appropriate arrows, write Avogadro’s number, Coefficients, and Molar mass. Explain that the only “transitions” are allowed between quantities connected by arrows. Point out that the required conversion factor to make a “transition” is written above each arrow. Encourage students to refer to the diagram when working practice problems.

Solve for the unknown.

Start with the given quantity, and convert from mass to moles.

29.2 g H2O ò

1 mol H2 18.0 g H2O

Then, convert from moles of reactant to moles of product.

29.2 g H2O ò

1 mol H2 1 mol O2 ò 18.0 g H2O 2 mol H2O

Finish by converting from moles to molecules.

29.2 g H2O ò

1 mol H2 1 mol O2 6.02 ò
1023 molecules O2 ò ò 18.0 g H2O 2 mol H2O 1 mol O2

Given quantity

Change to moles

Mole ratio

Remember to start your calculations with the given quantity, even if the given quantity is a product in the reaction.

Change to molecules

ä
4.88 ò
1023 molecules O2

™ Evaluate Does the result make sense? The given mass of water should produce a little less than 1 mol of oxygen, or a little less than Avogadro’s number of molecules. The answer should have three significant figures.

15. How many molecules of oxygen are produced by the decomposition of 6.54 g of potassium chlorate (KClO3)? 2KClO3(s)

2KCl(s) à 3O2(g)

16. The last step in the production of nitric acid is the reaction of nitrogen dioxide with water. 3NO2(g) à H2O(l)

2HNO3(aq) à NO(g)

How many grams of nitrogen dioxide must react with water to produce 5.00 ñ 1022 molecules of nitrogen monoxide? Stoichiometry 395

Foundations for Math CONVERSION FACTORS Students often struggle with the proper use of conversion factors. Conversion factors should always be oriented so that like units cancel each other, leaving the desired unit in the numerator. Explain to students that planning the steps of the equation can make the task simpler.

In Sample Problem 12.5, the goal is to find the number of molecules of O2 produced from 29.2 g of H2O. The necessary equation should end with molecules of O2 in the numerator of the ratio. With this in mind, students should first look for a molar ratio that is a direct comparison of H2O and O2. In this case, the ratio is 2 mol H2O to 1 mol O2. Now they know that the first step in their equation is to determine the number of moles in 29.2 g H2O. Then they can determine the number of moles of O2 that will be produced and finally the number of molecules of O2.

Answers FIGURE 12.5 6.02 × 1023 representative particles/

1 mol

15. 4.82 × 1022 molecules O2 16. 11.5 g NO2

Stoichiometry

395

LESSON 12.2

Sample Problem 12.5

LESSON 12.2

Sample Problem 12.6

Explore Class Activity PURPOSE Students practice sequencing the steps in

solving stoichiometric problems. MATERIALS 8 white index cards, 1 colored index card, paper punch, 2 brass paper fasteners PROCEDURE Distribute the white cards to the students. Have them divide the cards into two piles of four cards each. On the first card of the first pile, have them write Converting a given measured quantity to moles. On each of the three remaining cards, have students write the conversion factors for converting mass to moles, representative particles to moles, and volume to moles, respectively. For the second set of cards, have students label the first card Changing moles of wanted substances to a measured quantity. On each of the remaining cards, have them write the appropriate conversion factor. On the colored card, have students write Converting moles of given to moles of wanted using mole ratio from balanced chemical equation b mol W/a mol G. Have the students use the paper punch to punch each of the two sets of cards. Then have them fasten each set with a brass paper fastener. Allow students to practice using the cards to solve the Practice Problems. EXPECTED OUTCOME The cards should aid in sequencing the steps in solving stoichiometric problems.

Sample Practice Problem Ammonia (NH3) reacts with oxygen (O2) to produce nitrogen monoxide (NO) and water. 4NH3(g) + 5O2(g) → 4NO(g) + 6H2O(l)

Volume-Volume Stoichiometric Calculations Nitrogen monoxide and oxygen gas combine to form the brown gas nitrogen dioxide, which contributes to photochemical smog. How many liters of nitrogen dioxide are produced when 34 L of oxygen react with an excess of nitrogen monoxide? Assume conditions are at STP. 2NO(g) à O2(g)

2NO2(g)

— Analyze

List the knowns and the unknown. The following calculations need to be performed: L O2

mol O2

mol NO2

L NO2

KNOWNS volume of oxygen
ä
34 L O2 2 mol NO2/1 mol O2 (from balanced equation) 1 mol O2
ä
22.4 L O2 (at STP) 1 mol NO2
ä
22.4 L NO2 (at STP) UNKNOWN

For gaseous reactants and products at STP, 1 mol of a gas has a volume of 22.4 L.

˜ Calculate

volume of nitrogen dioxide
ä

L NO2

Solve for the unknown.

Start with the given quantity, and convert from volume to moles by using the mole-volume ratio.

34 L O2 ò

1 mol O2 22.4 L O2

Then, convert from moles of reactant to moles of product by using the correct mole ratio.

34 L O2 ò

2 mol NO2 1 mol O2 ò 22.4 L O2 1 mol O2

Finish by converting from moles to liters. Use the mole-volume ratio.

34 L O2 ò

2 mol NO2 22.4 L NO2 1 mol O2 ò ò ä
68 L NO2 22.4 L O2 1 mol O2 1 mol NO2

Given quantity

Change to moles

Mole ratio

Change to liters

™ Evaluate Does the result make sense? Because 2 mol NO2 are produced for each 1 mol O2 that reacts, the volume of NO2 should be twice the given volume of O2. The answer should have two significant figures. 17. The equation for the combustion of carbon monoxide is 2CO(g) à O2(g)

2CO2(g)

How many liters of oxygen are required to burn 3.86 L of carbon monoxide?

18. Phosphorus and hydrogen can be combined to form phosphine (PH3). P4(s) à 6H2(g)

4PH3(g)

How many liters of phosphine are formed when 0.42 L of hydrogen reacts with phosphorus?

How many liters of NO are produced when 1.40 L of oxygen reacts with ammonia? (1.12 L) 396 $IBQUFS

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Differentiated Instruction L1 STRUGGLING STUDENTS Encourage students to find a method of problem solving that capitalizes on their strengths, such as drawing pictures of reactants and products. Make molecular model kits available to help students visualize reactions. LPR LESS PROFICIENT READERS Direct students’ attention to the key questions and answers. Rewrite the answers on the board, and then revise them by writing simplified sentences or bulleted lists. L3 ADVANCED STUDENTS Have computer-literate students use the calculations in the sample problem as the basis for a general algorithm in a spreadsheet or computer program to solve stoichiometric problems. Have students demonstrate and explain their programs to interested classmates.

396

Chapter 12 • Lesson 2

Y TECHNOLOGY &YOU:

Steering wheel

Stoichiometric Safety

Air bag folded into steering wheel

In a car collision, proper inflation of an air bag may save your life. Too much air in the bag could make the bag too hard, which could cause injury because the bag wouldn’t effectively cushion the blow. Too little air in the bag could be insufficient to prevent a driver’s impact with the steering wheel. Engineers use stoichiometry to determine the exact quantity of each reactant in the air bag’s inflation system. When a crash occurs, a series of reactions happen. Sodium azide (NaN3) decomposes into sodium metal and nitrogen gas. The nitrogen gas causes the air bag to inflate, but the sodium can react explosively with water. So, air bags contain potassium nitrate (KNO3) to react with the sodium. Silicon dioxide is also included in the air bag to react with the products of the second reaction. This final reaction produces a harmless substance.

Ignition unit Igniter Sodium azide pellets

Steering wheel Igniter

Electrical signal from crash sensor

Sodium azide pellets decomposing 2NaN3(s) 2Na(s)  3N2(g) 10Na(s)  2KNO3(s) K2O(s)  5Na2O(s)  N2(g)

Take It Further CRASH TEST Air bag performance is tested using a crash test dummy. The production of nitrogen gas causes air bags to erupt from their storage site at speeds up to 200 miles per hour.

1. Draw Conclusions If a reaction in an air bag does not occur as intended, how might this affect the performance of an air bag? 2. Explain Research the regulations on automotive air bags, and explain why air bags are not safe for all passengers.

Chemistry & You 397

21st Century Learning To be successful in the 21st century, students need skills and learning experiences that extend beyond subject matter mastery. The following project helps students build 21st Century Skills. BROADCASTING FOR SAFETY Pose the following challenge to students: A major broadcasting corporation is creating a new automotive-themed podcast and has hired you as its host. Form groups of four to five students to do the following: • Write, produce, and record a 35-40 minute podcast, with one student serving as the host, one as an expert on air bag restraint systems, and two to three students as callers to the show. • The show host will conduct a 20-minute interview with the expert, eliciting important information about current air bag technologies and those in development for future car models. • The callers will use the final 15-20 minutes of the show to ask questions about safety and environmental concerns. The podcast will be submitted as an MP3 file either via e-mail or on a CD or DVD.

&

CHEMISTRY Y YO YOU U Write the following reactions on the board. Reaction I 2NaN3(s) → 2Na(s) + 3N2(g) Reaction II 10Na(s) + 2KNO3(s) → K2O(s) + 5Na2O(s) + N2(g) + heat Point out that the proper inflation of the air bag requires two reactions. Explain that an electrical current produced by the igniter causes the decomposition of sodium azide into sodium metal and nitrogen gas. Note that the sodium metal produced is dangerously reactive. In a second reaction, potassium nitrate reacts with the elemental sodium and forms potassium oxide, sodium oxide, and additional nitrogen gas. The heat causes all the solid products to fuse with SiO2, powdered sand, which is also part of the reaction mixture. The fused product is a safe, unreactive glass. Ask How many moles of potassium nitrate must be included in the reaction mixture to consume the sodium produced by the decomposition of one mole of sodium azide? (0.2 mol KNO3 ) Ask How many liters of N2 are produced at STP if 1.0 mole of sodium azide and 0.20 mole of potassium nitrate react? (36 L) Have students speculate how the pressure of the gas inside the air bag depends on the number of moles of nitrogen produced and the temperature inside the air bag. (Acceptable answers should indicate that because gas pressure depends on the number of gas particles present, pressure depends on the number of moles of gas particles present. The heat released by this reaction raises the temperature of the gaseous products, helping the bag inflate even faster.)

Extend Connect to

LANGUAGE ARTS

Explain to students that the use of air bag restraint systems (seatbelt/air bags) reduces the risk of fatalities in accidents by about 70%. However, not all passengers in a vehicle benefit from air bags, which can deliver a significant blow to a passenger when activated. Have students research the injuries that can occur as the result of air bag deployment, then have students write an argumentative essay that advocates the use of air bags despite the potential for injury. Essays should include current recommendations and restrictions for the use of air bags with small children and infants.

Answers 17. 1.93 L O2 18. 0.28 L PH3 TAKE IT FURTHER 1. Answers will vary. The air bag could under 2.

inflate or inflate too slowly. Answers will vary. Some students may find that passenger-side air bags are not safe for young children. Chemistry & You

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CHEMISTRY & YOU

CHEMISTRY Y

Evaluate

TU

Sample Sample Problem Problem 12.712.7

TOR

Finding the Volume of a Gas Needed for a Reaction Assuming STP, how many milliliters of oxygen are needed to produce 20.4 mL SO3 according to this balanced equation?

Informal Assessment Write a balanced equation on the board, such as H2(g) + I2(g) → 2HI(g). Have students orally state all the different mole ratios for the reaction; write all of the given ratios on the board. Then pose a problem, such as, How many moles of hydrogen iodide are formed when 0.75 mol I2 gas is reacted with excess hydrogen gas? Have students go to the board and place their initials next to the correct mole ratio for the problem. Repeat with various types of reactions. Then have students complete the 12.2 Lesson Check.

2SO2(g) à O2(g)

2SO3(g)

— Analyze List the knowns and the unknown. For a reaction involving gaseous reactants or products, the coefficients also indicate relative amounts of each gas. So, you can use volume ratios in the same way you have used mole ratios.

KNOWNS volume of sulfur trioxide
ä
20.4 mL 1 ml O2/2 ml SO3 (from balanced equation) UNKNOWN volume of oxygen
ä

mL O2

˜ Calculate

Solve for the unknown.

Multiply the given volume by the appropriate volume ratio.

1 mL O2 20.4 mL SO3
ò ä
10.2 mL O2 2 mL SO3

Reteach

The volume ratio can be written using milliliters as the units instead of liters.

™ Evaluate Does the result make sense? Because the volume ratio is 2 volumes SO3 to 1 volume O2, the volume of O2 should be half the volume of SO3. The answer should have three significant figures.

Use molecular models to review the importance of mole ratios. Illustrate how the mole ratios from the balanced chemical equation are related to the individual atoms, formula units, and molecules of the reactants and products as described by the equation.

Use the following chemical equation to answer Problems 19 and 20. CO2(g) à 2SO2(g) CS2(l) à 3O2(g) 19. Calculate the volume of sulfur dioxide, in milliliters, produced when 27.9 mL O2 reacts with carbon disulfide.

NLIN

PR

S

E

O

OBLE

M

LESSON 12.2

CHEM

20. How many deciliters of carbon dioxide are produced when 0.38 L SO2 is formed?

12.2 Lesso LessonCheck

21.

Explain How are mole ratios used in chemical calculations?

22.

Sequence Outline the sequence of steps needed to solve a typical stoichiometric problem.

23. Calculate The combustion of acetylene gas is represented by this equation: 2C2H2(g) à 5O2(g)

4CO2(g) à 2H2O(g)

a. How many grams of CO2 and grams of H2O are produced when 52.0 g C2H2 burn in oxygen? b. How many moles of H2O are produced when 64.0 g C2H2 burn in oxygen?

24. Apply Concepts Write the 12 mole ratios that can be derived from the equation for the combustion of isopropyl alcohol. 2C3H7OH(l) à 9O2(g)

6CO2(g) à 8H2O(g)

BIGIDEA

THE MOLE AND QUANTIFYING MATTER 25. Use what you have learned about stoichiometric calculations to explain the following statement: Stoichiometric calculations are not possible without a balanced chemical equation.

398 $IBQUFS

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Lesson Check Answers 21. Mole ratios are written using the coefficients from a balanced chemical equation.

They are used to relate moles of reactants and products in stoichiometric calculations. 22. Convert the given quantity to moles; use the mole ratio from the equations to find

the moles of the wanted; convert moles of wanted to the desired unit. 23. a. 176 g CO2, 36.0 g H2O

b. 2.46 mol H2O

24. 2 mol C3H7OH 2 mol C3 H7OH 2 mol C3H7OH 9 mol O2 9 mol O2 6 mol CO2 9 mol O2 6 mol CO2 8 mol H2O 6 mol CO2 8 mol H2O 8 mol H2O 9 mol O2 6 mol CO2 8 mol H2O 6 mol CO2 8 mol H2O 8 mol H2O 2 mol C3H7OH 2 mol C3H7OH 2 mol C3H7OH 9 mol O2 9 mol O2 6 mol CO2 25. A chemical reaction’s mole ratios are derived from the relationships between

coefficients in a balanced chemical equation.

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Chapter 12 • Lesson 2

LAB

V

Small-Scale Lab

Explore

Analysis of Baking Soda

Small-Scale Lab

Purpose To determine the mass of sodium hydrogen carbonate in a sample of baking soda, using stoichiometry

OBJECTIVE Students calculate the mass of NaHCO3 in a sample using stoichiometry. PREP TIME 1 hour CLASS TIME 30 minutes MATERIALS Baking soda; plastic cups; soda straws; mass balances; pipets of HCl, NaOH, and thymol blue; pH sensor (optional)

Materials r
baking soda r
3 plastic cups r
soda straw r
balance

r
pipets of HCl, NaOH, and thymol blue r
pH sensor (optional)

ADVANCE PREP

Procedure A. Measure the mass of a clean, dry plastic cup. B. Using the straw as a scoop, fill one end with baking soda to a depth of about 1 cm. Add the sample to the cup and measure its mass again. C. Place two HCl pipets that are about 3/4 full into a clean cup and measure the mass of the system. D. Transfer the contents of both HCl pipets to the cup containing baking soda. Swirl until the fizzing stops. Wait 5–10 minutes to be sure the reaction is complete. Measure the mass of the two empty HCl pipets in their cup again. E. Add 5 drops of thymol blue to the plastic cup. F. Place two full NaOH pipets in a clean cup and measure the mass of the system. G. Add NaOH slowly to the baking soda/HCl mixture until the pink color just disappears. Measure the mass of the NaOH pipets in their cup again.

Analyze Using your experimental data, record the answers to the following questions below your data table. 1. Evaluate Write a balanced equation for the reaction between baking soda (NaHCO3) and HCl. 2. Calculate Calculate the mass in grams of the baking soda. (Step B Ź Step A) 3. Calculate Calculate the total mmol of 1M HCl. Note: Every gram of HCl contains 1 mmol. (Step C Ź Step D) ñ
1.00 mmol/g

4. Calculate Calculate the total mmol of 0.5M NaOH. Note: Every gram of NaOH contains 0.5 mmol. (Step F Ź Step G) ñ 0.500 mmol/g 5. Calculate Calculate the mmol of HCl that reacted with the baking soda. Note: The NaOH measures the amount of HCl that did not react. (Step 3 Ź Step 4) 6. Calculate Calculate the mass of the baking soda from the reaction data. (0.084 g/mmol ñ Step 5) 7. Calculate Calculate the percent error of the experiment. (Step 2 Ź Step 6) ñ 100% Step 2

You’re the Chemist The following small-scale activities allow you to develop your own procedures and analyze the results. 1. Analyze Data For each calculation you did, substitute each quantity (number and unit) into the equation and cancel the units to explain why each step gives the quantity desired. 2. Design an Experiment Baking powder consists of a mixture of baking soda, sodium hydrogen carbonate, and a solid acid, usually calcium dihydrogen phosphate (Ca(H2PO4)2). Design and carry out an experiment to determine the percentage of baking soda in baking powder.

Small-Scale Lab 399

Solution

Preparation

0.5M NaOH

20.0 g in 1.0 L

1.0M HCl

82 mL of 12M in 1.0 L Caution Always add acid to water carefully and slowly.

0.04% TB

100 mg in 21.5 mL of 0.01M NaOH; dilute to 250 mL

SAFETY Have students wear safety glasses and

follow the standard safety procedures. TEACHING TIPS

• Stress that the procedure measures the amount of excess HCl that is not reacted with the baking soda (Step 4). Because this excess HCl reacts with the NaOH in a 1:1 mole ratio, the moles of NaOH equal the moles of HCl in excess. Subtracting the excess moles of HCl from the total moles used in the experiment (Step 5) yields the moles reacted with the baking soda, which is 100% NaHCO3. • If the mixture does not turn red when thymol blue is added, the student should find the mass of a third pipet and add just enough HCl to turn the mixture cherry red. Then the student should find the mass of the half-empty pipet so the mass of HCl added can be calculated and added to the total mass used. EXPECTED OUTCOME Sample data: Step A. 2.83 g,

B. 3.28 g, C. 10.70 g, D. 4.29 g, F. 10.53 g, G. 8.78 g ANALYZE

1. 2. 3. 4.

5.

6. 7.

HCl + NaHCO3(s) → CO2(g) + H2O + NaCl 3.28 g – 2.83 g = 0.45 g (10.70 – 4.29) g × 1.00 mmol/g = 6.41 mmol (10.53 – 8.78) g × 0.500 mmol/g = 0.875 mmol (0.875 mmol HCl unreacted) 6.41 mmol total – 0.875 mmol unreacted = 5.54 mmol (5.54 mmol NaHCO3) (0.0840 g/mmol) × 5.53 mmol = 0.46 g (0.46 – 0.45) g/0.45 g × 100% = 2% error (assuming baking soda

is one hundred percent sodium hydrogen carbonate) YOU’RE THE CHEMIST

1. See Steps 2–7. 2. Repeat Steps A–G and 1–7 using baking powder instead of baking soda. The percent error is the percent of baking soda in baking powder, assuming no other errors. FOR ENRICHMENT Ask students to

predict how much baking soda and 1 M HCl are needed to produce enough CO2 to fill a 1-L plastic bag. Have them write a procedure and then carry out the experiment.

Answers 19. 18.6 mL SO2 20. 1.9 dL CO2

Small-Scale Lab

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LESSON 12.2

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U IRT A