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6 Dalton’s Law of Partial Pressures

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271

9.5 Calculations Involving a Limiting Reactant

Grams

of H2

Molar

mass

of H2

Moles

of H2

H2

limiting

Grams

of N2

Molar

mass

of N2

Moles

of H2

2 mol NH3

3 mol H2

Moles

of NH3

Molar

mass

of NH3

Grams

of NH3

Moles

of N2

Figure 9.2

A map of the procedure used in Example 9.7.

R E A L I T Y C H E C K If neither reactant were limiting, we would expect an

answer of 30.0 kg of NH3 because mass is conserved (25.0 kg ϩ 5.0 kg ϭ 30.0

kg). Because one of the reactants (H2 in this case) is limiting, the answer

should be less than 30.0 kg, which it is. ■

The strategy used in Example 9.7 is summarized in Figure 9.2.

The following list summarizes the steps to take in solving stoichiometry problems in which the amounts of two (or more) reactants are given.

Steps for Solving Stoichiometry Problems Involving

Limiting Reactants

Step 1 Write and balance the equation for the reaction.

Step 2 Convert known masses of reactants to moles.

Step 3 Using the numbers of moles of reactants and the appropriate mole

ratios, determine which reactant is limiting.

Step 4 Using the amount of the limiting reactant and the appropriate mole

ratios, compute the number of moles of the desired product.

Step 5 Convert from moles of product to grams of product, using the molar

mass (if this is required by the problem).

EXAMPLE 9.8

Stoichiometric Calculations: Reactions Involving the Masses

of Two Reactants

Nitrogen gas can be prepared by passing gaseous ammonia over solid copper(II) oxide at high temperatures. The other products of the reaction are

solid copper and water vapor. How many grams of N2 are formed when 18.1

g of NH3 is reacted with 90.4 g of CuO?

SOLUTION

Where Are We Going?

We want to determine the mass of nitrogen produced given the masses of

both reactants.

272 Chapter 9 Chemical Quantities

What Do We Know?

• The names or formulas of the reactants and products.

• We start with 18.1 g of NH3 and 90.4 g of CuO.

• We can obtain the atomic masses from the periodic table.

What Do We Need To Know?

• We need to know the balanced equation for the reaction, but we

first have to write the formulas for the reactants and products.

Ken O’Donoghue

• We need the molar masses of NH3, CuO, and N2.

• We need to determine the limiting reactant.

How Do We Get There?

Copper(II) oxide reacting with

ammonia in a heated tube.

Step 1 From the description of the problem, we obtain the following balanced equation:

2NH3(g) ϩ 3CuO(s) → N2(g) ϩ 3Cu(s) ϩ 3H2O(g)

Step 2 Next, from the masses of reactants available we must compute the

moles of NH3 (molar mass ϭ 17.03 g) and of CuO (molar mass ϭ 79.55 g).

1 mol NH3

ϭ 1.06 mol NH3

17.03 g NH3

1 mol CuO

90.4 g CuO ϫ

ϭ 1.14 mol CuO

79.55 g CuO

18.1 g NH3 ϫ

Step 3 To determine which reactant is limiting, we use the mole ratio between CuO and NH3.

1.06 mol NH3 ϫ

3 mol CuO

ϭ 1.59 mol CuO

2 mol NH3

Then we compare how much CuO we have with how much of it we need.

Moles of

CuO

available

less

than

1.14

Li

Group

1

N

Group

5

Moles of CuO

needed to

react with

all the NH3

1.59

Therefore, 1.59 mol CuO is required to react with 1.06 mol NH3, but only

1.14 mol CuO is actually present. So the amount of CuO is limiting; CuO

will run out before NH3 does.

Step 4 CuO is the limiting reactant, so we must use the amount of CuO

in calculating the amount of N2 formed. Using the mole ratio between CuO

and N2 from the balanced equation, we have

1.14 mol CuO ϫ

1 mol N2

ϭ 0.380 mol N2

3 mol CuO

Step 5 Using the molar mass of N2 (28.02), we can now calculate the mass

of N2 produced.

0.380 mol N2 ϫ

28.02 g N2

ϭ 10.6 g N2

1 mol N2

9.6 Percent Yield

Self-Check

273

EXERCISE 9.6 Lithium nitride, an ionic compound containing the Liϩ and N3Ϫ ions, is

prepared by the reaction of lithium metal and nitrogen gas. Calculate the

mass of lithium nitride formed from 56.0 g of nitrogen gas and 56.0 g of

lithium in the unbalanced reaction

Li(s) ϩ N2(g) → Li3N(s)

See Problems 9.51 through 9.54. ■

9.6 Percent Yield

OBJECTIVE:

Percent yield is important as an

indicator of the efficiency of a

particular reaction.

To learn to calculate actual yield as a percentage of theoretical yield.

In the previous section we learned how to calculate the amount of products formed when specified amounts of reactants are mixed together. In doing these calculations, we used the fact that the amount of product is controlled by the limiting reactant. Products stop forming when one reactant

runs out.

The amount of product calculated in this way is called the theoretical yield of that product. It is the amount of product predicted from the

amounts of reactants used. For instance, in Example 9.8, 10.6 g of nitrogen

represents the theoretical yield. This is the maximum amount of nitrogen

that can be produced from the quantities of reactants used. Actually, however, the amount of product predicted (the theoretical yield) is seldom obtained. One reason for this is the presence of side reactions (other reactions

that consume one or more of the reactants or products).

The actual yield of product, which is the amount of product actually

obtained, is often compared to the theoretical yield. This comparison, usually expressed as a percentage, is called the percent yield.

Actual yield

ϫ 100% ϭ percent yield

Theoretical yield

For example, if the reaction considered in Example 9.8 actually gave 6.63 g

of nitrogen instead of the predicted 10.6 g, the percent yield of nitrogen

would be

6.63 g N2

ϫ 100% ϭ 62.5%

10.6 g N2

EXAMPLE 9.9

Stoichiometric Calculations: Determining Percent Yield

In Section 9.1, we saw that methanol can be produced by the reaction between carbon monoxide and hydrogen. Let’s consider this process again.

Suppose 68.5 kg (6.85 ϫ 104 g) of CO(g) is reacted with 8.60 kg (8.60 ϫ

103 g) of H2(g).

a. Calculate the theoretical yield of methanol.

b. If 3.57 ϫ 104 g of CH3OH is actually produced, what is the percent

yield of methanol?

SOLUTION (a)

Where Are We Going?

We want to determine the theoretical yield of methanol and the percent

yield given an actual yield.

274 Chapter 9 Chemical Quantities

What Do We Know?

• From Section 9.1 we know the balanced equation is

2H2 ϩ CO S CH3OH

• We start with 6.85 ϫ 104 g of CO and 8.60 ϫ 103 g of H2.

• We can obtain the atomic masses from the periodic table.

What Do We Need To Know?

• We need the molar masses of H2, CO, and CH3OH.

• We need to determine the limiting reactant.

How Do We Get There?

Step 1 The balanced equation is

2H2(g) ϩ CO(g) → CH3OH(l)

Step 2 Next we calculate the moles of reactants.

1 mol CO

ϭ 2.45 ϫ 103 mol CO

28.01 g CO

1 mol H2

8.60 ϫ 103 g H2 ϫ

ϭ 4.27 ϫ 103 mol H2

2.016 g H2

6.85 ϫ 104 g CO ϫ

Step 3 Now we determine which reactant is limiting. Using the mole ratio between CO and H2 from the balanced equation, we have

2.45 ϫ 103 mol CO ϫ

2 mol H2

ϭ 4.90 ϫ 103 mol H2

1 mol CO

Moles of H2

present

less

than

4.27 ϫ 103

Moles of H2

needed to

react with

all the CO

4.90 ϫ 103

We see that 2.45 ϫ 103 mol CO requires 4.90 ϫ 103 mol H2. Because only

4.27 ϫ 103 mol H2 is actually present, H2 is limiting.

Step 4 We must therefore use the amount of H2 and the mole ratio between H2 and CH3OH to determine the maximum amount of methanol that

can be produced in the reaction.

4.27 ϫ 103 mol H2 ϫ

1 mol CH3OH

ϭ 2.14 ϫ 103 mol CH3OH

2 mol H2

This represents the theoretical yield in moles.

Step 5 Using the molar mass of CH3OH (32.04 g), we can calculate the

theoretical yield in grams.

2.14 ϫ 103 mol CH3OH ϫ

32.04 g CH3OH

ϭ 6.86 ϫ 104 g CH3OH

1 mol CH3OH

So, from the amounts of reactants given, the maximum amount of CH3OH

that can be formed is 6.86 ϫ 104 g. This is the theoretical yield.

SOLUTION (b)

The percent yield is

Actual yield (grams)

Theoretical yield (grams)

ϫ 100% ϭ

3.57 ϫ 104 g CH3OH

6.86 ϫ 104 g CH3OH

ϫ 100% ϭ 52.0%

Chapter Review

Self-Check

275

EXERCISE 9.7 Titanium(IV) oxide is a white compound used as a coloring pigment. In

fact, the page you are now reading is white because of the presence of this

compound in the paper. Solid titanium(IV) oxide can be prepared by reacting gaseous titanium(IV) chloride with oxygen gas. A second product of

this reaction is chlorine gas.

TiCl4(g) ϩ O2(g) → TiO2(s) ϩ Cl2(g)

a. Suppose 6.71 ϫ 103 g of titanium(IV) chloride is reacted with

2.45 ϫ 103 g of oxygen. Calculate the maximum mass of

titanium(IV) oxide that can form.

b. If the percent yield of TiO2 is 75%, what mass is actually formed?

See Problems 9.63 and 9.64. ■

C H A P T E R

9

REVIEW

F

Key Terms

mole ratio (9.2)

stoichiometry (9.3)

limiting reactant

(limiting reagent) (9.4)

theoretical yield (9.6)

percent yield (9.6)

VP

directs you to the Chemistry in Focus feature in the chapter

indicates visual problems

interactive versions of these problems are assignable in OWL.

Summary

1. A balanced equation relates the numbers of molecules of reactants and products. It can also be expressed in terms of the numbers of moles of reactants and products.

2. The process of using a chemical equation to calculate the relative amounts of reactants and products

involved in the reaction is called doing stoichiometric calculations. To convert between moles of reactants and moles of products, we use mole ratios derived from the balanced equation.

3. Often reactants are not mixed in stoichiometric

quantities (they do not “run out” at the same time).

In that case, we must use the limiting reactant to calculate the amounts of products formed.

4. The actual yield of a reaction is usually less than its

theoretical yield. The actual yield is often expressed

as a percentage of the theoretical yield, which is

called the percent yield.

Active Learning Questions

These questions are designed to be considered by groups

of students in class. Often these questions work well for

introducing a particular topic in class.

1. Relate Active Learning Question 2 from Chapter 2 to

the concepts of chemical stoichiometry.

2. You are making cookies and are missing a key ingredient—eggs. You have plenty of the other ingredients, except that you have only 1.33 cups of butter

and no eggs. You note that the recipe calls for 2 cups

of butter and 3 eggs (plus the other ingredients) to

make 6 dozen cookies. You telephone a friend and

have him bring you some eggs.

a. How many eggs do you need?

b. If you use all the butter (and get enough eggs),

how many cookies can you make?

Unfortunately, your friend hangs up before you tell

him how many eggs you need. When he arrives, he

has a surprise for you—to save time he has broken

the eggs in a bowl for you. You ask him how many

he brought, and he replies, “All of them, but I spilled

some on the way over.” You weigh the eggs and find

that they weigh 62.1 g. Assuming that an average egg

weighs 34.21 g:

c. How much butter is needed to react with all the

eggs?

d. How many cookies can you make?

e. Which will you have left over, eggs or butter?

f. How much is left over?

g. Relate this question to the concepts of chemical

stoichiometry.

276 Chapter 9 Chemical Quantities

VP 3. Nitrogen (N2) and hydrogen (H2) react to form

ammonia (NH3). Consider the mixture of N2 (

)

and H2 (

) in a closed container as illustrated

below:

d. B is the limiting reactant because three A molecules react with every one B molecule.

e. Neither reactant is limiting.

For choices you did not pick, explain what you feel is

wrong with them, and justify the choice you did pick.

9. What happens to the weight of an iron bar when it

rusts?

Assuming the reaction goes to completion, draw a

representation of the product mixture. Explain how

you arrived at this representation.

4. Which of the following equations best represents the

reaction for Question 3?

a.

b.

c.

d.

e.

6N2 ϩ 6H2 S 4NH3 ϩ 4N2

N2 ϩ H2 S NH3

N ϩ 3H S NH3

N2 ϩ 3H2 S 2NH3

2N2 ϩ 6H2 S 4NH3

For choices you did not pick, explain what you feel is

wrong with them, and justify the choice you did pick.

a. There is no change because mass is always conserved.

b. The weight increases.

c. The weight increases, but if the rust is scraped off,

the bar has the original weight.

d. The weight decreases.

Justify your choice and, for choices you did not pick,

explain what is wrong with them. Explain what it

means for something to rust.

10. Consider the equation 2A ϩ B S A2B. If you mix

1.0 mole of A and 1.0 mole of B, how many moles

of A2B can be produced?

11. What is meant by the term mole ratio? Give an example of a mole ratio, and explain how it is used in

solving a stoichiometry problem.

5. You know that chemical A reacts with chemical B.

You react 10.0 g A with 10.0 g B. What information

do you need to know to determine the amount of

product that will be produced? Explain.

12. Which would produce a greater number of moles of

product: a given amount of hydrogen gas reacting

with an excess of oxygen gas to produce water, or

the same amount of hydrogen gas reacting with an

excess of nitrogen gas to make ammonia? Support

6. If 10.0 g of hydrogen gas is reacted with 10.0 g of

oxygen gas according to the equation

13. Consider a reaction represented by the following balanced equation

2H2 ϩ O2 S 2H2O

2A ϩ 3B S C ϩ 4D

we should not expect to form 20.0 g of water. Why

not? What mass of water can be produced with a

complete reaction?

You find that it requires equal masses of A and B so

that there are no reactants left over. Which of the

following is true? Justify your choice.

7. The limiting reactant in a reaction:

a. has the lowest coefficient in a balanced equation.

b. is the reactant for which you have the fewest number of moles.

c. has the lowest ratio: moles available/coefficient in

the balanced equation.

d. has the lowest ratio: coefficient in the balanced

equation/moles available.

d. None of the above.

For choices you did not pick, explain what you feel is

wrong with them, and justify the choice you did pick.

8. Given the equation 3A ϩ B S C ϩ D, if 4 moles of A

is reacted with 2 moles of B, which of the following

is true?

a. The limiting reactant is the one with the higher

molar mass.

b. A is the limiting reactant because you need 6

moles of A and have 4 moles.

c. B is the limiting reactant because you have fewer

moles of B than moles of A.

a. The molar mass of A must be greater than the

molar mass of B.

b. The molar mass of A must be less than the molar

mass of B.

c. The molar mass of A must be the same as the

molar mass of B.

14. Consider a chemical equation with two reactants

forming one product. If you know the mass of each

reactant, what else do you need to know to determine the mass of the product? Why isn’t the mass

necessarily the sum of the mass of the reactants? Provide a real example of such a reaction, and support

15. Consider the balanced chemical equation

A ϩ 5B S 3C ϩ 4D

When equal masses of A and B are reacted, which is

limiting, A or B? Justify your choice.

a. If the molar mass of A is greater than the molar

mass of B, then A must be limiting.

Chapter Review

Mass of NaCl (g)

b. If the molar mass of A is less than the molar mass

of B, then A must be limiting.

c. If the molar mass of A is greater than the molar

mass of B, then B must be limiting.

d. If the molar mass of A is less than the molar mass

of B, then B must be limiting.

277

16. Which of the following reaction mixtures would produce the greatest amount of product, assuming all

went to completion? Justify your choice.

Each involves the reaction symbolized by the equation

2H2 ϩ O2 S 2H2O

a.

b.

c.

d.

e.

2 moles of H2 and 2 moles of O2.

2 moles of H2 and 3 moles of O2.

2 moles of H2 and 1 mole of O2.

3 moles of H2 and 1 mole of O2.

Each would produce the same amount of product.

17. Baking powder is a mixture of cream of tartar

(KHC4H4O6) and baking soda (NaHCO3). When it is

placed in an oven at typical baking temperatures (as

part of a cake, for example), it undergoes the following reaction (CO2 makes the cake rise):

0

20

40

60

80

Mass of Sodium (g)

a. Explain the shape of the graph.

b. Calculate the mass of NaCl formed when 20.0 g

of sodium is used.

c. Calculate the mass of Cl2 in each container.

d. Calculate the mass of NaCl formed when 50.0 g

of sodium is used.

e. Identify the leftover reactant and determine its

mass for parts b and d above.

KHC4H4O6(s) ϩ NaHCO3(s) S

KNaC4H4O6(s) ϩ H2O(g) ϩ CO2(g) VP 19. You have a chemical in a sealed glass container filled

with air. The setup is sitting on a balance as shown

You decide to make a cake one day, and the recipe

below. The chemical is ignited by means of a magcalls for baking powder. Unfortunately, you have no

nifying glass focusing sunlight on the reactant. After

baking powder. You do have cream of tartar and bakthe chemical has completely burned, which of the

ing soda, so you use stoichiometry to figure out how

much of each to mix.

Of the following choices, which is the best way to

make baking powder? The amounts given in the

choices are in teaspoons (that is, you will use a teaspoon to measure the baking soda and cream of tartar). Justify your choice.

Assume a teaspoon of cream of tartar has the same

mass as a teaspoon of baking soda.

a. Add equal amounts of baking soda and cream of

tartar.

b. Add a bit more than twice as much cream of tartar as baking soda.

c. Add a bit more than twice as much baking soda

as cream of tartar.

d. Add more cream of tartar than baking soda, but VP 20.

not quite twice as much.

e. Add more baking soda than cream of tartar, but

not quite twice as much.

250.0g

a.

b.

c.

d.

Consider an iron bar on a balance as shown.

75.0g

VP 18. You have seven closed containers each with equal

masses of chlorine gas (Cl2). You add 10.0 g of sodium

to the first sample, 20.0 g of sodium to the second

sample, and so on (adding 70.0 g of sodium to the

seventh sample). Sodium and chloride react to form

sodium chloride according to the equation

2Na(s) ϩ Cl2(g) S 2NaCl(s)

After each reaction is complete, you collect and measure the amount of sodium chloride formed. A graph

of your results is shown below.

The balance will read less than 250.0 g.

The balance will read 250.0 g.

The balance will read greater than 250.0 g.

Cannot be determined without knowing the identity of the chemical.

As the iron bar rusts, which of the following is true?

a.

b.

c.

d.

The balance will read less than 75.0 g.

The balance will read 75.0 g.

The balance will read greater than 75.0 g.

The balance will read greater than 75.0 g, but if

the bar is removed, the rust scraped off, and the

bar replaced, the balance will read 75.0 g.

278 Chapter 9 Chemical Quantities

VP 21. Consider the reaction between NO(g) and O2(g) represented below.

9.2 Mole–Mole Relationships

QUESTIONS

7. Consider the reaction represented by the chemical

equation

KOH(s) ϩ SO2(g) S KHSO3(s)

Since the coefficients of the balanced chemical equation are all equal to 1, we know that exactly 1 g of

KOH will react with exactly 1 g of SO2. True or false?

Explain.

O2

NO

8. For the balanced chemical equation for the decomposition of hydrogen peroxide

NO2

2H2O2(aq) S 2H2O(l) ϩ O2(g)

What is the balanced equation for this reaction, and

what is the limiting reactant?

explain why we know that decomposition of 2 g of

hydrogen peroxide will not result in the production

of 2 g of water and 1 g of oxygen gas.

9. Consider the balanced chemical equation

4Al(s) ϩ 3O2(g) S 2Al2O3(s).

Questions and Problems

9.1 Information Given by Chemical Equations

QUESTIONS

1. What do the coefficients of a balanced chemical equation tell us about the proportions in which atoms and

molecules react on an individual (microscopic) basis?

2. What do the coefficients of a balanced chemical

equation tell us about the proportions in which substances react on a macroscopic (mole) basis?

3. Although mass is a property of matter we can conveniently measure in the laboratory, the coefficients

of a balanced chemical equation are not directly interpreted on the basis of mass. Explain why.

4. For the balanced chemical equation H2 ϩ Br2 S 2HBr,

explain why we do not expect to produce 2 g of HBr

if 1 g of H2 is reacted with 1 g of Br2.

PROBLEMS

5. For each of the following reactions, give the balanced

equation for the reaction and state the meaning of

the equation in terms of the numbers of individual

molecules and in terms of moles of molecules.

a.

b.

c.

d.

PCl3(l) ϩ H2O(l) S H3PO3(aq) ϩ ⌯Cl(g)

XeF2(g) ϩ H2O(l) S Xe(g) ϩ HF(g) ϩ O2(g)

S(s) ϩ HNO3(aq) S H2SO4(aq) ϩ H2O(l) ϩ NO2(g)

NaHSO3(s) S Na2SO3(s) ϩ SO2(g) ϩ H2O(l)

6. For each of the following reactions, balance the

chemical equation and state the stoichiometric meaning of the equation in terms of the numbers of individual molecules reacting and in terms of moles of molecules reacting.

a.

b.

c.

d.

(NH4)2CO3(s) S NH3(g) ϩ CO2(g) ϩ H2O(g)

Mg(s) ϩ P4(s) S Mg3P2(s)

Si(s) ϩ S8(s) S Si2S4(l)

C2H5OH(l) ϩ O2(g) S CO2(g) ϩ H2O(g)

What mole ratio would you use to calculate how

many moles of oxygen gas would be needed to react

completely with a given number of moles of aluminum metal? What mole ratio would you use to

calculate the number of moles of product that would

be expected if a given number of moles of aluminum

metal reacts completely?

10. Consider the balanced chemical equation

Fe2O3(s) ϩ 3H2SO4(aq) S Fe2(SO4)3(s) ϩ 3H2O(l).

What mole ratio would you use to calculate the number of moles of sulfuric acid needed to react completely with a given number of moles of iron(III) oxide? What mole ratios would you use to calculate the

number of moles of each product that would be produced if a given number of moles of Fe2O3(s) reacts

completely?

PROBLEMS

11. For each of the following balanced chemical equations, calculate how many moles of product(s) would

be produced if 0.500 mole of the first reactant were

to react completely.

a.

b.

c.

d.

CO2(g) ϩ 4H2(g) S CH4(g) ϩ 2H2O(l)

BaCl2(aq) ϩ 2AgNO3(aq) S 2AgCl(s) ϩ Ba(NO3)2(aq)

C3H8(g) ϩ 5O2(g) S 4H2O(l) ϩ 3CO2(g)

3H2SO4(aq) ϩ 2Fe(s) S Fe2(SO4)3(aq) ϩ 3H2(g)

12. For each of the following balanced chemical equations, calculate how many moles of product(s) would

be produced if 0.250 mole of the first reactant were

to react completely.

a.

b.

c.

d.

4Bi(s) ϩ 3O2(g) S 2Bi2O3(s)

SnO2(s) ϩ 2H2(g) S Sn(s) ϩ 2H2O(g)

SiCl4(l) ϩ 2H2O(l) S SiO2(s) ϩ 4HCl(g)

2N2(g) ϩ 5O2(g) ϩ 2H2O(l) S 4HNO3(aq)

13. For each of the following balanced chemical equations, calculate how many grams of the product(s)

All even-numbered Questions and Problems have answers in the back of this book and solutions in the Solutions Guide.

Chapter Review

would be produced by complete reaction of 0.125

mole of the first reactant.

a. AgNO3(aq) ϩ LiOH(aq) S AgOH(s) ϩ LiNO3(aq)

b. Al2(SO4)3(aq) ϩ 3CaCl2(aq) S

2AlCl3(aq) ϩ 3CaSO4(s)

c. CaCO3(s) ϩ 2HCl(aq) S

CaCl2(aq) ϩ CO2(g) ϩ H2O(l)

d. 2C4H10(g) ϩ 13O2(g) S 8CO2(g) ϩ 10H2O(g)

14. For each of the following balanced chemical equations, calculate how many grams of the product(s)

would be produced by complete reaction of 0.750

mole of the first (or only) reactant.

a.

b.

c.

d.

C5H12(l) ϩ 8O2(g) S 5CO2(g) ϩ 6H2O(l)

2CH3OH(l) ϩ 3O2(g) S 4H2O(l) ϩ 2CO2(g)

Ba(OH)2(aq) ϩ H3PO4(aq) S BaHPO4(s) ϩ 2H2O(l)

C6H12O6(aq) S 2C2H5OH(aq) ϩ 2CO2(g)

15. For each of the following unbalanced equations, indicate how many moles of the second reactant would

be required to react exactly with 0.275 mol of the first

reactant. State clearly the mole ratio used for the conversion.

a.

b.

c.

d.

Cl2(g) ϩ KI(aq) S I2(s) ϩ KCl(aq)

Co(s) ϩ P4(s) S Co3P2(s)

Zn(s) ϩ HNO3(aq) S ZnNO3(aq) ϩ H2(g)

C5H12(l) ϩ O2(g) S CO2(g) ϩ H2O(g)

16. For each of the following unbalanced equations, indicate how many moles of the first product are produced if 0.625 mole of the second product forms. State

clearly the mole ratio used for each conversion.

a.

b.

c.

d.

KO2(s) ϩ H2O(l) S O2(g) ϩ KOH(s)

SeO2(g) ϩ H2Se(g) S Se(s) ϩ H2O(g)

CH3CH2OH(l) ϩ O2(g) S CH3CHO(aq) ϩ H2O(l)

Fe2O3(s) ϩ Al(s) S Fe(l) ϩ Al2O3(s)

9.3 Mass Calculations

QUESTIONS

17. What quantity serves as the conversion factor between the mass of a sample and how many moles

the sample contains?

18. What does it mean to say that the balanced chemical equation for a reaction describes the stoichiometry of the reaction?

PROBLEMS

19. Using the average atomic masses given inside the

front cover of this book, calculate how many moles

of each substance the following masses represent.

a.

b.

c.

d.

e.

4.15 g of silicon, Si

2.72 mg of gold(III) chloride, AuCl3

1.05 kg of sulfur, S

0.000901 g of iron(III) chloride, FeCl3

5.62 ϫ 103 g of magnesium oxide, MgO

20. Using the average atomic masses given inside the

front cover of this book, calculate how many moles

of each substance the following masses represent.

a.

b.

c.

d.

e.

279

72.4 mg of argon, Ar

52.7 g of carbon disulfide, CS2

784 kg of iron, Fe

0.00104 g of calcium chloride, CaCl2

1.26 ϫ 103 g of nickel(II) sulfide, NiS

21. Using the average atomic masses given inside the

front cover of this book, calculate the mass in grams

of each of the following samples.

a. 2.17 moles of germanium, Ge

b. 4.24 mmol of lead(II) chloride (1 mmol ϭ 1/1000

mol)

c. 0.0971 mole of ammonia, NH3

d. 4.26 ϫ 103 moles of hexane, C6H14

e. 1.71 moles of iodine monochloride, ICl

22. Using the average atomic masses given inside the

front cover of this book, calculate the mass in grams

of each of the following samples.

a.

b.

c.

d.

e.

2.23 moles of propane, C3H8

9.03 mmol of argon, Ar (1 mmol ϭ 1/1000 mol)

5.91 ϫ 106 moles of silicon dioxide, SiO2

0.000104 mole of copper(II) chloride, CuCl2

0.000104 mole of copper(I) chloride, CuCl

23. For each of the following unbalanced equations, calculate how many moles of the second reactant would

be required to react completely with 0.413 moles of

the first reactant.

a.

b.

c.

d.

Co(s) ϩ F2(g) S CoF3(s)

Al(s) ϩ H2SO4(aq) S Al2(SO4)3(aq) ϩ H2(g)

K(s) ϩ H2O(l) S KOH(aq) ϩ H2(g)

Cu(s) ϩ O2(g) S Cu2O(s)

24. For each of the following unbalanced equations, calculate how many moles of the second reactant would

be required to react completely with 0.557 grams of

the first reactant.

a.

b.

c.

d.

Al(s) ϩ Br2(l) S AlBr3(s)

Hg(s) ϩ HClO4(aq) S Hg(ClO4)2(aq) ϩ H2(g)

K(s) ϩ P(s) S K3P(s)

CH4(g) ϩ Cl2(g) S CCl4(l) ϩ HCl(g)

25. For each of the following unbalanced equations, calculate how many grams of each product would be produced by complete reaction of 12.5 g of the reactant

indicated in boldface. Indicate clearly the mole ratio

used for the conversion.

a.

b.

c.

d.

TiBr4(g) ϩ H2(g) S Ti(s) ϩ HBr(g)

SiH4(g) ϩ NH3(g) S Si3N4(s) ϩ H2(g)

NO(g) ϩ H2(g) S N2(g) ϩ 2H2O(l)

Cu2S(s) S Cu(s) ϩ S(g)

26. For each of the following balanced equations, calculate how many grams of each product would be produced by complete reaction of 15.0 g of the reactant

indicated in boldface.

a.

b.

c.

d.

2BCl3(s) ϩ 3H2(g) S 2B(s) ϩ 6HCl(g)

2Cu2S(s) ϩ 3O2(g) S 2Cu2O(s) ϩ 2SO2(g)

2Cu2O(s) ϩ Cu2S(s) S 6Cu(s) ϩ SO2(g)

CaCO3(s) ϩ SiO2(s) S CaSiO3(s) ϩ CO2(g)

All even-numbered Questions and Problems have answers in the back of this book and solutions in the Solutions Guide.

280 Chapter 9 Chemical Quantities

27. “Smelling salts,” which are used to revive someone

who has fainted, typically contain ammonium carbonate, (NH4)2CO3. Ammonium carbonate decomposes readily to form ammonia, carbon dioxide, and

water. The strong odor of the ammonia usually restores consciousness in the person who has fainted.

The unbalanced equation is

(NH4)2CO3(s) S NH3(g) ϩ CO2(g) ϩ H2O(g)

Calculate the mass of ammonia gas that is produced

if 1.25 g of ammonium carbonate decomposes completely.

28. Calcium carbide, CaC2, can be produced in an electric furnace by strongly heating calcium oxide (lime)

with carbon. The unbalanced equation is

CaO(s) ϩ C(s) S CaC2(s) ϩ CO(g)

Calcium carbide is useful because it reacts readily

with water to form the flammable gas acetylene,

C2H2, which is used extensively in the welding industry. The unbalanced equation is

CaC2(s) ϩ H2O(l) S C2H2(g) ϩ Ca(OH)2(s)

What mass of acetylene gas, C2H2, would be produced

by complete reaction of 3.75 g of calcium carbide?

29. When elemental carbon is burned in the open atmosphere, with plenty of oxygen gas present, the product is carbon dioxide.

This is the reaction by which wines are produced

from grape juice. Calculate the mass of ethyl alcohol, C2H5OH, produced when 5.25 g of glucose,

C6H12O6, undergoes this reaction.

33. Sulfurous acid is unstable in aqueous solution and

gradually decomposes to water and sulfur dioxide gas

(which explains the choking odor associated with

sulfurous acid solutions).

H2SO3(aq) S H2O(l) ϩ SO2(g)

If 4.25 g of sulfurous acid undergoes this reaction,

what mass of sulfur dioxide is released?

34. Small quantities of ammonia gas can be generated in

the laboratory by heating an ammonium salt with a

strong base. For example, ammonium chloride reacts

with sodium hydroxide according to the following

balanced equation:

NH4Cl(s) ϩ NaOH(s) S NH3(g) ϩ NaCl(s) ϩ H2O(g)

What mass of ammonia gas is produced if 1.39 g of

ammonium chloride reacts completely?

35. Elemental phosphorus burns in oxygen with an intensely hot flame, producing a brilliant light and

clouds of the oxide product. These properties of the

combustion of phosphorus have led to its being used

in bombs and incendiary devices for warfare.

C(s) ϩ O2(g) S CO2(g)

P4(s) ϩ 5O2(g) S 2P2O5(s)

However, when the amount of oxygen present during the burning of the carbon is restricted, carbon

monoxide is more likely to result.

If 4.95 g of phosphorus is burned, what mass of oxygen does it combine with?

2C(s) ϩ O2(g) S 2CO(g)

What mass of each product is expected when a 5.00-g

sample of pure carbon is burned under each of these

conditions?

30. If baking soda (sodium hydrogen carbonate) is

heated strongly, the following reaction occurs:

36. Although we tend to make less use of mercury these

days because of the environmental problems created

by its improper disposal, mercury is still an important metal because of its unusual property of existing as a liquid at room temperature. One process by

which mercury is produced industrially is through

the heating of its common ore cinnabar (mercuric

sulfide, HgS) with lime (calcium oxide, CaO).

2NaHCO3(s) S Na2CO3(s) ϩ H2O(g) ϩ CO2(g)

4HgS(s) ϩ 4CaO(s) S 4Hg(l) ϩ 3CaS(s) ϩ CaSO4(s)

Calculate the mass of sodium carbonate that will remain if a 1.52-g sample of sodium hydrogen carbonate is heated.

What mass of mercury would be produced by complete reaction of 10.0 kg of HgS?

31. Although we usually think of substances as “burning”

only in oxygen gas, the process of rapid oxidation to

produce a flame may also take place in other strongly

oxidizing gases. For example, when iron is heated and

placed in pure chlorine gas, the iron “burns” according to the following (unbalanced) reaction:

Fe(s) ϩ Cl2(g) S FeCl3(s)

How many milligrams of iron(III) chloride result

when 15.5 mg of iron is reacted with an excess of

chlorine gas?

32. When yeast is added to a solution of glucose or fructose, the sugars are said to undergo fermentation and

ethyl alcohol is produced.

C6H12O6(aq) S 2C2H5OH(aq) ϩ 2CO2(g)

37. Ammonium nitrate has been used as a high explosive because it is unstable and decomposes into several gaseous substances. The rapid expansion of the

gaseous substances produces the explosive force.

NH4NO3(s) S N2(g) ϩ O2(g) ϩ H2O(g)

Calculate the mass of each product gas if 1.25 g of

ammonium nitrate reacts.

38. If common sugars are heated too strongly, they char

as they decompose into carbon and water vapor. For

example, if sucrose (table sugar) is heated, the reaction is

C12H22O11(s) S 12C(s) ϩ 11H2O(g)

What mass of carbon is produced if 1.19 g of sucrose

decomposes completely?

All even-numbered Questions and Problems have answers in the back of this book and solutions in the Solutions Guide.

Chapter Review

39. Thionyl chloride, SOCl2, is used as a very powerful

drying agent in many synthetic chemistry experiments in which the presence of even small amounts

of water would be detrimental. The unbalanced

chemical equation is

SOCl2(l) ϩ H2O(l) S SO2(g) ϩ HCl(g)

Calculate the mass of water consumed by complete

reaction of 35.0 g of SOCl2.

F

40. In the “Chemistry in Focus” segment Cars of the Future, the claim is made that the combustion of gasoline for some cars causes about 1 lb of CO2 to be produced for each mile traveled.

Estimate the gas mileage of a car that produces about

1 lb of CO2 per mile traveled. Assume gasoline has a

density of 0.75 g/mL and is 100% octane (C8H18).

While this last part is not true, it is close enough for

an estimation. The reaction can be represented by

the following unbalanced chemical equation:

C8H18 ϩ O2 S CO2 ϩ H2O

9.5 Calculations Involving a Limiting Reactant

QUESTIONS

41. Imagine you are chatting with a friend who has not

yet taken a chemistry course. How would you explain

the concept of limiting reactant to her? Your textbook

uses the analogy of an automobile manufacturer ordering four wheels for each engine ordered as an example. Can you think of another analogy that might

42. Explain how one determines which reactant in a

process is the limiting reactant. Does this depend

only on the masses of the reactant present? Is the

mole ratio in which the reactants combine involved?

43. What is the theoretical yield for a reaction, and how

does this quantity depend on the limiting reactant?

44. What does it mean to say a reactant is present “in

excess” in a process? Can the limiting reactant be present in excess? Does the presence of an excess of a

reactant affect the mass of products expected for a

reaction?

PROBLEMS

45. For each of the following unbalanced reactions, suppose exactly 5.00 g of each reactant is taken. Determine which reactant is limiting, and also determine

what mass of the excess reagent will remain after the

limiting reactant is consumed.

a. Na2B4O7(s) ϩ H2SO4(aq) ϩ H2O(l) S

H3BO3(s) ϩ Na2SO4(aq)

b. CaC2(s) ϩ H2O(l) S Ca(OH)2(s) ϩ C2H2(g)

c. NaCl(s) ϩ H2SO4(l) S HCl(g) ϩ Na2SO4(s)

d. SiO2(s) ϩ C(s) S Si(l) ϩ CO(g)

46. For each of the following unbalanced chemical equations, suppose that exactly 5.00 g of each reactant

281

is taken. Determine which reactant is limiting, and

calculate what mass of each product is expected

(assuming that the limiting reactant is completely

consumed).

a.

b.

c.

d.

S(s) ϩ H2SO4(aq) S SO2(g) ϩ H2O(l)

MnO2(s) ϩ H2SO4(l) S Mn(SO4)2(s) ϩ H2O(l)

H2S(g) ϩ O2(g) S SO2(g) ϩ H2O(l)

AgNO3(aq) ϩ Al(s) S Ag(s) ϩ Al(NO3)3(aq)

47. For each of the following unbalanced chemical equations, suppose 10.0 g of each reactant is taken. Show

by calculation which reactant is the limiting reagent.

Calculate the mass of each product that is expected.

a.

b.

c.

d.

C3H8(g) ϩ O2(g) S CO2(g) ϩ H2O(g)

Al(s) ϩ Cl2(g) S AlCl3(s)

NaOH(s) ϩ CO2(g) S Na2CO3(s) ϩ H2O(l)

NaHCO3(s) ϩ HCl(aq) S

NaCl(aq) ϩ H2O(l) ϩ CO2(g)

48. For each of the following unbalanced chemical equations, suppose that exactly 1.00 g of each reactant is

taken. Determine which reactant is limiting, and calculate what mass of the product in boldface is expected (assuming that the limiting reactant is completely consumed).

a.

b.

c.

d.

CS2(l) ϩ O2(g) S CO2(g) ϩ SO2(g)

NH3(g) ϩ CO2(g) S CN2H4O(s) ϩ H2O(g)

H2(g) ϩ MnO2(s) S MnO(s) ϩ H2O(g)

I2(l) ϩ Cl2(g) S ICl(g)

49. For each of the following unbalanced chemical equations, suppose 1.00 g of each reactant is taken. Show

by calculation which reactant is limiting. Calculate

the mass of each product that is expected.

a.

b.

c.

d.

UO2(s) ϩ HF(aq) S UF4(aq) ϩ H2O(l)

NaNO3(aq) ϩ H2SO4(aq) S Na2SO4(aq) ϩ HNO3(aq)

Zn(s) ϩ HCl(aq) S ZnCl2(aq) ϩ H2(g)

B(OH)3(s) ϩ CH3OH(l) S B(OCH3)3(s) ϩ H2O(l)

50. For each of the following unbalanced chemical equations, suppose 10.0 mg of each reactant is taken.

Show by calculation which reactant is limiting. Calculate the mass of each product that is expected.

a.

b.

c.

d.

CO(g) ϩ H2(g) S CH3OH(l)

Al(s) ϩ I2(s) S AlI3(s)

Ca(OH)2(aq) ϩ HBr(aq) S CaBr2(aq) ϩ H2O(l)

Cr(s) ϩ H3PO4(aq) S CrPO4(s) ϩ H2(g)

51. Lead(II) carbonate, also called “white lead,” was formerly used as a pigment in white paints. However,

because of its toxicity, lead can no longer be used in

paints intended for residential homes. Lead(II) carbonate is prepared industrially by reaction of aqueous lead(II) acetate with carbon dioxide gas. The unbalanced equation is

Pb(C2H3O2)2(aq) ϩ H2O(l) ϩ CO2(g) S

PbCO3(s) ϩ HC2H3O2(aq)

Suppose an aqueous solution containing 1.25 g of

lead(II) acetate is treated with 5.95 g of carbon dioxide. Calculate the theoretical yield of lead carbonate.

All even-numbered Questions and Problems have answers in the back of this book and solutions in the Solutions Guide.

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