SECTION 9.

Ideal Stoichiometric
Calculations
Teacher Notes and Answers
SECTION 2 Ideal Stoichiometric
Calculations
1. All reactants are completely converted into
products.
2. This procedure is the same as the procedure
given for finding the mass of an unknown
substance, in the chapter “Stoichiometry,” in
reverse.

Practice
A. 2KCl​O3​ ​(aq) ⟶ 2KCl(aq) + ​3O​2​(g);
10. mol KCl​O​3​
B. 3​H2​ ​(g) + ​N2​ ​(g) ⟶ 2N​H3​ ​(g); 4 mol N​H3​ ​
C. 80.6 g MgO
1 mol ​O​ ​
D. molar mass of oxygen, ​ __________
2  ​;
32.00 g ​O2​ ​
6 mol ​H​2​O
mole ratio of oxygen to water, ​ __________  ​
6 mol ​O2​ ​
E. 2.6 kg Al; 72 mol O

Review
1. 4N​H3​ ​+ 3​O2​ ​⟶ 2​N2​ ​+ 6​H2​ ​O
1a. 3 mol ​O2​ ​; 2 mol ​N​2​; 6 mol ​H2​ ​O
1b. 6.0 mol N​H3​ ​; 3.0 mol ​N​2​; 9.0 mol ​H2​ ​O
2. 182 g HCl
3. 24.0 g C and 32.0 g ​O2​ ​; the law of conservation
of mass

Stoichiometry 1
SECTION 9.2

Ideal Stoichiometric
Calculations
Balanced chemical equations are important for s­ toichiometric
calculations. This is because the mole ratio can be directly
found from balanced chemical equations. With a chemical
equation, you can predict the relative amounts of the reactants
and products that are needed for or produced in the reaction.
READING CHECK
The chemical equation predicts what will happen for a
1. What happens in reactions that
reaction that takes place under ideal conditions. Under ideal take place under ideal conditions?
conditions, all the reactants are completely converted into
the products. Many real reactions proceed in a such a way
that not all reactants are converted to products. However,
stoichiometric calculations will tell you the maximum amount
of the products that can form for a given amount of reactants.

Balanced equations give amounts of reactants and

products under ideal conditions.

You are given the quantity in moles of one of the s­ ubstances

in a reaction. You must find the quantity in moles of another
substance in the reaction. The general plan is shown below.

amount of amount of
convert given into unknown
substance (mol) substance (mol)

This plan requires only one conversion factor—the mole TIP Use the coefficients in the
ratio of the unknown substance to the given substance. To chemical equation to figure
out the appropriate mole ratio
solve this problem, multiply the known amount by the conversion factors.
conversion factor to get the unknown amount.
Mole ratio
(Balanced equation)
Amount of Amount of
given mol unknown unknown
× =
substance mol given substance
(mol) (mol)
CONVERSION FACTOR
GIVEN IN CALCULATED
THE PROBLEM

2 CH A P TER 9
 SAMPLE PROBLEM
In a spacecraft, the carbon dioxide exhaled by astronauts can be
removed by its reaction with lithium hydroxide, LiOH, according to
the following chemical equation.
C​O2​ ​(g) + 2LiOH(s) → L​i2​ ​C​O3​ ​(s) + H
​ 2​ ​O(l)
How many moles of lithium hydroxide are required to react with
20 mol C​O2​ ​, the average amount exhaled by a person each day?

1 ANALYZE Determine the information that is given and unknown.

Given: amount of C​O2​ ​= 20 mol
Unknown: amount of LiOH in moles

2 PLAN Write an equation that can be used to find the unknown.

The mole ratio is obtained from the balanced chemical
equation. Because you are given moles of C​O2​ ​, select a
mole ratio that will cancel mol C​O2​ ​and give you
mol LiOH in your final answer. The correct ratio has the
following units.
​ mol LiOH ​
__________
mol C​O2​ ​
This ratio cancels mol C​O2​ ​and gives the units mol LiOH in
the answer.
​ mol LiOH ​= mol LiOH
mol C​O2​ ×​__________
mol C​O2​ ​

mole ratio

3 SOLVE Substitute the values in the equation and compute the answer.
​ 2 mol LiOH
20 mol C​O2​ = 20 mol C​O2​ ​× ___________    ​= 40 mol LiOH
1 mol C​O2​ ​

4 CHECK Check the answer to determine if it makes sense.

YOUR
The answer is written correctly with one significant figure
WORK
to match the number of significant figures in the given value
of 20 mol C​O2​ ​. The units correctly cancel to leave mol LiOH,
which is the unknown.The equation shows that twice the
amount of LiOH reacts with C​O2​ ​. Therefore, the answer
should be 2 × 20 = 40.

Stoichiometry 3
PRACTICE

A. The decomposition of potassium chlorate, KCl​O3​ ​, is used as

a source of oxygen in the laboratory. How many moles of ­
potassium chlorate are needed to produce 15 mol of oxygen gas?
Write the balanced equation for the decomposition reaction.
Refer to Section 2 of the chapter “Chemical Equations and
Reactions” for more information about decomposition reactions.

What is the given quantity?

What is the unknown quantity?

Use the chemical equation to find the appropriate mole ratio

and write the conversion equation.

Substitute numbers into the equation and calculate your answer.

B. Ammonia, NH​3, iswidely used as a fertilizer and in many

household cleaners. How many moles of ammonia are produced
when 6 mol of hydrogen gas react with an excess of nitrogen gas?
Write the balanced equation for the synthesis reaction.

Use the chemical equation to find the appropriate mole ratio

and write the conversion equation. Then substitute numbers into
the equation and calculate your answer.

4 CH A P TER 9
 Mole-to-gram calculations require two conversion factors.

You are asked to calculate the mass (usually in grams) of a

substance that will react with or be produced from a given
amount in moles of a second substance. The plan for these
mole-to-gram conversions is given below.

amount of amount of mass of

convert given into unknown into unknown
substance (mol) substance (mol) substance (g)

Two conversion factors are needed. The mole ratio of the

unknown substance to the given substance is needed, as is the
molar mass of the unknown substance.

Mole ratio Molar mass factor

(Balanced equation) (Periodic table)
Amount of Mass of
mol given
given × × Molar mass of unknown (in g) = unknown
substance mol unknown 1 mol unknown substance
(mol) (g)
CONVERSION FACTORS
GIVEN IN CALCULATED
THE PROBLEM

SAMPLE PROBLEM
In photosynthesis, plants use energy from the sun to produce
​ 6​ ​​H​12​​O​6​, and oxygen from the reaction of carbon
glucose, C
dioxide and water. What mass, in grams, of glucose is
­produced when 3.00 mol of water react with carbon dioxide?

SOLUTION

1 Analyze Determine the information that is given and unknown.

Given: amount of H
​ 2​ ​O = 3.00 mol
Unknown: mass of ​C6​ ​​H​12​​O​6​produced in grams

2 Plan Write an equation that can be used to find the unknown.

Two conversion factors are needed—the mass ratio of
glucose to water and the molar mass of glucose.

mol C
​ 6​ ​​H​12​​O​6​ g C​6​​H​12​​O​6​
​ 2​ ​O × ____________
mol H ​      ​  × ___
​    ​  = g ​C6​ ​​H​12​​O​6​
mol H​ 2​ ​O mol C​6​​H​12​​O​6

molar mass
mole ratio
factor

Stoichiometry 5
3 SOLVE Substitute the values in the equation and compute the answer.
First, write the balanced equation for the reaction.
6C​O2​ ​(g) + 6​H2​ ​O(l) → C
​ 6​ ​​H​12​​O​6​(s) + 6​O2​ ​(g)
Then, compute the molar mass of C
​ 6​ ​​H​12​​O​6​.
g/mol C​ 6​ ​​H​12​​O​6​
= 6(12.01 g/mol C) + 12(1.01 g/mol H) + 6 (16.00 g/mol O)
= 180.18 g/mol
Finally, use both conversion factors to find the answer.
180.19 g ​C6​ ​​H​12​​O​6​
​ 6​ ​​H​12​​O​6​ ____
1 mol C
3.00 mol ​H2​ ​O × ______________
​    
    ​ × ​    
   ​ ​6​​H​12​​O​6​
 ​ = 90.1 g C
6 mol H​ 2​ ​O 1 mol ​C6​ ​​H​12​​O​6​

4 CHECK Check the answer to determine if it makes sense.

YOUR
The answer is correctly rounded to three significant figures,
WORK
to match those in 3.00 mol H ​ 2​ ​O. The units cancel correctly,
​ 6​ ​​H​12​​O​6​as the units for the answer. The answer
leaving g C
is reasonable because it is about three-sixths, or one-half, of 180.

PRACTICE

C. When magnesium burns in air, it combines with oxygen

to form magnesium oxide according to the following
equation. What mass in grams of magnesium oxide is
produced from 2.00 mol of magnesium?
2Mg(s) + ​O2​ ​(g) → 2MgO(s)

What is the given quantity?

What is the unknown quantity?

Write the two conversion factors needed to solve the problem.

Calculate the molar mass of the unknown using the given

quantity and the two conversion factors.

6 CH A P TER 9
 Gram-to-mole conversions require the molar mass of
the given substance and the mole ratio.

You are asked to calculate the amount in moles of one

substance that will react with or be produced from a given
mass of another substance. In this type of problem, you are
starting with a mass (probably in grams) of some substance.
The plan for this conversion is given below.

mass of amount of amount of

convert given into given into unknown
substance (g) substance (mol) substance (mol)

This procedure is similar to the previous procedure. You

Critical Thinking
need two additional pieces of data—the molar mass of the
2. Compare and Contrast How
given substance and the mole ratio of the two substances. You
does this procedure compare to the
can use the units of the molar mass conversion factor to guide previous procedure?
you in your calculations. Because the known quantity is a
mass, the conversion factor will need to be 1 mol divided by
the molar mass. This will cancel grams and leave moles.

Molar mass factor Mole ratio

(Periodic table) (Balanced equation)
Mass of Amount of
1 mol given mol unknown
given × × = unknown
Molar mass of mol given
substance substance
given (g)
(g) (mol)
CONVERSION FACTORS
GIVEN IN CALCULATED
THE PROBLEM

PRACTICE

D. The following reaction produced 10.0 g of O

​ 2​ ​.
6C​O2​ ​(g) + 6​H2​ ​O(l) → C
​ 6​ ​​H​12​​O​6​(aq) + 6​O2​ ​(g)
What two conversion factors would you need in order
to determine the number of moles of H​2​O used to run
the reaction?

Stoichiometry 7
 SAMPLE PROBLEM
The first step in the industrial manufacture of nitric acid is
the catalytic oxidation of ammonia.
N​H​3​(g) + O
​ 2​ ​(g) → NO(g) + H
​ 2​ ​O(g) (unbalanced)
The reaction is run using 824 g N​H3​ ​and excess oxygen. How
many moles of NO are formed?

SOLUTION

1 ANALYZE Determine the information that is given and unknown.

Given: mass of N​H3​ ​= 824 g
Unknown: amount of NO produced in moles

2 PLAN Write an equation that can be used to find the unknown.

Two conversion factors are needed—the molar mass factor
for N​H3​ ​and the mole ratio of NO to N​H3​ ​.

mol NH​3​ mol NO  ​   =   mol NO

g N​H​3​    ×   ​ __ ​    ×   ​ __
g N​H3​ ​ mol NH​​3​

molar mass factor mole ratio

3 SOLVE Substitute the values in the equation and compute the answer.
First, balance the equation for the reaction.
 14.01 g/mol N + 3(1.01 g/mol H) = 17.04 g/mol N​H3​ ​
molar mass =
Then use the periodic table to compute the molar mass of N​H3​ and
use the chemical equation to find the mole ratio. Then substitute
the numbers into the conversion equation to find the answer.
4N​H3​ ​(g) + 5​O2​ ​(g) → 4NO(g) + 6​H2​ ​O(g)
Finally, compute the molar mass of N​H3​ and apply the conversion
factors to find the answer.

1 mol NH​​3​ __
824 g N​H3​ ​× ___
​   ​× ​ 4 mol NO  ​= 4 8.4 mol NO
17.04 g N​H​3​ 4 mol NH​3​

4 CHECK Check the answer to determine if it makes sense.

YOUR
The answer is correctly given to three significant figures. The units
WORK
cancel out to leave the unknown.

8 CH A P TER 9
 Mass-to-mass calculations use the mole ratio and the
molar masses of the given and unknown substances.

Mass-mass calculations are usually more useful than the other

calculations. You cannot measure moles directly, but you can TIP Mass-mass problems can
be viewed as the combina-
measure the masses of the products and reactants involved. tion of the other types of problems.
The plan for solving mass-mass problems is given below.

mass of amount of amount of mass of

convert given into given into unknown into unknown
substance (g) substance (mol) substance (mol) substance (g)

To solve mass-mass problems, you need three conversion

factors. They are the molar mass of the given substance, the
mole ratio, and the molar mass of the unknown substance.

Molar mass factor Mole ratio Molar mass factor

(Periodic table) (Balanced equation) (Periodic table)
Mass of 1 mol given mol unknown Molar mass Mass of
given × × × = unknown
Molar mass of mol given of unknown (g)
substance substance
(g) given (g) 1 mol unknown (g)
CONVERSION FACTORS
GIVEN IN CALCULATED
THE PROBLEM

SAMPLE PROBLEM
How many grams of Sn​F2​ ​are produced from the reaction of
30.00 g HF with Sn? The reaction is given by this equation.
Sn(s) + 2HF(g) → Sn​F2​ ​(s) + H
​ 2​ ​(g)

SOLUTION

1 Analyze Given: amount of HF = 30.00 g

Unknown: mass of Sn​F2​ ​produced in grams

2 Plan Three conversion factors are needed.

mol Sn​F​ ​ g Sn​F​2​

​ mol HF
g HF × __  ​ × ​ __2 ​ × __​   ​ = g Sn​F2​ ​
g HF mol HF mol Sn​F2​ ​

3 SOLVE The molar masses are 20.01 g/mol HF and 1​ 56.71 g/mol Sn​F2​ .

1 mol Sn​F2​ ​ 156.71 g Sn​F2​ ​

​  mol HF  ​ ×
30.00 g HF × __ __
​   ​ × ___
​      ​ = 117.5 g Sn​F2​ ​
20.01 g HF 2 mol HF mol Sn​F2​ ​

Stoichiometry 9
 PRACTICE

E. What mass of aluminum is produced by the decomposition

of 5.0 kg A​l​2​​O​3​? How many moles of oxygen are produced?
What is the given quantity?
What is the unknown quantity?

Write the balanced decomposition reaction.

What conversion factors are needed to find the mass of ­

aluminum produced? The moles of oxygen produced?
mass Al

mol O

Find the molar mass ratios needed for both problems.

Substitute numbers into the conversion factors and calculate

your answers.
mass Al

mol O

Check your answers.

10 CH A P TER 9
 SECTION 9.2 REVIEW
REVIEW
1. Balance the following equation. Then, given the moles of reactant or
­ roduct below, determine the corresponding amount in moles of each
p
of the other reactants and products.

N​H3​ ​+ ​O2​ ​→ N
​ 2​ ​+ ​H2​ ​O

a. 4 mol N​H​3 ​

b. 4.5 mol ​O​2​

2. One reaction that produces hydrogen gas can be represented by the

­following unbalanced chemical equation:

Mg(s) + HCl(aq) → MgC​l2​ ​(aq) + H

​ 2​ ​(g)

What mass of HCl is consumed by the reaction of 2.50 mol of magnesium?

Critical Thinking
3. RELATING IDEAS Carbon and oxygen react to form carbon monoxide as in
​ 2​ ​→ 2CO. What masses of carbon and oxygen are
the equation 2C + O
needed to make 56.0 g CO?

Which law does this illustrate?

Stoichiometry 11