Introductory Chemistry: An Active Learning Approach

Mark S. Cracolice, Edward I. Peters

Chapter 14

The Ideal Gas Law and Its Applications - all with Video Answers

Educators

Chapter Questions

Problem 1

Compare the volumes of $1 \times 10^{23}$ hydrogen molecules,
$1 \times 10^{23}$ oxygen molecules, and $2 \times 10^{23}$ nitrogen molecules, all at the same temperature and pressure.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 2

largest volume, if all samples are at the same temperature and pressure? (a) 263 grams of $\mathrm{Xe} ;$ (b) $5 \times 10^{23}$ molecules of $\mathrm{H}_{2}$
(c) 4.00 moles of $\mathrm{CO}_{2} ;$ (d) they would all have the same volume.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 3

Find the pressure in torr produced by 0.0888 mol of carbon dioxide in a 5.00 -liter vessel at $36^{\circ} \mathrm{C}$.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 4

A 0.917 -mol sample of hydrogen gas at a temperature of $25.0^{8} \mathrm{C}$ is found to occupy a volume of 21.7 liters. What is the pressure of this gas sample in torr?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 5

The pressure exerted by 6.04 mol of nitrogen monoxide at a temperature of $18^{\circ} \mathrm{C}$ is 17.2 atm. What is the volume of the gas in liters?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 6

A 0.512 -mol sample of argon gas is collected at a pressure of 872 torr and a temperature of $18^{\circ} \mathrm{C} .$ What is the volume (L) of the sample?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 7

A 784 -mL hydrogen lecture bottle is left with the valve slightly open. Assuming no air has mixed with the hydrogen, how many moles of hydrogen are left in the bottle after the pressure has become equal to an atmospheric pressure of 752 torr at a temperature of $22^{\circ} \mathrm{C} ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 8

A sample of xenon gas collected at a pressure of 1.18 atm and a temperature of $18^{\circ} \mathrm{C}$ is found to occupy a volume of 26.7 liters. How many moles of Xe gas are in the sample?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 9

At what temperature $\left(^{\circ} \mathrm{C}\right)$ will 0.810 mol of chlorine in a 15.7-L vessel exert a pressure of 756 torr?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 10

A 0.142 -mol sample of argon gas has a volume of 834 millilitres at a pressure of 4.83 atm. What is the temperature of the Ar gas sample on the Celsius scale?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 11

How many moles of carbon monoxide must be placed into a $40.0-\mathrm{L}$ tank to develop a pressure of 965 torr at $18^{\circ} \mathrm{C} ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 12

A sample of neon gas collected at a pressure of 0.946 atm and a temperature of $276 \mathrm{K}$ is found to occupy a volume of
712 milliliters. How many moles of Ne gas are in the sample?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 13

Find the volume of 0.621 mol of helium at $-32^{\circ} \mathrm{C}$ and 0.771 atm.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 14

A sample of neon gas collected at a pressure of $531 \mathrm{mm}$ Hg and a temperature of 291 K has a mass of 10.2 grams. What is the volume (L) of the sample?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 15

The STP density of an unknown gas is found to be $2.32 \mathrm{g} / \mathrm{L}$. What is the molar mass of the gas?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 16

What is the density of a sample of oxygen gas at a pressure of 1.40 atm and a temperature of $49^{8} \mathrm{C} ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 17

The "effective" molar mass of air is $29 \mathrm{g} / \mathrm{mol.~Use~this~value}$ to calculate the density of air (a) at STP and (b) at $20^{\circ} \mathrm{C}$ and
751 torr.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 18

A 2.94 -gram sample of an unknown gas is found to occupy a volume of $2.06 \mathrm{L}$ at a pressure of 1.16 atm and a temperature of $46^{\circ} \mathrm{C}$. What is the molar mass of the unknown gas?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 19

If the density of an unknown gas at $41^{\circ} \mathrm{C}$ and 2.61 atm is 1.61 $\mathrm{g} / \mathrm{L},$ what is its molar mass?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 20

A sample of an unknown gas is found to have a density of $2.00 \mathrm{g} / \mathrm{L}$ at a pressure of 0.939 atm and a temperature of $40.0^{\circ} \mathrm{C}$. What is the molar mass of the unknown gas?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 21

The gas in an 8.07 -liter cylinder at $13^{\circ} \mathrm{C}$ has a mass of 33.5 grams and exerts a pressure of 3.25 atm. Find the molar mass of the gas.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 22

A 0.201 -mol sample of an unknown gas contained in a $5.00 \mathrm{L}$ flask is found to have a density of $1.72 \mathrm{g} / \mathrm{L} .$ What is the molar mass of the unknown gas?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 23

$\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4}$ both have the same empirical (simplest) formula. At a temperature and pressure at which both substances are gases, can you tell without calculating which gas is more dense? Explain.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 24

A 0.284 -mol sample of Xe gas is contained in a $7.00 \mathrm{L}$ flask at room temperature and pressure. What is the density of the gas, in grams/liter, under these conditions?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 25

Compare the molar volumes of helium and neon at $30^{\circ} \mathrm{C}$ and
1.10 torr. What are their values in $\mathrm{L} / \mathrm{mol} ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 26

What is the molar volume of carbon dioxide gas at a pressure of 0.974 atm and a temperature of $43^{\circ} \mathrm{C} ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 27

Find the molar volume of acetylene, $\mathrm{C}_{2} \mathrm{H}_{2},$ at $21^{\circ} \mathrm{C}$ and 0.908 atm.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 28

The molar volume for oxygen gas at a pressure of 0.684 atm and a temperature of $31^{\circ} \mathrm{C}$ is $36.5 \mathrm{L} / \mathrm{mol}$. What is the volume occupied by 1.31 moles of $\mathrm{O}_{2}$ gas at the same temperature and pressure?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 29

One small-scale laboratory method for preparing oxygen is to heat potassium chlorate in the presence of a catalyst:
$2 \mathrm{KClO}_{3}(\mathrm{s}) \rightarrow 2 \mathrm{KCl}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) .$ Find the STP volume of oxy-
gen that can be produced by $5.74 \mathrm{g} \mathrm{KClO}_{3}$.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 30

What volume of carbon dioxide is produced at $0^{\circ} \mathrm{C}$ and 1 atm when $64.2 \mathrm{g}$ of calcium carbonate reacts completely according to the reaction $\mathrm{CaCO}_{3}(\mathrm{s}) \rightarrow \mathrm{CaO}(\mathrm{s})+\mathrm{CO}_{2}(\mathrm{g}) ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 31

The reaction used to produce chlorine in the laboratory is $2 \mathrm{KMnO}_{4}(\mathrm{aq})+16 \mathrm{HCl}(\mathrm{aq}) \rightarrow 2 \mathrm{MnCl}_{2}(\mathrm{aq})+5 \mathrm{Cl}_{2}(\mathrm{aq})+$
$8 \mathrm{H}_{2} \mathrm{O}(\mathrm{aq})+2 \mathrm{KCl}(\mathrm{aq}) .$ Calculate the number of grams of potas-
sium permanganate, $\mathrm{KMnO}_{4}$, that are needed to produce $9.81 \mathrm{L}$ of chlorine, measured at STP.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 32

How many grams of carbon (graphite) are required to react completely with $42.5 \mathrm{L}$ of oxygen gas at $0^{\circ} \mathrm{C}$ and 1 atm according to the reaction $\mathrm{C}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{CO}_{2}(\mathrm{g}) ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 33

may be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back-
ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied.
One source of sulfur dioxide used in making sulfuric acid comes from sulfide ores by the reaction $4 \mathrm{FeS}_{2}(\mathrm{s})+11 \mathrm{O}_{2}(\mathrm{g}) \rightarrow$
$2 \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{s})+8 \mathrm{SO}_{2}(\mathrm{g}) .$ How many liters of $\mathrm{SO}_{2},$ measured at 983
torr and $214^{\circ} \mathrm{C},$ are produced by the reaction of $598 \mathrm{g} \mathrm{FeS}_{2} ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 34

may be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back-
ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied.
What volume of chlorine gas at $42.0^{\circ} \mathrm{C}$ and 1.33 atm is required to react completely with $41.5 \mathrm{g}$ of phosphorus according to the reaction $P_{4}(s)+6 C l_{2}(g) \rightarrow 4 P C l_{3}(\ell) ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 35

May be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back-
ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied.
How many grams of water must decompose by electrolysis to produce $23.9 \mathrm{L} \mathrm{H}_{2}$, measured at $28^{\circ} \mathrm{C}$ and 728 torr?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 36

May be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back-
ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied.
What volume of hydrogen gas at $29^{\circ} \mathrm{C}$ and 0.809 atm is produced when $31.8 \mathrm{g}$ of iron reacts completely according to the reaction $\mathrm{Fe}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{FeCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g}) ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 37

May be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back-
ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied.
The reaction chamber in a modified Haber process for making ammonia by the direct combination of its elements is operated at $575^{\circ} \mathrm{C}$ and 248 atm. How many liters of nitrogen, measured at these conditions, will react to produce $9.16 \times 10^{3}$ grams of ammonia?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 38

May be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back-
ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied.
How many grams of iron are required to react completely with 5.49 L of oxygen gas at $41^{\circ} \mathrm{C}$ and 1.41 atm according to the reaction $2 \mathrm{Fe}(\mathrm{s})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{FeO}(\mathrm{s}) ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 39

May be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back-
ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied.
When properly detonated, ammonium nitrate explodes violently, releasing hot gases: $\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{s}) \rightarrow \mathrm{N}_{2} \mathrm{O}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) .$ If
the total volume of gas produced, both dinitrogen and steam, is $82.3 \mathrm{L}$ at $447^{\circ} \mathrm{C}$ and 896 torr, how many grams of $\mathrm{NH}_{4} \mathrm{NO}_{3}$
exploded?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 40

May be solved by the molar volume method (Section 14.7 ) or by the ideal gas equation method (Section 14.8 ). In the answer section, the setups are given first for the molar volume method, printed over a tan background. Then, over a green back-
ground, the answers are given for the ideal gas equation method. Check your work according to the section you studied.
How many grams of sodium are needed to produce $25.3 \mathrm{L}$ of hydrogen gas at $43^{\circ} \mathrm{C}$ and 0.886 atm according to the reaction $2 \mathrm{Na}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow 2 \mathrm{NaOH}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g}) ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 41

Sulfur burns to $\mathrm{SO}_{2}$ with a beautiful deep blue-purple flame, but with a foul, suffocating odor: $2 \mathrm{S}+\mathrm{O}_{2} \rightarrow 2 \mathrm{SO}_{2}$. (a) How many liters of $\mathrm{O}_{2}$ are needed to form $35.2 \mathrm{L} \mathrm{SO}_{2}$, both gases being measured at 741 torr and $26^{\circ} \mathrm{C} ?$ (b) What if only the $\mathrm{SO}_{2}$ is at those conditions, but the $\mathrm{O}_{2}$ is at $17^{\circ} \mathrm{C}$ and 847 torr?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 42

Consider the following gas phase reaction: $4 \mathrm{NH}_{3}(g)+$ $5 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{NO}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) .$ If 6.98 liters of $\mathrm{O}_{2}(\mathrm{g})$ gas at
$129^{\circ} \mathrm{C}$ and 0.836 atm are reacted, what volume of $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$ will be produced if it is collected at $74^{\circ} \mathrm{C}$ and 0.630 atm?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 43

Gaseous chlorine dioxide, $\mathrm{ClO}_{2},$ is used to bleach flour and in water treatment. It is produced by the reaction of chlorine with sodium chlorite: $\mathrm{Cl}_{2}+2 \mathrm{NaClO}_{2} \rightarrow 2 \mathrm{ClO}_{2}+2 \mathrm{NaCl}$. How many
liters of $\mathrm{ClO}_{2}$, measured at 0.961 atm and $31^{\circ} \mathrm{C},$ will be produced by $283 \mathrm{L} \mathrm{Cl}_{2}$ at 2.92 atm and $21^{\circ} \mathrm{C} ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 44

Consider the following gas phase reaction: $\mathrm{N}_{2}(\mathrm{g})+$ $2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) .$ If 8.44 liters of $\mathrm{N}_{2}(\mathrm{g})$ gas at $127^{\circ} \mathrm{C}$ and
0.638 atm is used, what volume of $\mathrm{NO}_{2}(\mathrm{g})$ gas will be formed if it is collected at $187^{\circ} \mathrm{C}$ and 0.982 atm?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 45

In the natural oxidation of hydrogen sulfide released by decaying organic matter, the following reaction occurs: $2 \mathrm{H}_{2} \mathrm{S}+$ $3 \mathrm{O}_{2} \rightarrow 2 \mathrm{SO}_{2}+2 \mathrm{H}_{2} \mathrm{O} .$ How many milliliters of hydrogen sul-
fide, measured at $19^{\circ} \mathrm{C}$ and 549 torr, will be used in a reaction that also uses $704 \mathrm{mL} \mathrm{O}_{2}$ at 159 torr and $26^{\circ} \mathrm{C} ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 46

Consider the following gas phase reaction: $\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(\mathrm{g})$ $\rightarrow 2 \mathrm{HCl}(\mathrm{g}) .$ If 8.36 liters of $\mathrm{Cl}_{2}(\mathrm{g})$ gas at $113^{\circ} \mathrm{C}$ and 0.693 atm is
used, what volume of HCl(g) gas will be formed if it is collected at $64^{\circ} \mathrm{C}$ and 0,355 atm?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 47

Distinguish precisely, and in scientific terms, the differences among items in each of the following pairs or groups.
a) Avogadro's Law, Law of Combining Volumes
b) Gas density, molar volume, molar mass
c) Ideal gas equation, combined gas equation

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 48

Determine whether each of the following statements is true or false:
a) The molar volume of a gas at 1.06 atm and $212^{\circ} \mathrm{C}$ is less than 22.4 L/mol.
b) The mass of $5.00 \mathrm{L}$ of $\mathrm{NH}_{3}$ is the same as the mass of $5.00 \mathrm{L}$ of CO if both volumes are measured at the same temperature and pressure.
c) At a given temperature and pressure, the densities of two gases are proportional to their molar masses.
d) To change liters of a gas to moles, multiply by RT/P.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 49

Calculate the volume of $6.74 \mathrm{g} \mathrm{C}_{2} \mathrm{H}_{4}(\mathrm{g})$ at $41^{\circ} \mathrm{C}$ and 733 torr.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 50

Find the mass of 57.9 liters of krypton at 775 torr and $6^{\circ} \mathrm{C}$.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 51

What is the density of $\mathrm{H}_{2} \mathrm{S}$ at 0.972 atm and $14^{\circ} \mathrm{C} ?$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 52

At $17^{\circ} \mathrm{C}$ and 0.835 atm, 16.2 liters of ammonia has a mass of 9.68 g. What is the molar volume of ammonia at those conditions? (This is easier than it may seem!)

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 53

A $7.60-\mathrm{g}$ sample of pure liquid is vaporized at $183^{\circ} \mathrm{C}$ and 179 torr. At these conditions it occupies 3.87 L. What is the molar mass of the substance?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 54

The density of nitrogen at 0.913 atm and $18^{\circ} \mathrm{C}$ is $1.07 \mathrm{g} / \mathrm{L}$ Explain how this shows that the formula of nitrogen is $\mathrm{N}_{2}$ rather than just N.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 55

The answer to Question 56 follows from the answer to Question
55. Answer Question 55 first.
At a given temperature and pressure, what mathematical relationship exists between the density and molar mass of a gas? Explain your answer.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 56

The answer to Question 56 follows from the answer to Question
55. Answer Question 55 first.
Labels have become detached from cylinders of two gases, one of which is known to be propane, $\mathrm{C}_{3} \mathrm{H}_{8}$, and the other butane, $\mathrm{C}_{4} \mathrm{H}_{10} .$ The densities of the two gases are compared at the same temperature and pressure. The density of gas $A$ is $1.37 \mathrm{g} / \mathrm{L},$ and the density of gas $\mathbf{B}$ is higher. Which gas is A and which is B? What is the density of B?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 57

An organic chemist has produced a solid she believes to be pure; she expects a molar mass of $346 \mathrm{g} / \mathrm{mol}$. Using 4.08 grams of the solid, she melts and then boils it in a 3.36 -L vacuum chamber at 117 torr and $243^{\circ} \mathrm{C}$. She is disappointed; the molar mass is close to what she expected, but not close enough. (a) What molar mass did she find? (b) Her finding suggested to her what her mistake might have been. Does it suggest anything to you? [Part (b) is beyond the scope of Chapter $14,$ but you might have an inspiration if you have studied Chapter 13.]

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator