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Chapter 5

Gases

Educators


Problem 1

What is pressure? What causes pressure?

Sisi G.
Numerade Educator

Problem 2

Explain what happens when a person inhales. What forces airinto the lungs?

Matthew B.
Numerade Educator

Problem 3

Explain what happens when a person exhales. What forces airout of the lungs?

Sisi G.
Numerade Educator

Problem 4

What are the common units of pressure? List them in order of smallest to largest unit.

Matthew B.
Numerade Educator

Problem 5

What is a manometer? How does it measure the pressure of a sample of gas?

Sisi G.
Numerade Educator

Problem 6

Summarize each of the simple gas laws (Boyle's law, Charles's law, and Avogadro's law). For each, explain the relationship between the two variables and also state which variables must be kept constant.

Matthew B.
Numerade Educator

Problem 7

Explain why people may experience ear pain after a rapid change in altitude.

Sisi G.
Numerade Educator

Problem 8

Explain why scuba divers should never hold their breath when they ascend to the surface.

Matthew B.
Numerade Educator

Problem 9

Why is it impossible to breathe air through an extra-long snorkel (longer than a couple of meters) while swimming under water?

Sisi G.
Numerade Educator

Problem 10

Explain why hot-air balloons float above the ground and why the second story of a two-story home is often warmer than the ground story.

Matthew B.
Numerade Educator

Problem 11

What is the ideal gas law? Why is it useful?

Sisi G.
Numerade Educator

Problem 12

Explain how the ideal gas law contains within it the simple gas laws (show an example).

Matthew B.
Numerade Educator

Problem 13

Define molar volume and lists its value for a gas at STP.

Sisi G.
Numerade Educator

Problem 14

How does the density of a gas depend on temperature? Pressure? How does it depend on the molar mass of the gas?

Matthew B.
Numerade Educator

Problem 15

What is partial pressure? What is the relationship between the partial pressures of each gas in a sample and the total pressure of gas in the sample?

Sisi G.
Numerade Educator

Problem 16

Why do deep-sea divers breathe a mixture of helium and oxygen?

Matthew B.
Numerade Educator

Problem 17

When a gas is collected over water, is the gas pure? Why or why not? How can the partial pressure of the collected gas be determined?

Sisi G.
Numerade Educator

Problem 18

If a reaction occurs in the gas phase at STP, we can determine the mass of a product from the volumes of reactants. Explain.

Matthew B.
Numerade Educator

Problem 19

What are the basic postulates of kinetic molecular theory? How does the concept of pressure follow from kinetic molecular theory?

Sisi G.
Numerade Educator

Problem 20

Explain how Boyle's law, Charles's law, Avogadro's law, and Dalton's law all follow from kinetic molecular theory.

Matthew B.
Numerade Educator

Problem 21

How is the kinetic energy of a gas related to temperature? How is the root mean square velocity of a gas related to its molar mass?

Sisi G.
Numerade Educator

Problem 22

Describe how the molecules in a perfume bottle travel from the bottle to your nose. What is mean free path?

Matthew B.
Numerade Educator

Problem 23

Explain the difference between diffusion and effusion. How is the effusion rate of a gas related to its molar mass?

Sisi G.
Numerade Educator

Problem 24

Deviations from the ideal gas law are observed at high pressure and low temperature. Explain this in light of kinetic molecular theory.

Matthew B.
Numerade Educator

Problem 25

The pressure in Denver, Colorado (elevation 5280 $\mathrm{ft}$ , averages about 24.9 in $\mathrm{Hg}$ . Convert this pressure to each indicated unit.
$$\text { a. atm } \quad \text { b. } \mathrm{mmHg} \quad \text { c. psi } \quad \text { d. } \mathrm{Pa}$$

Sisi G.
Numerade Educator

Problem 26

The pressure on top of Mount Everest $(29,029 \mathrm{ft})$ averages about 235 $\mathrm{mm} \mathrm{Hg} .$ Convert this pressure to each indicated unit.
$$\text { a. torr }\quad \text { b. psi } \quad \text { c. in Hg } \quad \text { d. atm }$$

Matthew B.
Numerade Educator

Problem 27

The North American record for highest recorded barometric pressure is 31.85 in Hg, set in 1989 in Northway, Alaska. Convert this pressure to each indicated unit.
$$\text { a. mmHg }\quad \text { b. atm } \quad \text { c. torr } \quad \text { d. kPa (kilopascals) }$$

Sisi G.
Numerade Educator

Problem 28

The world record for lowest pressure (at sea level) was 652.5 mmHg recorded inside Typhoon Tip on October $12,1979$ , in the western Pacific Ocean. Convert this pressure to each indicated unit.
$$\text { a. torr }\quad \text { b. atm } \quad \text { c. in Hg } \quad\text { d. psi }$$

Matthew B.
Numerade Educator

Problem 29

Given a barometric pressure of 762.4 $\mathrm{mmHg}$ , calculate the pressure of each gas sample as indicated by the manometer.

Sisi G.
Numerade Educator

Problem 30

Given a barometric pressure of 751.5 $\mathrm{mmHg}$ , calculate the pressure of each gas sample as indicated by the manometer.

Matthew B.
Numerade Educator

Problem 31

A sample of gas has an initial volume of 5.6 $\mathrm{L}$ at a pressure of 735 $\mathrm{mm} \mathrm{Hg} .$ If the volume of the gas is increased to $9.4 \mathrm{L},$ what is its pressure?

Sisi G.
Numerade Educator

Problem 32

A sample of gas has an initial volume of 13.9 $\mathrm{L}$ at a pressure of 1.22 atm. If the sample is compressed to a volume of 10.3 $\mathrm{L}$ , what is its pressure?

Matthew B.
Numerade Educator

Problem 33

A 48.3 -mL sample of gas in a cylinder is warmed from $22^{\circ} \mathrm{C}$ . $87^{\circ} \mathrm{C} .$ What is its volume at the final temperature?

Sisi G.
Numerade Educator

Problem 34

A syringe containing 1.55 $\mathrm{mL}$ of oxygen gas is cooled from $95.3^{\circ} \mathrm{C}$ to $0.0^{\circ} \mathrm{C} .$ What is the final volume of oxygen gas?

Matthew B.
Numerade Educator

Problem 35

A balloon contains 0.158 mol of gas and has a volume of 2.46 $\mathrm{L}$ . If an additional 0.113 mol of gas is added to the balloon (at the same temperature and pressure), what is its final volume?

Bailey M.
Numerade Educator

Problem 36

A cylinder with a moveable piston contains 0.553 mol of gas and has a volume of 253 mL. What is its volume if an additional 0.365 mol of gas is added to the cylinder? (Assume constant temperature and pressure.)

Matthew B.
Numerade Educator

Problem 37

What volume is occupied by 0.118 mol of helium gas at a pressure of 0.97 atm and a temperature of 305 $\mathrm{K}$ ? Would the volume be different if the gas was argon (under the same conditions)?

Sisi G.
Numerade Educator

Problem 38

What volume is occupied by 12.5 $\mathrm{g}$ of argon gas at a pressure of 1.05 atm and a temperature of 322 $\mathrm{K}$ ? Would the volume be different if the sample were 12.5 $\mathrm{g}$ of helium (under identical conditions)?

Matthew B.
Numerade Educator

Problem 39

What is the pressure in a 10.0 -L cylinder filled with 0.448 mol of nitrogen gas at a temperature of 315 $\mathrm{K}$ ?

Sisi G.
Numerade Educator

Problem 40

What is the pressure in a $15.0-$ cylinder filled with 32.7 g of oxygen gas at a temperature of 302 $\mathrm{K} ?$

Matthew B.
Numerade Educator

Problem 41

A cylinder contains 28.5 L of oxygen gas at a pressure of 1.8 atm and a temperature of 298 $\mathrm{K}$ . How much gas (in moles) is in the cylinder?

Sisi G.
Numerade Educator

Problem 42

What is the temperature of 0.52 mol of gas at a pressure of 1.3 atm and a volume of 11.8 $\mathrm{L}$ ?

Matthew B.
Numerade Educator

Problem 43

An automobile tire has a maximum rating of 38.0 psi (gauge pressure). The tire is inflated (while cold) to a volume of 11.8 $\mathrm{L}$ and a gauge pressure of 36.0 psi at a temperature of $12.0^{\circ} \mathrm{C}$ . On a hot day, the tire warms to $65.0^{\circ} \mathrm{C},$ and its volume expands to
12.2 L. Does the pressure in the tire exceed its maximum rating? (Note: The gauge pressure is the difference between the total pressure and atmospheric pressure. In this case, assume that atmospheric pressure is 14.7 psi.)

Sisi G.
Numerade Educator

Problem 44

A weather balloon is inflated to a volume of 28.5 $\mathrm{L}$ at a pressure of 748 $\mathrm{mm} \mathrm{Hg}$ and a temperature of $28.0^{\circ} \mathrm{C}$ The balloon rises in the atmosphere to an altitude of approximately $25,000 \mathrm{ft},$ where the pressure is 385 $\mathrm{mm} \mathrm{Hg}$ and the temperature is $-15.0^{\circ} \mathrm{C}$ . Assuming the balloon can freely expand, calculate the volume of the balloon at this altitude.

Matthew B.
Numerade Educator

Problem 45

A piece of dry ice (solid carbon dioxide) with a mass of 28.8 $\mathrm{g}$ sublimes (converts from solid to gas) into a large balloon. Assuming that all of the carbon dioxide ends up in the balloon, what is thevolume of the balloon at $22^{\circ} \mathrm{C}$ and a pressure of 742 $\mathrm{mm} \mathrm{Hg}$ ?

Sisi G.
Numerade Educator

Problem 46

A 1.0 -L container of liquid nitrogen is kept in a closet measuring 1.0 $\mathrm{m}$ by 1.0 $\mathrm{m}$ by 2.0 $\mathrm{m}$ . Assuming that the container is completely full, that the temperature is $25.0^{\circ} \mathrm{C},$ and that the atmospheric pressure is 1.0 atm, calculate the percent (by volume) of air that is displaced if all of the liquid nitrogen evaporates. (Liquid nitrogen has a density of 0.807 $\mathrm{g} / \mathrm{mL.}$ )

Matthew B.
Numerade Educator

Problem 47

A wine-dispensing system uses argon canisters to pressurize and preserve wine in the bottle. An argon canister for the system has a volume of 55.0 mL and contains 26.0 $\mathrm{g}$ of argon. Assuming ideal gas behavior, what is the pressure in the canister at 295 $\mathrm{K}$ ? When the argon is released from the canister, it expands to fill the wine bottle. How many 750.0 -mL wine bottles can be purged with the argon in the canister at a pressure of 1.20 atm and a temperature of 295 $\mathrm{K}$ ?

Sisi G.
Numerade Educator

Problem 48

Cyclists sometimes use pressurized carbon dioxide inflators to inflate a bicycle tire in the event of a flat. These inflators use metal cartridges that contain 16.0 g of carbon dioxide. At 298 $\mathrm{K}$ ,
to what pressure (in psi) can the carbon dioxide in the cartridge inflate a 3.45 - mountain bike tire? (Note: The gauge pressure is the difference between the total pressure and atmospheric pressure. In this case, assume that atmospheric pressure is 14.7 psi.

Matthew B.
Numerade Educator

Problem 49

Which gas sample has the greatest pressure? Assume that all the samples are at the same temperature. Explain.

Sisi G.
Numerade Educator

Problem 50

This picture represents a sample of gas at a pressure of 1 atm, a volume of 1 . and a temperature of 25 'C. Draw a similar picture showing what would happen to the sample if the volume were reduced to 0.5 $\mathrm{L}$ and the temperature were increased to $250^{\circ} \mathrm{C}$ . What would happen to the pressure?

Matthew B.
Numerade Educator

Problem 51

Aerosol cans carry clear warnings against incineration because of the high pressures that can develop upon heating. Suppose that a can contains a residual amount of gas at a pressure of 755 $\mathrm{mmHg}$ and a temperature of $25^{\circ} \mathrm{C} .$ What would the pressure be if the can were heated to $1155^{\circ} \mathrm{C} ?$

Sisi G.
Numerade Educator

Problem 52

A sample of nitrogen gas in a $1.75-$ container exerts a pressure of 1.35 atm at $25^{\circ} \mathrm{C}$ . What is the pressure if the volume of the container is maintained constant and the temperature is raised to $355^{\circ} \mathrm{C} ?$

Matthew B.
Numerade Educator

Problem 53

Use the molar volume of a gas at STP to determine the volume (in L) occupied by 33.6 $\mathrm{g}$ of neon at STP.

Sisi G.
Numerade Educator

Problem 54

Use the molar volume of a gas at STP to calculate the density (in g/L) of nitrogen gas at STP.

Matthew B.
Numerade Educator

Problem 55

What is the density (in g/L) of hydrogen gas at $20.0^{\circ} \mathrm{C}$ and a pressure of 1655 psi?

Ly T.
Numerade Educator

Problem 56

A sample of $\mathrm{N}_{2} \mathrm{O}$ gas has a density of 2.85 $\mathrm{g} / \mathrm{L}$ at 298 $\mathrm{K}$ . What is the pressure of the gas (in mmHg)?

Matthew B.
Numerade Educator

Problem 57

A 248 -mL gas sample has a mass of 0.433 g at a pressure of 745 $\mathrm{mm} \mathrm{Hg}$ and a temperature of $28^{\circ} \mathrm{C} .$ What is the molar mass of the gas?

Sisi G.
Numerade Educator

Problem 58

A 113 -mL gas sample has a mass of 0.171 $\mathrm{g}$ at a pressure of 721 $\mathrm{mm} \mathrm{Hg}$ and a temperature of $32^{\circ} \mathrm{C} .$ What is the molar mass of the gas?

Matthew B.
Numerade Educator

Problem 59

A sample of gas has a mass of 38.8 $\mathrm{mg}$ . Its volume is 224 $\mathrm{mL}$ at a temperature of $55^{\circ} \mathrm{C}$ and a pressure of 886 torr. Find the molar mass of the gas.

Sisi G.
Numerade Educator

Problem 60

A sample of gas has a mass of 0.555 g. Its volume is 117 mL at a temperature of $85^{\circ} \mathrm{C}$ and a pressure of 753 $\mathrm{mm} \mathrm{g}$ . Find the molar mass of the gas.

Matthew B.
Numerade Educator

Problem 61

A gas mixture contains each of the following gases at the indicated partial pressures: $\mathrm{N}_{2}, 215$ torr; $\mathrm{O}_{2}, 102$ torr; and He, 117 torr. What is the total pressure of the mixture? What mass of each gas is present in a 1.35 -L sample of this mixture at $25.0^{\circ} \mathrm{C}$ ?

Sisi G.
Numerade Educator

Problem 62

A gas mixture with a total pressure of 745 $\mathrm{mm} \mathrm{Hg}$ contains each of the following gases at the indicated partial pressures: $\mathrm{CO}_{2}$ $125 \mathrm{mm} \mathrm{Hg} ; \mathrm{Ar}, 214 \mathrm{mm} \mathrm{Hg} ;$ and $\mathrm{O}_{2}, 187 \mathrm{mm} \mathrm{Hg}$ . The mixture also contains helium gas. What is the partial pressure of the helium gas? What mass of helium gas is present in a 12.0 -L sample of this mixture at 273 $\mathrm{K}$ ?

Matthew B.
Numerade Educator

Problem 63

A 1.20 -g sample of dry ice is added to a 755 mL flask containing nitrogen gas at a temperature of $25.0^{\circ} \mathrm{C}$ and a pressure of 725mmHg. The dry ice sublimes (converts from solid to gas), and the mixture returns to $25.0^{\circ} \mathrm{C} .$ What is the total pressure in the flask?

Sisi G.
Numerade Educator

Problem 64

A 275 -mL flask contains pure helium at a pressure of 752 torr. A second flask with a volume of 475 mL contains pure argon at a pressure of 722 torr. If we connect the two flasks through a stopcock and we open the stopcock, what is the partial pressure of each gas and the total pressure?

Matthew B.
Numerade Educator

Problem 65

A gas mixture contains 1.25 $\mathrm{g} \mathrm{N}_{2}$ and 0.85 $\mathrm{gO}_{2}$ in a 1.55 $\mathrm{L}$ container at $18^{\circ} \mathrm{C}$ . Calculate the mole fraction and partial pressure of each component in the gas mixture.

Sisi G.
Numerade Educator

Problem 66

What is the mole fraction of oxygen gas in air (see Table 5.3$) ?$ What volume of air contains 10.0 g of oxygen gas at 273 $\mathrm{K}$ and 1.00 atm?

Matthew B.
Numerade Educator

Problem 67

The hydrogen gas formed in a chemical reaction is collected over water at $30.0^{\circ} \mathrm{C}$ at a total pressure of 732 $\mathrm{mm} \mathrm{Hg.}$ . What is the partial pressure of the hydrogen gas collected in this way? If the total volume of gas collected is $722 \mathrm{mL},$ what mass of hydrogen gas is collected?

Sisi G.
Numerade Educator

Problem 68

The air in a bicycle tire is bubbled through water and collected at $25^{\circ} \mathrm{C}$ . If the total volume of gas collected is 5.45 $\mathrm{L}$ at a temperature of $25^{\circ} \mathrm{C}$ and a pressure of 745 torr, how many moles of gas were in the bicycle tire?

Matthew B.
Numerade Educator

Problem 69

The zinc in a copper-plated penny will dissolve in hydrochloric acid if the copper coating is filed down in several spots (so that the hydrochloric acid can get to the zinc). The reaction between the acid and the zinc is $2 \mathrm{H}^{+}(a q)+\mathrm{Zn}(s) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{Zn}^{2+}(a q)$. When the zinc in a certain penny dissolves, the total volume of gas collected over water at $25^{\circ} \mathrm{C}$ is 0.951 $\mathrm{L}$ at a total pressure of 748 $\mathrm{mm} \mathrm{Hg}$ . What mass of hydrogen gas is collected?

Sisi G.
Numerade Educator

Problem 70

A heliox deep-sea diving mixture contains 2.0 $\mathrm{g}$ of oxygen to every 98.0 $\mathrm{g}$ of helium. What is the partial pressure of oxygen when this mixture is delivered at a total pressure of 8.5 $\mathrm{atm}$ ?

Matthew B.
Numerade Educator

Problem 71

Consider the chemical reaction:
$$\mathrm{C}(s)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+\mathrm{H}_{2}(g)$$
How many liters of hydrogen gas are formed from the complete reaction of 15.7 $\mathrm{g}$ C? Assume that the hydrogen gas is collected at a pressure of 1.0 atm and a temperature of 355 $\mathrm{K}$.

Sisi G.
Numerade Educator

Problem 72

Consider the chemical reaction:
$$2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{H}_{2}(g)+\mathrm{O}_{2}(g)$$
What mass of $\mathrm{H}_{2} \mathrm{O}$ is required to form 1.4 $\mathrm{L}$ of $\mathrm{O}_{2}$ at a temperature of 315 $\mathrm{K}$ and a pressure of 0.957 $\mathrm{atm}$ ?

Matthew B.
Numerade Educator

Problem 73

$\mathrm{CH}_{3} \mathrm{OH}$ can be synthesized by the reaction:
$$\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)$$
What volume of $\mathrm{H}_{2}$ gas (in $\mathrm{L} ),$ at 748 $\mathrm{mmHg}$ and $86^{\circ} \mathrm{C},$ is required to synthesize 25.8 $\mathrm{g} \mathrm{CH}_{3} \mathrm{OH}$ . How many liters of CO gas, measured under the same conditions, are required?

Sisi G.
Numerade Educator

Problem 74

Oxygen gas reacts with powdered aluminum according to thereaction:
$$4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s) $$
What volume of $\mathrm{O}_{2}$ gas (in L), measured at 782 $\mathrm{mm} \mathrm{Hg}$ and $25^{\circ} \mathrm{C},$ completely reacts with 53.2 g $\mathrm{} \mathrm{Al}$ ?

Matthew B.
Numerade Educator

Problem 75

Automobile air bags inflate following a serious impact. The impact triggers the chemical reaction:
$$2 \mathrm{NaN}_{3}(s) \longrightarrow 2 \mathrm{Na}(s)+3 \mathrm{N}_{2}(g)$$
If an automobile air bag has a volume of $11.8 \mathrm{L},$ what mass of $\mathrm{NaN}_{3}(\mathrm{ing})$ is required to fully inflate the air bag upon impact? Assume STP conditions.

Sisi G.
Numerade Educator

Problem 76

Lithium reacts with nitrogen gas according to the reaction:
$$6 \mathrm{Li}(s)+\mathrm{N}_{2}(g) \longrightarrow 2 \mathrm{Li}_{3} \mathrm{N}(s)$$
What mass of lithium (in g) reacts completely with 58.5 $\mathrm{mL}$ of $\mathrm{N}_{2}$ gas at STp?

Matthew B.
Numerade Educator

Problem 77

Hydrogen gas (a potential future fuel) can be formed by the reaction of methane with water according to the equation:
$$\mathrm{CH}_{4}(g)+\mathrm{H}_{2} \mathrm{O}(g) \longrightarrow \mathrm{CO}(g)+3 \mathrm{H}_{2}(g)$$
In a particular reaction, 25.5 $\mathrm{L}$ of methane gas (measured at a pressure of 732 torr and a temperature of $25^{\circ} \mathrm{C} )$ mixes with 22.8 $\mathrm{L}$ of water vapor (measured at a pressure of 702 torr and a temperature of $125^{\circ} \mathrm{C}$ ). The reaction produces 26.2 $\mathrm{L}$ of hydrogen gas at STP. What is the percent yield of the reaction?

Sisi G.
Numerade Educator

Problem 78

Ozone is depleted in the stratosphere by chlorine from $\mathrm{CF}_{3} \mathrm{Cl}$
according to this set of equations:
\begin{equation}
\begin{array}{c}{\mathrm{CF}_{3} \mathrm{Cl}+\mathrm{UV} \text { light } \longrightarrow \mathrm{CF}_{3}+\mathrm{Cl}} \\ {\mathrm{Cl}+\mathrm{O}_{3} \longrightarrow \mathrm{ClO}+\mathrm{O}_{2}} \\ {\mathrm{O}_{3}+\mathrm{UV} \text { light } \longrightarrow \mathrm{O}_{2}+\mathrm{O}} \\ {\mathrm{ClO}+\mathrm{O} \longrightarrow \mathrm{Cl}+\mathrm{O}_{2}}\end{array}
\end{equation}
What total volume of ozone at a pressure of 25.0 $\mathrm{mm} \mathrm{Hg}$ and a temperature of 225 $\mathrm{K}$ is destroyed when all of the chlorine from 15.0 $\mathrm{g}$ of $\mathrm{CF}_{3} \mathrm{Cl}$ goes through 10 cycles of the given reactions?

Matthew B.
Numerade Educator

Problem 79

Chlorine gas reacts with fluorine gas to form chlorine trifluoride.
$$\mathrm{Cl}_{2}(g)+3 \mathrm{F}_{2}(g) \longrightarrow 2 \mathrm{ClF}_{3}(g)$$
A 2.00 -L reaction vessel, initially at 298 $\mathrm{K}$ , contains chlorine gas at a partial pressure of 337 $\mathrm{mmg}$ and fluorine gas at a partial pressure of 729 $\mathrm{mm} \mathrm{Hg}$ . Identify the limiting reactant and determine the theoretical yield of $\mathrm{ClF}_{3}$ in grams.

Sisi G.
Numerade Educator

Problem 80

Carbon monoxide gas reacts with hydrogen gas to form methanol.
$$\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)$$
A $1.50-$ Lreaction vessel, initially at 305 $\mathrm{K}$ , contains carbon monoxide gas at a partial pressure of 232 $\mathrm{mm} \mathrm{Hg}$ and hydrogen gas at a partial pressure of 397 $\mathrm{mm} \mathrm{g}$ . Identify the limiting reactant and determine the theoretical yield of methanol in grams.

Matthew B.
Numerade Educator

Problem 81

Consider a 1.0 -L sample of helium gas and a 1.0 -L sample of argon gas, both at room temperature and atmospheric pressure.
a. Do the atoms in the helium sample have the same average kinetic energy as the atoms in the argon sample?
b. Do the atoms in the helium sample have the same average velocity as the atoms in the argon sample?
c. Do the argon atoms, because they are more massive, exert a greater pressure on the walls of the container? Explain.
d. Which gas sample has the faster rate of effusion?

Sisi G.
Numerade Educator

Problem 82

A flask at room temperature contains exactly equal amounts (in moles) of nitrogen and xenon.
\begin{equation}
\begin{array}{l}{\text { a. Which of the two gases exerts the greater partial pressure? }} \\ {\text { b. The molecules or atoms of which gas have the greater average }} \\ {\text { velocity? }} \\ {\text { c. The molecules of which gas have the greater average kinetic }} \\ {\text { energy? }} \\ {\text { d. If a small hole were opened in the flask, which gas effuses }} \\ {\text { more quickly? }}\end{array}
\end{equation}

Matthew B.
Numerade Educator

Problem 83

Calculate the root mean square velocity and kinetic energy of $\mathrm{F}_{2}, \mathrm{Cl}_{2},$ and $\mathrm{Br}_{2}$ at 298 $\mathrm{K}$ . Rank these three halogens with respect to their rate of effusion.

Sisi G.
Numerade Educator

Problem 84

Calculate the root mean square velocity and kinetic energy of $\mathrm{CO}, \mathrm{CO}_{2},$ and $\mathrm{SO}_{3}$ at 298 $\mathrm{K}$ . Which gas has the greatest velocity? The greatest kinetic energy? The greatest effusion rate?

Matthew B.
Numerade Educator

Problem 85

We separate U- 235 from $\mathrm{U}-238$ by fluorinating a sample of uranium to form UF $_{6}($ which is a gas) and then taking advantage of the different rates of effusion and diffusion for compounds containing the two isotopes. Calculate the ratio of effusion rates for $^{238} \mathrm{UF}_{6}$ and $^{235} \mathrm{UF}_{6}$. The atomic mass of $\mathrm{U}-235$ is 235.054 amu and that of $\mathrm{U}-238$ is 238.051 amu.

Sisi G.
Numerade Educator

Problem 86

Calculate the ratio of effusion rates for Ar and Kr.

Matthew B.
Numerade Educator

Problem 87

A sample of neon effuses from a container in 76 seconds. The same amount of an unknown noble gas requires 155 seconds. Identify the second gas.

Sisi G.
Numerade Educator

Problem 88

A sample of $\mathrm{N}_{2} \mathrm{O}$ effuses from a container in 42 seconds. How long will it take the same amount of gaseous $\mathrm{I}_{2}$ to effuse from the same container under identical conditions?

Matthew B.
Numerade Educator

Problem 89

The graph shows the distribution of molecular velocities for two different molecules $(A$ and $B)$ at the same temperature. Which molecule has the higher molar mass? Which molecule has the higher rate of effusion?

Sisi G.
Numerade Educator

Problem 90

The graph shows the distribution of molecular velocities for the same molecule at two different temperatures $\left(T_{1}$ and $T_{2}\right) .$ Which temperature is greater? Explain.

Matthew B.
Numerade Educator

Problem 91

Which postulate of the kinetic molecular theory breaks down under conditions of high pressure? Explain.

Sisi G.
Numerade Educator

Problem 92

Which postulate of the kinetic molecular theory breaks down under conditions of low temperature? Explain.

Matthew B.
Numerade Educator

Problem 93

Use the van der Walls equation and the ideal gas equation to calculate the volume of 1.000 mol of neon at a pressure of 500.0 atm and a temperature of 355.0 $\mathrm{K}$ . Explain why the two values are different. (Hint: One way to solve the van der Waals equation for $V$ is to use successive approximations. Use the ideal gas law to get a preliminary estimate for $V .$ )

Sisi G.
Numerade Educator

Problem 94

Use the van der Waals equation and the ideal gas equation to calculate the pressure exerted by 1.000 mol of $\mathrm{Cl}_{2}$ in a volume of 5.000 $\mathrm{L}$ at a temperature of 273.0 $\mathrm{K}$ . Explain why the two values are different.

Matthew B.
Numerade Educator

Problem 95

Modern pennies are composed of zinc coated with copper. A student determines the mass of a penny to be 2.482 $\mathrm{g}$ and then makes several scratches in the copper coating (to expose the underlying zinc). The student puts the scratched penny in hydrochloric acid, where the following reaction occurs between the zinc and the HCl (the copper remains undissolved):
$$\mathrm{Zn}(\mathrm{s})+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{H}_{2}(g)+\mathrm{ZnCl}_{2}(a q)$$
The student collects the hydrogen produced over water at $25^{\circ} \mathrm{C}$ . The collected gas occupies a volume of 0.899 $\mathrm{L}$ at a total pressure of 791 $\mathrm{mmHg}$ . Calculate the percent zinc (by mass) in the penny. (Assume that all the Zn in the penny dissolves.)

Sisi G.
Numerade Educator

Problem 96

A 2.85 -g sample of an unknown chlorofluorocarbon decomposes and produces 564 mL of chlorine gas at a pressure of 752 $\mathrm{mm} \mathrm{Hg}$ and a temperature of 298 $\mathrm{K}$ . What is the percent chlorine (by mass) in the unknown chlorofluorocarbon?

Matthew B.
Numerade Educator

Problem 97

The mass of an evacuated 255 $\mathrm{mL}$ flask is 143.187 $\mathrm{g}$ . The mass of the flask filled with 267 torr of an unknown gas at $25^{\circ} \mathrm{C}$ is 143.289 $\mathrm{g} .$ Calculate the molar mass of the unknown gas.

Sisi G.
Numerade Educator

Problem 98

A 118 -mL flask is evacuated and found to have a mass of 97.129 $\mathrm{g}$ . When the flask is filled with 768 torr of helium gas at $35^{\circ} \mathrm{C},$ it has a mass of 97.171 $\mathrm{g}$ . Was the helium gas pure?

Matthew B.
Numerade Educator

Problem 99

A gaseous hydrogen- and carbon-containing compound is decomposed and found to contain 82.666 carbon and 17.34$\%$ hydrogen by mass. The mass of 158 mL of the gas, measured at 556 mmHg and $25^{\circ} \mathrm{C},$ was 0.275 $\mathrm{g} .$ What is the molecular formula of the compound?

Sisi G.
Numerade Educator

Problem 100

A gaseous hydrogen- and carbon-containing compound is decomposed and found to contain 85.63$\% \mathrm{C}$ and 14.37$\% \mathrm{H}$ by mass. The mass of 258 $\mathrm{mL}$ of the gas, measured at Srp, was 0.646 $\mathrm{g} .$ What is the molecular formula of the compound?

Matthew B.
Numerade Educator

Problem 101

Consider the reaction:
$$2 \mathrm{NiO}(s) \longrightarrow 2 \mathrm{Ni}(s)+\mathrm{O}_{2}(g)$$
If $\mathrm{O}_{2}$ is collected over water at $40.0^{\circ} \mathrm{C}$ and a total pressure of
$745 \mathrm{mm} \mathrm{Hg},$ what volume of gas is collected for the complete reaction of 24.78 $\mathrm{g}$ of NiO?

Sisi G.
Numerade Educator

Problem 102

Consider the reaction:
$$2 \mathrm{Ag}_{2} \mathrm{O}(s) \longrightarrow 4 \mathrm{Ag}(s)+\mathrm{O}_{2}(g)$$
If this reaction produces 15.8 $\mathrm{g}$ of $\mathrm{Ag}(\mathrm{s}),$ what total volume of gas can be collected over water at a temperature of $25^{\circ} \mathrm{C}$ and a total
pressure of 752 $\mathrm{mm} \mathrm{Hg}$ ?

Matthew B.
Numerade Educator

Problem 103

When hydrochloric acid is poured over potassium sulfide, 42.9 $\mathrm{mL}$ of hydrogen sulfide gas is produced at a pressure of 752 torr and $25.8^{\circ} \mathrm{C}$ . Write an equation for the gas-evolution reaction and determine how much potassium sulfide (in grams) reacted.

Sisi G.
Numerade Educator

Problem 104

Consider the reaction:
$$2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g)$$
a. If 285.5 $\mathrm{mL}$ of $\mathrm{SO}_{2}$ reacts with 158.9 $\mathrm{mL}$ of $\mathrm{O}_{2}$ (both measured at 315 $\mathrm{K}$ and 50.0 $\mathrm{mm} \mathrm{Hg}$ ), what is the limiting reactant and the theoretical yield of $\mathrm{SO}_{3} ?$
b. If 187.2 $\mathrm{mL}$ of $\mathrm{SO}_{3}$ is collected (measured at 315 $\mathrm{K}$ and 50.0 $\mathrm{mmHg}$ , what is the percent yield for the reaction?

Matthew B.
Numerade Educator

Problem 105

Ammonium carbonate decomposes upon heating according to the balanced equation:
$$\left(\mathrm{NH}_{\mathrm{d}}\right)_{2} \mathrm{CO}_{3}(\mathrm{s}) \longrightarrow 2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)$$
Calculate the total volume of gas produced at $22^{\circ} \mathrm{C}$ and 1.02 $\mathrm{atm}$ by the complete decomposition of 11.83 $\mathrm{g}$ of ammonium carbonate.

Sisi G.
Numerade Educator

Problem 106

Ammonium nitrate decomposes explosively upon heating according to the balanced equation:
$$2 \mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{s}) \longrightarrow 2 \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)$$
Calculate the total volume of gas (at $125^{\circ} \mathrm{C}$ and 748 $\mathrm{mm} \mathrm{Hg}$ ) produced by the complete decomposition of 1.55 $\mathrm{kg}$ of ammonium
nitrate.

Matthew B.
Numerade Educator

Problem 107

Olympic cyclists fill their tires with helium to make them lighter. Calculate the mass of air in an air-filled tire and the mass of helium in a helium-filled tire. What is the mass difference between the two? Assume that the volume of the tire is 855 $\mathrm{mL}$ , that it is filled to a total pressure of 125 $\mathrm{psi}$ , and that the temperature is $25^{\circ} \mathrm{C}$ . Also, assume an average molar mass for air of 28.8 $\mathrm{g} / \mathrm{mol} .$

Sisi G.
Numerade Educator

Problem 108

In a common classroom demonstration, a balloon is filled with air and submerged in liquid nitrogen. The balloon contracts as the gases within the balloon cool. Suppose a balloon initially contains 2.95 L of air at a temperature of $25.0^{\circ} \mathrm{C}$ and a pressure of 0.998 atm. Calculate the expected volume of the balloon upon cooling to $-196^{\circ} \mathrm{C}$ (the boiling point of liquid nitrogen). When the demonstration is carried out, the actual volume of the balloon decreases to 0.61 $\mathrm{L} .$ How does the observed volume of the balloon compare to your calculated value? Explain the difference.

Matthew B.
Numerade Educator

Problem 109

Gaseous ammonia is injected into the exhaust stream of a coal- burning power plant to reduce the pollutant NO to $\mathrm{N}_{2}$ according to the reaction:
$$4 \mathrm{NH}_{3}(g)+4 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$
Suppose that the exhaust stream of a power plant has a flow rate of 335 $\mathrm{L} / \mathrm{s}$ at a temperature of 955 $\mathrm{K}$ , and the exhaust contains a partial pressure of $\mathrm{NO}$ of 22.4 torr. What should be the flow rate of ammonia delivered at 755 torr and 298 $\mathrm{K}$ into the stream to react completely with the NO if the ammonia is 65.2$\%$ pure (by volume)?

Sisi G.
Numerade Educator

Problem 110

The emission of $\mathrm{NO}_{2}$ by fossil fuel combustion can be prevented
by injecting gaseous urea into the combustion mixture. The urea reduces NO (which oxidizes in air to form $\mathrm{NO}_{2} )$ according to the reaction:
$$\begin{aligned} 2 \mathrm{CO}\left(\mathrm{NH}_{2}\right)_{2}(g)+4 \mathrm{NO}(g)+\mathrm{O}_{2}(g) & \longrightarrow \\ & 4 \mathrm{N}_{2}(g)+2 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g) \end{aligned}$$
Suppose that the exhaust stream of an automobile has a flow rate of 2.55 $\mathrm{L} / \mathrm{s}$ at 655 $\mathrm{K}$ and contains a partial pressure of NO of 12.4 torr. What total mass of urea is necessary to react completely with the NO formed during 8.0 hours of driving?

Matthew B.
Numerade Educator

Problem 111

An ordinary gasoline can measuring 30.0 $\mathrm{cm}$ by 20.0 $\mathrm{cm}$ by 15.0 $\mathrm{cm}$ is evacuated with a vacuum pump. Assuming that virtually all of the air can be removed from inside the can and that atmospheric pressure is 14.7 psi, what is the total force (in pounds) on the surface of the can? Do you think that the can could withstand the force?

Sisi G.
Numerade Educator

Problem 112

Twenty-five milliliters of liquid nitrogen (density $=$ 0.807 $\mathrm{g} / \mathrm{mL}$ ) is poured into a cylindrical container with a radius of 10.0 $\mathrm{cm}$ and a length of 20.0 $\mathrm{cm} .$ The container initially contains only air at a pressure of 760.0 $\mathrm{mmHg}$ (atmospheric pressure) and a temperature of 298 $\mathrm{K}$ . If the liquid nitrogen completely vaporizes, what is the total force (in lb) on the interior of the container at 298 $\mathrm{K}$ ?

Matthew B.
Numerade Educator

Problem 113

A 160.0 -L. helium tank contains pure helium at a pressure of 1855 psi and a temperature of 298 $\mathrm{K}$ . How many $3.5-$ helium balloons will the helium in the tank fill? (Assume an atmospheric pressure of 1.0 $\mathrm{atm}$ and a temperature of 298 $\mathrm{K.}$

Sisi G.
Numerade Educator

Problem 114

An 11.5 -mL sample of liquid butane (density $=0.573 \mathrm{g} / \mathrm{mL}$ ) is evaporated in an otherwise empty container at a temperature of $28.5^{\circ} \mathrm{C}$ . The pressure in the container following evaporation is 892 torr. What is the volume of the container?

Matthew B.
Numerade Educator

Problem 115

A scuba diver creates a spherical bubble with a radius of 2.5 $\mathrm{cm}$ at a depth of 30.0 $\mathrm{m}$ where the total pressure (including atmospheric pressure) is 4.00 atm. What is the radius of the bubble when it reaches the surface of the water? (Assume that the atmospheric pressure is 1.00 atm and the temperature is 298 $\mathrm{K} .$ .

Sisi G.
Numerade Educator

Problem 116

A particular balloon can be stretched to a maximum surface area of 1257 $\mathrm{cm}^{2} .$ The balloon is filled with 3.0 L of helium gas at a pressure of 755 torr and a temperature of 298 $\mathrm{K}$ . The balloon is then allowed to rise in the atmosphere. If the atmospheric temperature is $273 \mathrm{K},$ at what pressure will the balloon burst? (Assume the balloon is the shape of a sphere.)

Matthew B.
Numerade Educator

Problem 117

A catalytic converter in an automobile uses a palladium or platinum catalyst (a substance that increases the rate of a reaction without being consumed by the reaction) to convert carbon monoxide gas to carbon dioxide according to the reaction:
$$2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)$$
A chemist researching the effectiveness of a new catalyst combines a $2.0 : 1.0$ mole ratio mixture of carbon monoxide and oxygen gas (respectively) over the catalyst in a $2.45-\mathrm{L}$ flask at a total pressure of 745 torr and a temperature of $552^{\circ} \mathrm{C}$ . When the reaction is complete, the pressure in the flask has dropped to 552 torr. What percentage of the carbon monoxide was converted to carbon dioxide?

Sisi G.
Numerade Educator

Problem 118

A quantity of $\mathrm{N}_{2}$ occupies a volume of 1.0 $\mathrm{Lat} 300 \mathrm{K}$ and 1.0 $\mathrm{atm}$ . The gas expands to a volume of 3.0 $\mathrm{L}$ as the result of a change in both temperature and pressure. Find the density of the gas at these new conditions.

Matthew B.
Numerade Educator

Problem 119

A mixture of $\mathrm{CO}(g)$ and $\mathrm{O}_{2}(g)$ in a $1.0-$ -L container at $1.0 \times 10^{3} \mathrm{K}$ has a total pressure of 2.2 atm. After some time, the total pressure falls to 1.9 atm as the result of the formation of $\mathrm{CO}_{2}$ . Determine the mass (in grams) of $\mathrm{CO}_{2}$ that forms.

Sisi G.
Numerade Educator

Problem 120

The radius of a xenon atom is $1.3 \times 10^{-8} \mathrm{cm} . \mathrm{A} 100$ -mL flask is filled with Xe at a pressure of 1.0 atm and a temperature of 273 $\mathrm{K}$ . Calculate the fraction of the volume that is occupied by $\mathrm{xe}$ atoms. (Hint: The atoms are spheres.)

Matthew B.
Numerade Educator

Problem 121

A natural gas storage tank is a cylinder with a moveable top. Its volume can change only as its height changes, and its radius remains fixed. The height of the cylinder is 22.6 $\mathrm{m}$ on a day when the temperature is $22^{\circ} \mathrm{C}$ . The next day the height of the cylinder increases to 23.8 $\mathrm{m}$ when the gas expands because of a heat wave. Determine the temperature on the second day, assuming that the pressure and amount of gas in the storage tank have not changed.

Sisi G.
Numerade Educator

Problem 122

A mixture of 8.0 $\mathrm{g} \mathrm{CH}_{4}$ and 8.0 $\mathrm{g}$ Xe is placed in a container and the total pressure is found to be 0.44 atm. Determine the partial pressure of $\mathrm{CH}_{4} .$

Matthew B.
Numerade Educator

Problem 123

A steel container of volume 0.35 L can withstand pressures up to 88 atm before exploding. What mass of helium can be stored in this container at 299 $\mathrm{K}$ ?

Sisi G.
Numerade Educator

Problem 124

Binary compounds of alkali metals and hydrogen react with water to liberate $\mathrm{H}_{2}(g) .$ The $\mathrm{H}_{2}$ from the reaction of a sample of NaH with an excess of water fills a volume of 0.490 L above the water. The temperature of the gas is $35^{\circ} \mathrm{C}$ and the total pressure is 758 $\mathrm{mm} \mathrm{Hg}$ . Determine the mass of $\mathrm{H}_{2}$ liberated and the mass of $\mathrm{NaH}$ that reacted.

Matthew B.
Numerade Educator

Problem 125

In a given diffusion apparatus, 15.0 $\mathrm{mL}$ of HBr gas diffuses in 1.0 $\mathrm{min}$ . In the same apparatus and under the same conditions, 20.3 $\mathrm{mL}$ of an unknown gas diffuses in 1.0 $\mathrm{min}$ . The unknown gas is a hydrocarbon. Find its molecular formula.

Sisi G.
Numerade Educator

Problem 126

A sample of $\mathrm{N}_{2} \mathrm{O}_{3}(g)$ has a pressure of 0.017 atm. The temperature (in $\mathrm{K}$ ) is doubled and thel $\mathrm{N}_{2} \mathrm{O}_{3}$ undergoes complete decomposition to $\mathrm{NO}_{2}(g)$ and $\mathrm{NO}(g) .$ Find the total pressure of the mixture of gases assuming constant volume and no additional temperature change.

Matthew B.
Numerade Educator

Problem 127

When 0.583 g of neon is added to an 800 -cm' bulb containing a sample of argon, the total pressure of the gases is 1.17 atm at a temperature of 295 $\mathrm{K}$ . Find the mass of the argon in the bulb.

Sisi G.
Numerade Educator

Problem 128

A gas mixture composed of helium and argon has a density of 0.670 $\mathrm{g} / \mathrm{L}$ at a 755 $\mathrm{mm} \mathrm{g}$ and 298 $\mathrm{K} .$ What is the composition of the mixture by volume?

Matthew B.
Numerade Educator

Problem 129

A gas mixture contains 75.2$\%$ nitrogen and 24.8$\%$ krypton by mass. What is the partial pressure of krypton in the mixture if the total pressure is 745 $\mathrm{mm} \mathrm{Hg}$ ?

Sisi G.
Numerade Educator

Problem 130

A 10 -L container is filled with 0.10 mol of $\mathrm{H}_{2}(g)$ and heated to $3000 \mathrm{K},$ causing some of the $\mathrm{H}_{2}(g)$ to decompose into $\mathrm{H}(g)$ . The pressure is found to be 3.0 atm. Find the partial pressure of the $\mathrm{H}(g)$ that forms from $\mathrm{H}_{2}$ at this temperature. (Assume two significant figures for the temperature.)

Matthew B.
Numerade Educator

Problem 131

A mixture of $\mathrm{NH}_{3}(g)$ and $\mathrm{N}_{2} \mathrm{H}_{4}(g)$ is placed in a sealed container at 300 $\mathrm{K}$ . The total pressure is 0.50 atm. The container is heated to 1200 $\mathrm{K}$ at which time both substances decompose completely according to the equations $2 \mathrm{NH}_{3}(g) \longrightarrow \mathrm{N}_{2}(g)+3 \mathrm{H}_{2}(g)$ $\mathrm{N}_{2} \mathrm{H}_{4}(g) \longrightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2}(g) .$ After decomposition is complete, the total pressure at 1200 $\mathrm{K}$ is found to be 4.5 atm. Find the percent of $\mathrm{N}_{2} \mathrm{H}_{4}(g)$ in the original mixture. (Assume two significant figures for the temperature.)

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Problem 132

A quantity of CO gas occupies a volume of 0.48 L at 1.0 atm and 275 $\mathrm{K}$ . The pressure of the gas is lowered, and its temperature is raised until its volume is 1.3 $\mathrm{L}$ . Determine the density of the CO under the new conditions.

Matthew B.
Numerade Educator

Problem 133

When $\mathrm{CO}_{2}(g)$ is put in a sealed container at 701 $\mathrm{K}$ and a pressure of 10.0 atm and is heated to $1401 \mathrm{K},$ the pressure rises to 22.5 $\mathrm{atm}$ . Some of the $\mathrm{CO}_{2}$ decomposes to CO and $\mathrm{O}_{2}$ . Calculate the mole percent of $\mathrm{CO}_{2}$ that decomposes.

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Problem 134

The world burns approximately $3.7 \times 10^{12} \mathrm{kg}$ of fossil fuel per
year. Use the combustion of octane as the representative reaction and determine the mass of carbon dioxide (the most significant greenhouse gas) formed per year. The current concentration of carbon dioxide in the atmosphere is approximately 399 ppm (by volume). By what percentage does the concentration increase each year due to fossil fuel combustion? Approximate the average properties of the entire atmosphere by assuming that the atmosphere extends from sea level to 15 $\mathrm{km}$ and that it has an average pressure of 381 torr and average temperature of 275 $\mathrm{K}$ . Assume Earth is a perfect sphere with a radius of 6371 $\mathrm{km}$ .

Matthew B.
Numerade Educator

Problem 135

The atmosphere slowly oxidizes hydrocarbons in a number of steps that eventually convert the hydrocarbon into carbon dioxide and water. The overall reaction of a number of such steps for methane gas is
$$\begin{aligned} \mathrm{CH}_{4}(g)+5 \mathrm{O}_{2}(g)+5 \mathrm{NO}(g) & \longrightarrow \\ & \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)+5 \mathrm{NO}_{2}(g)+2 \mathrm{OH}(g) \end{aligned}$$
Suppose that an atmospheric chemist combines 155 mL of methane at $S \mathrm{TP}, 885 \mathrm{mL}$ of oxygen at STP, and 55.5 $\mathrm{mL}$ of NO at STP in a 2.0 Lflask. The flask is allowed to stand for several weeks at 275 $\mathrm{K}$ . If the reaction reaches 90.0$\%$ of completion 90.0$\%$ of the limiting reactant is consumed), what is the partial pressure of each of the reactants and products in the flask at 275 $\mathrm{K}$ ? What
is the total pressure in the flask?

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Problem 136

Two identical balloons are filled to the same volume, one with air and one with helium. The next day, the volume of the air-filled balloon has decreased by 5.0$\%$ . By what percent has the volume of the helium-filled balloon decreased? (Assume that the air is four-fifths nitrogen and one-fifth oxygen and that the temperature did not change.)

Matthew B.
Numerade Educator

Problem 137

A mixture of $\mathrm{CH}_{4}(g)$ and $\mathrm{C}_{2} \mathrm{H}_{6}(g)$ has a total pressure of 0.53 atm. Just enough $\mathrm{O}_{2}(g)$ is added to the mixture to bring about its complete combustion to $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g) .$ The total pressure of the two product gases is 2.2 atm. Assuming constant volume and temperature, find the mole fraction of $\mathrm{CH}_{4}$ in the mixture.

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Problem 138

A sample of $\mathrm{C}_{2} \mathrm{H}_{2}(g)$ has a pressure of 7.8 $\mathrm{kPa}$ . After some time a portion of it reacts to form $\mathrm{C}_{6} \mathrm{H}_{6}(g) .$ The total pressure of the mixture of gases is then 3.9 $\mathrm{kP}$ . Assume the volume and the temperature do not change. What fraction of $\mathrm{C}_{2} \mathrm{H}_{2}(g)$ has undergone reaction?

Matthew B.
Numerade Educator

Problem 139

When the driver of an automobile applies the brakes, the passengers are pushed toward the front of the car, but a helium balloon is pushed toward the back of the car. Upon forward acceleration, the passengers are pushed toward the back of the car, but the helium balloon is pushed toward the front of the car. Why?

Sisi G.
Numerade Educator

Problem 140

Suppose that a liquid is 10 times denser than water. If you were to sip this liquid at sea level using a straw, what is the maximum length your straw would be?

Matthew B.
Numerade Educator

Problem 141

This reaction occurs in a closed container:
$$\mathrm{A}(g)+2 \mathrm{B}(g) \longrightarrow 2 \mathrm{C}(g)$$
A reaction mixture initially contains 1.5 $\mathrm{L}$ of $\mathrm{A}$ and 2.0 $\mathrm{L}$ of $\mathrm{B}$ . Assuming that the volume and temperature of the reaction mixture remain constant, what is the percent change in pressure if the reaction goes to completion?

Sisi G.
Numerade Educator

Problem 142

One mole of nitrogen and one mole of neon are combined in a closed container at STP. How big is the container?

Matthew B.
Numerade Educator

Problem 143

Exactly equal amounts (in moles) of gas A and gas $\mathrm{B}$ are combined in a $1-\mathrm{container}$ at room temperature. Gas $\mathrm{B}$ has a molar mass that is twice that of gas A. Which statement is true for the mixture of gases and why?
\begin{equation}
\begin{array}{l}{\text { a. The molecules of gas B have greater kinetic energy than those }} \\ {\text { of gas A. }} \\ {\text { b. Gas } B \text { has a greater partial pressure than gas A. }} \\ {\text { c. The molecules of gas B have a greater average velocity than }} \\ {\text { those of gas A. }} \\ {\text { d. Gas B makes a greater contribution to the average density of }} \\ {\text { the mixture than gas A. }}\end{array}
\end{equation}

Sisi G.
Numerade Educator

Problem 144

Which gas would you expect to deviate most from ideal behavior under conditions of low temperature: $F_{2}, \mathrm{Cl}_{2},$ or $\mathrm{Br}_{2}$ ? Explain.

Matthew B.
Numerade Educator

Problem 145

The volume of a sample of a fixed amount of gas is decreased from 2.0 L to 1.0 L. The temperature of the gas in kelvins is then doubled. What is the final pressure of the gas in terms of the initial pressure?

Sisi G.
Numerade Educator

Problem 146

Which gas sample has the greatest volume at STP?
a. 10.0 $\mathrm{gKr} \quad$ b. 10.0 $\mathrm{g} \mathrm{xe} \quad$ c. 10.0 $\mathrm{gHe}$

Matthew B.
Numerade Educator

Problem 147

Draw a depiction of a gas sample, as described by kinetic molecular theory, containing equal molar amounts of helium, neon, and krypton. Use different color dots to represent each, element. Give each atom a "tail" to represent its velocity relative to the others in the mixture.

Sisi G.
Numerade Educator

Problem 148

Assign one of the three simple gas laws to each member of your group. For the assigned gas law, have each member write two equations, draw a graph, and describe it in a complete sentence. Have each group member present his or her law to the group.

Matthew B.
Numerade Educator

Problem 149

Review the ideal gas law. Without referring back to the text, use algebra to write the ideal gas law and solve for each of the individual variables it contains. Have each group member solve for a different variable and present answers to the group.

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Problem 150

Hydrogen peroxide $\left(\mathrm{H}_{2} \mathrm{O}_{2}\right)$ decomposes in the presence of a catalyst to form water and oxygen. The catalyst is added to 5.00 $\mathrm{mL}$ of a hydrogen peroxide solution at $25.0^{\circ} \mathrm{C}$ and 49.5 $\mathrm{mL}$ of gas is
collected over water at a total pressure of 763.8 $\mathrm{mmHg.}$
\begin{equation}
\begin{array}{l}{\text { a. Write and balance the chemical reaction (note: catalysts do }} \\ {\text { not appear in balanced chemical equations). }} \\ {\text { b. Look up the vapor pressure of water under these conditions. }} \\ {\text { c. What is the partial pressure of oxygen collected over the }} \\ {\text { water? }} \\ {\text { d. How many moles of oxygen are collected? }}\\{\text { e. How many grams of hydrogen peroxide were in the origi- }} \\ {\text { nal sample? }} \\ {\text { f. What is the concentration (in mol/L) of the hydrogen }} \\ {\text { peroxide solution? }} \\ {\text { g. Which part of this process is conceptually most difficult for }} \\ {\text { your group? }}\end{array}
\end{equation}

Matthew B.
Numerade Educator

Problem 151

A box contains equal amounts of helium, argon, and krypton (all gases) at $25^{\circ} \mathrm{C}$ . Using complete sentences, describe the temperatures, masses, average velocities, and average kinetic energy of the three kinds of gas in the mixture. What do they have in common? What are the differences? How are these properties related?

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Problem 152

Calculate the pressure exerted by 1 mol of an ideal gas in a box that is 0.500 $\mathrm{L}$ and 298 $\mathrm{K}$ . Have each group member calculate the pressure of 1 $\mathrm{mol}$ of the following gases in the same box at the same temperature: He, Ne, $\mathrm{H}_{2}, \mathrm{CH}_{4},$ and $\mathrm{CO}_{2} .$ Compare group members' answers as well as all answers with the pressure of an ideal gas. Assuming that the van der Waals equation predictions are accurate, account for why the pressure of each gas is higher or lower than that predicted for an ideal gas.

Matthew B.
Numerade Educator

Problem 153

Air contains about 78.08$\%$ nitrogen gas, 20.95$\%$ oxygen gas, and 0.97$\%$ other gases by volume. When air is combusted in automobile engines, nitrogen oxide gases form. One of these gases, nitric oxide (NO), rapidly oxidizes in air to form nitrogen dioxide $\left(\mathrm{NO}_{2}\right)$ .
Scientists are concerned about the level of $\mathrm{NO}_{\mathrm{x}}$ gas $(\mathrm{NO}_{\mathrm{x}}$ is the term used to refer collectively to nitrogen oxide gases) being emitted by automobile exhaust. People breathing air with elevated levels of $\mathrm{NO}_{2}$ gas are susceptible to increased incidence of asthma attacks, respiratory infection, and inflammation of the breathing airways, which leads to coughing and wheezing. As a result, government and state regulations require new cars to emit less nitrogen oxide gas than new cars did in the past and older cars to have yearly inspections to check the efficiency of their engines. One purpose of a three-way catalytic converter is to convert the $\mathrm{NO}_{\mathrm{x}}$ gases produced as a by- product of the combustion of gasoline with air to $\mathrm{N}_{2}$ and $\mathrm{O}_{2}$ .
The EPA mandates that the overall average concentration of nitrogen dioxide in the air not exceed 0.053 ppmv and not exceed a one-hour average of 0.100 ppmv. Monitoring gas pollutants in cities allows engineers and scientists to caution the public about possible health risks. Figure a charts the average concentration of nitrogen dioxide $\left(\mathrm{NO}_{2}\right)$ and ozone (O $_{3} )$ gases over seven days from nine gas detection stations located equal distances from each other in a city. The particular gas detection system employed in this city can measure the concentration of $\mathrm{NO}_{2}, \mathrm{O}_{3},$ and $\mathrm{CO}$ gases but does not measure the concentration of $\mathrm{NO}$ .

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