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Chemistry

Raymond Chang, Jason Overby

Chapter 5

Gases - all with Video Answers

Educators

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Chapter Questions

00:51

Problem 1

Name five elements and five compounds that exist as gases at room temperature.

Marissa Turner
Marissa Turner
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04:20

Problem 2

List the physical characteristics of gases.

Rey Law
Rey Law
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01:09

Problem 3

Define pressure and give the common units for pressure.

Shivani Naidu
Shivani Naidu
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01:16

Problem 4

When you are in a plane flying at high altitudes, your ears often experience pain. This discomfort can be temporarily relieved by yawning or swallowing some water. Explain.

Rey Law
Rey Law
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00:47

Problem 5

Why is mercury a more suitable substance to use in a barometer than water?

Marissa Turner
Marissa Turner
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02:07

Problem 6

Explain why the height of mercury in a barometer is independent of the cross-sectional area of the tube. Would the barometer still work if the tubing were tilted at an angle, say 15 degrees (see Figure 5.3 )?

Rey Law
Rey Law
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01:04

Problem 7

Explain how a unit of length (mmHg) can be used as a unit for pressure.

Shivani Naidu
Shivani Naidu
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00:48

Problem 8

Describe what would happen to the column of mercury in these manometers when the stopcock is opened.

Rey Law
Rey Law
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Problem 9

What is the difference between a gas and a vapor? At $25^{\circ} \mathrm{C},$ which of the following substances in the gas phase should be properly called a gas and which should be called a vapor: molecular nitrogen $\left(\mathrm{N}_{2}\right)$, mercury?

Shivani Naidu
Shivani Naidu
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Problem 10

If the maximum distance that water may be brought up a well by a suction pump is $34 \mathrm{ft}(10.3 \mathrm{~m})$, how is it possible to obtain water and oil from hundreds of feet below the surface of Earth?

Susan Hallstrom
Susan Hallstrom
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00:49

Problem 11

Why is it that if the barometer reading falls in one part of the world, it must rise somewhere else?

Marissa Turner
Marissa Turner
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01:30

Problem 12

Why do astronauts have to wear protective suits when they are on the surface of the moon?

Rey Law
Rey Law
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01:18

Problem 13

Convert $562 \mathrm{mmHg}$ to atm.

Shivani Naidu
Shivani Naidu
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01:26

Problem 14

The atmospheric pressure at the summit of Denali (formerly known as Mt. McKinley) is $606 \mathrm{mmHg}$ on a certain day. What is the pressure in atm and in kPa?

Narayan Hari
Narayan Hari
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04:05

Problem 15

State the following gas laws in words and also in the form of an equation: Boyle's law, Charles' law, Avogadro's law. In each case, indicate the conditions under which the law is applicable, and give the units for each quantity in the equation.

Shivani Naidu
Shivani Naidu
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04:26

Problem 16

A certain amount of gas is contained in a closed mercury manometer as shown here. Assuming no other parameters change, would $h$ increase, decrease, or remain the same if (a) the amount of the gas were increased; (b) the molar mass of the gas were doubled; (c) the temperature of the gas was increased; (d) the atmospheric pressure in the room was increased; (e) the mercury in the tube were replaced with a less dense fluid; (f) some gas was added to the vacuum at the top of the right-side tube; $(\mathrm{g})$ a hole was drilled in the top of the rightside tube?

Rey Law
Rey Law
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Problem 17

A gaseous sample of a substance is cooled at constant pressure. Which of the diagrams (a)-(d) best represents the situation if the final temperature is
(i) above the boiling point of the substance, and
(ii) below the boiling point but above the freezing point of the substance?

Tom Comey
Tom Comey
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04:18

Problem 18

Consider the following gaseous sample in a cylinder fitted with a movable piston. Initially there are $n$ moles of the gas at temperature $T,$ pressure $P,$ and volume $V$.
Choose the cylinder that correctly represents the gas after each of the following changes. (1) The pressure on the piston is tripled at constant $n$ and $T$.
(2) The temperature is doubled at constant $n$ and $P$.
(3) $n$ moles of another gas are added at constant $T$ and $P .(4) T$ is halved and pressure on the piston is reduced to a quarter of its original value.

Rey Law
Rey Law
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01:43

Problem 19

A gas occupying a volume of $725 \mathrm{~mL}$ at a pressure of 0.970 atm is allowed to expand at constant temperature until its pressure reaches 0.541 atm. What is its final volume?

Shivani Naidu
Shivani Naidu
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01:43

Problem 20

A gas occupying a volume of $725 \mathrm{~mL}$ at a pressure of 0.970 atm is allowed to expand at constant temperature until its pressure reaches 0.541 atm. What is its final volume?

Shivani Naidu
Shivani Naidu
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02:14

Problem 21

The volume of a gas is $5.80 \mathrm{~L}$, measured at 1.00 atm. What is the pressure of the gas in $\mathrm{mmHg}$ if the volume is changed to $9.65 \mathrm{~L} ?$ (The temperature remains constant.)

Shivani Naidu
Shivani Naidu
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01:19

Problem 22

A sample of air occupies $3.8 \mathrm{~L}$ when the pressure is 1.2 atm.
(a) What volume does it occupy at 6.6 atm?
(b) What pressure is required in order to compress it to $0.075 \mathrm{~L} ?$ (The temperature is kept constant.)

Rey Law
Rey Law
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02:00

Problem 23

A 36.4-L volume of methane gas is heated from $25^{\circ} \mathrm{C}$ to $88^{\circ} \mathrm{C}$ at constant pressure. What is the final volume of the gas?

Shivani Naidu
Shivani Naidu
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06:04

Problem 24

Under constant-pressure conditions a sample of hydrogen gas initially at $88^{\circ} \mathrm{C}$ and $9.6 \mathrm{~L}$ is cooled until its final volume is $3.4 \mathrm{~L}$. What is its final temperature?

Jennifer Hudspeth
Jennifer Hudspeth
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02:46

Problem 25

Ammonia burns in oxygen gas to form nitric oxide (NO) and water vapor. How many volumes of NO are obtained from one volume of ammonia at the
same temperature and pressure?

Marissa Turner
Marissa Turner
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01:21

Problem 26

Molecular chlorine and molecular fluorine combine to form a gaseous product. Under the same conditions of temperature and pressure it is found that one volume of $\mathrm{Cl}_{2}$ reacts with three volumes of $\mathrm{F}_{2}$ to yield two volumes of the product. What is the formula of the product?

Rey Law
Rey Law
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02:17

Problem 27

List the characteristics of an ideal gas. Write the ideal gas equation and also state it in words. Give the units for each term in the equation.

Shivani Naidu
Shivani Naidu
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03:02

Problem 28

Use Equation (5.9) to derive all the gas laws.

Charles Thomas
Charles Thomas
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01:02

Problem 29

What are standard temperature and pressure (STP)? What is the significance of STP in relation to the volume of 1 mole of an ideal gas?

Shivani Naidu
Shivani Naidu
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01:20

Problem 30

Why is the density of a gas much lower than that of a liquid or solid under atmospheric conditions? What units are normally used to express the density of gases?

Rey Law
Rey Law
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01:37

Problem 31

A sample of nitrogen gas kept in a container of volume $2.3 \mathrm{~L}$ and at a temperature of $32^{\circ} \mathrm{C}$ exerts a pressure of 4.7 atm. Calculate the number of moles of gas present.

Shivani Naidu
Shivani Naidu
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01:21

Problem 32

Given that 6.9 moles of carbon monoxide gas are present in a container of volume $30.4 \mathrm{~L},$ what is the pressure of the gas (in atm) if the temperature is $62^{\circ} \mathrm{C} ?$

Rey Law
Rey Law
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01:40

Problem 33

What volume will 5.6 moles of sulfur hexafluoride $\left(\mathrm{SF}_{6}\right)$ gas occupy if the temperature and pressure of the gas are $128^{\circ} \mathrm{C}$ and 9.4 atm?

Shivani Naidu
Shivani Naidu
Numerade Educator
01:21

Problem 34

A certain amount of gas at $25^{\circ} \mathrm{C}$ and at a pressure of 0.800 atm is contained in a glass vessel. Suppose that the vessel can withstand a pressure of 2.00 atm. How high can you raise the temperature of the gas without bursting the vessel?

Rey Law
Rey Law
Numerade Educator
01:59

Problem 35

A gas-filled balloon having a volume of $2.50 \mathrm{~L}$ at 1.2 atm and $25^{\circ} \mathrm{C}$ is allowed to rise to the stratosphere (about $30 \mathrm{~km}$ above the surface of Earth), where the temperature and pressure are $-23^{\circ} \mathrm{C}$ and $3.00 \times 10^{-3}$ atm, respectively. Calculate the final volume of the balloon.

Shivani Naidu
Shivani Naidu
Numerade Educator
01:17

Problem 36

The temperature of $2.5 \mathrm{~L}$ of a gas initially at $\mathrm{STP}$ is raised to $250^{\circ} \mathrm{C}$ at constant volume. Calculate the final pressure of the gas in atm.

Rey Law
Rey Law
Numerade Educator
02:44

Problem 37

The pressure of $6.0 \mathrm{~L}$ of an ideal gas in a flexible container is decreased to one-third of its original pressure, and its absolute temperature is decreased by one-half. What is the final volume of the gas?

Cheryl Glor
Cheryl Glor
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01:24

Problem 38

A gas evolved during the fermentation of glucose (wine making) has a volume of $0.78 \mathrm{~L}$ at $20.1^{\circ} \mathrm{C}$ and 1.00 atm. What was the volume of this gas at the fermentation temperature of $36.5^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}$ pressure?

Rey Law
Rey Law
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02:16

Problem 39

An ideal gas originally at 0.85 atm and $66^{\circ} \mathrm{C}$ was allowed to expand until its final volume, pressure, and temperature were $94 \mathrm{~mL}, 0.60 \mathrm{~atm},$ and $45^{\circ} \mathrm{C}$ respectively. What was its initial volume?

Shivani Naidu
Shivani Naidu
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01:13

Problem 40

Calculate its volume (in liters) of $88.4 \mathrm{~g}$ of $\mathrm{CO}_{2}$ at STP.

Rey Law
Rey Law
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02:10

Problem 41

A gas at $772 \mathrm{mmHg}$ and $35.0^{\circ} \mathrm{C}$ occupies a volume of $6.85 \mathrm{~L}$. Calculate its volume at STP.

Shivani Naidu
Shivani Naidu
Numerade Educator
03:53

Problem 42

Dry ice is solid carbon dioxide. A $0.050-\mathrm{g}$ sample of dry ice is placed in an evacuated $4.6-\mathrm{L}$ vessel at $30^{\circ} \mathrm{C} .$ Calculate the pressure inside the vessel after all the dry ice has been converted to $\mathrm{CO}_{2}$ gas.

Marissa Turner
Marissa Turner
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02:17

Problem 43

At STP, $0.280 \mathrm{~L}$ of a gas weighs $0.400 \mathrm{~g}$. Calculate the molar mass of the gas.

Marissa Turner
Marissa Turner
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03:06

Problem 44

At 741 torr and $44^{\circ} \mathrm{C}, 7.10 \mathrm{~g}$ of a gas occupy a volume of $5.40 \mathrm{~L}$. What is the molar mass of the gas?

Rey Law
Rey Law
Numerade Educator
02:47

Problem 45

Ozone molecules in the stratosphere absorb much of the harmful radiation from the sun. Typically, the temperature and pressure of ozone in the stratosphere are $250 \mathrm{~K}$ and $1.0 \times 10^{-3}$ atm, respectively. How many ozone molecules are present in $1.0 \mathrm{~L}$ of air under these conditions?

Shivani Naidu
Shivani Naidu
Numerade Educator
04:47

Problem 46

Assuming that air contains 78 percent $\mathrm{N}_{2}, 21$ percent $\mathrm{O}_{2}$, and 1 percent Ar, all by volume, how many molecules of each type of gas are present in $1.0 \mathrm{~L}$ of air at STP?

Marissa Turner
Marissa Turner
Numerade Educator
02:25

Problem 47

A 2.10-L vessel contains 4.65 g of a gas at 1.00 atm and $27.0^{\circ} \mathrm{C}$. (a) Calculate the density of the gas in grams per liter. (b) What is the molar mass of the gas?

Shalini Tyagi
Shalini Tyagi
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03:03

Problem 48

Calculate the density of hydrogen bromide (HBr) gas in grams per liter at $733 \mathrm{mmHg}$ and $46^{\circ} \mathrm{C}$.

Rey Law
Rey Law
Numerade Educator
08:21

Problem 49

A certain anesthetic contains 64.9 percent $\mathrm{C}, 13.5$ percent $\mathrm{H},$ and 21.6 percent $\mathrm{O}$ by mass. At $120^{\circ} \mathrm{C}$ and $750 \mathrm{mmHg}, 1.00 \mathrm{~L}$ of the gaseous compound weighs $2.30 \mathrm{~g}$. What is the molecular formula of the compound?

Marissa Turner
Marissa Turner
Numerade Educator
04:44

Problem 50

A compound has the empirical formula $\mathrm{SF}_{4}$. At $20^{\circ} \mathrm{C}, 0.100 \mathrm{~g}$ of the gaseous compound occupies a volume of $22.1 \mathrm{~mL}$ and exerts a pressure of 1.02 atm. What is the molecular formula of the gas?

Marissa Turner
Marissa Turner
Numerade Educator
15:41

Problem 51

What pressure will be required for neon at $30^{\circ} \mathrm{C}$ to have the same density as nitrogen at $20^{\circ} \mathrm{C}$ and $1.0 \mathrm{~atm} ?$

Shazia Naz
Shazia Naz
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05:08

Problem 52

The density of a mixture of fluorine and chlorine gases is $1.77 \mathrm{~g} / \mathrm{L}$ at $14^{\circ} \mathrm{C}$ and 0.893 atm. Calculate the mass percent of the gases.

Charles Thomas
Charles Thomas
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10:00

Problem 53

Consider the formation of nitrogen dioxide from nitric oxide and oxygen:
$$
2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{NO}_{2}(g)
$$
If $9.0 \mathrm{~L}$ of $\mathrm{NO}$ are reacted with excess $\mathrm{O}_{2}$ at $\mathrm{STP}$, what is the volume in liters of the $\mathrm{NO}_{2}$ produced?

Shazia Naz
Shazia Naz
Numerade Educator
01:43

Problem 54

Methane, the principal component of natural gas, is used for heating and cooking. The combustion process is
$$
\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)
$$
If 15.0 moles of $\mathrm{CH}_{4}$ are reacted, what is the volume of $\mathrm{CO}_{2}$ (in liters) produced at $23.0^{\circ} \mathrm{C}$ and 0.985 atm?

Rey Law
Rey Law
Numerade Educator
12:16

Problem 55

When coal is burned, the sulfur present in coal is converted to sulfur dioxide $\left(\mathrm{SO}_{2}\right),$ which is responsible for the acid rain phenomenon.
$$
\mathrm{S}(s)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{SO}_{2}(g)
$$
If $2.54 \mathrm{~kg}$ of $\mathrm{S}$ are reacted with oxygen, calculate the volume of $\mathrm{SO}_{2}$ gas (in $\mathrm{mL}$ ) formed at $30.5^{\circ} \mathrm{C}$ and 1.12 atm.

Shazia Naz
Shazia Naz
Numerade Educator
03:14

Problem 56

In alcohol fermentation, yeast converts glucose to ethanol and carbon dioxide:
$$
\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+2 \mathrm{CO}_{2}(g)
$$
If $5.97 \mathrm{~g}$ of glucose are reacted and $1.44 \mathrm{~L}$ of $\mathrm{CO}_{2}$ gas are collected at $293 \mathrm{~K}$ and $0.984 \mathrm{~atm},$ what is the percent yield of the reaction?

Rey Law
Rey Law
Numerade Educator
25:52

Problem 57

A compound of $\mathrm{P}$ and $\mathrm{F}$ was analyzed as follows:
Heating $0.2324 \mathrm{~g}$ of the compound in a $378-\mathrm{cm}^{3}$ container turned all of it to gas, which had a pressure of $97.3 \mathrm{mmHg}$ at $77^{\circ} \mathrm{C}$. Then the gas was mixed with calcium chloride solution, which turned all of the $\mathrm{F}$ to $0.2631 \mathrm{~g}$ of $\mathrm{CaF}_{2}$. Determine the molecular formula of the compound.

Shazia Naz
Shazia Naz
Numerade Educator
06:14

Problem 58

A quantity of $0.225 \mathrm{~g}$ of a metal $\mathrm{M}$ (molar mass = $27.0 \mathrm{~g} / \mathrm{mol}$ ) liberated $0.303 \mathrm{~L}$ of molecular hydrogen (measured at $17^{\circ} \mathrm{C}$ and $741 \mathrm{mmHg}$ ) from an excess of hydrochloric acid. Deduce from these data the corresponding equation and write formulas for the oxide and sulfate of M.

Marissa Turner
Marissa Turner
Numerade Educator
04:46

Problem 59

What is the mass of the solid $\mathrm{NH}_{4} \mathrm{Cl}$ formed when $73.0 \mathrm{~g}$ of $\mathrm{NH}_{3}$ are mixed with an equal mass of HCl? What is the volume of the gas remaining, measured at $14.0^{\circ} \mathrm{C}$ and $752 \mathrm{mmHg}$ ? What gas is it?

Nicole Smina
Nicole Smina
Numerade Educator
02:44

Problem 60

Dissolving $3.00 \mathrm{~g}$ of an impure sample of calcium carbonate in hydrochloric acid produced $0.656 \mathrm{~L}$ of carbon dioxide (measured at $20.0^{\circ} \mathrm{C}$ and $792 \mathrm{mmHg}$ ). Calculate the percent by mass of calcium carbonate in the sample. State any assumptions.

Rey Law
Rey Law
Numerade Educator
03:28

Problem 61

Calculate the mass in grams of hydrogen chloride produced when $5.6 \mathrm{~L}$ of molecular hydrogen measured at STP react with an excess of molecular chlorine gas.

Marissa Turner
Marissa Turner
Numerade Educator
04:27

Problem 62

Ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$ burns in air:
$$
\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)
$$
Balance the equation and determine the volume of air in liters at $35.0^{\circ} \mathrm{C}$ and $790 \mathrm{mmHg}$ required to burn $227 \mathrm{~g}$ of ethanol. Assume that air is 21.0 percent $\mathrm{O}_{2}$ by volume.

Rey Law
Rey Law
Numerade Educator
10:10

Problem 63

(a) What volumes (in liters) of ammonia and oxygen must react to form $12.8 \mathrm{~L}$ of nitric oxide according to the equation at the same temperature and pressure?
$$
4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \longrightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)
$$
(b) What volumes (in liters) of propane and water vapor must react to form $8.96 \mathrm{~L}$ of hydrogen according to the equation at the same temperature and pressure?
$$
\mathrm{C}_{3} \mathrm{H}_{8}(g)+3 \mathrm{H}_{2} \mathrm{O}(g) \longrightarrow 3 \mathrm{CO}(g)+7 \mathrm{H}_{2}(g)
$$

Shazia Naz
Shazia Naz
Numerade Educator
03:00

Problem 64

A 4.00-g sample of FeS containing nonsulfide impurities reacted with $\mathrm{HCl}$ to give $896 \mathrm{~mL}$ of $\mathrm{H}_{2} \mathrm{~S}$ at $14^{\circ} \mathrm{C}$ and $782 \mathrm{mmHg} .$ Calculate mass percent purity of the sample.

Rey Law
Rey Law
Numerade Educator
01:50

Problem 65

State Dalton's law of partial pressures and explain what mole fraction is. Does mole fraction have units?

Marissa Turner
Marissa Turner
Numerade Educator
00:53

Problem 66

A sample of air contains only nitrogen and oxygen gases whose partial pressures are 0.80 atm and 0.20 atm, respectively. Calculate the total pressure and the mole fractions of the gases.

Rey Law
Rey Law
Numerade Educator
02:01

Problem 67

A mixture of gases contains $0.31 \mathrm{~mol} \mathrm{CH}_{4}, 0.25 \mathrm{~mol}$ $\mathrm{C}_{2} \mathrm{H}_{6},$ and $0.29 \mathrm{~mol} \mathrm{C}_{3} \mathrm{H}_{8} .$ The total pressure is 1.50 atm. Calculate the partial pressures of the gases.

Marissa Turner
Marissa Turner
Numerade Educator
02:51

Problem 68

A 2.5 -L flask at $15^{\circ} \mathrm{C}$ contains a mixture of $\mathrm{N}_{2}, \mathrm{He}$ and Ne at partial pressures of 0.32 atm for $\mathrm{N}_{2}$, 0.15 atm for $\mathrm{He},$ and 0.42 atm for $\mathrm{Ne} .$ (a) Calculate the total pressure of the mixture. (b) Calculate the volume in liters at STP occupied by He and Ne if the $\mathrm{N}_{2}$ is removed selectively.

Rey Law
Rey Law
Numerade Educator
06:55

Problem 69

Dry air near sea level has the following composition by volume: $\mathrm{N}_{2}, 78.08$ percent; $\mathrm{O}_{2}, 20.94$ percent; Ar, 0.93 percent; $\mathrm{CO}_{2}, 0.05$ percent. The atmospheric pressure is 1.00 atm. Calculate (a) the partial pressure of each gas in atm and (b) the concentration of each gas in moles per liter at $0^{\circ} \mathrm{C}$.

Ankit Pandey
Ankit Pandey
Numerade Educator
01:06

Problem 70

A mixture of helium and neon gases is collected over water at $28.0^{\circ} \mathrm{C}$ and $745 \mathrm{mmHg} .$ If the partial pressure of helium is $368 \mathrm{mmHg}$, what is the partial pressure of neon? (Vapor pressure of water at $28^{\circ} \mathrm{C}=$ $28.3 \mathrm{mmHg} .$ )

Rey Law
Rey Law
Numerade Educator
04:32

Problem 71

A piece of sodium metal reacts completely with water as follows:
$$
2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g)
$$
The hydrogen gas generated is collected over water at $25.0^{\circ} \mathrm{C}$. The volume of the gas is $246 \mathrm{~mL}$ measured at 1.00 atm. Calculate the number of grams of sodium used in the reaction. (Vapor pressure of water at $25^{\circ} \mathrm{C}=0.0313$ atm. $)$

Marissa Turner
Marissa Turner
Numerade Educator
03:35

Problem 72

A sample of zinc metal reacts completely with an excess of hydrochloric acid:
$$
\operatorname{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g)
$$
The hydrogen gas produced is collected over water at $25.0^{\circ} \mathrm{C}$ using an arrangement similar to that shown in Figure $5.15 .$ The volume of the gas is $7.80 \mathrm{~L},$ and the pressure is $0.980 \mathrm{~atm} .$ Calculate the amount of zinc metal in grams consumed in the reaction. (Vapor pressure of water at $25^{\circ} \mathrm{C}=23.8 \mathrm{mmHg} .$ )

Rey Law
Rey Law
Numerade Educator
02:45

Problem 73

Helium is mixed with oxygen gas for deep-sea divers. Calculate the percent by volume of oxygen gas in the mixture if the diver has to submerge to a depth where the total pressure is 4.2 atm. The partial pressure of oxygen is maintained at 0.20 atm at this depth.

Shazia Naz
Shazia Naz
Numerade Educator
02:09

Problem 74

A sample of ammonia $\left(\mathrm{NH}_{3}\right)$ gas is completely decomposed to nitrogen and hydrogen gases over heated iron wool. If the total pressure is $866 \mathrm{mmHg}$, calculate the partial pressures of $\mathrm{N}_{2}$ and $\mathrm{H}_{2}$.

Rey Law
Rey Law
Numerade Educator
View

Problem 75

Consider the three gas containers (i)-(iii). All of them have the same volume and are at the same temperature. (a) Which container has the smallest mole fraction of gas A (blue sphere)? (b) Which container has the highest partial pressure of gas $\mathrm{B}$ (green sphere)?

Tom Comey
Tom Comey
Numerade Educator
02:44

Problem 76

The volume of the box on the right is twice that of the box on the left. The boxes contain helium atoms (red) and hydrogen molecules (green) at the same temperature.
(a) Which box has a higher total pressure? (b) Which box has a lower partial pressure of helium?

Rey Law
Rey Law
Numerade Educator
04:00

Problem 77

What are the basic assumptions of the kinetic molecular theory of gases? How does the kinetic molecular theory explain Boyle's law, Charles' law, Avogadro's law, and Dalton's law of partial pressures?

Crystal Wang
Crystal Wang
Numerade Educator
00:54

Problem 78

What does the Maxwell speed distribution curve tell us? Does Maxwell's theory work for a sample of 200 molecules? Explain.

Rey Law
Rey Law
Numerade Educator
05:37

Problem 79

Which of the following statements is correct?
(a) Heat is produced by the collision of gas molecules against one another. (b) When a gas is heated, the molecules collide with one another more often.

Shazia Naz
Shazia Naz
Numerade Educator
01:10

Problem 80

What is the difference between gas diffusion and effusion? State Graham's law and define the terms in Equation (5.17)

Rey Law
Rey Law
Numerade Educator
03:24

Problem 81

Compare the root-mean-square speeds of $\mathrm{O}_{2}$ and $\mathrm{UF}_{6}$ at $65^{\circ} \mathrm{C}$

Marissa Turner
Marissa Turner
Numerade Educator
04:43

Problem 82

The temperature in the stratosphere is $-23^{\circ} \mathrm{C}$. Calculate the root-mean-square speeds of $\mathrm{N}_{2}, \mathrm{O}_{2}$ and $\mathrm{O}_{3}$ molecules in this region.

Marissa Turner
Marissa Turner
Numerade Educator
02:07

Problem 83

The average distance traveled by a molecule between successive collisions is called mean free path. For a given amount of a gas, how does the mean free path of a gas depend on (a) density, (b) temperature at constant volume, (c) pressure at constant temperature, (d) volume at constant temperature, and (e) size of the atoms?

Marissa Turner
Marissa Turner
Numerade Educator
01:44

Problem 84

At a certain temperature the speeds of six gaseous molecules in a container are $2.0 \mathrm{~m} / \mathrm{s}, 2.2 \mathrm{~m} / \mathrm{s}, 2.6 \mathrm{~m} / \mathrm{s}$ $2.7 \mathrm{~m} / \mathrm{s}, 3.3 \mathrm{~m} / \mathrm{s},$ and $3.5 \mathrm{~m} / \mathrm{s} .$ Calculate the root-
mean-square speed and the average speed of the molecules. These two average values are close to each other, but the root-mean-square value is always the larger of the two. Why?

Charles Thomas
Charles Thomas
Numerade Educator
07:49

Problem 85

Based on your knowledge of the kinetic theory of gases, derive Graham's law [Equation (5.17)].

Shazia Naz
Shazia Naz
Numerade Educator
01:10

Problem 86

The ${ }^{235} \mathrm{U}$ isotope undergoes fission when bombarded with neutrons. However, its natural abundance is only 0.72 percent. To separate it from the more abundant ${ }^{238} \mathrm{U}$ isotope, uranium is first converted to UF $_{6}$, which is easily vaporized above room temperature. The mixture of the ${ }^{235} \mathrm{UF}_{6}$ and ${ }^{238} \mathrm{UF}_{6}$ gases is then subjected to many stages of effusion. Calculate the separation factor, that is, the enrichment of ${ }^{235} \mathrm{U}$ relative to ${ }^{238} \mathrm{U}$ after one stage of effusion.

Rey Law
Rey Law
Numerade Educator
07:29

Problem 87

A gas evolved from the fermentation of glucose is found to effuse through a porous barrier in $15.0 \mathrm{~min} .$ Under the same conditions of temperature and pressure, it takes an equal volume of $\mathrm{N}_{2} 12.0 \mathrm{~min}$ to effuse through the same barrier. Calculate the molar mass of the gas and suggest what the gas might be.

Shazia Naz
Shazia Naz
Numerade Educator
03:31

Problem 88

Nickel forms a gaseous compound of the formula $\mathrm{Ni}(\mathrm{CO})_{x} .$ What is the value of $x$ given the fact that under the same conditions of temperature and pressure, methane $\left(\mathrm{CH}_{4}\right)$ effuses 3.3 times faster than the compound?

Marissa Turner
Marissa Turner
Numerade Educator
01:38

Problem 89

Cite two pieces of evidence to show that gases do not behave ideally under all conditions.

Marissa Turner
Marissa Turner
Numerade Educator
01:59

Problem 90

Under what set of conditions would a gas be expected to behave most ideally: (a) high temperature and low pressure, (b) high temperature and high pressure, (c) low temperature and high pressure, or (d) low temperature and low pressure?

Marissa Turner
Marissa Turner
Numerade Educator
04:11

Problem 91

Shown are plots of $P V / R T$ against $P$ for one mole of a nonideal gas at two different temperatures. Which curve is at the higher temperature?

Shazia Naz
Shazia Naz
Numerade Educator
02:02

Problem 92

(a) A real gas is introduced into a flask of volume $V$. Is the corrected volume of the gas greater or less than $V ?$ (b) Ammonia has a larger $a$ value than neon does (see Table 5.4 ). What can you conclude about the relative strength of the attractive forces between molecules of ammonia and between atoms of neon?

Charles Thomas
Charles Thomas
Numerade Educator
08:25

Problem 93

Using the data shown in Table $5.4,$ calculate the pressure exerted by 2.50 moles of $\mathrm{CO}_{2}$ confined in a volume of $5.00 \mathrm{~L}$ at $450 \mathrm{~K}$. Compare the pressure with that predicted by the ideal gas equation.

Shazia Naz
Shazia Naz
Numerade Educator
00:57

Problem 94

At $27^{\circ} \mathrm{C}, 10.0$ moles of a gas in a 1.50 -L container exert a pressure of 130 atm. Is this an ideal gas?

Marissa Turner
Marissa Turner
Numerade Educator
02:18

Problem 95

Discuss the following phenomena in terms of the gas laws: (a) the pressure increase in an automobile tire on a hot day; (b) the "popping" of a paper bag; (c) the expansion of a weather balloon as it rises in the air; (d) the loud noise heard when a lightbulb shatters.

Marissa Turner
Marissa Turner
Numerade Educator
01:32

Problem 96

Under the same conditions of temperature and pressure, which of the following gases would behave most ideally: Ne, $\mathrm{N}_{2}$, or $\mathrm{CH}_{4}$ ? Explain.

Marissa Turner
Marissa Turner
Numerade Educator
06:29

Problem 97

Nitroglycerin, an explosive compound, decomposes according to the equation
$4 \mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(s) \longrightarrow$
$$
12 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)+6 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g)
$$
Calculate the total volume of gases when collected at 1.2 atm and $25^{\circ} \mathrm{C}$ from $2.6 \times 10^{2} \mathrm{~g}$ of nitroglycerin. What are the partial pressures of the gases under these conditions?

Marissa Turner
Marissa Turner
Numerade Educator
02:21

Problem 98

The empirical formula of a compound is $\mathrm{CH}$. At $200^{\circ} \mathrm{C}, 0.145 \mathrm{~g}$ of this compound occupies $97.2 \mathrm{~mL}$
at a pressure of 0.74 atm. What is the molecular formula of the compound?

Marissa Turner
Marissa Turner
Numerade Educator
03:17

Problem 99

When ammonium nitrite $\left(\mathrm{NH}_{4} \mathrm{NO}_{2}\right)$ is heated, it decomposes to give nitrogen gas. This property is used to inflate some tennis balls.
(a) Write a balanced equation for the reaction. (b) Calculate the quantity (in grams) of $\mathrm{NH}_{4} \mathrm{NO}_{2}$ needed to inflate a tennis ball to a volume of $86.2 \mathrm{~mL}$ at $1.20 \mathrm{~atm}$ and $22^{\circ} \mathrm{C}$.

Marissa Turner
Marissa Turner
Numerade Educator
05:23

Problem 100

The percent by mass of bicarbonate $\left(\mathrm{HCO}_{3}^{-}\right)$ in a certain Alka-Seltzer product is 32.5 percent. Calculate the volume of $\mathrm{CO}_{2}$ generated (in $\mathrm{mL}$ ) at $37^{\circ} \mathrm{C}$ and 1.00 atm when a person ingests a $3.29-\mathrm{g}$ tablet. (Hint: The reaction is between $\mathrm{HCO}_{3}^{-}$ and $\mathrm{HCl}$ acid in the stomach.

Marissa Turner
Marissa Turner
Numerade Educator
02:40

Problem 101

The boiling point of liquid nitrogen is $-196^{\circ} \mathrm{C}$. On the basis of this information alone, do you think nitrogen is an ideal gas?

Shazia Naz
Shazia Naz
Numerade Educator
02:33

Problem 102

In the metallurgical process of refining nickel, the metal is first combined with carbon monoxide to form tetracarbonylnickel, which is a gas at $43^{\circ} \mathrm{C}$ :
$$
\mathrm{Ni}(s)+4 \mathrm{CO}(g) \longrightarrow \mathrm{Ni}(\mathrm{CO})_{4}(g)
$$
This reaction separates nickel from other solid impurities. (a) Starting with $86.4 \mathrm{~g}$ of $\mathrm{Ni}$, calculate the pressure of $\mathrm{Ni}(\mathrm{CO})_{4}$ in a container of volume $4.00 \mathrm{~L}$. (Assume the above reaction goes to completion.)
(b) At temperatures above $43^{\circ} \mathrm{C}$, the pressure of the gas is observed to increase much more rapidly than predicted by the ideal gas equation. Explain.

Charles Thomas
Charles Thomas
Numerade Educator
01:31

Problem 103

The partial pressure of carbon dioxide varies with seasons. Would you expect the partial pressure in the Northern Hemisphere to be higher in the summer or winter? Explain.

Marissa Turner
Marissa Turner
Numerade Educator
03:11

Problem 104

A healthy adult exhales about $5.0 \times 10^{2} \mathrm{~mL}$ of a gaseous mixture with each breath. Calculate the number of molecules present in this volume at $37^{\circ} \mathrm{C}$ and 1.1 atm. List the major components of this gaseous mixture.

Marissa Turner
Marissa Turner
Numerade Educator
12:37

Problem 105

Sodium bicarbonate $\left(\mathrm{NaHCO}_{3}\right)$ is called baking soda because when heated, it releases carbon dioxide gas, which is responsible for the rising of cookies, doughnuts, and bread. (a) Calculate the volume (in liters) of $\mathrm{CO}_{2}$ produced by heating $5.0 \mathrm{~g}$ of $\mathrm{NaHCO}_{3}$ at $180^{\circ} \mathrm{C}$ and 1.3 atm. (b) Ammonium bicarbonate $\left(\mathrm{NH}_{4} \mathrm{HCO}_{3}\right)$ has also been used for the same purpose. Suggest one advantage and one disadvantage of using $\mathrm{NH}_{4} \mathrm{HCO}_{3}$ instead of $\mathrm{NaHCO}_{3}$ for baking.

Shazia Naz
Shazia Naz
Numerade Educator
03:14

Problem 106

A barometer having a cross-sectional area of $1.00 \mathrm{~cm}^{2}$ at sea level measures a pressure of $76.0 \mathrm{~cm}$ of mercury. The pressure exerted by this column of mercury is equal to the pressure exerted by all the air on $1 \mathrm{~cm}^{2}$ of Earth's surface. Given that the density of mercury is $13.6 \mathrm{~g} / \mathrm{mL}$ and the average radius of Earth is $6371 \mathrm{~km},$ calculate the total mass of Earth's atmosphere in kilograms. (Hint: The surface area of a sphere is $4 \pi r^{2},$ where $r$ is the radius of the sphere.)

Charles Thomas
Charles Thomas
Numerade Educator
02:44

Problem 107

Some commercial drain cleaners contain a mixture of sodium hydroxide and aluminum powder. When the mixture is poured down a clogged drain, the following reaction occurs:
$$
\begin{array}{r}
2 \mathrm{NaOH}(a q)+2 \mathrm{Al}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \\
2 \mathrm{NaAl}(\mathrm{OH})_{4}(a q)+3 \mathrm{H}_{2}(g)
\end{array}
$$
The heat generated in this reaction helps melt away obstructions such as grease, and the hydrogen gas released stirs up the solids clogging the drain. Calculate the volume of $\mathrm{H}_{2}$ formed at $23^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}$ if $3.12 \mathrm{~g}$ of $\mathrm{Al}$ are treated with an excess of $\mathrm{NaOH}$.

Marissa Turner
Marissa Turner
Numerade Educator
02:36

Problem 108

The volume of a sample of pure HCl gas was $189 \mathrm{~mL}$ at $25^{\circ} \mathrm{C}$ and $108 \mathrm{mmHg} .$ It was completely dissolved in about $60 \mathrm{~mL}$ of water and titrated with an $\mathrm{NaOH}$ solution; $15.7 \mathrm{~mL}$ of the $\mathrm{NaOH}$ solution were required to neutralize the $\mathrm{HCl}$. Calculate the molarity of the $\mathrm{NaOH}$ solution.

Marissa Turner
Marissa Turner
Numerade Educator
03:59

Problem 109

Propane $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)$ burns in oxygen to produce carbon dioxide gas and water vapor. (a) Write a balanced equation for this reaction.
(b) Calculate the number of liters of carbon dioxide measured at STP that could be produced from $7.45 \mathrm{~g}$ of propane.

Marissa Turner
Marissa Turner
Numerade Educator
05:21

Problem 110

Consider this apparatus. Calculate the partial pressures of helium and neon after the stopcock is open. The temperature remains constant at $16^{\circ} \mathrm{C}$.

Marissa Turner
Marissa Turner
Numerade Educator
View

Problem 111

Nitric oxide (NO) reacts with molecular oxygen as follows:
$$
\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)
$$
Initially NO and $\mathrm{O}_{2}$ are separated as shown here. When the valve is opened, the reaction quickly goes to completion. Determine what gases remain at the end and calculate their partial pressures. Assume that the temperature remains constant at $25^{\circ} \mathrm{C}$.

Tom Comey
Tom Comey
Numerade Educator
01:20

Problem 112

Consider this apparatus. When a small amount of water is introduced into the flask by squeezing the bulb of the medicine dropper, water is squirted upward out of the long glass tubing. Explain this observation. (Hint: Hydrogen chloride gas is soluble in water.)

Marissa Turner
Marissa Turner
Numerade Educator
03:08

Problem 113

Describe how you would measure, by either chemical or physical means, the partial pressures of a mixture of gases of the following composition:
(a) $\mathrm{CO}_{2}$ and $\mathrm{H}_{2,}(\mathrm{~b}) \mathrm{He}$ and $\mathrm{N}_{2}$

Marissa Turner
Marissa Turner
Numerade Educator
View

Problem 114

A certain hydrate has the formula $\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}$. A quantity of $54.2 \mathrm{~g}$ of the compound is heated in an oven to drive off the water. If the steam generated exerts a pressure of 24.8 atm in a $2.00-\mathrm{L}$ container $\mathrm{at}$ $120^{\circ} \mathrm{C},$ calculate $x$

Tom Comey
Tom Comey
Numerade Educator
16:09

Problem 115

A mixture of $\mathrm{Na}_{2} \mathrm{CO}_{3}$ and $\mathrm{MgCO}_{3}$ of mass $7.63 \mathrm{~g}$ is reacted with an excess of hydrochloric acid. The $\mathrm{CO}_{2}$ gas generated occupies a volume of $1.67 \mathrm{~L}$ at 1.24 atm and $26^{\circ} \mathrm{C}$. From these data, calculate the percent composition by mass of $\mathrm{Na}_{2} \mathrm{CO}_{3}$ in the mixture.

Shazia Naz
Shazia Naz
Numerade Educator
05:31

Problem 116

The following apparatus can be used to measure atomic and molecular speed. Suppose that a beam of metal atoms is directed at a rotating cylinder in a vacuum. A small opening in the cylinder allows the atoms to strike a target area. Because the cylinder is rotating, atoms traveling at different speeds will strike the target at different positions. In time, a layer of the metal will deposit on the target area, and the variation in its thickness is found to correspond to Maxwell's speed distribution. In one experiment it is found that at $850^{\circ} \mathrm{C}$ some bismuth (Bi) atoms struck the target at a point $2.80 \mathrm{~cm}$ from the spot directly opposite the slit. The diameter of the cylinder is $15.0 \mathrm{~cm}$ and it is rotating at 130 revolutions per second. (a) Calculate the speed (m/s) at which the target is moving. (Hint: The circumference of a circle is given by $2 \pi r,$ where $r$ is the radius. $)$
(b) Calculate the time (in seconds) it takes for the target to travel $2.80 \mathrm{~cm} .$ (c) Determine the speed of the Bi atoms. Compare your result in (c) with the $u_{\mathrm{rms}}$ of $\mathrm{Bi}$ at $850^{\circ} \mathrm{C}$. Comment on the difference.

Rashmi Sinha
Rashmi Sinha
Numerade Educator
02:18

Problem 117

If $10.00 \mathrm{~g}$ of water are introduced into an evacuated flask of volume $2.500 \mathrm{~L}$ at $65^{\circ} \mathrm{C},$ calculate the mass of water vaporized. (Hint: Assume that the volume of the remaining liquid water is negligible; the vapor pressure of water at $65^{\circ} \mathrm{C}$ is $187.5 \mathrm{mmHg} .$

Marissa Turner
Marissa Turner
Numerade Educator
01:58

Problem 118

Commercially, compressed oxygen is sold in metal cylinders. If a 120-L cylinder is filled with oxygen to a pressure of 132 atm at $22^{\circ} \mathrm{C},$ what is the mass (in grams) of $\mathrm{O}_{2}$ present? How many liters of $\mathrm{O}_{2}$ gas at 1.00 atm and $22^{\circ} \mathrm{C}$ could the cylinder produce? (Assume ideal behavior.)

Charles Thomas
Charles Thomas
Numerade Educator
01:20

Problem 119

The shells of hard-boiled eggs sometimes crack due to the rapid thermal expansion of the shells at high temperatures. Suggest another reason why the shells may crack.

Marissa Turner
Marissa Turner
Numerade Educator
01:02

Problem 120

Ethylene gas $\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)$ is emitted by fruits and is known to be responsible for their ripening. Based on this information, explain why a bunch of bananas ripens faster in a closed paper bag than in a bowl.

Charles Thomas
Charles Thomas
Numerade Educator
04:49

Problem 121

About $8.0 \times 10^{6}$ tons of urea $\left[\left(\mathrm{NH}_{2}\right)_{2} \mathrm{CO}\right]$ are used annually as a fertilizer. The urea is prepared at $200^{\circ} \mathrm{C}$ and under high-pressure conditions from carbon dioxide and ammonia (the products are urea and steam). Calculate the volume of ammonia (in liters) measured at 150 atm needed to prepare 1.0 ton of urea.

Marissa Turner
Marissa Turner
Numerade Educator
01:11

Problem 122

Some ballpoint pens have a small hole in the main body of the pen. What is the purpose of this hole?

Marissa Turner
Marissa Turner
Numerade Educator
10:22

Problem 123

The gas laws are vitally important to scuba divers. The pressure exerted by $33 \mathrm{ft}$ of seawater is equivalent to 1 atm pressure. (a) A diver ascends quickly to the surface of the water from a depth of $36 \mathrm{ft}$ without exhaling gas from his lungs. By what factor will the volume of his lungs increase by the time he reaches the surface? Assume that the temperature is constant. (b) The partial pressure of oxygen in air is about 0.20 atm. (Air is 20 percent oxygen by volume.) In deep-sea diving, the composition of air the diver breathes must be changed to maintain this partial pressure. What must the oxygen content (in percent by volume) be when the total pressure exerted on the diver is 4.0 atm? (At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gases.) (Hint: See the Chemistry in Action essay "Scuba Diving and the Gas Laws" in Section $5.6 . ?$

Shazia Naz
Shazia Naz
Numerade Educator
04:30

Problem 124

Nitrous oxide $\left(\mathrm{N}_{2} \mathrm{O}\right)$ can be obtained by the thermal decomposition of ammonium nitrate $\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right) .$ (a) Write a balanced equation for the reaction. (b) In a certain experiment, a student obtains $0.340 \mathrm{~L}$ of the gas at $718 \mathrm{mmHg}$ and $24^{\circ} \mathrm{C}$. If the gas weighs $0.580 \mathrm{~g},$ calculate the value of the gas constant.

Marissa Turner
Marissa Turner
Numerade Educator
04:06

Problem 125

Two vessels are labeled A and B. Vessel A contains $\mathrm{NH}_{3}$ gas at $70^{\circ} \mathrm{C},$ and vessel $\mathrm{B}$ contains $\mathrm{Ne}$ gas at the same temperature. If the average kinetic energy of $\mathrm{NH}_{3}$ is $7.1 \times 10^{-21} \mathrm{~J} / \mathrm{molecule},$ calculate the rootmean-square speed of Ne atoms.

Crystal Wang
Crystal Wang
Numerade Educator
02:06

Problem 126

Which of the following molecules has the largest $a$ value: $\mathrm{CH}_{4}, \mathrm{~F}_{2}, \mathrm{C}_{6} \mathrm{H}_{6}, \mathrm{Ne} ?$

Marissa Turner
Marissa Turner
Numerade Educator
03:05

Problem 127

The following procedure is a simple though somewhat crude way to measure the molar mass of a gas. A liquid of mass $0.0184 \mathrm{~g}$ is introduced into a syringe like the one shown here by injection through the rubber tip using a hypodermic needle. The syringe is then transferred to a temperature bath heated to $45^{\circ} \mathrm{C},$ and the liquid vaporizes. The final volume of the vapor (measured by the outward movement of the plunger) is $5.58 \mathrm{~mL}$ and the atmospheric pressure is $760 \mathrm{mmHg}$. Given that the compound's empirical formula is $\mathrm{CH}_{2}$, determine the molar mass of the compound.

Marissa Turner
Marissa Turner
Numerade Educator
01:38

Problem 128

In 1995 a man suffocated as he walked by an abandoned mine in England. At that moment there was a sharp drop in atmospheric pressure due to a change in the weather. Suggest what might have caused the man's death.

Marissa Turner
Marissa Turner
Numerade Educator
14:43

Problem 129

Acidic oxides such as carbon dioxide react with basic oxides like calcium oxide (CaO) and barium oxide $(\mathrm{BaO})$ to form salts (metal carbonates).
(a) Write equations representing these two reactions. (b) A student placed a mixture of $\mathrm{BaO}$ and $\mathrm{CaO}$ of combined mass $4.88 \mathrm{~g}$ in a 1.46 - $\mathrm{L}$ flask containing carbon dioxide gas at $35^{\circ} \mathrm{C}$ and $746 \mathrm{mmHg}$. After the reactions were complete, she found that the $\mathrm{CO}_{2}$ pressure had dropped to $252 \mathrm{mmHg}$. Calculate the percent composition by mass of the mixture. Assume volumes of the solids are negligible.

Marissa Turner
Marissa Turner
Numerade Educator
01:56

Problem 130

Identify the Maxwell speed distribution curves shown here with the following gases: $\mathrm{Br}_{2}, \mathrm{CH}_{4}$ $\mathrm{N}_{2}, \mathrm{SO}_{3}$

Charles Thomas
Charles Thomas
Numerade Educator
08:58

Problem 131

The running engine of an automobile produces carbon monoxide (CO), a toxic gas, at the rate of about $188 \mathrm{~g}$ CO per hour. A car is left idling in a poorly ventilated garage that is $6.0 \mathrm{~m}$ long, $4.0 \mathrm{~m}$ wide, and $2.2 \mathrm{~m}$ high at $20^{\circ} \mathrm{C}$
(a) Calculate the rate of $\mathrm{CO}$ production in moles per minute. (b) How long would it take to build up a lethal concentration of $\mathrm{CO}$ of 1000 ppmv (parts per million by volume)?

Shazia Naz
Shazia Naz
Numerade Educator
04:15

Problem 132

Interstellar space contains mostly hydrogen atoms at a concentration of about 1 atom $/ \mathrm{cm}^{3}$. (a) Calculate the pressure of the $\mathrm{H}$ atoms. (b) Calculate the volume (in liters) that contains $1.0 \mathrm{~g}$ of $\mathrm{H}$ atoms. The temperature is $3 \mathrm{~K}$

Marissa Turner
Marissa Turner
Numerade Educator
04:25

Problem 133

Atop Mt. Everest, the atmospheric pressure is $210 \mathrm{mmHg}$ and the air density is $0.426 \mathrm{~kg} / \mathrm{m}^{3}$
(a) Calculate the air temperature, given that the molar mass of air is $29.0 \mathrm{~g} / \mathrm{mol}$.
(b) Assuming no change in air composition, calculate the percent decrease in oxygen gas from sea level to the top of Mt. Everest.

Marissa Turner
Marissa Turner
Numerade Educator
01:17

Problem 134

Relative humidity is defined as the ratio (expressed as a percentage) of the partial pressure of water vapor in the air to the equilibrium vapor pressure (see Table 5.3 ) at a given temperature. On a certain summer day in North Carolina the partial pressure of water vapor in the air is $3.9 \times 10^{3} \mathrm{~Pa}$ at $30^{\circ} \mathrm{C}$. Calculate the relative humidity.

Charles Thomas
Charles Thomas
Numerade Educator
01:34

Problem 135

Under the same conditions of temperature and pressure, why does $1 \mathrm{~L}$ of moist air weigh less than $1 \mathrm{~L}$ of dry air? In weather forecasts, an oncoming lowpressure front usually means imminent rainfall. Explain.

Marissa Turner
Marissa Turner
Numerade Educator
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Problem 136

Air entering the lungs ends up in tiny sacs called alveoli. It is from the alveoli that oxygen diffuses into the blood. The average radius of the alveoli is $0.0050 \mathrm{~cm}$ and the air inside contains 14 percent oxygen. Assuming that the pressure in the alveoli is 1.0 atm and the temperature is $37^{\circ} \mathrm{C},$ calculate the number of oxygen molecules in one of the alveoli.

Tom Comey
Tom Comey
Numerade Educator
10:03

Problem 137

A student breaks a thermometer and spills most of the mercury (Hg) onto the floor of a laboratory that measures $15.2 \mathrm{~m}$ long, $6.6 \mathrm{~m}$ wide, and $2.4 \mathrm{~m}$ high.
(a) Calculate the mass of mercury vapor (in grams) in the room at $20^{\circ} \mathrm{C}$. The vapor pressure of mercury at $20^{\circ} \mathrm{C}$ is $1.7 \times 10^{-6} \mathrm{~atm} .$ (b) Does the concentration of mercury vapor exceed the air quality regulation of $0.050 \mathrm{mg} \mathrm{Hg} / \mathrm{m}^{3}$ of air? (c) One way to treat small quantities of spilled mercury is to spray sulfur powder over the metal. Suggest a physical and a chemical reason for this action.

Shazia Naz
Shazia Naz
Numerade Educator
01:31

Problem 138

Consider two bulbs containing argon (left) and oxygen (right) gases. After the stopcock is opened, the pressure of the combined gases is 1.08 atm. Calculate the volume of the right bulb. The temperature is kept at $20^{\circ} \mathrm{C}$. Assume ideal behavior.

Charles Thomas
Charles Thomas
Numerade Educator
04:43

Problem 139

Nitrogen dioxide $\left(\mathrm{NO}_{2}\right)$ cannot be obtained in a pure form in the gas phase because it exists as a mixture of $\mathrm{NO}_{2}$ and $\mathrm{N}_{2} \mathrm{O}_{4}$. At $25^{\circ} \mathrm{C}$ and 0.98 atm, the density of this gas mixture is $2.7 \mathrm{~g} / \mathrm{L}$. What is the partial pressure of each gas?

Marissa Turner
Marissa Turner
Numerade Educator
03:56

Problem 140

The Chemistry in Action essay "Super Cold Atoms" in Section $5.7 .$ describes the cooling of rubidium vapor to $5.0 \times 10^{-8} \mathrm{~K}$. Calculate the root-mean-square speed and average kinetic energy of a $\mathrm{Rb}$ atom at this temperature.

Charles Thomas
Charles Thomas
Numerade Educator
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Problem 141

Lithium hydride reacts with water as follows:
$$
\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(l)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(l)
$$
During World War II, U.S. pilots carried LiH tablets. In the event of a crash landing at sea, the $\mathrm{LiH}$ would react with the seawater and fill their life belts and lifeboats with hydrogen gas. How many grams of $\mathrm{LiH}$ are needed to fill a 4.1 -L life belt at 0.97 atm and $12^{\circ} \mathrm{C} ?$

Tom Comey
Tom Comey
Numerade Educator
02:30

Problem 142

The atmosphere on Mars is composed mainly of carbon dioxide. The surface temperature is $220 \mathrm{~K}$ and the atmospheric pressure is about $6.0 \mathrm{mmHg}$. Taking these values as Martian "STP," calculate the molar volume in liters of an ideal gas on Mars.

Marissa Turner
Marissa Turner
Numerade Educator
02:35

Problem 143

The atmosphere on Venus is composed of 96.5 percent $\mathrm{CO}_{2}, 3.5$ percent $\mathrm{N}_{2},$ and 0.015 percent $\mathrm{SO}_{2}$ by volume. Its standard atmospheric pressure is $9.0 \times 10^{6} \mathrm{~Pa}$. Calculate the partial pressures of the gases in pascals.

Cheryl Glor
Cheryl Glor
Numerade Educator
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Problem 144

A student tries to determine the volume of a bulb
like the one shown in Figure $5.12 .$ These are her results: Mass of the bulb filled with dry air at $23^{\circ} \mathrm{C}$ and $744 \mathrm{mmHg}=91.6843 \mathrm{~g} ;$ mass of evacuated bulb $=91.4715 \mathrm{~g} .$ Assume the composition of air is 78 percent $\mathrm{N}_{2}, 21$ percent $\mathrm{O}_{2},$ and 1 percent argon. What is the volume (in milliliters) of the bulb?

Tom Comey
Tom Comey
Numerade Educator
05:05

Problem 145

Apply your knowledge of the kinetic theory of gases to the following situations.
(a) Two flasks of volumes $V_{1}$ and $V_{2}\left(V_{2}>V_{1}\right)$ contain the same number of helium atoms at the same temperature.
(i) Compare the root-mean-square (rms) speeds and average kinetic energies of the helium (He) atoms in the flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers. (b) Equal numbers of He atoms are placed in two flasks of the same volume at temperatures $T_{1}$ and $T_{2}\left(T_{2}>T_{1}\right) .$ (i) Compare the rms speeds of the atoms in the two flasks. (ii) Compare the frequency and the force with which the He atoms collide with the walls of their containers.
(c) Equal numbers of He and neon (Ne) atoms are placed in two flasks of the same volume, and the temperature of both gases is $74^{\circ} \mathrm{C}$. Comment on the validity of the following statements: (i) The rms speed of He is equal to that of Ne. (ii) The average kinetic energies of the two gases are equal. (iii) The rms speed of each He atom is $1.47 \times 10^{3} \mathrm{~m} / \mathrm{s}$

Marissa Turner
Marissa Turner
Numerade Educator
03:48

Problem 146

It has been said that every breath we take, on average, contains molecules that were once exhaled by Wolfgang Amadeus Mozart ( $1756-1791$ ) . The following calculations demonstrate the validity of this statement. (a) Calculate the total number of molecules in the atmosphere. (Hint: Use the result in Problem 5.106 and $29.0 \mathrm{~g} / \mathrm{mol}$ as the molar mass of air.) (b) Assuming the volume of every breath (inhale or exhale) is $500 \mathrm{~mL}$, calculate the number of molecules exhaled in each breath at $37^{\circ} \mathrm{C},$ which is the body temperature. (c) If Mozart's life span was exactly 35 years, what is the number of molecules he exhaled in that period? (Given that an average person breathes 12 times per minute.) (d) Calculate the fraction of molecules in the atmosphere that was exhaled by Mozart. How many of Mozart's molecules do we breathe in with every inhalation of air? Round off your answer to one significant figure. (e) List three important assumptions in these calculations.

Charles Thomas
Charles Thomas
Numerade Educator
03:36

Problem 147

At what temperature will He atoms have the same $u_{\mathrm{rms}}$ value as $\mathrm{N}_{2}$ molecules at $25^{\circ} \mathrm{C} ?$

Marissa Turner
Marissa Turner
Numerade Educator
03:43

Problem 148

Estimate the distance (in nanometers) between molecules of water vapor at $100^{\circ} \mathrm{C}$ and 1.0 atm. Assume ideal behavior. Repeat the calculation for liquid water at $100^{\circ} \mathrm{C}$, given that the density of water is $0.96 \mathrm{~g} / \mathrm{cm}^{3}$ at that temperature. Comment on your results. (Assume water molecule to be a sphere with a diameter of $0.3 \mathrm{nm} .$ ) (Hint: First calculate the number density of water molecules. Next, convert the number density to linear density, that is, number of molecules in one direction.)

Charles Thomas
Charles Thomas
Numerade Educator
00:23

Problem 149

Which of the noble gases would not behave ideally under any circumstance? Why?

Victoria Moyer
Victoria Moyer
Numerade Educator
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Problem 150

A relation known as the barometric formula is useful for estimating the change in atmospheric pressure with altitude. The formula is given by $P=P_{0} e^{-g .1 h / R T},$ where $P$ and $P_{0}$ are the pressures at height $h$ and sea level, respectively; $g$ is the acceleration due to gravity $\left(9.8 \mathrm{~m} / \mathrm{s}^{2}\right) ; \mathscr{M}$ is the average molar mass of air $(29.0 \mathrm{~g} / \mathrm{mol}) ;$ and $R$ is the gas constant. Calculate the atmospheric pressure in atm at a height of $5.0 \mathrm{~km}$, assuming the temperature is constant at $5^{\circ} \mathrm{C}$ and $P_{0}=1.0 \mathrm{~atm} .$

Tom Comey
Tom Comey
Numerade Educator
05:54

Problem 151

A 5.72-g sample of graphite was heated with $68.4 \mathrm{~g}$ of $\mathrm{O}_{2}$ in a $8.00-\mathrm{L}$ flask. The reaction that took place was
$$
\mathrm{C}(\text { graphite })+\mathrm{O}_{2}(g) \longrightarrow \mathrm{CO}_{2}(g)
$$
After the reaction was complete, the temperature in the flask was $182^{\circ} \mathrm{C}$. What was the total pressure inside the flask?

Marissa Turner
Marissa Turner
Numerade Educator
01:52

Problem 152

An equimolar mixture of $\mathrm{H}_{2}$ and $\mathrm{D}_{2}$ effuses through an orifice (small hole) at a certain temperature. Calculate the composition (in mole fractions) of the gases that pass through the orifice. The molar mass of $\mathrm{D}_{2}$ is $2.014 \mathrm{~g} / \mathrm{mol}$

Charles Thomas
Charles Thomas
Numerade Educator
13:49

Problem 153

A mixture of calcium carbonate $\left(\mathrm{CaCO}_{3}\right)$ and magnesium carbonate $\left(\mathrm{MgCO}_{3}\right)$ of mass $6.26 \mathrm{~g}$ reacts completely with hydrochloric acid (HCl) to generate $1.73 \mathrm{~L}$ of $\mathrm{CO}_{2}$ at $48^{\circ} \mathrm{C}$ and 1.12 atm. Calculate the mass percentages of $\mathrm{CaCO}_{3}$ and $\mathrm{MgCO}_{3}$ in the mixture.

Shazia Naz
Shazia Naz
Numerade Educator
02:02

Problem 154

A 6.11 -g sample of a Cu-Zn alloy reacts with HCl acid to produce hydrogen gas. If the hydrogen gas has a volume of $1.26 \mathrm{~L}$ at $22^{\circ} \mathrm{C}$ and $728 \mathrm{mmHg}$, what is the percent of Zn in the alloy?

Narayan Hari
Narayan Hari
Numerade Educator
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Problem 155

A stockroom supervisor measured the contents of a partially filled 25.0 -gallon acetone drum on a day when the temperature was $18.0^{\circ} \mathrm{C}$ and atmospheric pressure was $750 \mathrm{mmHg}$, and found that 15.4 gallons of the solvent remained. After tightly sealing the drum, an assistant dropped the drum while carrying it upstairs to the organic laboratory. The drum was dented and its internal volume was decreased to 20.4 gallons. What is the total pressure inside the drum after the accident? The vapor pressure of acetone at $18.0^{\circ} \mathrm{C}$ is $400 \mathrm{mmHg} .$

Tom Comey
Tom Comey
Numerade Educator
02:54

Problem 156

In 2.00 min, $29.7 \mathrm{~mL}$ of He effuse through a small hole. Under the same conditions of pressure and temperature, $10.0 \mathrm{~mL}$ of a mixture of $\mathrm{CO}$ and $\mathrm{CO}_{2}$ effuse through the hole in the same amount of time. Calculate the percent composition by volume of the mixture.

Charles Thomas
Charles Thomas
Numerade Educator
09:22

Problem 157

Referring to Figure $5.22,$ explain the following:
(a) Why do the curves dip below the horizontal line labeled ideal gas at low pressures and then why do they arise above the horizontal line at high pressures? (b) Why do the curves all converge to 1 at very low pressures? (c) Each curve intercepts the horizontal line labeled ideal gas. Does it mean that at that point the gas behaves ideally?

Shazia Naz
Shazia Naz
Numerade Educator
04:52

Problem 158

A mixture of methane $\left(\mathrm{CH}_{4}\right)$ and ethane $\left(\mathrm{C}_{2} \mathrm{H}_{6}\right)$ is stored in a container at $294 \mathrm{mmHg} .$ The gases are burned in air to form $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$. If the pressure of $\mathrm{CO}_{2}$ is $356 \mathrm{mmHg}$ measured at the same temperature and volume as the original mixture, calculate the mole fractions of the gases.

Marissa Turner
Marissa Turner
Numerade Educator
01:40

Problem 159

Use the kinetic theory of gases to explain why hot air rises.

Marissa Turner
Marissa Turner
Numerade Educator
03:27

Problem 160

One way to gain a physical understanding of $b$ in the van der Waals equation is to calculate the "excluded volume." Assume that the distance of closest approach between two similar atoms is the sum of their radii $(2 r) .$ (a) Calculate the volume around each atom into which the center of another atom cannot penetrate. (b) From your result in (a), calculate the excluded volume for 1 mole of the atoms, which is the constant $b$. How does this volume compare with the sum of the volumes of 1 mole of the atoms?

Adriano Chikande
Adriano Chikande
Numerade Educator
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Problem 161

Use the van der Waals constants in Table 5.4 to estimate the radius of argon in picometers.

Tom Comey
Tom Comey
Numerade Educator
01:41

Problem 162

Identify the gas whose root-mean-square speed is 2.82 times that of hydrogen iodide (HI) at the same temperature.

Charles Thomas
Charles Thomas
Numerade Educator
05:46

Problem 163

A 5.00-mole sample of $\mathrm{NH}_{3}$ gas is kept in a 1.92 -L container at $300 \mathrm{~K}$. If the van der Waals equation is assumed to give the correct answer for the pressure of the gas, calculate the percent error made in using the ideal gas equation to calculate the pressure.

Marissa Turner
Marissa Turner
Numerade Educator
03:06

Problem 164

The root-mean-square speed of a certain gaseous oxide is $493 \mathrm{~m} / \mathrm{s}$ at $20^{\circ} \mathrm{C}$. What is the molecular formula of the compound?

Marissa Turner
Marissa Turner
Numerade Educator
04:56

Problem 165

Referring to Figure $5.17,$ we see that the maximum of each speed distribution plot is called the most probable speed $\left(u_{\mathrm{mp}}\right)$ because it is the speed possessed by the largest number of molecules. It is given by $u_{\mathrm{mp}}=\sqrt{2 R T / \mathscr{M}}$. (a) Compare $u_{\mathrm{mp}}$ with $u_{\mathrm{rms}}$ for nitrogen at $25^{\circ} \mathrm{C}$. (b) The following diagram shows the Maxwell speed distribution curves for an ideal gas at two different temperatures $T_{1}$ and $T_{2}$. Calculate the value of $T_{2}$.

Crystal Wang
Crystal Wang
Numerade Educator
02:30

Problem 166

A gaseous reaction takes place at constant volume and constant pressure in this cylinder. Which of the following equations best describes the reaction? The initial temperature $\left(T_{1}\right)$ is twice that of the final temperature $\left(T_{2}\right)$
(a) $\mathrm{A}+\mathrm{B} \longrightarrow \mathrm{C}$
(b) $\mathrm{AB} \longrightarrow \mathrm{C}+\mathrm{D}$
(c) $A+B \longrightarrow C+D$
(d) $A+B \longrightarrow 2 C+D$

Marissa Turner
Marissa Turner
Numerade Educator
19:15

Problem 167

A gaseous hydrocarbon (containing C and H atoms) in a container of volume $20.2 \mathrm{~L}$ at $350 \mathrm{~K}$ and 6.63 atm reacts with an excess of oxygen to form $205.1 \mathrm{~g}$ of $\mathrm{CO}_{2}$ and $168.0 \mathrm{~g}$ of $\mathrm{H}_{2} \mathrm{O} .$ What is the
molecular formula of the hydrocarbon?

Shazia Naz
Shazia Naz
Numerade Educator
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Problem 168

Three flasks (a)-(c) contain gases A (red) and B (green). (i) If the pressure in (a) is 4.0 atm, what are the pressures in (b) and (c)? (ii) Calculate the total pressure and partial pressure of each gas after the valves are opened. The volumes of (a) and (c) are $4.0 \mathrm{~L}$ each and that of $(\mathrm{b})$ is $2.0 \mathrm{~L}$. The temperature is the same throughout.

Tom Comey
Tom Comey
Numerade Educator
12:00

Problem 169

(a) Show that the pressure exerted by a fluid $P$ (in pascals) is given by $P=h d g,$ where $h$ is the column of the fluid in meters, $d$ is the density in $\mathrm{kg} / \mathrm{m}^{3},$ and $g$ is the acceleration due to gravity $\left(9.81 \mathrm{~m} / \mathrm{s}^{2}\right)$ (Hint: See Appendix 1.) (b) The volume of an air bubble that starts at the bottom of a lake at $5.24^{\circ} \mathrm{C}$ increases by a factor of 6 as it rises to the surface of water where the temperature is $18.73^{\circ} \mathrm{C}$ and the air pressure is 0.973 atm. The density of the lake water is $1.02 \mathrm{~g} / \mathrm{cm}^{3}$. Use the equation in (a) to determine the depth of the lake in meters.

Shazia Naz
Shazia Naz
Numerade Educator
02:06

Problem 170

A student first measured the total pressure of a mixture of gases methane $\left(\mathrm{CH}_{4}\right),$ ethane $\left(\mathrm{C}_{2} \mathrm{H}_{6}\right),$ and propane $\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)$ at a certain temperature, which turned out to be 4.50 atm. She then recorded the mass spectra of the gases shown here. Calculate the partial pressure of the gases.

Charles Thomas
Charles Thomas
Numerade Educator
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Problem 171

In 2012 , Felix Baumgartner jumped from a balloon roughly $24 \mathrm{mi}$ above Earth, breaking the record for the highest skydive. He reached speeds of more than 700 miles per hour and became the first skydiver to exceed the speed of sound during free fall. The helium-filled plastic balloon used to carry Baumgartner to the edge of space was designed to expand to $8.5 \times 10^{8} \mathrm{~L}$ in order to accommodate the low pressures at the altitude required to break the record. (a) Calculate the mass of helium in the balloon from the conditions at the time of the jump $(8.5 \times$ $\left.10^{8} \mathrm{~L},-67.8^{\circ} \mathrm{C}, 0.027 \mathrm{mmHg}\right) .$ (b) Determine the volume of the helium in the balloon just before it was released, assuming a pressure of 1.0 atm and a temperature of $23^{\circ} \mathrm{C}$.

Tom Comey
Tom Comey
Numerade Educator
01:47

Problem 172

Which of the following has a greater mass: a sample of air of volume $V$ at a certain temperature $T$ and pressure $P$ or a sample of air plus water vapor having the same volume and at the same temperature and pressure?

Charles Thomas
Charles Thomas
Numerade Educator
07:32

Problem 173

A flask with a volume of $14.5 \mathrm{~L}$ contains $1.25 \mathrm{moles}$ of helium gas. Estimate the average distance between He atoms in nanometers.

Shazia Naz
Shazia Naz
Numerade Educator
02:32

Problem 174

Hyperbaric oxygen therapy (HBOT) is very effective in treating burns, crush injuries that impede blood flow, and tissue-damaging infections, as well as carbon monoxide poisoning. However, it has generated some controversy in its application to other maladies (for example, autism, multiple sclerosis). A typical oxygen hyperbaric chamber is shown here. HBOT can be administered using pressure up to six atmospheres, but lower pressures are more common. (a) If this chamber was pressurized to 3.0 atm with pure oxygen, how many moles of $\mathrm{O}_{2}$ would be contained in an empty chamber? (b) Given that a full tank of oxygen contains about 2500 moles of the gas, how many times could the chamber be filled with a single tank of oxygen?

Rajesh Singh
Rajesh Singh
Numerade Educator
10:27

Problem 175

(a) Fluorescent lightbulbs contain a small amount of mercury, giving a mercury vapor pressure of around $1 \times 10^{-5}$ atm. When excited electrically, the $\mathrm{Hg}$ atoms emit UV light, which excites the phosphor coating of the inner tube, which then emits visible (white) light. Estimate the mass of Hg vapor present in the type of long, thin fluorescent tubes used in offices. (b) Ordinary tungsten incandescent lightbulbs used in households are filled with argon gas at about 0.5 atm to retard the sublimation of the tungsten filament. Estimate the number of moles of Ar in a typical lightbulb.

Shazia Naz
Shazia Naz
Numerade Educator
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Problem 176

(a) Estimate the volume of air at $1.0 \mathrm{~atm}$ and $22^{\circ} \mathrm{C}$ needed to fill a bicycle tire to a pressure of 5.0 atm at the same temperature. (Note that the $5.0 \mathrm{~atm}$ is the gauge pressure, which is the difference between the pressure in the tire and atmospheric pressure.)
(b) The tire is pumped by filling the cylinder of a hand pump with air at 1.0 atm and then, by compressing the gas in the cylinder, adding all the air in the pump to the air in the tire. If the volume of the pump is 33 percent of the tire's volume, what is the gauge pressure in the tire after three full strokes of the pump?

Tom Comey
Tom Comey
Numerade Educator
11:28

Problem 177

On October $15,2009,$ a homemade helium balloon was released, and for a while authorities were led to believe that a 6 -year-old boy had been carried away in the balloon. (The incident was later revealed to be a hoax.) The balloon traveled more than $50 \mathrm{mi}$ and reached a height of $7000 \mathrm{ft}$. The shape and span of the balloon are shown in the figure. How much weight could this balloon lift? (A helium balloon can lift a mass equal to the difference in the mass of air and the mass of helium that would be contained in the balloon.) Could it actually lift a 6 -year-old boy?

Shazia Naz
Shazia Naz
Numerade Educator