Chemistry The Molecular Science

John W. Moore, Conrad L. Stanitski

Chapter 8

Properties of Gases - all with Video Answers

Educators

Chapter Questions

Problem 1

Name the three gas laws and explain how they interrelate $P, V, T,$ and $n$. Explain the relationships in words and with equations.

Mukesh Devi

Mukesh Devi

Numerade Educator

Problem 2

What are the conditions represented by STP?

Mukesh Devi

Numerade Educator

Problem 3

What is the volume occupied by $1 \mathrm{~mol}$ of an ideal gas at STP?

Mukesh Devi

Numerade Educator

Problem 4

What is the definition of pressure?

Theodore Donnell

Theodore Donnell

Numerade Educator

Problem 5

State Avogadro's law. Explain why two volumes of hydrogen react with one volume of oxygen to form two volumes of steam.

Mukesh Devi

Numerade Educator

Problem 6

State Dalton's law of partial pressures. If the air we breathe is $78 \% \mathrm{~N}_{2}$ and $21 \% \mathrm{O}_{2}$ on a mole basis, calculate the mole fraction of $\mathrm{O}_{2}$. Calculate the partial pressure of $\mathrm{O}_{2}$ if the total pressure is $720 \mathrm{mmHg}$.

Mukesh Devi

Numerade Educator

Problem 7

Explain Boyle's law on the basis of the kinetic-molecular theory.

Mukesh Devi

Numerade Educator

Problem 8

Explain why a gas at low temperature and high pressure does not obey the ideal gas equation as well as the same gas at high temperature and low pressure.

Mukesh Devi

Numerade Educator

Problem 9

Gaseous water and carbon dioxide each absorb infrared radiation. Does either of them absorb ultraviolet radiation? Explain your answer.

Mukesh Devi

Numerade Educator

Problem 10

Gas pressures can be expressed in units of $\mathrm{mmHg}$, atm, torr, and kPa. Convert these pressure values.
(a) $720 . \mathrm{mmHg}$ to atm
(b) 1.25 atm to $\mathrm{mmHg}$
(c) $542 . \mathrm{mmHg}$ to torr
(d) $740 . \mathrm{mmHg}$ to $\mathrm{kPa}$
(e) $700 . \mathrm{kPa}$ to $\mathrm{atm}$

Mukesh Devi

Numerade Educator

Problem 11

Convert these pressure values.
(a) $120 . \mathrm{mmHg}$ to atm
(b) $2.00 \mathrm{~atm}$ to $\mathrm{mmHg}$
(c) $100 . \mathrm{kPa}$ to $\mathrm{mmHg}$
(d) $200 . \mathrm{kPa}$ to $\mathrm{atm}$
(e) $36.0 \mathrm{kPa}$ to atm
(f) $600 . \mathrm{kPa}$ to $\mathrm{mmHg}$

Mukesh Devi

Numerade Educator

Problem 12

Mercury has a density of $13.55 \mathrm{~g} / \mathrm{cm}^{3}$. A barometer is constructed using an oil with a density of $0.75 \mathrm{~g} / \mathrm{cm}^{3} .$ If the atmospheric pressure is 1.0 atm, calculate the height in meters of the oil column in the barometer.

Mukesh Devi

Numerade Educator

Problem 13

Why can't a hand-driven pump on a water well pull underground water from depths more than $33 \mathrm{ft}$ ? Would it help to have a motor-driven vacuum pump?

Mukesh Devi

Numerade Educator

Problem 14

A scuba diver taking photos of a coral reef 60 ft below the ocean surface breathes out a stream of bubbles. What is the total gas pressure of these bubbles at the moment they are released? What is the gas pressure in the bubbles when they reach the surface of the ocean?

Mukesh Devi

Numerade Educator

Problem 15

List the five basic postulates of the kinetic-molecular theory. Which assumption is incorrect at very high pressures? Which one is incorrect at low temperatures? Which assumption is probably most nearly correct?

Mukesh Devi

Numerade Educator

Problem 16

Use the postulates of the kinetic-molecular theory to explain each phenomenon.
(a) $\mathrm{Br}_{2}(\mathrm{~g})$ is reddish brown and transparent; $\mathrm{Br}_{2}(\ell)$ is very dark brown and very little light passes through it.
(b) When equal volumes of $\mathrm{Br}_{2}(\mathrm{~g})$ and $\mathrm{N}_{2}(\mathrm{~g})$ at the same $T$ and $P$ are brought into contact, they mix rapidly and the color is only half as dark as the initial $\mathrm{Br}_{2}$ color.

Mukesh Devi

Numerade Educator

Problem 17

If $50.75 \mathrm{~g}$ of a gas occupies $10.0 \mathrm{~L}$ at $\mathrm{STP},$ calculate the volume $129.3 \mathrm{~g}$ of the gas occupies at $\mathrm{STP}$.

Mukesh Devi

Numerade Educator

Problem 18

A sample of a gas has a pressure of $100 . \mathrm{mmHg}$ in a sealed $125-\mathrm{mL}$. flask. This gas sample is transferred to another flask with a volume of $200 . \mathrm{mL}$. Calculate the new pressure. Assume that the temperature remains constant.

Mukesh Devi

Numerade Educator

Problem 19

Some butane, the fuel used in backyard grills, is placed in a sealed 3.50 -L container at $25^{\circ} \mathrm{C} ;$ its pressure is $735 \mathrm{mmHg}$. You transfer the gas to a sealed 15.0 - $\mathrm{L}$ container, also at $25^{\circ} \mathrm{C}$. Calculate the pressure of the gas in the larger container.

Mukesh Devi

Numerade Educator

Problem 20

A sample of gas at $30 .{ }^{\circ} \mathrm{C}$ has a pressure of $2.0 \mathrm{~atm}$ in a sealed 1.0 - $\mathrm{L}$ container. Calculate the pressure it will exert in a 4.0 -L container. The temperature does not change.

Mukesh Devi

Numerade Educator

Problem 21

Suppose you have a sample of $\mathrm{CO}_{2}$ in a gas-tight syringe with a movable piston. The gas volume is $25.0 \mathrm{~mL}$ at a room temperature of $20 .{ }^{\circ} \mathrm{C} .$ Calculate the final volume of the gas if you hold the syringe in your hand to raise the gas temperature to $37^{\circ} \mathrm{C}$.

Mukesh Devi

Numerade Educator

Problem 22

A sample of gas has a volume of $2.50 \mathrm{~L}$ at a pressure of $670 . \mathrm{mmHg}$ and a temperature of $80 .{ }^{\circ} \mathrm{C} .$ If the pressure remains constant but the temperature is decreased, the gas occupies $1.25 \mathrm{~L}$. Determine this new temperature, in degrees Celsius.

Mukesh Devi

Numerade Educator

Problem 23

A bicycle tire is inflated to a pressure of 3.74 atm at $15^{\circ} \mathrm{C}$. The tire is heated to $35^{\circ} \mathrm{C}$. Calculate the pressure in the tire. Assume the tire volume doesn't change.

Mukesh Devi

Numerade Educator

Problem 24

An automobile tire is inflated to a pressure of 3.05 atm on a rather warm day when the temperature is $40 .{ }^{\circ} \mathrm{C}$. The car is then driven to the mountains and parked overnight. The morning temperature is $-5.0{ }^{\circ} \mathrm{C}$. Calculate the gas pressure in the tire. Assume the volume of the tire doesn't change.

Mukesh Devi

Numerade Educator

Problem 25

A sample of gas occupies $754 \mathrm{~mL}$ at $22^{\circ} \mathrm{C}$ and a pressure of $165 \mathrm{mmHg}$. Calculate its volume if the temperature is raised to $42^{\circ} \mathrm{C}$ and the pressure is raised to $265 \mathrm{mmHg}$. (The amount of gas does not change.)

Mukesh Devi

Numerade Educator

Problem 26

A balloon is filled with helium to a volume of $1.05 \times 10^{3} \mathrm{~L}$ on the ground, where the pressure is $745 \mathrm{mmHg}$ and the temperature is $20 .{ }^{\circ} \mathrm{C}$.
(a) Calculate the amount (mol) of helium in the balloon.
(b) Calculate the volume of helium when the balloon ascends to a height of 2 miles, where the pressure is only $600, \mathrm{mmHg}$ and the temperature is $-33{ }^{\circ} \mathrm{C}$.

Mukesh Devi

Numerade Educator

Problem 27

Calculate the pressure exerted by $1.55 \mathrm{~g}$ Xe gas at $20 .{ }^{\circ} \mathrm{C}$ in a sealed $560-\mathrm{mL}$ flask.

Mukesh Devi

Numerade Educator

Problem 28

A $1.00-\mathrm{g}$ sample of water is allowed to vaporize completely inside a sealed $10.0-\mathrm{L}$ container. Calculate the pressure of the water vapor at a temperature of $150 .{ }^{\circ} \mathrm{C}$.

Mukesh Devi

Numerade Educator

Problem 29

Which of these gas samples contains the largest number of molecules and which contains the smallest?
(a) $1.0 \mathrm{~L} \mathrm{H}_{2}$ at $\mathrm{STP}$
(b) $1.0 \mathrm{~L} \mathrm{~N}_{2}$ at $\mathrm{STP}$
(c) $1.0 \mathrm{~L} \mathrm{H}_{2}$ at $27{ }^{\circ} \mathrm{C}$ and $760 . \mathrm{mmHg}$
(d) $1.0 \mathrm{~L} \mathrm{CO}_{2}$ at $0{ }^{\circ} \mathrm{C}$ and $800 . \mathrm{mmHg}$

Mukesh Devi

Numerade Educator

Problem 30

Ozone molecules attack rubber and cause cracks to appear. If enough cracks occur in a rubber tire, for example, it will be weakened, and the tread will wear away much faster. As little as $0.020 \mathrm{ppm} \mathrm{O}_{3}$ will cause cracks to appear in rubber in about 1 hour. Assume that a $1.0-\mathrm{cm}^{3}$ sample of air containing $0.020 \mathrm{ppm} \mathrm{O}_{3}$ is brought in contact with a sample of rubber that is $1.0 \mathrm{~cm}^{2}$ in area. Calculate the number of $\mathrm{O}_{3}$ molecules that are available to collide with the rubber surface. The temperature of the air sample is $25^{\circ} \mathrm{C}$ and the pressure is $0.95 \mathrm{~atm}$.

Mukesh Devi

Numerade Educator

Problem 31

To find the volume of a flask, the flask is evacuated so it contains no gas. Next, $4.4 \mathrm{~g} \mathrm{CO}_{2}$ is introduced into the flask. On warming to $27^{\circ} \mathrm{C}$, the gas exerts a pressure of $730 . \mathrm{mmHg}$. Calculate the volume of the flask in milliliters.

Mukesh Devi

Numerade Educator

Problem 32

Determine the mass of helium required to fill a $5.0-\mathrm{L}$ balloon to a pressure of $1.1 \mathrm{~atm}$ at $25^{\circ} \mathrm{C}$.

Mukesh Devi

Numerade Educator

Problem 33

Calculate the molar mass of a gas that has a density of $5.75 \mathrm{~g} / \mathrm{L}$ at STP.

Mukesh Devi

Numerade Educator

Problem 34

A 0.423 -g sample of an unknown gas exerts a pressure of 0.965 atm in a 1.00 -L container at $445.7 \mathrm{~K}$. Calculate the molar mass of the gas.

Mukesh Devi

Numerade Educator

Problem 35

Forty miles above Earth's surface the temperature is $-23^{\circ} \mathrm{C},$ and the pressure is only $0.20 \mathrm{mmHg}$. Determine the density of air (molar mass $=29.0 \mathrm{~g} / \mathrm{mol}$ ) at this altitude.

Mukesh Devi

Numerade Educator

Problem 36

A newly discovered gas has a density of $2.39 \mathrm{~g} / \mathrm{L}$ at $23.0^{\circ} \mathrm{C}$ and $715 \mathrm{mmHg}$. Determine the molar mass of the gas.

Mukesh Devi

Numerade Educator

Problem 37

Consider two 5.0 - $\mathrm{L}$ containers, each filled with gas at $25^{\circ} \mathrm{C}$. One container is filled with helium and the other with $\mathrm{N}_{2}$. The density of gas in the two containers is the same. What is the relationship between the pressures in the two containers?

Mukesh Devi

Numerade Educator

Problem 38

A hydrocarbon with the general formula $\mathrm{C}_{x} \mathrm{H}_{y}$ is $92.26 \%$ carbon. Experiment shows that $0.293 \mathrm{~g}$ hydrocarbon fills a $185-\mathrm{mL}$ flask at $23^{\circ} \mathrm{C}$ with a pressure of $374 \mathrm{mmHg}$. Calculate the molecular formula for this compound.

Mukesh Devi

Numerade Educator

Problem 39

When a commercial drain cleaner containing sodium hydroxide and small pieces of aluminum is poured, along with water, into a clogged drain, this reaction occurs:
$$
\begin{aligned}
2 \mathrm{Al}(\mathrm{s})+2 \mathrm{NaOH}(\mathrm{aq})+6 \mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \\
2 \mathrm{NaAl}(\mathrm{OH})_{4}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{~g})
\end{aligned}
$$
If $6.5 \mathrm{~g} \mathrm{Al}$ and excess $\mathrm{NaOH}$ are reacted, calculate the volume of $\mathrm{H}_{2}$ gas produced at $742 \mathrm{mmHg}$ and $22.0^{\circ} \mathrm{C}$.

Mukesh Devi

Numerade Educator

Problem 40

Water can be made by combining gaseous $\mathrm{O}_{2}$ and $\mathrm{H}_{2}$. You begin with $1.5 \mathrm{~L} \mathrm{H}_{2}(\mathrm{~g})$ at $360 . \mathrm{mmHg}$ and $23{ }^{\circ} \mathrm{C}$. Calculate the volume in liters of $\mathrm{O}_{2}(\mathrm{~g})$ needed for complete reaction if the $\mathrm{O}_{2}$ gas is also measured at $360 . \mathrm{mmHg}$ and $23^{\circ} \mathrm{C}$.

Mukesh Devi

Numerade Educator

Problem 41

Gaseous silane, $\mathrm{SiH}_{4}$, ignites spontaneously in air according to the equation
$$\mathrm{SiH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{SiO}_{2}(\mathrm{~s})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$
If $5.2 \mathrm{~L} \mathrm{SiH}_{4}$ reacts with $\mathrm{O}_{2},$ determine the volume in liters of $\mathrm{O}_{2}$ required for complete reaction. Determine the volume of $\mathrm{H}_{2} \mathrm{O}$ vapor produced. Assume all gases are measured at the same temperature and pressure.

Mukesh Devi

Numerade Educator

Problem 42

A $0.05-\mathrm{g}$ sample of the boron hydride, $\mathrm{B}_{4} \mathrm{H}_{10},$ is burned in pure oxygen to give $\mathrm{B}_{2} \mathrm{O}_{3}$ and $\mathrm{H}_{2} \mathrm{O}$.
$$2 \mathrm{~B}_{4} \mathrm{H}_{10}(\mathrm{~s})+11 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 4 \mathrm{~B}_{2} \mathrm{O}_{3}(\mathrm{~s})+10 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$
Calculate the pressure of the gaseous water in a $4.25-\mathrm{L}$ flask at $30 .{ }^{\circ} \mathrm{C}$.

Mukesh Devi

Numerade Educator

Problem 43

If $1.0 \times 10^{3} \mathrm{~g}$ uranium metal is converted to gaseous $\mathrm{UF}_{6},$ calculate the pressure of $\mathrm{UF}_{6}$ at $62{ }^{\circ} \mathrm{C}$ in a chamber that has a volume of $3.0 \times 10^{2} \mathrm{~L}$.

Mukesh Devi

Numerade Educator

Problem 44

Ten liters of $\mathrm{F}_{2}$ gas at $1.00 \mathrm{~atm}$ and $100.0{ }^{\circ} \mathrm{C}$ reacts with $99.9 \mathrm{~g} \mathrm{CaBr}_{2}$ to form $\mathrm{CaF}_{2}$ and bromine gas. Calculate the volume of $\mathrm{Br}_{2}$ gas formed at this temperature and pressure.

Mukesh Devi

Numerade Educator

Problem 45

Metal carbonates decompose to the metal oxide and $\mathrm{CO}_{2}$ on heating according to this general equation.
$$\mathrm{M}_{x}\left(\mathrm{CO}_{3}\right)_{y}(\mathrm{~s}) \longrightarrow \mathrm{M}_{x} \mathrm{O}_{y}(\mathrm{~s})+y \mathrm{CO}_{2}(\mathrm{~g})$$
You heat $0.158 \mathrm{~g}$ of a white, solid carbonate of a Group 2A metal and find that the evolved $\mathrm{CO}_{2}$ has a pressure of $69.8 \mathrm{mmHg}$ in a $285-\mathrm{mL}$ flask at $25^{\circ} \mathrm{C}$. Determine the molar mass of the metal carbonate.

Mukesh Devi

Numerade Educator

Problem 46

Nickel carbonyl, $\mathrm{Ni}(\mathrm{CO})_{4},$ can be made by the roomtemperature reaction of finely divided nickel metal with gaseous CO. This is the basis for purifying nickel on an industrial scale. If you have CO in a sealed $1.50-\mathrm{L}$ flask at a pressure of $418 \mathrm{mmHg}$ at $25.0^{\circ} \mathrm{C},$ calculate the maximum mass in grams of $\mathrm{Ni}(\mathrm{CO})_{4}$ that can be made.

Mukesh Devi

Numerade Educator

Problem 47

Assume that a car burns octane, $\mathrm{C}_{8} \mathrm{H}_{18}\left(d=0.703 \mathrm{~g} / \mathrm{cm}^{3}\right)$.
(a) Write the balanced equation for burning octane in air. forming $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O} .$
(b) The car has a fuel efficiency of 32 miles per gallon of octane; determine the volume of $\mathrm{CO}_{2}$ at $25{ }^{\circ} \mathrm{C}$ and $1.0 \mathrm{~atm}$ that is generated when the car goes on a 10 -mile trip.

Mukesh Devi

Numerade Educator

Problem 48

Follow the directions in the previous question, but use methanol, $\mathrm{CH}_{3} \mathrm{OH}\left(d=0.791 \mathrm{~g} / \mathrm{cm}^{3}\right)$ as the fuel. Assume
the fuel efficiency is $20 .$ miles per gallon.

Mukesh Devi

Numerade Educator

Problem 49

The build-up of excess carbon dioxide in the air of a submerged submarine is prevented by reacting $\mathrm{CO}_{2}$ with sodium peroxide, $\mathrm{Na}_{2} \mathrm{O}_{2}$
$$2 \mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{~s})+2 \mathrm{CO}_{2}(\mathrm{~g}) \rightarrow 2 \mathrm{Na}_{2} \mathrm{CO}_{3}(\mathrm{~s})+\mathrm{O}_{2}(\mathrm{~g})$$
Calculate the mass of $\mathrm{Na}_{2} \mathrm{O}_{2}$ needed in a $24.0-\mathrm{h}$ period per submariner if each exhales $240 \mathrm{~mL} \mathrm{CO}_{2}$ per minute
at $21^{\circ} \mathrm{C}$ and $1.02 \mathrm{~atm} .$

Mukesh Devi

Numerade Educator

Problem 50

Calculate the total pressure of a mixture of $1.50 \mathrm{~g} \mathrm{H}_{2}$ and $5.00 \mathrm{~g} \mathrm{~N}_{2}$ in a sealed $5.0-\mathrm{L}$ vessel at $25^{\circ} \mathrm{C}$.

Mukesh Devi

Numerade Educator

Problem 51

At $298 \mathrm{~K},$ a sealed $750-\mathrm{mL}$ vessel contains equimolar amounts of $\mathrm{O}_{2}, \mathrm{H}_{2}$, and He at a total pressure of 3.85 atm. Determine the partial pressure of the $\mathrm{H}_{2}$ gas.

Mukesh Devi

Numerade Educator

Problem 52

A sample of the atmosphere at a total pressure of $740 . \mathrm{mmHg}$ is analyzed to give these partial pressures:
$$P\left(\mathrm{~N}_{2}\right)=575 \mathrm{mmHg} ; P(\mathrm{Ar})=6.9 \mathrm{mmHg} ; P\left(\mathrm{CO}_{2}\right)=$$
$0.2 \mathrm{mmHg} ; P\left(\mathrm{H}_{2} \mathrm{O}\right)=4.0 \mathrm{mmHg} .$ No other gases except
$\mathrm{O}_{2}$ have appreciable partial pressures. Calculate
(a) the partial pressure of $\mathrm{O}_{2}$
(b) the mole fraction of each gas.
(c) the composition of this sample in percentage by volume. Compare your results with those of Table 8.6 .

Mukesh Devi

Numerade Educator

Problem 53

Gaseous CO exerts a pressure of $45.6 \mathrm{mmHg}$ in a $56.0-\mathrm{L}$ tank at $22.0{ }^{\circ} \mathrm{C}$. This gas is released into a room with a volume of $2.70 \times 10^{4} \mathrm{~L} ;$ determine the partial pressure of $\mathrm{CO}$ (in $\mathrm{mmHg}$ ) in the room at $22{ }^{\circ} \mathrm{C}$.

Mukesh Devi

Numerade Educator

Problem 54

Three flasks are connected as shown. The starting conditions, with the stopcocks closed, are shown. Assume $T$ does not change.
(a) Determine the final pressure inside the system when all the stopcocks are open.
(b) Calculate the partial pressure of each of the three gases. Assume that the connecting tube has negligible volume.

Mukesh Devi

Numerade Educator

Problem 55

The density of air at $20.0 \mathrm{~km}$ above Earth's surface is $92 \mathrm{~g} / \mathrm{m}^{3}$. The pressure is $42 \mathrm{mmHg}$ and the temperature is $-63^{\circ}$ C. Assuming the atmosphere contains only $\mathrm{O}_{2}$ and $\mathrm{N}_{2},$ calculate
(a) the average molar mass of the air at $20.0 \mathrm{~km}$.
(b) the mole fraction of each gas.

Mukesh Devi

Numerade Educator

Problem 56

Benzene has acute health effects. For example, it causes mucous membrane irritation at a concentration of 100 ppm and fatal narcosis at 20,000 ppm (by volume). Calculate the partial pressures in atmospheres at STP corresponding to these concentrations.

Mukesh Devi

Numerade Educator

Problem 57

The mean fraction by mass of water vapor and cloud water in Earth's atmosphere is about 0.0025 . Assume that the atmosphere contains two components: "air," with a molar mass of $29.2 \mathrm{~g} / \mathrm{mol}$, and water vapor. Determine the mean mole fraction of water vapor in Earth's atmosphere. Determine the mean partial pressure of water vapor. Why is this so much smaller than the typical partial pressure of water vapor at Earth's surface on a rainy summer day ( $25 \mathrm{mmHg}$ )?

Aadit Sharma

Numerade Educator

Problem 58

Acetylene can be made by reacting calcium carbide with water.
$$\mathrm{CaC}_{2}(\mathrm{~s})+2 \mathrm{H}_{2} \mathrm{O}(\ell) \longrightarrow \mathrm{C}_{2} \mathrm{H}_{2}(\mathrm{~g})+\mathrm{Ca}(\mathrm{OH})_{2}(\mathrm{aq})$$
Assume that you place $2.65 \mathrm{~g} \mathrm{CaC}_{2}$ in excess water and collect the acetylene over water. The volume of the acetylene and water vapor is $795 \mathrm{~mL}$ at $25.0^{\circ} \mathrm{C}$ and a barometric pressure of $735.2 \mathrm{mmHg}$. Calculate the percent yield of acetylene. The vapor pressure of water at $25^{\circ} \mathrm{C}$ is $23.8 \mathrm{mmHg}$.

Sandra Lundell

Numerade Educator

Problem 59

Potassium chlorate, $\mathrm{KClO}_{3}$, can be decomposed by heating.
$$2 \mathrm{KClO}_{3}(\mathrm{~s}) \longrightarrow 2 \mathrm{KCl}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{~g})$$
If $465 \mathrm{~mL}$ gas was collected over water at a total pressure of $750 . \mathrm{mmHg}$ and a temperature of $25^{\circ} \mathrm{C},$ calculate the mass of $\mathrm{O}_{2}$ collected.

Mukesh Devi

Numerade Educator

Problem 60

You are given two flasks of equal volume. Flask A contains $\mathrm{H}_{2}$ at $0{ }^{\circ} \mathrm{C}$ and 1 atm pressure. Flask $\mathrm{B}$ contains $\mathrm{CO}_{2}$ gas at $0{ }^{\circ} \mathrm{C}$ and 2 atm pressure. Compare these two samples with respect to each of these properties.
(a) Average kinetic energy per molecule
(b) Average molecular velocity
(c) Number of molecules

Sandra Lundell

Numerade Educator

Problem 61

Place these gases in order of increasing average molecular speed at $25^{\circ} \mathrm{C}: \mathrm{Kr}, \mathrm{CH}_{4}, \mathrm{~N}_{2},$ and $\mathrm{CH}_{2} \mathrm{Cl}_{2}$.

Mukesh Devi

Numerade Educator

Problem 62

Arrange these four gases in order of increasing average molecular speed at $25^{\circ} \mathrm{C}: \mathrm{Cl}_{2}, \mathrm{~F}_{2}, \mathrm{~N}_{2},$ and $\mathrm{O}_{2}$.

Mukesh Devi

Numerade Educator

Problem 63

If equal amounts of the four inert gases $\mathrm{Ar}, \mathrm{Ne}, \mathrm{Kr},$ and Xe are released at the same time at one end of a long, evacuated tube, which gas will reach the other end of the tube first? Explain your answer.

Aadit Sharma

Numerade Educator

Problem 64

The reaction of $\mathrm{SO}_{2}$ with $\mathrm{Cl}_{2}$ to give dichlorine oxide is
$$\mathrm{SO}_{2}(\mathrm{~g})+2 \mathrm{Cl}_{2}(\mathrm{~g}) \longrightarrow \mathrm{SOCl}_{2}(\mathrm{~g})+\mathrm{Cl}_{2} \mathrm{O}(\mathrm{g})$$
Place all molecules in the equation in order of increasing rate of effusion.

Aadit Sharma

Numerade Educator

Problem 65

List all the gases in the atmosphere (Table 8.5 ) in order of decreasing average molecular speed. Concern has been expressed about one of these gases escaping into outer space because a significant fraction of its molecules have velocities large enough to break free from Earth's gravitational field. Which gas is it? (Assume the same $T$ for all gases.)

Aadit Sharma

Numerade Educator

Problem 66

From the density of liquid water and its molar mass, calculate the volume that 1 mol liquid water occupies. If water were an ideal gas at STP, what volume would a mole of water vapor occupy? Can we achieve the STP conditions for water vapor? Why or why not?

Aadit Sharma

Numerade Educator

Problem 67

At low temperatures and very low pressures, gases behave ideally, but as the pressure is increased the product $P V$ becomes less than the product $n R T$. Give a molecular-level explanation of this fact.

Aadit Sharma

Numerade Educator

Problem 68

At high temperatures and low pressures, gases behave ideally, but as the pressure is increased the product $P V$ becomes greater than the product $n R T$. Give a molecularlevel explanation of this fact.

Aadit Sharma

Numerade Educator

Problem 69

The densities of liquid noble gases and their normal boiling points are given in this table.
$$
\begin{array}{lcc}
\hline & \begin{array}{l}
\text { Normal Boiling } \\
\text { Paint (K) }
\end{array} & \begin{array}{c}
\text { Liquid Density } \\
\left(g / \mathrm{cm}^{3}\right)
\end{array} \\
\hline \mathrm{He} & 4.2 & 0.125 \\
\mathrm{Ne} & 27.1 & 1.20 \\
\mathrm{Ar} & 87.3 & 1.40 \\
\mathrm{Kr} & 120 . & 2.42 \\
\mathrm{Xe} & 165 & 2.95 \\
\hline
\end{array}
$$
Calculate the volume occupied by 1 mol of each of these liquids. Comment on any trend that you see. Determine the volume occupied by exactly $1 \mathrm{~mol}$ of each of these substances as an ideal gas at STP. Which gas would you expect to show the largest deviations from ideality at room temperature? Why?

Aadit Sharma

Numerade Educator

Problem 70

Use the van der Waals constants in Table 8.5 to predict whether $\mathrm{N}_{2}$ or $\mathrm{CO}_{2}$ behaves more like an ideal gas at high pressures.

Aadit Sharma

Numerade Educator

Problem 71

Calculate the pressure of $7.0 \mathrm{~mol} \mathrm{CO}_{2}$ in a sealed $2.00-\mathrm{L}$ vessel at $50^{\circ} \mathrm{C}$ using
(a) the ideal gas equation.
(b) the van der Waals equation.

Aadit Sharma

Numerade Educator

Problem 72

Without looking at Table $8.5,$ predict which of these gases: $\mathrm{Ne} ; \mathrm{N}_{2} ; \mathrm{H}_{2} \mathrm{O} ;$ or $\mathrm{CH}_{4}$
(a) has the largest van der Waals constant $a$.
(b) has the smallest van der Waals constant $b$.

Aadit Sharma

Numerade Educator

Problem 73

Explain the major roles played by nitrogen in the atmosphere. Do the same for oxygen.

Aadit Sharma

Numerade Educator

Problem 74

Beginning at Earth's surface and proceeding upward, name the first two layers or regions of the atmosphere. Describe, in general, the kinds of chemical reactions that occur in each layer.

Aadit Sharma

Numerade Educator

Problem 75

(a) Calculate the volume of air in liters that you would inhale in 24 hours assuming that you inhaled 16 breaths per minute and each breath had a volume of approximately $0.50 \mathrm{~L} .\left(T=18.0^{\circ} \mathrm{C} ; P=0.970 \mathrm{~atm} .\right)$
(b) Compare that total volume to the volume of air in a typical residence hall room, approximately $864 \mathrm{ft}^{3}$ (approx. $\left.28 \mathrm{~L} / \mathrm{ft}^{3}\right)$
(c) Calculate the number of oxygen molecules you inhaled during that time.

Aadit Sharma

Numerade Educator

Problem 76

At a spot 3,000 feet above sea level you take a sip of water through a straw before you begin a mountain hike. You take another sip when you reach the top at $10,400 \mathrm{ft}$. At which elevation is it easier to sip the water? Explain.

Aadit Sharma

Numerade Educator

Problem 77

Felix Baumgartner, wearing a special pressurized suit, set a new skydiving record on October 14,2012 by free falling from an altitude of $39 \mathrm{~km}$, near the top of the stratosphere. Baumgartner was in a state of weightlessness for the first $25 \mathrm{~s}$ of his free fall. Explain why he was able to gain maneuverability and ultimately deploy his parachute only after reaching the troposphere.

Aadit Sharma

Numerade Educator

Problem 78

Write the products for these reactions that take place in the stratosphere.
(a) $\mathrm{CF}_{3} \mathrm{Cl} \stackrel{h v}{\longrightarrow}$
(b) $\cdot \mathrm{Cl}+\cdot \mathrm{O} \cdot \longrightarrow$
(c) $\mathrm{ClO} \cdot+\cdot \mathrm{O} \cdot \longrightarrow$

Aadit Sharma

Numerade Educator

Problem 79

Can ozone form in the stratosphere at night? Explain why or why not.

Aadit Sharma

Numerade Educator

Problem 80

The molecule $\mathrm{CH}_{3} \mathrm{~F}$ has much less ozone-depletion potential than the corresponding molecule $\mathrm{CH}_{3} \mathrm{Cl}$. Explain why.

Aadit Sharma

Numerade Educator

Problem 81

Can CFCs catalyze the destruction of ozone in the stratosphere at night? Explain.

Aadit Sharma

Numerade Educator

Problem 82

Are CFCs toxic? Compare the toxicity of CFCs with that of compounds used for refrigeration before CFCs were invented. Look up the toxicity of these compounds on the Internet.

Aadit Sharma

Numerade Educator

Problem 83

What is the difference between the greenhouse effect and global warming? How are they related?

Aadit Sharma

Numerade Educator

Problem 84

Name four greenhouse gases, and explain why they are called that.

Aadit Sharma

Numerade Educator

Problem 85

Carbon dioxide is known to be a major contributor to the greenhouse effect. List some of its sources in our atmosphere and some of the processes that remove it. Currently, which predominates - the production of $\mathrm{CO}_{2}$ or its removal?

Aadit Sharma

Numerade Educator

Problem 86

Name a favorable effect of the global increase of $\mathrm{CO}_{2}$ in the atmosphere.

Aadit Sharma

Numerade Educator

Problem 87

Define air pollution in terms of the kinds of pollutants, their sources, and the ways they are harmful.

Aadit Sharma

Numerade Educator

Problem 88

Assume that limestone, $\mathrm{CaCO}_{3}$, is used to remove $90 . \%$ of the sulfur from 4.0 metric tons of coal containing $2.0 \% \mathrm{~S} .$ The product is $\mathrm{CaSO}_{4}$
$$\mathrm{CaCO}_{3}(\mathrm{~s})+\mathrm{SO}_{3}(\mathrm{~g}) \longrightarrow \mathrm{CaSO}_{4}(\mathrm{~s})+\mathrm{CO}_{2}(\mathrm{~g})$$
Calculate the mass of limestone required. Express your answer in metric tons.

Aadit Sharma

Numerade Educator

Problem 89

Approximately 65 million metric tons of $\mathrm{SO}_{2}$ enter the atmosphere every year from the burning of coal. If coal, on average, contains $2.0 \% \mathrm{~S},$ calculate how many metric tons of coal were burned to produce this much $\mathrm{SO}_{2}$. A 1000-MW power plant burns about 700 . metric tons of coal per hour. Calculate the number of hours the quantity of coal will burn in one of these power plants.

Aadit Sharma

Numerade Educator

Problem 90

Calculate the mass of gasoline that must be burned according to the reaction
$$\mathrm{C}_{8} \mathrm{H}_{18}(\ell)+8.5 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow 8 \mathrm{CO}(\mathrm{g})+9 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$
to raise the CO concentration to 1000 . ppm in a garage that measures $7.00 \mathrm{~m} \times 3.00 \mathrm{~m} \times 3.00 \mathrm{~m}$. (Assume STP conditions.)

Aadit Sharma

Numerade Educator

Problem 91

What atmospheric reaction produces nitrogen monoxide, NO?

Aadit Sharma

Numerade Educator

Problem 92

Give an example of a situation where atmospheric ozone is beneficial and an example of a situation where it is harmful. Explain how ozone is beneficial and how it is harmful.

Aadit Sharma

Numerade Educator

Problem 93

The air pollutant sulfur dioxide, $\mathrm{SO}_{2},$ is known to increase mortality in people exposed to it for 24 hours at a concentration of $0.175 \mathrm{ppm}$.
(a) Calculate the mole fraction of $\mathrm{SO}_{2}$ when its mass fraction is 0.175 ppm.
(b) Calculate the partial pressure of $\mathrm{SO}_{2}$ at the same mass fraction.
(c) Calculate the mass in micrograms of $\mathrm{SO}_{2}$ in $1 \mathrm{~m}^{3}$ of air at STP.

Aadit Sharma

Numerade Educator

Problem 94

$\mathrm{HCl}$ can be made by the direct reaction of $\mathrm{H}_{2}$ and $\mathrm{Cl}_{2}$ in the presence of light. Assume that $3.0 \mathrm{~g} \mathrm{H}_{2}$ and $140 . \mathrm{g}$ $\mathrm{Cl}_{2}$ are mixed in a $10-\mathrm{L}$ flask at $28{ }^{\circ} \mathrm{C}$, and the flask is sealed. Before the reaction:
(a) Calculate the partial pressures of the two reactants.
(b) Calculate the total pressure in the flask. After the reaction:
(c) Calculate the total pressure in the flask.
(d) What reactant remains in the flask? Calculate the amount (mol) that remains.
(e) Calculate the partial pressure of each gas.
(f) Calculate the pressure inside the flask if the temperature is increased to $40 .{ }^{\circ} \mathrm{C}$.

Aadit Sharma

Numerade Educator

Problem 95

Worldwide, about $100 .$ million metric tons of $\mathrm{H}_{2} \mathrm{~S}$ are produced annually from sources that include the oceans, bogs, swamps, and tidal flats. One of the major sources of $\mathrm{SO}_{2}$ in the atmosphere is the oxidation of $\mathrm{H}_{2} \mathrm{~S}$, produced by the decay of organic matter. The reaction in which $\mathrm{H}_{2} \mathrm{~S}$ molecules are oxidized to $\mathrm{SO}_{2}$ involves $\mathrm{O}_{3}$ Write an equation showing that one molecule of each reactant combines to form two product molecules, one of them being $\mathrm{SO}_{2}$. Then, calculate the annual production in tons of $\mathrm{H}_{2} \mathrm{SO}_{4},$ assuming all of this $\mathrm{SO}_{2}$ is converted to sulfuric acid.

Aadit Sharma

Numerade Educator

Problem 96

Calculate the densities of $\mathrm{Cl}_{2}$ and of $\mathrm{SO}_{2}$ at $25^{\circ} \mathrm{C}$ and $0.750 \mathrm{~atm} .$ Then, calculate the density of $\mathrm{Cl}_{2}$ at $35^{\circ} \mathrm{C}$ and $0.750 \mathrm{~atm}$ and the density of $\mathrm{SO}_{2}$ at $25^{\circ} \mathrm{C}$ and $2.60 \mathrm{~atm} .$

Aadit Sharma

Numerade Educator

Problem 97

The gas burner in a stove or furnace admits enough air so that methane gas can react completely with oxygen in the air according to the equation
$$\mathrm{CH}_{4}(\mathrm{~g})+2 \mathrm{O}_{2}(\mathrm{~g}) \longrightarrow \mathrm{CO}_{2}(\mathrm{~g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$
Air is one-fifth oxygen by volume. Both air and methane gas are supplied to the flame by passing them through separate small tubes. Compared with the tube for the methane gas, determine how much bigger the cross section of the tube for the air needs to be. Assume that both gases are at the same $T$ and $P$.

Aadit Sharma

Numerade Educator

Problem 98

You have 100 balloons of equal volume filled with a total of $26.8 \mathrm{~g}$ helium gas at $23.0^{\circ} \mathrm{C}$ and $748 \mathrm{mmHg}$. The total volume of these balloons is $168 \mathrm{~L}$. You are given 150 more balloons of the same size and $41.8 \mathrm{~g}$ He gas. The temperature and pressure remain the same. Determine by calculation whether you will be able to fill all the balloons with the He you have available.

Aadit Sharma

Numerade Educator

Problem 99

The statement is made in Section $8-9$ that the mass of Earth's atmosphere is $5.3 \times 10^{15}$ metric tons. Perform calculations to show that this value is correct. 1 metric ton $=10^{3} \mathrm{~kg}$. The surface area of Earth is $5.1 \times 10^{8} \mathrm{~km}^{2}$.

Aadit Sharma

Numerade Educator

Problem 100

Argon is the most abundant atmospheric gas after nitrogen and oxygen. At a volume percent of $0.934,$ you might not consider argon as being "abundant". Calculate the mass $(\mathrm{kg})$ of argon in the atmosphere. Assume the density of argon to be $1.6 \mathrm{~g} / \mathrm{L}$.

Aadit Sharma

Numerade Educator

Problem 101

At $25^{\circ} \mathrm{C}$, the measured pressure of acetic acid vapor, $\mathrm{CH}_{3} \mathrm{COOH}(\mathrm{g})$, is significantly lower than that predicted by the ideal gas law. Explain this difference.

Aadit Sharma

Numerade Educator

Problem 102

The air in a flask is evacuated by a high-quality vacuum system. The vacuum created corresponds to $1.0 \times 10^{-8}$ Torr at $25^{\circ} \mathrm{C}$. Calculate the number of molecules of air per $\mathrm{cm}^{3}$ remaining in the apparatus at this temperature and pressure.

Aadit Sharma

Numerade Educator

Problem 103

If all the ozone, $\mathrm{O}_{3}$, in the atmosphere could be isolated and brought to Earth's surface at standard temperature and pressure, the ozone would form a $3-\mathrm{mm}$ thick layer around Earth. Assume that the volume of this ozone layer around Earth equals the thickness multiplied by the area,
$A: A=4 \pi r^{2} ; r$ is the radius of Earth, $6.37 \times 10^{3} \mathrm{~km} .$
(a) Calculate the number of ozone molecules that would be in this layer.
(b) To put this number of ozone molecules into perspective, compare it to the number of carbon dioxide molecules emitted annually by human activities such as the burning fossil fuels, cement production, and deforestation. It is estimated that $7.90 \times 10^{15} \mathrm{~g} \mathrm{CO}_{2}$ is generated in this way.

Aadit Sharma

Numerade Educator

Problem 104

The average kinetic energy of a gas molecule at $20.0{ }^{\circ} \mathrm{C}$ is $3.66 \times 10^{3} \mathrm{~J} / \mathrm{mol} .$ Calculate the average velocity of carbon dioxide molecules in air at a temperature of $20.0^{\circ} \mathrm{C}$. Compare this average velocity with that of nitrogen molecules in the air at the same temperature. Calculate by what percent the average velocities differ. Explain the difference.

Aadit Sharma

Numerade Educator

Problem 105

Consider a sample of $\mathrm{N}_{2}$ gas under conditions in which it obeys the ideal gas law exactly. Which of these statements is/are true?
(a) A sample of $\mathrm{Ne}(\mathrm{g})$ under the same conditions must obey the ideal gas law exactly.
(b) The speed at which one particular $\mathrm{N}_{2}$ molecule is moving changes from time to time.
(c) Some $\mathrm{N}_{2}$ molecules are moving more slowly than some of the molecules in a sample of $\mathrm{O}_{2}(\mathrm{~g})$ under the same conditions.
(d) Some $\mathrm{N}_{2}$ molecules are moving more slowly than some of the molecules in a sample of $\mathrm{Ne}(\mathrm{g})$ under the same conditions.
(e) When two $\mathrm{N}_{2}$ molecules collide, it is possible that both may be moving faster after the collision than they were before.

Aadit Sharma

Numerade Educator

Problem 106

Which of these graphs best represents the distribution of molecular speeds for the gases acetylene, $\mathrm{C}_{2} \mathrm{H}_{2},$ and $\mathrm{N}_{2}$ ? Both gases are in the same sealed flask with a total pressure of $750 . \mathrm{mmHg}$. The partial pressure of $\mathrm{N}_{2}$ is $500 . \mathrm{mmHg}$.

Aadit Sharma

Numerade Educator

Problem 107

Draw a graph representing the distribution of molecular speeds for the gases ethane, $\mathrm{C}_{2} \mathrm{H}_{6}$, and $\mathrm{F}_{2}$ when both are in the same sealed flask with a total pressure of $720 . \mathrm{mmHg}$ and a partial pressure of $540 . \mathrm{mmHg}$ for $\mathrm{F}_{2}$.

Aadit Sharma

Numerade Educator

Problem 108

In this chapter Boyle's, Charles's, and Avogadro's laws were presented as word statements and mathematical relationships. Express each of these laws graphically.

Aadit Sharma

Numerade Educator

Problem 109

Consider these four samples of helium (green spheres represent He atoms), all at the same temperature. The larger boxes have twice the volume of the smaller boxes. Rank the gas samples with respect to: (a) pressure,
(b) density, (c) average kinetic energy, and (d) average molecular speed.

Aadit Sharma

Numerade Educator

Problem 110

Consider these four gas samples, all at the same temperature. The larger boxes have twice the volume of the smaller boxes. Rank the gas samples with respect to:
(a) pressure,
(b) density, (c) average kinetic energy, and
(d) average molecular speed. (Green spheres are He; violet spheres are Ne.)

Aadit Sharma

Numerade Educator

Problem 111

Consider these four gas samples, all at the same temperature. The larger boxes have twice the volume of the smaller boxes. Rank the gas samples with respect to:
(a) pressure, (b) density, (c) average kinetic energy, and (d) average molecular speed.

Aadit Sharma

Numerade Educator

Problem 112

The figure for Question 112 represents a gas collected in a syringe (the needle end was sealed after collecting) at room temperature and pressure. Assume that the plunger can move freely, but no gas can escape. Redraw the syringe and gas to show what it would look like under each set of conditions.
(a) The temperature of the gas is decreased by one half.
(b) The pressure of the gas is decreased to one half of its initial value.
(c) The temperature of the gas is tripled and the pressure is doubled.

Aadit Sharma

Numerade Educator

Problem 113

A gas phase reaction takes place in a syringe at a constant temperature and pressure. If the initial volume is
40. $\mathrm{cm}^{3}$ and the final volume is $60 . \mathrm{cm}^{3},$ which of these general reactions took place? Explain your reasoning.
(a) $\mathrm{A}(\mathrm{g})+\mathrm{B}(\mathrm{g}) \longrightarrow \mathrm{AB}(\mathrm{g})$
(b) $2 \mathrm{~A}(\mathrm{~g})+\mathrm{B}(\mathrm{g}) \longrightarrow \mathrm{A}_{2} \mathrm{~B}(\mathrm{~g})$
(c) $2 \mathrm{AB}_{2}(\mathrm{~g}) \longrightarrow \mathrm{A}_{2}(\mathrm{~g})+2 \mathrm{~B}_{2}(\mathrm{~g})$
(d) $2 \mathrm{AB}(\mathrm{g}) \longrightarrow \mathrm{A}_{2}(\mathrm{~g})+\mathrm{B}_{2}(\mathrm{~g})$
(e) $2 \mathrm{~A}_{2}(\mathrm{~g})+4 \mathrm{~B}(\mathrm{~g}) \longrightarrow 4 \mathrm{AB}(\mathrm{g})$

Aadit Sharma

Numerade Educator

Problem 114

The gas molecules in the box undergo a reaction at constant temperature and pressure.
If the initial volume is $1.8 \mathrm{~L}$ and the final volume is $0.9 \mathrm{~L},$ which of the boxes (a) through (e) could be the products of the reaction? Explain your reasoning.
(a)
(b)
(c)
(d)
(e)

Aadit Sharma

Numerade Educator

Problem 115

A substance is analyzed and found to contain $85.7 \%$ carbon and $14.3 \%$ hydrogen by mass. A gaseous sample of the substance is found to have a density of $1.87 \mathrm{~g} / \mathrm{L}$ at STP.
(a) Calculate the molar mass of the compound.
(b) Determine the empirical and molecular formulas of the compound.
(c) Draw two possible Lewis structures for molecules of the compound.

Aadit Sharma

Numerade Educator

Problem 116

A compound consists of $37.5 \% \mathrm{C}, 3.15 \% \mathrm{H},$ and $59.3 \%$ $\mathrm{F}$ by mass. When $0.298 \mathrm{~g}$ of the compound is heated to
50. ${ }^{\circ} \mathrm{C}$ in an evacuated $125-\mathrm{mL}$ flask, the pressure is observed to be $750 . \mathrm{mmHg}$. The compound has three isomers.
(a) Calculate the molar mass of the compound.
(b) Determine the empirical and molecular formulas of the compound.
(c) Draw the Lewis structure for each isomer of the compound.

Aadit Sharma

Numerade Educator

Problem 117

One very cold winter day you and a friend purchase a helium-filled balloon. As you leave the store and walk down the street, your friend notices the balloon is not as full as it was a moment ago in the store. He says the balloon is defective and he is taking it back. Do you agree with him? Explain why you do or do not agree.

Aadit Sharma

Numerade Educator

Problem 118

A $2.69-\mathrm{g} \mathrm{PCl}_{5}$ sample was completely vaporized in a 1.00-L flask at $250 .{ }^{\circ} \mathrm{C}$. The resulting pressure in the flask was 1.00 atm. At this temperature, there is the possibility that some $\mathrm{PCl}_{5}(\mathrm{~g})$ decomposed to $\mathrm{PCl}_{3}(\mathrm{~g})$ and $\mathrm{Cl}_{2}(\mathrm{~g}) .$
(a) Show calculations to determine whether any of the $\mathrm{PCl}_{5}(\mathrm{~g})$ decomposed.
(b) If some of the $\mathrm{PCl}_{5}(\mathrm{~g})$ decomposed, calculate the partial pressures of each of the three gaseous species under these experimental conditions.

Aadit Sharma

Numerade Educator

Problem 119

The mean free path in a gas is the average distance traveled by a molecule (or atom of monoatomic gas) between its collision with another molecule (or atom). As expected, the mean free path depends on the number of molecules (or atoms) per cubic centimeter and upon the sizes of the molecules (or atoms) themselves. The mean free path can be calculated using the equation
$$\lambda=\frac{1}{\sqrt{2} \pi N \sigma^{2}}$$
in which $\sigma$ represents the diameter of the atom or molecule, $\lambda$ the distance traveled between collisions, and $N$, the number of molecules (or atoms) per cubic centimeter.
(a) Calculate the mean free path of gaseous argon atoms at $0.0^{\circ} \mathrm{C}$ and $1.0 \mathrm{~atm}$. The radius of an argon atom is $91 \mathrm{pm}$.
(b) Calculate how much greater the mean free path of argon atoms is compared to the diameter of the argon atom.
(c) Calculate the pressure (atm) required to change the mean free path of argon to $1.0 \mathrm{~cm}$ at $0.0^{\circ} \mathrm{C}$.

Aadit Sharma

Numerade Educator

Problem 120

The relation between the average kinetic energy of a molecule, $\frac{1}{2} m v^{2},$ and the absolute temperature is
$$\frac{1}{2} m v^{2}=\frac{3}{2} k T$$
$m$ is the mass of the molecule; $v$ is its average velocity; $k$ is $1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K} ; T$ is the absolute temperature. $1 \mathrm{~J}=1 \mathrm{~kg} \mathrm{~m}^{2} \mathrm{~s}^{-2}$. Calculate the average velocity of a nitrogen dioxide molecule in the atmosphere at $27.0^{\circ} \mathrm{C}$.

Aadit Sharma

Numerade Educator

Problem 121

The reaction between the gases $\mathrm{NH}_{3}$ and HBr produces $\mathrm{NH}_{4} \mathrm{Br}$, a white solid. The two gases are introduced simultaneously at opposite ends of an evacuated glass tube that is $1.0 \mathrm{~m}$ long. Calculate how far from the $\mathrm{NH}_{3}$ end of the tube the white solid will form.

Aadit Sharma

Numerade Educator

Problem 122

It is estimated that $50 \mathrm{~g}$ He are lost per second from the uppermost part of Earth's atmosphere. At this point, about $500 \mathrm{~km}$ above Earth's surface, there are so few atoms present that collisions between them are exceptionally rare and the helium atoms simply leave the top of the atmosphere and go into outer space.
(a) Use the equation given in question 120 to calculate the average velocity $(\mathrm{km} / \mathrm{s})$ of a helium atom at $1.0 \times 10^{3} \mathrm{~K}$, the typical temperature of the atmosphere at $500 \mathrm{~km}$ above Earth's surface.
(b) To escape from the atmosphere, any object (including a molecule) must be traveling at $11 \mathrm{~km} / \mathrm{s}$ or more. In light of the answer to part (a), explain how helium escapes from Earth's atmosphere.

Aadit Sharma

Numerade Educator

Problem 123

A neon atom has a radius of $68 \mathrm{pm}$.
(a) Calculate the volume of $1 \mathrm{~mol} \mathrm{Ne}$ atoms; $V=4 \pi r^{3} / 3$.
(b) Calculate the fraction of the total volume of $\mathrm{Ne}(\mathrm{g})$ at
20. ${ }^{\circ} \mathrm{C}$ and 50 . atm that is occupied by $\mathrm{Ne}$ atoms.

Aadit Sharma

Numerade Educator

Problem 124

Acetic acid vapor contains both single acetic acid molecules and dimers of acetic acid in which two molecules of acetic acid are hydrogen bonded to each other. At $77^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm},$ the density of the vapor is $3.23 \mathrm{~g} / \mathrm{L}$. Calculate the percentage of acetic acid vapor that exists in the dimer form at these conditions. Does this percent increase or decrease with increasing temperature? Explain.

Aadit Sharma

Numerade Educator

Problem 125

An ideal gas was contained in a glass vessel of unknown volume with a pressure of $0.960 \mathrm{~atm} .$ Some of the gas was withdrawn from the vessel and used to fill a $25.0-\mathrm{mL}$ glass bulb to a pressure of $1.00 \mathrm{~atm}$. The pressure of the gas remaining in the vessel of unknown volume was 0.882 atm. All the measurements were done at the same temperature. Determine the volume of the vessel.

Aadit Sharma

Numerade Educator

Problem 126

You are holding two balloons, an orange balloon and a blue balloon, both at the same temperature and pressure. The orange balloon is filled with neon gas and the blue balloon is filled with argon gas. The orange balloon has twice the volume of the blue balloon. Determine the mass ratio of Ne to Ar in the two balloons.

Aadit Sharma

Numerade Educator

Problem 127

A container of gas has a pressure of $550 .$ Torr. A chemical change then occurs that consumes half of the molecules present at the start and produces two new molecules for each three consumed. Calculate the new pressure in the container if $T$ and $V$ are unchanged.

Aadit Sharma

Numerade Educator

Problem 128

The effects of intermolecular interactions on gas properties depend on $T$ and $P .$ Do these effects become more or less significant when each change occurs? Why?
(a) A sealed container of gas is compressed to a smaller volume at constant temperature.
(b) A container of gas has more gas added into the same volume at constant temperature.
(c) The gas in a container of variable volume is heated at constant pressure.

Aadit Sharma

Numerade Educator

Problem 129

Formaldehyde, $\mathrm{CH}_{2} \mathrm{O},$ is a volatile organic compound that is sometimes released from insulation used in home construction, and it can be trapped and build up inside the home. When this happens, people exposed to the formaldehyde can suffer adverse health effects. The U. S. National Institute of Occupational Health and Safety (NIOSH) guideline for the maximum allowable concentration of formaldehyde in air in the workplace is $16 \mathrm{ppb}$ (parts per billion) for an eight-hour average exposure.
(a) Determine the partial pressure of formaldehyde at the maximum allowable level of $16 \mathrm{ppb}$.
(b) Calculate how many molecules of formaldehyde are present in each cubic centimeter of air when formaldehyde is present at $16 \mathrm{ppb}$.
(c) Calculate how many total molecules of formaldehyde are present in a room: $15.0 \mathrm{ft}$ long $\times 10.0 \mathrm{ft}$ wide $X$ $8.00 \mathrm{ft}$ high (at $16 \mathrm{ppb}$ ).

Aadit Sharma

Numerade Educator