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CHEMISTRY: The Molecular Nature of Matter and Change 2016

Martin S. Silberberg, Patricia G. Amateis

Chapter 5

Gases and the Kinetic-Molecular Theory

Educators


Problem 1

How does a sample of gas differ in its behavior from a sample of liquid in each of the following situations?
(a) The sample is transferred from one container to a larger one.
(b) The sample is heated in an expandable container, but no change of state occurs.
(c) The sample is placed in a cylinder with a piston, and an external force is applied.

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Problem 2

Are the particles in a gas farther apart or closer together than the particles in a liquid? Use your answer to explain each of the following general observations:
(a) Gases are more compressible than liquids.
(b) Gases have lower viscosities than liquids.
(c) After thorough stirring, all gas mixtures are solutions.
(d) The density of a substance in the gas state is lower than in the liquid state.

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Problem 3

How does a barometer work? Is the column of mercury in a barometer shorter when it is on a mountaintop or at sea level? Explain.

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Problem 4

How can a unit of length such as millimeter of mercury (mmHg) be used as a unit of pressure, which has the dimensions of force per unit area?

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Problem 5

n a closed-end manometer, the mercury level in the arm attached to the flask can never be higher than the mercury level in the other arm, whereas in an open-end manometer, it can be higher. Explain.

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Problem 6

On a cool, rainy day, the barometric pressure is 730 $\mathrm{mmHg}$ . Calculate the barometric pressure in centimeters of water (cm $\mathrm{H}_{2} \mathrm{O} )$ (d of $\mathrm{Hg}=13.5 \mathrm{g} / \mathrm{mL} ; d$ of $\mathrm{H}_{2} \mathrm{O}=1.00 \mathrm{g} / \mathrm{mL} )$

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Problem 7

A long glass tube, sealed at one end, has an inner diameter of 10.0 $\mathrm{mm}$ . The tube is filled with water and inverted into a pail of water. If the atmospheric pressure is 755 $\mathrm{mmHg}$ , how high (in $\mathrm{mmH}_{2} \mathrm{O}$ ) is the column of water in the tube $(d \text { of } \mathrm{Hg}=13.5 \mathrm{g} / \mathrm{mL}$ $d$ of $\mathrm{H}_{2} \mathrm{O}=1.00 \mathrm{g} / \mathrm{mL} ) ?$

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Problem 8

Convert the following:
$$
\begin{array}{ll}{\text { (a) } 0.745 \text { atm to mmHg }} & {\text { (b) } 992 \text { torr to bar }} \\ {\text { (c) } 365 \mathrm{kPa} \text { to atm }} & {\text { (d) } 804 \mathrm{mmH} \mathrm{g} \text { to kPa }}\end{array}
$$

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Problem 9

Convert the following:
$$
\begin{array}{ll}{\text { (a) } 76.8 \mathrm{cmHg} \text { to atm }} & {\text { (b) } 27.5 \text { atm to kPa }} \\ {\text { (c) } 6.50 \mathrm{atm} \text { to bar }} & {\text { (d) } 0.937 \mathrm{kPa} \text { to torr }}\end{array}
$$

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Problem 10

In Figure P5.10, what is the pressure of the gas in the flask (in atm) if the barometer reads 738.5 torr?

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Problem 11

In Figure P5.11, what is the pressure of the gas in the flask (in kPa) if the barometer reads 765.2 mmHg?

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Problem 12

If the sample flask in Figure P5.12 is open to the air, what is the atmospheric pressure (in atm)?

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Problem 13

In Figure P5.13, what is the pressure (in Pa) of the gas in the flask?

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Problem 14

Convert each of the pressures described below to atm:
(a) At the peak of Mt. Everest, atmospheric pressure is only $2.75 \times 10^{2}$ mmHg.
(b) A cyclist fills her bike tires to 86 psi.
(c) The surface of Venus has an atmospheric pressure of $9.15 \times 10^{6} \mathrm{Pa}$ .
(d) At 100 $\mathrm{ft}$ below sea level, a scuba diver experiences a pressure of $2.54 \times 10^{4}$ torr.

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Problem 15

The gravitational force exerted by an object is given by $F=m g,$ where $F$ is the force in newtons, $m$ is the mass in kilograms, and $g$ is the acceleration due to gravity $\left(9.81 \mathrm{m} / \mathrm{s}^{2}\right) .$
(a) Use the definition of the pascal to calculate the mass (in $\mathrm{kg}$ ) of the atmosphere above 1 $\mathrm{m}^{2}$ of ocean.
(b) Osmium $(Z=76)$ is a transition metal in Group 8 $\mathrm{B}(8)$ and has the highest density of any element $(22.6 \mathrm{g} / \mathrm{mL})$ . If an osmium column is 1 $\mathrm{m}^{2}$ in area, how high must it be for its pressure to equal atmospheric pressure? [Use the answer from part (a) in your calculation. $]$

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Problem 16

A student states Boyle's law as follows: "The volume of a gas is inversely proportional to its pressure." How is this statement incomplete? Give a correct statement of Boyle's law.

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Problem 17

In the following relationships, which quantities are variables and which are fixed: (a) Charles’s law; (b) Avogadro’s law; (c) Amontons’s law?

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Problem 18

Boyle’s law relates gas volume to pressure, and Avogadro’s law relates gas volume to amount (mol). State a relationship between gas pressure and amount (mol).

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Problem 19

Each of the following processes caused the gas volume to double, as shown. For each process, tell how the remaining gas variable changed or state that it remained fixed:
(a) $T$ doubles at fixed $P .$
(b) $T$ and $n$ are fixed.
(c) At fixed $T$ , the reaction is $\mathrm{CD}_{2}(g) \longrightarrow \mathrm{C}(g)+\mathrm{D}_{2}(g)$
(d) At fixed $P,$ the reaction is $\mathrm{A}_{2}(g)+\mathrm{B}_{2}(g) \longrightarrow 2 \mathrm{AB}(g)$

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Problem 20

What is the effect of the following on the volume of 1 mol of an ideal gas?
(a) The pressure is tripled (at constant T).
(b) The absolute temperature is increased by a factor of 3.0 (at constant P).
(c) Three more moles of the gas are added (at constant P and T).

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Problem 21

What is the effect of the following on the volume of 1 mol of an ideal gas?
(a) The pressure changes from 760 torr to 202 $\mathrm{kPa}$ , and the temperature changes from $37^{\circ} \mathrm{C}$ to 155 $\mathrm{K}$ .
(b) The temperature changes from 305 $\mathrm{K}$ to $32^{\circ} \mathrm{C},$ and the pressure changes from 2 atm to 101 $\mathrm{kPa}$ .
(c) The pressure is reduced by a factor of 4 (at constant $T )$ .

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Problem 22

What is the effect of the following on the volume of 1 mol of an ideal gas?
(a) Temperature decreases from 800 $\mathrm{K}$ to 400 $\mathrm{K}$ (at constant $P )$
(b) Temperature increases from $250^{\circ} \mathrm{C}$ to $500^{\circ} \mathrm{C}$ (at constant $P )$
(c) Pressure increases from 2 atm to 6 atm (at constant $T )$

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Problem 23

What is the effect of the following on the volume of 1 $\mathrm{mol}$ of an ideal gas?
(a) The initial pressure is 722 torr, and the final pressure is 0.950 atm; the initial temperature is $32^{\circ} \mathrm{F},$ and the final temperature is 273 $\mathrm{K}$
(b) Half the gas escapes (at constant $P$ and $T ) .$
(c) Both the pressure and temperature decrease to one-fourth of their initial values.

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Problem 24

A weather balloon is filled with helium to a volume of 1.61 L at 734 torr. What is the volume of the balloon after it has been released and its pressure has dropped to 0.844 atm? Assume that the temperature remains constant.

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Problem 25

A sample of methane is placed in a $10.0-\mathrm{L}$ container at $25^{\circ} \mathrm{C}$ and 725 $\mathrm{mm} \mathrm{Hg}$ . The gas sample is then moved to a 7.50 $\mathrm{-L}$ container at $25^{\circ} \mathrm{C}$ . What is the gas pressure in the second container?

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Problem 26

A sample of sulfur hexafluoride gas occupies 9.10 $\mathrm{L}$ at $198^{\circ} \mathrm{C}$ . Assuming that the pressure remains constant, what temperature (in $^{\circ} \mathrm{C} )$ is needed to reduce the volume to 2.50 $\mathrm{L} ?$

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Problem 27

A 93 -L sample of dry air cools from $145^{\circ} \mathrm{C}$ to $-22^{\circ} \mathrm{C}$ while the pressure is maintained at 2.85 atm. What is the final volume?

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Problem 28

A gas cylinder is filled with argon at a pressure of 177 atm and $25^{\circ} \mathrm{C}$ . What is the gas pressure when the temperature of the cylinder and its contents are heated to $195^{\circ} \mathrm{C}$ by exposure to fire?

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Problem 29

A bicycle tire is filled to a pressure of $110 .$ psi at a temperature of $30.0^{\circ} \mathrm{C}$ . At what temperature will the air pressure in the tire decrease to 105 psi? Assume that the volume of the tire remains constant.

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Problem 30

A balloon filled with 1.92 $\mathrm{g}$ of helium has a volume of 12.5 $\mathrm{L}$ . What is the balloon's volume after 0.850 $\mathrm{g}$ of helium has leaked out through a small hole (assume constant pressure and temperature)?

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Problem 31

The average person takes 500 $\mathrm{mL}$ of air into the lungs with each normal inhalation, which corresponds to approximately $1 \times 10^{22}$ molecules of air. Calculate the number of molecules of air inhaled by a person with a respiratory problem who takes in only 350 $\mathrm{mL}$ of air with each breath. Assume constant pressure and temperature.

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Problem 32

A sample of Freon-12 $\left(\mathrm{CF}_{2} \mathrm{Cl}_{2}\right)$ occupies 25.5 $\mathrm{L}$ at 298 $\mathrm{K}$ and 153.3 $\mathrm{kPa}$ . Find its volume at STP.

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Problem 33

A sample of carbon monoxide occupies 3.65 $\mathrm{L}$ at 298 $\mathrm{K}$ and 745 torr. Find its volume at $-14^{\mathrm{C}} \mathrm{C}$ and 367 $\mathrm{torr.}$

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Problem 34

A sample of chlorine gas is confined in a 5.0 -L container at 328 torr and $37^{\circ}$ C. How many moles of gas are in the sample?

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Problem 35

If $1.47 \times 10^{-3}$ mol of argon occupies a $75.0-\mathrm{mL}$ container at $26^{\circ} \mathrm{C},$ what is the pressure (in torr)?

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Problem 36

You have 357 $\mathrm{mL}$ of chlorine trifluoride gas at 699 $\mathrm{mmHg}$ and $45^{\circ} \mathrm{C} .$ What is the mass (in $\mathrm{g} )$ of the sample?

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Problem 37

$ \mathrm{A} 75.0-\mathrm{g}$ sample of dinitrogen monoxide is confined in a
$3.1-\mathrm{L}$ vessel. What is the pressure (in atm) at $115^{\circ} \mathrm{C} ?$

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Problem 38

In preparation for a demonstration, your professor brings a $1.5-$ L bottle of sulfur dioxide into the lecture hall before class to allow the gas to reach room temperature. If the pressure gauge reads 85 psi and the temperature in the classroom is $23^{\circ} \mathrm{C},$ how many moles of sulfur dioxide are in the bottle? (Hint: The gauge reads zero when the gas pressure in the bottle is 14.7 $\mathrm{psi.}$ )

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Problem 39

A gas-filled weather balloon with a volume of 65.0 $\mathrm{L}$ is released at sea-level conditions of 745 torr and $25^{\circ} \mathrm{C}$ . The balloon can expand to a maximum volume of 835 $\mathrm{L}$ . When the balloon rises to an altitude at which the temperature is $-5^{\circ} \mathrm{C}$ and the pres- sure is 0.066 $\mathrm{atm}$ , will it reach its maximum volume?

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Problem 40

Why is moist air less dense than dry air?

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Problem 41

To collect a beaker of $\mathrm{H}_{2}$ gas by displacing the air already in the beaker, would you hold the beaker upright or inverted? Why? How would you hold the beaker to collect $\mathrm{CO}_{2} ?$

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Problem 42

Why can we use a gas mixture, such as air, to study the general behavior of an ideal gas under ordinary conditions?

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Problem 43

How does the partial pressure of gas A in a mixture compare to its mole fraction in the mixture? Explain.

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Problem 44

The scene at right represents a portion of a mixture of four gases A (purple), B (black), C (green), and D_ (orange).
(a) Which has the highest partial pressure?
(b) Which has the lowest partial pressure?
(c) If the total pressure is 0.75 atm, what is the partial pressure of $\mathrm{D}_{2} ?$

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Problem 45

What is the density of Xe gas at STP?

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Problem 46

Find the density of Freon-11 $\left(\mathrm{CFCl}_{3}\right)$ at $120^{\circ} \mathrm{C}$ and 1.5 $\mathrm{atm}$ .

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Problem 47

How many moles of gaseous arsine (AsH_ ) occupy 0.0400 $\mathrm{L}$ at STP? What is the density of gaseous arsine?

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Problem 48

The density of a noble gas is 2.71 $\mathrm{g} / \mathrm{L}$ at 3.00 atm and $0^{\circ} \mathrm{C}$ .
Identify the gas.

Angela D.
Numerade Educator

Problem 49

Calculate the molar mass of a gas at 388 torr and $45^{\circ} \mathrm{C}$ if 206 ng occupies 0.206$\mu \mathrm{L}$ .

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Problem 50

When an evacuated 63.8 -mL glass bulb is filled with a gas at $22^{\circ} \mathrm{C}$ and 747 $\mathrm{mmHg}$ , the bulb gains 0.103 $\mathrm{g}$ in mass. Is the gas $\mathrm{N}_{2},$ Ne, or Ar?

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Problem 51

After 0.600 L of Ar at 1.20 atm and $227^{\circ} \mathrm{C}$ is mixed with 0.200 $\mathrm{L}$ of $\mathrm{O}_{2}$ at 501 $\mathrm{torr}$ and $127^{\circ} \mathrm{C}$ in a 400 -mL flask at $27^{\circ} \mathrm{C},$ what is the pressure in the flask?

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Problem 52

A 355 -mL container holds 0.146 $\mathrm{g}$ of Ne and an unknown amount of Ar at $35^{\circ} \mathrm{C}$ and a total pressure of 626 $\mathrm{mm} \mathrm{Hg}$ . Calculate the number of moles of Ar present.

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Problem 53

How many grams of phosphorus react with 35.5 $\mathrm{L}$ of $\mathrm{O}_{2}$ at STP to form tetraphosphorus decoxide?
$$\mathrm{P}_{4}(s)+5 \mathrm{O}_{2}(g) \longrightarrow \mathrm{P}_{4} \mathrm{O}_{10}(s)$$

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Problem 54

How many grams of potassium chlorate decompose to potassium chloride and 638 $\mathrm{mL}$ of $\mathrm{O}_{2}$ at $128^{\circ} \mathrm{C}$ and 752 torr?
$$2 \mathrm{KClO}_{3}(s) \longrightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$$

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Problem 55

How many grams of phosphine (PH_ $_{3} )$ can form when 37.5 $\mathrm{g}$ of phosphorus and 83.0 $\mathrm{L}$ of hydrogen gas react at STP?
$$
\mathrm{P}_{4}(s)+\mathrm{H}_{2}(g) \longrightarrow \mathrm{PH}_{3}(g) \quad[\text { unbalanced }]
$$

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Problem 56

When 35.6 $\mathrm{L}$ of ammonia and 40.5 $\mathrm{L}$ of oxygen gas at $\mathrm{STP}$ burn, nitrogen monoxide and water form. After the products return to STP, how many grams of nitrogen monoxide are present?
$$\mathrm{NH}_{3}(g)+\mathrm{O}_{2}(g) \longrightarrow \mathrm{NO}(g)+\mathrm{H}_{2} \mathrm{O}(l) \quad[\text { unbalanced }]$$

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Problem 57

Aluminum reacts with excess hydrochloric acid to form aqueous aluminum chloride and 35.8 $\mathrm{mL}$ of hydrogen gas over water at $27^{\circ} \mathrm{C}$ and 751 $\mathrm{mm} \mathrm{Hg}$ . How many grams of aluminum reacted?

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Problem 58

How many liters of hydrogen gas are collected over water at $18^{\circ} \mathrm{C}$ and 725 $\mathrm{mm} \mathrm{mg}$ when 0.84 $\mathrm{g}$ of lithium reacts with water? Aqueous lithium hydroxide also forms.

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Problem 59

The air in a hot-air balloon at 744 torr is heated from $17^{\circ} \mathrm{C}$ to $60.0^{\circ} \mathrm{C}$ . Assuming that the amount (mol) of air and the pressure remain constant, what is the density of the air at each temperature? (The average molar mass of air is 28.8 $\mathrm{g} / \mathrm{mol.}$ )

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Problem 60

On a certain winter day in Utah, the average atmospheric pressure is 650 . torr. What is the molar density (in mol/L) of the air if the temperature is $-25^{\circ} \mathrm{C} ?$

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Problem 61

A sample of a liquid hydrocarbon known to consist of molecules with five carbon atoms is vaporized in a $0.204-\mathrm{L}$ flask by immersion in a water bath at $101^{\circ} \mathrm{C} .$ The barometric pressure is 767 torr, and the remaining gas weighs 0.482 $\mathrm{g} .$ What is the molecular formula of the hydrocarbon?

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Problem 62

A sample of air contains 78.08$\%$ nitrogen, 20.94$\%$ oxygen, 0.05$\%$ carbon dioxide, and 0.93$\%$ argon, by volume. How many molecules of each gas are present in 1.00 $\mathrm{L}$ of the sample at $25^{\circ} \mathrm{C}$ and 1.00 $\mathrm{atm}$ ?

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Problem 63

An environmental chemist sampling industrial exhaust gases from a coal-burning plant collects a $\mathrm{CO}_{2}-\mathrm{SO}_{2}-\mathrm{H}_{2} \mathrm{O}$ mixture in a 21 -L steel tank until the pressure reaches 850 . torr at $45^{\circ} \mathrm{C}$ .
(a) How many moles of gas are collected?
(b) If the $\mathrm{SO}_{2}$ concentration in the mixture is $7.95 \times 10^{3}$ parts per million by volume (ppmv), what is its partial pressure? [Hint: ppmv $=$ (volume of component/volume of mixture) $\times 10^{6} . ]$

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Problem 64

"Strike anywhere" matches contain the compound tetraphosphorus trisulfide, which burns to form tetraphosphorus decoxide and sulfur dioxide gas. How many milliliters of sulfur dioxide, measured at 725 torr and $32^{\circ} \mathrm{C},$ can be produced from burning 0.800 $\mathrm{g}$ of tetraphosphorus trisulfide?

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Problem 65

Freon- $12\left(\mathrm{CF}_{2} \mathrm{Cl}_{2}\right),$ widely used as a refrigerant and aerosol propellant, is a dangerous air pollutant. In the troposphere, it traps heat 25 times as effectively as $\mathrm{CO}_{2},$ and in the stratosphere, it participates in the breakdown of ozone. Freon-12 is prepared industrially by reaction of gaseous carbon tetrachloride with hydrogen fluoride. Hydrogen chloride gas also forms. How many grams of carbon tetrachloride are required for the production of 16.0 $\mathrm{dm}^{3}$ of Freon- 12 at $27^{\circ} \mathrm{C}$ and 1.20 atm?

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Problem 66

Xenon hexafluoride was one of the first noble gas compounds synthesized. The solid reacts rapidly with the silicon dioxide in glass or quartz containers to form liquid $\mathrm{XeOF}_{4}$ and gaseous silicon tetrafluoride. What is the pressure in a $1.00-\mathrm{L}$ container at $25^{\circ} \mathrm{C}$ after 2.00 $\mathrm{g}$ of xenon hexafluoride reacts? (Assume that silicon tetrafluoride is the only gas present and that it occupies the entire volume.)

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Problem 67

In the four piston-cylinder assemblies below, the reactant in the left cylinder is about to undergo a reaction at constant $T$ and $P :$
Which of the other three depictions best represents the products of the reaction?

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Problem 68

Roasting galena [lead(II) sulfide] is a step in the industrial isolation of lead. How many liters of sulfur dioxide, measured at STP, are produced by the reaction of 3.75 $\mathrm{kg}$ of galena with 228 $\mathrm{L}$ of oxygen gas at $220^{\circ} \mathrm{C}$ and 2.0 atm? Lead(II) oxide also forms.

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Problem 69

In one of his most critical studies into the nature of combustion, Lavoisier heated mercury(Il) oxide and isolated elemental mercury and oxygen gas. If 40.0 $\mathrm{g}$ of mercury $(\mathrm{II})$ oxide is heated in a 502 -mL vessel and 20.0$\%$ (by mass) decomposes, what is the pressure (in atm) of the oxygen that forms at $25.0^{\circ} \mathrm{C} ?$ (Assume that the gas occupies the entire volume.)

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Problem 70

Use the kinetic-molecular theory to explain the change in gas pressure that results from warming a sample of gas.

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Problem 71

How does the kinetic-molecular theory explain why 1 mol of krypton and 1 mol of helium have the same volume at STP?

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Problem 72

Is the rate of effusion of a gas higher than, lower than, or equal to its rate of diffusion? Explain. For two gases with molecules of approximately the same size, is the ratio of their effusion rates higher than, lower than, or equal to the ratio of their diffusion rates? Explain.

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Problem 73

Consider two $1-\mathrm{L}$ samples of gas: one is $\mathrm{H}_{2}$ and the other is $\mathrm{O}_{2}$ . Both are at 1 atm and $25^{\circ} \mathrm{C}$ . How do the samples compare in terms of (a) mass, (b) density, (c) mean free path, (d) aver- age molecular kinetic energy, (e) average molecular speed, and (f) time for a given fraction of molecules to effuse?

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Problem 74

Three $5-\mathrm{L}$ flasks, fixed with pressure gauges and small valves, each contain 4 $\mathrm{g}$ of gas at 273 $\mathrm{K}$ . Flask A contains $\mathrm{H}_{2},$ flask $\mathrm{B}$ contains He, and flask $\mathrm{C}$ contains $\mathrm{CH}_{4}$ . Rank the flask contents in terms of (a) pressure, (b) average molecular kinetic energy, (c) diffusion rate after the valve is opened, (d) total kinetic energy of the molecules, (e) density, and (f) collision frequency.

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Problem 75

What is the ratio of effusion rates for the lightest gas, $\mathrm{H}_{2},$ and the heaviest known gas, UF $_{6} ?$

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Problem 76

What is the ratio of effusion rates for $\mathrm{O}_{2}$ and $\mathrm{Kr} ?$

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Problem 77

The graph below shows the distribution of molecular speeds for argon and helium at the same temperature.
(a) Does curve 1 or 2 better represent the behavior of argon?
(b) Which curve represents the gas that effuses more slowly?
(c) Which curve more closely represents the behavior of fluorine gas? Explain.

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Problem 78

The graph below shows the distribution of molecular speeds for a gas at two different temperatures.
(a) Does curve 1 or 2 better represent the behavior of the gas at the lower temperature?
(b) Which curve represents the gas when it has a higher $\overline{E_{\mathrm{k}}} ?$
(c) Which curve is consistent with a higher diffusion rate?

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Problem 79

At a given pressure and temperature, it takes 4.85 min for a 1.5 -L sample of He to effuse through a membrane. How long does it take for 1.5 $\mathrm{L}$ of $\mathrm{F}_{2}$ to effuse under the same conditions?

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Problem 80

A sample of an unknown gas effuses in 11.1 $\mathrm{min}$ . An equal volume of $\mathrm{H}_{2}$ in the same apparatus under the same conditions effuses in 2.42 $\mathrm{min}$ . What is the molar mass of the unknown gas?

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Problem 81

White phosphorus melts and then vaporizes at high temperature. The gas effuses at a rate that is 0.404 times that of neon in the same apparatus under the same conditions. How many atoms are in a molecule of gaseous white phosphorus?

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Problem 82

Helium (He) is the lightest noble gas component of air, and xenon (Xe) is the heaviest. [For this problem, use $R=8.314 \mathrm{J} / \mathrm{mol} \cdot \mathrm{K}$ ) and $\mathscr{M}$ in $\mathrm{kg} / \mathrm{mol} . ]$
(a) Find the rms speed of He in winter $\left(0 .^{\circ} \mathrm{C}\right)$ and in summer $\left(30 .^{\circ} \mathrm{C}\right) .$
(b) Compare the rms speed of He with that of $\mathrm{Xe}$ at $30 .^{\circ} \mathrm{C} .$
(c) Find the average kinetic energy per mole of He and of Xe at $30 .^{\circ} \mathrm{C} .$
(d) Find the average kinetic energy per molecule of He at $30 .^{\circ} \mathrm{C}$ .

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Problem 83

A mixture of gaseous disulfur difluoride, dinitrogen tetra- fluoride, and sulfur tetrafluoride is placed in an effusion apparatus.
(a) Rank the gases in order of increasing effusion rate.
(b) Find the ratio of effusion rates of disulfur diffuoride and dinitrogen tetrafluoride.
(c) If gas X is added, and it effuses at 0.935 times the rate of sulfur tetrafluoride, find the molar mass of X.

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Problem 84

Do interparticle attractions cause negative or positive deviations from the $P V / R T$ ratio of an ideal gas? Use Table 5.3 to rank $\mathrm{Kr}, \mathrm{CO}_{2},$ and $\mathrm{N}_{2}$ in order of increasing magnitude of these deviations.

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Problem 85

Does particle volume cause negative or positive deviations from the $P V / R T$ ratio of an ideal gas? Use Table 5.3 to rank $\mathrm{Cl}_{2}$ , $\mathrm{H}_{2},$ and $\mathrm{O}_{2}$ in order of increasing magnitude of these deviations.

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Problem 86

Does $\mathrm{N}_{2}$ behave more ideally at 1 atm or at 500 atm? Explain.

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Problem 87

Does $\mathrm{SF}_{6}$ (boiling point $=16^{\circ} \mathrm{C}$ at 1 atm ) behave more ideally at $150^{\circ} \mathrm{C}$ or at $20^{\circ} \mathrm{C} ?$ Explain.

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Problem 88

An "empty" gasoline can with dimensions 15.0 $\mathrm{cm}$ by 40.0 $\mathrm{cm}$ by 12.5 $\mathrm{cm}$ is attached to a vacuum pump and evacuated. If the atmospheric pressure is 14.7 $\mathrm{lb} / \mathrm{in}^{2}$ , what is the total force (in pounds) on the outside of the can?

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Problem 89

Hemoglobin is the protein that transports $\mathrm{O}_{2}$ through the blood from the lungs to the rest of the body. To do so, each molecule of hemoglobin combines with four molecules of $\mathrm{O}_{2}$ . If 1.00 $\mathrm{g}$ of hemoglobin combines with 1.53 $\mathrm{mL}$ of $\mathrm{O}_{2}$ at $37^{\circ} \mathrm{C}$ and 743 torr, what is the molar mass of hemoglobin?

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Problem 90

A baker uses sodium hydrogen carbonate (baking soda) as the leavening agent in a banana-nut quickbread. The baking soda decomposes in either of two possible reactions:
$$
\begin{array}{l}{\text { (1) } 2 \mathrm{NaHCO}_{3}(s) \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)} \\ {\text { (2) } \mathrm{NaHCO}_{3}(s)+\mathrm{H}^{+}(a q) \longrightarrow \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{CO}_{2}(g)+\mathrm{Na}^{+}(a q)}\end{array}
$$
Calculate the volume (in mL) of $\mathrm{CO}_{2}$ that forms at $200 .^{\circ} \mathrm{C}$ and 0.975 atm per gram of $\mathrm{NaHCO}_{3}$ by each of the reaction processes.

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Problem 91

A weather balloon containing $600 .$ L of He is released near the equator at 1.01 atm and 305 $\mathrm{K}$ . It rises to a point where conditions are 0.489 atm and 218 $\mathrm{K}$ and eventually lands in the northern hemisphere under conditions of 1.01 atm and 250 $\mathrm{K}$ . If one-fourth of the helium leaked out during this journey, what is the volume (in L) of the balloon at landing?

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Problem 92

Chlorine is produced from sodium chloride by the electro-chemical chlor-alkali process. During the process, the chlorine is collected in a container that is isolated from the other products to prevent unwanted (and explosive) reactions. If a $15.50-\mathrm{L}$ container holds 0.5950 $\mathrm{kg}$ of $\mathrm{Cl}_{2}$ gas at $2225^{\circ} \mathrm{C}$ , calculate:
$$
\text {(a)} P_{\mathrm{IGL}} \quad \text { (b) } P_{\mathrm{vDW}}\left(\text { use } R=0.08206 \frac{\mathrm{atm} \cdot \mathrm{L}}{\mathrm{mol} \cdot \mathrm{K}}\right)
$$

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Problem 93

In a certain experiment, magnesium boride $\left(\mathrm{Mg}_{3} \mathrm{B}_{2}\right)$ reacted with acid to form a mixture of four boron hydrides $\left(\mathrm{B}_{x} \mathrm{H}_{y}\right),$ three as liquids (labeled I, II, and III) and one as a gas (IV).
(a) When a 0.1000 -g sample of each liquid was transferred to an evacuated 750.0 -mL container and volatilized at $70.00^{\circ} \mathrm{C},$ sample I had a pressure of 0.05951 atm; sample II, 0.07045 atm; and sample $\mathrm{III}, 0.05767 \mathrm{atm}$ . What is the molar mass of each liquid?
(b) Boron is 85.63$\%$ by mass in sample I, 81.10$\%$ in II, and 82.98$\%$ in III. What is the molecular formula of each sample?
(c) Sample IV was found to be 78.14$\%$ boron. Its rate of effusion was compared to that of sulfur dioxide; under identical conditions, 350.0 $\mathrm{mL}$ of sample IV effused in 12.00 $\mathrm{min}$ and 250.0 $\mathrm{mL}$ of sulfur dioxide effused in 13.04 $\mathrm{min}$ . What is the molecular formula of sample IV?

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Problem 94

Three equal volumes of gas mixtures, all at the same $T$ , are depicted below (with gas A red, gas B green, and gas Cblue):
(a) Which sample, if any, has the highest partial pressure of A?
(b) Which sample, if any, has the lowest partial pressure of $\mathrm{B} ?$
(c) In which sample, if any, do the gas particles have the highest average kinetic energy?

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Problem 95

Will the volume of a gas increase, decrease, or remain unchanged for each of the following sets of changes?
(a) The pressure is decreased from 2 atm to 1 atm, while the temperature is decreased from $200^{\circ} \mathrm{C}$ to $100^{\circ} \mathrm{C} .$
(b) The pressure is increased from 1 atm to 3 atm, while the temperature is increased from $100^{\circ} \mathrm{C}$ to $300^{\circ} \mathrm{C} .$
(c) The pressure is increased from 3 atm to $6 \mathrm{atm},$ while the temperature is increased from $-73^{\circ} \mathrm{C}$ to $127^{\circ} \mathrm{C}$ .
(d) The pressure is increased from 0.2 atm to 0.4 atm, while the temperature is decreased from $300^{\circ} \mathrm{C}$ to $150^{\circ} \mathrm{C} .$

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Problem 96

When air is inhaled, it enters the alveoli of the lungs, and varying amounts of the component gases exchange with dissolved gases in the blood. The resulting alveolar gas mixture is quite different from the atmospheric mixture. The following table presents selected data on the composition and partial pressure of four gases in the atmosphere and in the alveoli: If the total pressure of each gas mixture is 1.00 atm, calculate:
(a) The partial pressure (in torr) of each gas in the atmosphere
(b) The mole $\%$ of each gas in the alveoli
(c) The number of $\mathrm{O}_{2}$ molecules in 0.50 $\mathrm{L}$ of alveolar air (volume of an average breath of a person at rest) at $37^{\circ} \mathrm{C}$

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Problem 97

Radon (Rn) is the heaviest, and only radioactive, member of Group 8 $\mathrm{A}(18)$ (noble gases). It is a product of the disintegration of heavier radioactive nuclei found in minute concentrations in many common rocks used for building and construction. In recent years, there has been growing concern about the cancers caused from inhaled residential radon. If $1.0 \times 10^{15}$ atoms of radium (Ra) produce an average of $1.373 \times 10^{4}$ atoms of Rn per second, how many liters of Rn, measured at STP, are produced per day by 1.0 $\mathrm{g}$ of Ra? inhaled residential radon. If $1.0 \times 10^{15}$ atoms of radium (Ra) produce an average of $1.373 \times 10^{4}$ atoms of Rn per second, how many liters of Rn, measured at STP, are produced per day by 1.0 $\mathrm{g}$ of Ra?

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Problem 98

At $1450 .$ mmHg and $286 \mathrm{K},$ a skin diver exhales a $208-\mathrm{mL}$ bubble of air that is $77 \% \mathrm{N}_{2}, 17 \% \mathrm{O}_{2},$ and 6.0$\% \mathrm{CO}_{2}$ by volume.
(a) How many milliliters would the volume of the bubble be if it were exhaled at the surface at 1 $\mathrm{atm}$ and 298 $\mathrm{K}$ ?
(b) How many moles of $\mathrm{N}_{2}$ are in the bubble?

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Problem 99

Nitrogen dioxide is used industrially to produce nitric acid, but it contributes to acid rain and photochemical smog. What volume (in L) of nitrogen dioxide is formed at 735 torr and $28.2^{\circ} \mathrm{Cby}$ reacting 4.95 $\mathrm{cm}^{3}$ of copper $\left(d=8.95 \mathrm{g} / \mathrm{cm}^{3}\right)$ with 230.0 $\mathrm{mL}$ of nitric acid $\left(d=1.42 \mathrm{g} / \mathrm{cm}^{3}, 68.0 \% \mathrm{HNO}_{3} \text { by mass)? }\right.$
$$
\mathrm{Cu}(s)+4 \mathrm{HNO}_{3}(a q) \rightarrow \mathrm{Cu}\left(\mathrm{NO}_{3}\right)_{2}(a q)+2 \mathrm{NO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(l)
$$

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Problem 100

In the average adult male, the residual volume (RV) of the lungs, the volume of air remaining after a forced exhalation, is 1200 $\mathrm{mL}$ (a) How many moles of air are present in the RV at 1.0 atm and $37^{\circ} \mathrm{C} ?$ (b) How many molecules of gas are present under these conditions?

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Problem 101

In a bromine-producing plant, how many liters of gaseous elemental bromine at $300^{\circ} \mathrm{C}$ and 0.855 atm are formed by the reaction of 275 g of sodium bromide and 175.6 $\mathrm{g}$ of sodium bromate in aqueous acid solution? (Assume that no $\mathrm{Br}_{2}$ dissolves.)
$$
\begin{aligned} 5 \mathrm{NaBr}(a q)+\mathrm{NaBrO}_{3}(a q) &+3 \mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \\ & 3 \mathrm{Br}_{2}(g)+3 \mathrm{Na}_{2} \mathrm{SO}_{4}(a q)+3 \mathrm{H}_{2} \mathrm{O}(g) \end{aligned}
$$

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Problem 102

In a collision of sufficient force, automobile air bags respond by electrically triggering the explosive decomposition of sodium azide (NaN $_{3} )$ to its elements. A 50.0 -g sample of sodium
azide was decomposed, and the nitrogen gas generated was collected over water at $26^{\circ} \mathrm{C}$ . The total pressure was 745.5 $\mathrm{mmHg}$ . How many liters of dry $\mathrm{N}_{2}$ were generated?

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Problem 103

An anesthetic gas contains 64.81$\%$ carbon, 13.60$\%$ hydro- gen, and 21.59$\%$ oxygen, by mass. If 2.00 $\mathrm{L}$ of the gas at $25^{\circ} \mathrm{C}$ and 0.420 atm weighs $2.57 \mathrm{g},$ what is the molecular formula of the anesthetic?

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Problem 104

Aluminum chloride is easily vaporized above $180^{\circ} \mathrm{C}$ . The gas escapes through a pinhole 0.122 times as fast as helium at the same conditions of temperature and pressure in the same apparatus. What is the molecular formula of aluminum chloride gas?

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Problem 105

(a) What is the total volume (in L) of gaseous products, measured at $350^{\circ} \mathrm{C}$ and 735 torr, when an automobile engine burns $100 . \mathrm{g}$ of $\mathrm{C}_{8} \mathrm{H}_{18}(\text { a typical component of gasoline)? }$
(b) For part (a), the source of $\mathrm{O}_{2}$ is air, which is $78 \% \mathrm{N}_{2}, 21 \% \mathrm{O}_{2}$ and 1.0$\%$ Ar by volume. Assuming all the $\mathrm{O}_{2}$ reacts, but no $\mathrm{N}_{2}$ or Ar does, what is the total volume (in L) of gaseous exhaust?

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Problem 106

An atmospheric chemist studying the pollutant $\mathrm{SO}_{2}$ places a mixture of $\mathrm{SO}_{2}$ and $\mathrm{O}_{2}$ in a $2.00-\mathrm{L}$ container at $800 . \mathrm{K}$ and
1.90 $\mathrm{atm}$ . When the reaction occurs, gaseous $\mathrm{SO}_{3}$ forms, and the pressure falls to 1.65 atm. How many moles of $\mathrm{SO}_{3}$ form?

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Problem 107

The thermal decomposition of ethylene occurs during the compound's transit in pipelines and during the formation of polyethylene. The decomposition reaction is
$$\mathrm{CH}_{2}=\mathrm{CH}_{2}(g) \longrightarrow \mathrm{CH}_{4}(g)+\mathrm{C}(\text { graphite })$$
If the decomposition begins at $10^{\circ} \mathrm{C}$ and 50.0 atm with a gas den- sity of 0.215 $\mathrm{g} / \mathrm{mL}$ and the temperature increases by 950 $\mathrm{K}$ ,
(a) What is the final pressure of the confined gas (ignore the volume of graphite and use the van der Waals equation)?
(b) How does the $P V / R T$ value of $\mathrm{CH}_{4}$ compare to that in Figure 5.23$?$ Explain.

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Problem 108

Ammonium nitrate, a common fertilizer, was used by terrorists in the tragic explosion in Oklahoma City in $1995 .$ How many liters of gas at $307^{\circ} \mathrm{C}$ and 1.00 atm are formed by the explosive decomposition of 15.0 $\mathrm{kg}$ of ammonium nitrate to nitrogen, oxygen, and water vapor?

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Problem 109

An environmental engineer analyzes a sample of air contaminated with sulfur dioxide. To a 500 -mL sample at 700 . torr and $38^{\circ} \mathrm{C},$ she adds 20.00 $\mathrm{mL}$ of 0.01017 $\mathrm{M}$ aqueous iodine, which reacts as follows:
$$\begin{aligned} \mathrm{SO}_{2}(g)+\mathrm{I}_{2}(a q) &+\mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \\ & \text { HSO }_{4}^{-}(a q)+\mathrm{I}^{-}(a q)+\mathrm{H}^{+}(a q) \end{aligned}$$
$$
\begin{array}{l}{\text { Excess I_ reacts with } 11.37 \mathrm{mL} \text { of } 0.0105 M \text { sodium thiosulfate: }} \\ {\mathrm{I}_{2}(a q)+\mathrm{S}_{2} \mathrm{O}_{3}^{2-}(a q) \longrightarrow \mathrm{I}^{-}(a q)+\mathrm{S}_{4} \mathrm{O}_{6}^{2-}(a q) \quad[\text { unbalanced }]} \\ {\text { What is the volume } \% \text { of } \mathrm{SO}_{2} \text { in the air sample? }}\end{array}
$$

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Problem 110

Canadian chemists have developed a modern variation of the 1899 Mond process for preparing extremely pure metallic nickel. A sample of impure nickel reacts with carbon monoxide at $50^{\circ} \mathrm{C}$ to form gaseous nickel carbonyl, Ni(CO).
(a) How many grams of nickel can be converted to the carbonyl with 3.55 $\mathrm{m}^{3}$ of $\mathrm{CO}$ at 100.7 $\mathrm{kPa}$ ?
(b) The carbonyl is then decomposed at 21 atm and $155^{\circ} \mathrm{C}$ to pure $(>99.95 \%)$ nickel. How many grams of nickel are obtained per cubic meter of the carbonyl?
(c) The released carbon monoxide is cooled and collected for reuse by passing it through water at $35^{\circ} \mathrm{C}$ . If the barometric pressure is 769 torr, what volume (in $\mathrm{m}^{3} )$ of $\mathrm{CO}$ is formed per cubic meter of carbonyl?

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Problem 111

Analysis of a newly discovered gaseous silicon-fluorine compound shows that it contains 33.01 mass $\%$ silicon. At $27^{\circ} \mathrm{C},$ 2.60 $\mathrm{g}$ of the compound exerts a pressure of 1.50 $\mathrm{atm}$ in a 0.250 $\mathrm{-L}$ vessel. What is the molecular formula of the compound?

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Problem 112

A gaseous organic compound containing only carbon, hydrogen, and nitrogen is burned in oxygen gas, and the volume of each reactant and product is measured under the same conditions of temperature and pressure. Reaction of four volumes of the compound produces four volumes of $\mathrm{CO}_{2},$ two volumes of $\mathrm{N}_{2},$ and ten volumes of water vapor. (a) How many volumes of $\mathrm{O}_{2}$ were required? (b) What is the empirical formula of the compound?

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Problem 113

Containers A, B, and C are attached by closed stopcocks of negligible volume. If each particle shown in the picture represents $10^{6}$ particles,
(a) How many blue particles and black particles are in $\mathrm{B}$ after the stopcocks are opened and the system reaches equilibrium?
(b) How many blue particles and black particles are in A after the stopcocks are opened and the system reaches equilibrium?
(c) If the pressure in $\mathrm{C}, P_{\mathrm{C}},$ is 750 torr before the stopcocks are opened, what is $P_{\mathrm{C}}$ afterward?
(d) What is $P_{\mathrm{B}}$ afterward?

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Problem 114

Combustible vapor-air mixtures are flammable over a limited range of concentrations. The minimum volume $\mathscr{G}$ of vapor that gives a combustible mixture is called the lower flammable limit (LFL). Generally, the LFL is about half the stoichiometric mixture, the concentration required for complete combustion of the vapor in air. (a) If oxygen is 20.9 vol $\%$ of air, estimate the LFL for $n$ -hexane, $\mathrm{C}_{6} \mathrm{H}_{14},$ (b) What volume (in mL) of $n$ -hexane $\left(d=0.660 \mathrm{g} / \mathrm{cm}^{3}\right)$ is required to produce a flammable mixture of hexane in 1.000 $\mathrm{m}^{3}$ of air at STP?

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Problem 115

By what factor would a scuba diver's lungs expand if she ascended rapidly to the surface from a depth of 125 $\mathrm{ft}$ without inhaling or exhaling? If an expansion factor greater than 1.5 causes lung rupture, how far could she safely ascend from 125 $\mathrm{ft}$ without breathing? Assume constant temperature ( $d$ of seawater $=1.04 \mathrm{g} / \mathrm{mL}$ $d$ of $\mathrm{Hg}=13.5 \mathrm{g} / \mathrm{mL} )$

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Problem 116

When 15.0 g of fluorite (CaF) reacts with excess sulfuric acid, hydrogen fluoride gas is collected at 744 torr and $25.5^{\circ} \mathrm{C}$ . Solid calcium sulfate is the other product. What gas temperature is
required to store the gas in an $8.63-\mathrm{L}$ container at 875 torr?

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Problem 117

Dilute aqueous hydrogen peroxide is used as a bleaching agent and for disinfecting surfaces and small cuts. Its concentration is sometimes given as a certain number of "volumes hydrogen peroxide," which refers to the number of volumes of $\mathrm{O}_{2}$ gas, measured at STP, that a given volume of hydrogen peroxide solution will release when it decomposes to $\mathrm{O}_{2}$ and liquid $\mathrm{H}_{2} \mathrm{O}$ . How many grams of hydrogen peroxide are in 0.100 $\mathrm{L}$ of "20 volumes hydrogen peroxide" solution?

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Problem 118

At a height of 300 $\mathrm{km}$ above Earth's surface, an astronaut finds that the atmospheric pressure is about $10^{-8}$ mmHg and the temperature is 500 $\mathrm{K}$ . How many molecules of gas are there per milliter at this altitude?

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Problem 119

(a) What is the ms speed of $\mathrm{O}_{2}$ at STP? (b) If the mean free path of $\mathrm{O}_{2}$ molecules at $\mathrm{STP}$ is $6.33 \times 10^{-8} \mathrm{m},$ what is their collision frequency? [Use $R=8.314 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})$ and $\mathscr{M}$ in kg/mol.]

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Problem 120

Acrylic acid $\left(\mathrm{CH}_{2}=\mathrm{CHCOOH}\right)$ is used to prepare polymers, adhesives, and paints. The first step in making acrylic acid involves the vapor-phase oxidation of propylene $\left(\mathrm{CH}_{2}=\mathrm{CHCH}_{3}\right)$ to acrolein $\left(\mathrm{CH}_{2}=\mathrm{CHCHO}\right) .$ This step is carried out at $330^{\circ} \mathrm{C}$ and 2.5 atm in a large bundle of tubes around which a heat- transfer agent circulates. The reactants spend an average of 1.8 $\mathrm{s}$ in the tubes, which have a void space of 100 $\mathrm{ft}^{3} .$ How many pounds of propylene must be added per hour in a mixture whose mole fractions are 0.07 propylene, 0.35 steam, and 0.58 air?

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Problem 121

Standard conditions are based on relevant environmental conditions. If normal average surface temperature and pressure on Venus are $730 . \mathrm{K}$ and $90 \mathrm{atm},$ respectively, what is the standard molar volume of an ideal gas on Venus?

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Problem 122

A barometer tube is $1.00 \times 10^{2} \mathrm{cm}$ long and has a cross- sectional area of 1.20 $\mathrm{cm}^{2}$ . The height of the mercury column is $74.0 \mathrm{cm},$ and the temperature is $24^{\circ} \mathrm{C}$ . A small amount of $\mathrm{N}_{2}$ is introduced into the evacuated space above the mercury, which causes the mercury level to drop to a height of 64.0 $\mathrm{cm} .$ How many grams of $\mathrm{N}_{2}$ were introduced?

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Problem 123

What is the molarity of the cleaning solution formed when 10.0 $\mathrm{L}$ of ammonia gas at $33^{\circ} \mathrm{C}$ and 735 torr dissolves in enough water to give a final volume of 0.750 $\mathrm{L}$ ?

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Problem 124

The Hawaiian volcano Kilauea emits an average of $1.5 \times 10^{3} \mathrm{m}^{3}$ of gas each day, when corrected to 298 $\mathrm{K}$ and 1.00 $\mathrm{atm}$ . The mixture contains gases that contribute to global warming and acid rain, and some are toxic. An atmospheric chemist analyzes a sample and finds the following mole fractions: $0.4896 \mathrm{CO}_{2}, 0.0146 \mathrm{CO}, 0.3710 \mathrm{H}_{2} \mathrm{O}, 0.1185 \mathrm{SO}_{2}, 0.0003 \mathrm{S}_{2}$
$0.0047 \mathrm{H}_{2}, 0.0008 \mathrm{HCl},$ and 0.0003 $\mathrm{H}_{2} \mathrm{S}$ . How many metric tons (t) of each gas are emitted per year $(1 \mathrm{t}=1000 \mathrm{kg}) ?$

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Problem 125

To study a key fuel-cell reaction, a chemical engineer has 20.0 -L tanks of $\mathrm{H}_{2}$ and of $\mathrm{O}_{2}$ and wants to use up both tanks to form 28.0 $\mathrm{mol}$ of water at $23.8^{\circ} \mathrm{C}$ . (a) Use the ideal gas law to find the pressure needed in each tank. (b) Use the van der Waals equation to find the pressure needed in each tank.(c) Compare the results from the two equations.

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Problem 126

For each of the following, which shows the greater deviation from ideal behavior at the same set of conditions? Explain.
$$
\begin{array}{ll}{\text { (a) Argon or xenon }} & {\text { (b) Water vapor or neon }} \\ {\text { (c) Mercury vapor or radon }} & {\text { (d) Water vapor or methane }}\end{array}
$$

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Problem 127

How many liters of gaseous hydrogen bromide at $29^{\circ} \mathrm{C}$ and 0.965 atm will a chemist need if she wishes to prepare 3.50 $\mathrm{L}$ of 1.20 M hydrobromic acid?

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Problem 128

A mixture consisting of 7.0 $\mathrm{g}$ of $\mathrm{CO}$ and 10.0 $\mathrm{g}$ of $\mathrm{SO}_{2},$ two atmospheric pollutants, has a pressure of 0.33 atm when placed in a sealed container. What is the partial pressure of $\mathrm{CO} ?$

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Problem 129

Sulfur dioxide is used to make sulfuric acid. One method of producing it is by roasting mineral sulfides, for example,
$$\mathrm{FeS}_{2}(s)+\mathrm{O}_{2}(g) \stackrel{\Delta}{\longrightarrow} \mathrm{SO}_{2}(g)+\mathrm{Fe}_{2} \mathrm{O}_{3}(s) \quad[\text { unbalanced }]$$
A production error leads to the sulfide being placed in a $950-\mathrm{L}$ vessel with insufficient oxygen. Initially, the partial pressure of $\mathrm{O}_{2}$ is 0.64 $\mathrm{atm}$ , and the total pressure is 1.05 atm, with the balance due to $\mathrm{N}_{2}$ . The reaction is run until 85$\%$ of the $\mathrm{O}_{2}$ is consumed, and the vessel is then cooled to its initial temperature. What is the total pressure in the vessel and the partial pressure of each gas in it?

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Problem 130

A mixture of $\mathrm{CO}_{2}$ and $\mathrm{Kr}$ weighs 35.0 $\mathrm{g}$ and exerts a pressure of 0.708 $\mathrm{atm}$ in its container. Since $\mathrm{Kr}$ is expensive, you wish to recover it from the mixture. After the $\mathrm{CO}_{2}$ is completely removed by absorption with $\mathrm{NaOH}(s),$ the pressure in the container is 0.250 atm. How many grams of $\mathrm{CO}_{2}$ were originally present? How many grams of Kr can you recover?

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Problem 131

When a car accelerates quickly, the passengers feel a force that presses them back into their seats, but a balloon filled with helium floats forward. Why?

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Problem 132

Gases such as CO are gradually oxidized in the atmosphere, not by $\mathrm{O}_{2}$ but by the hydroxyl radical, $\cdot \mathrm{OH},$ a species with one fewer electron than a hydroxide ion. At night, the \cdotOH concentration is nearly zero, but it increases to $2.5 \times 10^{12}$ molecules/m $^{3}$ in polluted air during the day. At daytime conditions of 1.00 atm and $22^{\circ} \mathrm{C},$ what is the partial pressure and mole percent of $\cdot \mathrm{OH}$ in air?

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Problem 133

Aqueous sulfurous acid $\left(\mathrm{H}_{2} \mathrm{SO}_{3}\right)$ was made by dissolving 0.200 $\mathrm{L}$ of sulfur dioxide gas at $19^{\circ} \mathrm{C}$ and 745 $\mathrm{mm} \mathrm{Hg}$ in water to yield 500.0 $\mathrm{mL}$ of solution. The acid solution required 10.0 $\mathrm{mL}$ of
sodium hydroxide solution to reach the titration end point. What was the molarity of the sodium hydroxide solution?

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Problem 134

In the $19^{\text { th }}$ century, J. B. A. Dumas devised a method for finding the molar mass of a volatile liquid from the volume, temperature, pressure, and mass of its vapor (next column). He placed a sample of such a liquid in a flask that was closed with a stopper fitted with a narrow tube, immersed the flask in a hot water bath to vaporize the liquid, and then cooled the flask. Find the molar mass of a volatile liquid from the following:
Mass of empty flask $=65.347 \mathrm{g}$
Mass of flask filled with water at $25^{\circ} \mathrm{C}=327.4 \mathrm{g}$
Density of water at $25^{\circ} \mathrm{C}=0.997 \mathrm{g} / \mathrm{mL}$
Mass of flask plus condensed unknown liquid $=65.739 \mathrm{g}$
Barometric pressure $=101.2 \mathrm{kPa}$
Temperature of water bath $=99.8^{\circ} \mathrm{C}$

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Problem 135

During World War II, a portable source of hydrogen gas was needed for weather balloons, and solid metal hydrides were the most convenient form. Many metal hydrides react with water to generate the metal hydroxide and hydrogen. Two candidates were lithium hydride and magnesium hydride. What volume (in L) of gas is formed from 1.00 lb of each hydride reacting with excess water at 750 . torr and $27^{\circ} \mathrm{C} ?$

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Problem 136

The lunar surface reaches 370 $\mathrm{K}$ at midday. The atmo- sphere consists of neon, argon, and helium at a total pressure of only $2 \times 10^{-14} \mathrm{atm}$ . Calculate the rms speed of each component in the lunar atmosphere. [Use $R=8.314 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})$ and $\mathscr{M}$ in $\mathrm{kg} / \mathrm{mol} . ]$

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Problem 137

A person inhales air richer in $\mathrm{O}_{2}$ and exhales air richer in $\mathrm{CO}_{2}$ and water vapor. During each hour of sleep, a person exhales $\mathrm{a}$ total of about 300 $\mathrm{L}$ of this $\mathrm{CO}_{2}$ -enriched and $\mathrm{H}_{2} \mathrm{O}$ -enriched air. (a) If the partial pressures of $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ in exhaled air are each 30.0 torr at $37.0^{\circ} \mathrm{C},$ calculate the mass (g) of $\mathrm{CO}_{2}$ and of $\mathrm{H}_{2} \mathrm{O}$ exhaled in 1 $\mathrm{h}$ of sleep. (b) How many grams of body mass does the person lose in 8 $\mathrm{h}$ of sleep if all the $\mathrm{CO}_{2}$ and $\mathrm{H}_{2} \mathrm{O}$ exhaled come from the metabolism of glucose?
$$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$

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Problem 138

Popcorn pops because the horny endosperm, a tough, elastic material, resists gas pressure within the heated kernel until it reaches explosive force. A $0.25-\mathrm{mL}$ kernel has a water content of 1.6$\%$ by mass, and the water vapor reaches $170^{\circ} \mathrm{C}$ and 9.0 atm before the kernel ruptures. Assume that water vapor can occupy 75$\%$ of the kernel's volume. (a) What is the mass (in $\mathrm{g}$ of the kernel? How many milliliters would this amount of water vapor occupy at $25^{\circ} \mathrm{C}$ and 1.00 $\mathrm{atm}$ ?

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Problem 139

Sulfur dioxide emissions from coal-burning power plants are removed by flue-gas desulfurization. The flue gas passes through a scrubber, and a slurry of wet calcium carbonate reacts with it to form carbon dioxide and calcium sulfite. The calcium sulfite then reacts with oxygen to form calcium sulfium sulfate, which is sold as gypsum. (a) If the sulfur dioxide concentration is 1000 times higher than its mole fraction in clean dry air $\left(2 \times 10^{-10}\right),$ how much calcium sulcium sulfate (kg) can be made from scrubbing 4 GL of flue gas $\left(1 \mathrm{GL}=1 \times 10^{9} \mathrm{L}\right) ?$ A state-of-the-art scrubber removes at least 95$\%$ of the sulfur dioxide. (b) If the mole fraction of oxygen in air is 0.209 , what volume (L) of air at 1.00 atm and $25^{\circ} \mathrm{C}$ is needed to react with all the calcium sulfite?

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Problem 140

Many water treatment plants use chlorine gas to kill micro-organisms before the water is released for residential use. A plant engineer has to maintain the chlorine pressure in a tank below the 85.0 -atm rating and, to be safe, decides to fill the tank to 80.0$\%$ of this maximum pressure. (a) How many moles of $\mathrm{Cl}_{2}$ gas can be kept in an 850 -L tank at 298 $\mathrm{K}$ if she uses the ideal gas law in the calculation? ( b) What is the tank pressure if she uses the van der Waals equation for this amount of gas? (c) Did the engineer fill the tank to the desired pressure?

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Problem 141

At $10.0^{\circ} \mathrm{C}$ and 102.5 $\mathrm{kPa}$ , the density of dry air is 1.26 $\mathrm{g} / \mathrm{L}$ . What is the average "molar mass" of dry air at these conditions?

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Problem 142

In A, the picture shows a cylinder with 0.1 $\mathrm{mol}$ of a gas that behaves ideally. Choose the cylinder (B, C, or D) that cor- rectly represents the volume of the gas after each of the following changes. If none of the cylinders is correct, specify "none."
(a) $P$ is doubled at fixed $n$ and $T .$
(b) $T$ is reduced from 400 $\mathrm{K}$ to 200 $\mathrm{K}$ at fixed $n$ and $P$
(c) $T$ is increased from $100^{\circ} \mathrm{C}$ to $200^{\circ} \mathrm{C}$ at fixed $n$ and $P$
(d) 0.1 mol of gas is added at fixed $P$ and $T$
(e) 0.1 mol of gas is added and $P$ is doubled at fixed $T$

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Problem 143

Ammonia is essential to so many industries that, on a molar basis, it is the most heavily produced substance in the world. Calculate $P_{\mathrm{IGL}}$ and $P_{\mathrm{VDW}}(\text { in atm })$ of 51.1 $\mathrm{g}$ of ammonia in a $3.000-L$ container at $0^{\circ} \mathrm{C}$ and $400 .^{\circ} \mathrm{C},$ the industrial temperature. (See Table 5.4 for the values of the van der Waals constants.)

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Problem 144

A $6.0-$ - flask contains a mixture of methane $\left(\mathrm{CH}_{4}\right),$ argon, and helium at $45^{\circ} \mathrm{C}$ and 1.75 atm. If the mole fractions of helium and argon are 0.25 and $0.35,$ respectively, how many molecules of methane are present?

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Problem 145

A large portion of metabolic energy arises from the biological combustion of glucose:
$$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(s)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$
(a) If this reaction is carried out in an expandable container at $37^{\circ} \mathrm{C}$ and $780 .$ torr, what volume of $\mathrm{CO}_{2}$ is produced from 20.0 $\mathrm{g}$ of glucose and excess $\mathrm{O}_{2} ?$
(b) If the reaction is carried out at the same conditions with the stoichiometric amount of $\mathrm{O}_{2},$ what is the partial pressure of each gas when the reaction is 50$\%$ complete $(10.0 \mathrm{g} \text { of glucose }$ remains)?

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Problem 146

What is the average kinetic energy and rms speed of $\mathrm{N}_{2}$ molecules at STP? Compare these values with those of $\mathrm{H}_{2}$ molecules at STP. [Use $R=8.314 \mathrm{J} /(\mathrm{mol} \cdot \mathrm{K})$ and $\mathscr{M}$ in $\mathrm{kg} / \mathrm{mol} . ]$

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Problem 147

According to government standards, the 8 -h threshold limit value is 5000 ppmv for $\mathrm{CO}_{2}$ and 0.1 ppmy for $\mathrm{Br}_{2}$ (1 ppmy is 1 part by volume in $10^{6}$ parts by volume). Exposure to either gas for 8 h above these limits is unsafe. At STP, which of the following would be unsafe for 8 h of exposure?
(a) Air with a partial pressure of 0.2 torr of $\mathrm{Br}_{2}$
(b) Air with a partial pressure of 0.2 torr of $\mathrm{CO}_{2}$
(c) 1000 $\mathrm{L}$ of air containing 0.0004 $\mathrm{g}$ of $\mathrm{Br}_{2}$ gas
(d) 1000 $\mathrm{L}$ of air containing $2.8 \times 10^{22}$ molecules of $\mathrm{CO}_{2}$

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Problem 148

One way to prevent emission of the pollutant NO from industrial plants is by a catalyzed reaction with $\mathrm{NH}_{3} :$
$$4 \mathrm{NH}_{3}(g)+4 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \stackrel{\text { catalyst }}{\longrightarrow} 4 \mathrm{N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$
(a) If the NO has a partial pressure of $4.5 \times 10^{-5}$ atm in the flue gas, how many liters of $\mathrm{NH}_{3}$ are needed per liter of flue gas at 1.00 $\mathrm{atm} ?$ (b) If the reaction takes place at 1.00 atm and $365^{\circ} \mathrm{C},$ how many grams of $\mathrm{NH}_{3}$ are needed per kL of flue gas?

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Problem 149

An equimolar mixture of Ne and Xe is accidentally placed in a container that has a tiny leak. After a short while, a very small proportion of the mixture has escaped. What is the mole fraction of Ne in the effusing gas?

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Problem 150

From the relative rates of effusion of 235 $\mathrm{UF}_{6}$ and $238 \mathrm{UF}_{6},$ find the number of steps needed to produce a sample of the enriched fuel used in many nuclear reactors, which is 3.0 mole $\%$ 35 U. The natural abundance of $^{235} \mathrm{U}$ is 0.72$\%$

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Problem 151

A slight deviation from ideal behavior exists even at normal conditions. If it behaved ideally, 1 mol of $\mathrm{CO}$ would occupy 22.414 $\mathrm{L}$ and exert 1 atm pressure at 273.15 $\mathrm{K}$ . Calculate $P_{\text { VDW }}$
for 1.000 mol of $\mathrm{CO}$ at 273.15 $\mathrm{K} .\left(\text { Use } R=0.08206 \frac{\mathrm{atm} \cdot \mathrm{L}}{\mathrm{mol} \cdot \mathrm{K}}\right)^{\mathrm{VDW}}$

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Problem 152

In preparation for a combustion demonstration, a professor fills a balloon with equal molar amounts of $\mathrm{H}_{2}$ and $\mathrm{O}_{2},$ but the demonstration has to be postponed until the next day. During the night, both gases leak through pores in the balloon. If 35$\%$ of the $\mathrm{H}_{2}$ leaks, what is the $\mathrm{O}_{2} / \mathrm{H}_{2}$ ratio in the balloon the next day?

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Problem 153

Phosphorus trichloride is important in the manufacture of insecticides, fuel additives, and flame retardants. Phosphorus has only one naturally occurring isotope, $31 \mathrm{P},$ whereas chlorine has two, 35 $\mathrm{Cl}(75 \%)$ and $^{37} \mathrm{Cl}(25 \%)$ . (a) What different molecular masses (in amu) can be found for $\mathrm{PCl}_{3} ?$ (b) Which is the most abundant? (c) What is the ratio of the effusion rates of the heaviest and the lightest $\mathrm{PCl}_{3}$ molecules?

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Problem 154

A truck tire has a volume of 218 $\mathrm{L}$ and is filled with air to 35.0 psi at 295 $\mathrm{K}$ . After a drive, the air heats up to 318 $\mathrm{K}$ . (a) If the tire volume is constant, what is the pressure (in psi)? (b) If the tire volume increases 2.0$\%$ , what is the pressure (in psi)? (c) If the tire
leaks 1.5 $\mathrm{g}$ of air per minute and the temperature is constant, how many minutes will it take for the to reach the original pressure of 35.0 $\mathrm{psi}(\mathscr{M} \text { of air }=28.8 \mathrm{g} / \mathrm{mol}) ?$

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Problem 155

Allotropes are different molecular forms of an element, such as dioxygen $\left(\mathrm{O}_{2}\right)$ and ozone $\left(\mathrm{O}_{3}\right) .$ (a) What is the density of each oxygen allotrope at $0^{\circ} \mathrm{C}$ and 760 torr? (b) Calculate the ratio of densities, $d_{\mathrm{O}_{3}} / d_{\mathrm{O}_{2}},$ and explain the significance of this number.

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Problem 156

When gaseous $\mathrm{F}_{2}$ and solid $\mathrm{I}_{2}$ are heated to high temperatures, the $\mathrm{I}_{2}$ sublimes and gaseous iodine heptafluoride forms. If 350 . torr of $\mathrm{F}_{2}$ and 2.50 $\mathrm{g}$ of solid $\mathrm{I}_{2}$ are put into a $2.50-\mathrm{L}$ container at $250 . \mathrm{K}$ and the container is heated to $550 . \mathrm{K}$ , what is the final pressure (in torr)? What is the partial pressure of $\mathrm{I}_{2}$ gas?

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