Chemistry

Steven S. Zumdahl, Susan A. Zumdahls

Chapter 5

Gases - all with Video Answers

Educators

+ 2 more educators

Chapter Questions

Problem 1

Consider the following apparatus: a test tube covered with a nonpermeable elastic membrane inside a container that is closed with a cork. A syringe goes through the cork.
a. As you push down on the syringe, how does the membrane covering the test tube change?
b. You stop pushing the syringe but continue to hold it down. In a few seconds, what happens to the membrane?

Cathy Geisel

Cathy Geisel

Numerade Educator

Problem 2

Figure $5.2$ shows a picture of a barometer. Which of the following statements is the best explanation of how this barometer works?
a. Air pressure outside the tube causes the mercury to move in the tube until the air pressure inside and outside the tube is equal.
b. Air pressure inside the tube causes the mercury to move in the tube until the air pressure inside and outside the tube is equal.
c. Air pressure outside the tube counterbalances the weight of the mercury in the tube.
d. Capillary action of the mercury causes the mercury to go up the tube.
e. The vacuum that is formed at the top of the tube holds up the mercury. Justify your choice, and for the choices you did not pick, explain what is wrong with them. Pictures help!

Matthew Confer

Numerade Educator

Problem 3

The barometer below shows the level of mercury at a given at mospheric pressure. Fill all the other barometers with mercury for that same atmospheric pressure. Explain your answer.

David Collins

Numerade Educator

Problem 4

As you increase the temperature of a gas in a sealed, rigid container, what happens to the density of the gas? Would the results be the same if you did the same experiment in a container with a piston at constant pressure? (See Figure 5.17.)

Matthew Confer

Numerade Educator

Problem 5

A diagram in a chemistry book shows a magnified view of a flask of air as follows:
What do you suppose is between the dots (the dots represent air molecules)?
a. air
b. dust
c. pollutants
d. oxygen
e. nothing

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 6

If you put a drinking straw in water, place your finger over the opening, and lift the straw out of the water, some water stays in the straw. Explain.

Matthew Confer

Numerade Educator

Problem 7

A chemistry student relates the following story: I noticed my tires were a bit low and went to the gas station. As I was filling the tires, I thought about the kinetic molecular theory (KMT). I noticed the tires because the volume was low, and I realized that I was increasing both the pressure and volume of the tires. "Hmmm," I thought, "that goes against what I learned in chemistry, where I was told pressure and volume are inversely proportional." What is the fault in the logic of the chemistry student in this situation? Explain why we think pressure and volume to be inversely related (draw pictures and use the KMT).

Cathy Geisel

Numerade Educator

Problem 8

Chemicals $X$ and $Y$ (both gases) react to form the gas $X Y$, but it takes a bit of time for the reaction to occur. Both $X$ and $Y$ are placed in a container with a piston (free to move), and you note the volume. As the reaction occurs, what happens to the volume of the container? (See Fig. 5.18.)

Matthew Confer

Numerade Educator

Problem 9

Which statement best explains why a hot-air balloon rises when the air in the balloon is heated?
a. According to Charles's law, the temperature of a gas is directly related to its volume. Thus the volume of the balloon increases, making the density smaller. This lifts the balloon.
b. Hot air rises inside the balloon, and this lifts the balloon.
c. The temperature of a gas is directly related to its pressure. The pressure therefore increases, and this lifts the balloon.
d. Some of the gas escapes from the bottom of the balloon, thus decreasing the mass of gas in the balloon. This decreases the density of the gas in the balloon, which lifts the balloon.
e. Temperature is related to the root mean square velocity of the gas molecules. Thus the molecules are moving faster, hitting the balloon more, and thus lifting the balloon. Justify your choice, and for the choices you did not pick, explain what is wrong with them.

Cathy Geisel

Numerade Educator

Problem 10

Draw a highly magnified view of a sealed, rigid container filled with a gas. Then draw what it would look like if you cooled the gas significantly but kept the temperature above the boiling point of the substance in the container. Also draw what it would look like if you heated the gas significantly. Finally, draw what each situation would look like if you evacuated enough of the gas to decrease the pressure by a factor of $2 .$

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 11

If you release a helium balloon, it soars upward and eventually pops. Explain this behavior.

Cathy Geisel

Numerade Educator

Problem 12

If you have any two gases in different containers that are the same size at the same pressure and same temperature, what is true about the moles of each gas? Why is this true?

Cathy Geisel

Numerade Educator

Problem 13

Explain the following seeming contradiction: You have two gases, $A$ and $B$, in two separate containers of equal volume and at equal pressure and temperature. Therefore, you must have the same number of moles of each gas. Because the two temperatures are equal, the average kinetic energies of the two samples are equal. Therefore, since the energy given such a system will be converted to translational motion (that is, move the molecules), the root mean square velocities of the two are equal, and thus the particles in each sample move, on average, with the same relative speed. Since $A$ and $B$ are different gases, they each must have a different molar mass. If $A$ has higher molar mass than $B$, the particles of $A$ must be hitting the sides of the container with more force. Thus the pressure in the container of gas $A$ must be higher than that in the container with gas $B$. However, one of our initial assumptions was that the pressures were equal.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 14

You have a balloon covering the mouth of a flask filled with air at 1 atm. You apply heat to the bottom of the flask until the volume of the balloon is equal to that of the flask.
a. Which has more air in it, the balloon or the flask? Or do both have the same amount? Explain.
b. In which is the pressure greater, the balloon or the flask? Or is the pressure the same? Explain.

Cathy Geisel

Numerade Educator

Problem 15

How does Dalton's law of partial pressures help us with our model of ideal gases? That is, what postulates of the kinetic molecular theory does it support?

Cathy Geisel

Numerade Educator

Problem 16

At room temperature, water is a liquid with a molar volume of $18 \mathrm{~mL}$. At $105^{\circ} \mathrm{C}$ and 1 atm pressure, water is a gas and has a molar volume of over $30 \mathrm{~L}$. Explain the large difference in molar volumes.

Cathy Geisel

Numerade Educator

Problem 17

If a barometer were built using water $\left(d=1.0 \mathrm{~g} / \mathrm{cm}^{3}\right)$ instead of mercury $\left(d=13.6 \mathrm{~g} / \mathrm{cm}^{3}\right)$, would the column of water be higher than, lower than, or the same as the column of mercury at $1.00 \mathrm{~atm} ?$ If the level is different, by what factor? Explain.

Cathy Geisel

Numerade Educator

Problem 18

A bag of potato chips is packed and sealed in Los Angeles, California, and then shipped to Lake Tahoe, Nevada, during ski season. It is noticed that the volume of the bag of potato chips has increased upon its arrival in Lake Tahoe. What external conditions would most likely cause the volume increase?

Cathy Geisel

Numerade Educator

Problem 19

Boyle's law can be represented graphically in several ways. Which of the following plots does not correctly represent Boyle's law (assuming constant $T$ and $n$ )? Explain.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 20

As weather balloons rise from the earth's surface, the pressure of the atmosphere becomes less, tending to cause the volume of the balloons to expand. However, the temperature is much lower in the upper atmosphere than at sea level. Would this temperature effect tend to make such a balloon expand or contract? Weather balloons do, in fact, expand as they rise. What does this tell you?

Cathy Geisel

Numerade Educator

Problem 21

Which noble gas has the smallest density at STP? Explain.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 22

Consider two different containers, each filled with 2 moles of $\mathrm{Ne}(\mathrm{g})$. One of the containers is rigid and has constant volume. The other container is flexible (like a balloon) and is capable of changing its volume to keep the external pressure and internal pressure equal to each other. If you raise the temperature in both containers, what happens to the pressure and density of the gas inside each container? Assume a constant external pressure.

Matthew Confer

Numerade Educator

Problem 23

Do all the molecules in a 1-mol sample of $\mathrm{CH}_{4}(\mathrm{~g}$ ) have the same kinetic energy at $273 \mathrm{~K}$ ? Do all molecules in a 1 -mol sample of $\mathrm{N}_{2}(g)$ have the same velocity at $546 \mathrm{~K}$ ? Explain.

Tom Comey

Numerade Educator

Problem 24

Consider the following samples of gases at the same temperature. Arrange each of these samples in order from lowest to highest:
a. pressure
b. average kinetic energy
c. density
d. root mean square velocity Note: Some samples of gases may have equal values for these attributes. Assume the larger containers have a volume twice the volume of the smaller containers and assume the mass of an argon atom is twice the mass of a neon atom.

Matthew Confer

Numerade Educator

Problem 25

As $\mathrm{NH}_{3}(g)$ is decomposed into nitrogen gas and hydrogen gas at constant pressure and temperature, the volume of the product gases collected is twice the volume of $\mathrm{NH}_{3}$ reacted. Explain. As $\mathrm{NH}_{3}(g)$ is decomposed into nitrogen gas and hydrogen gas at constant volume and temperature, the total pressure increases by some factor. Why the increase in pressure and by what factor does the total pressure increase when reactants are completely converted into products? How do the partial pressures of the product gases compare to each other and to the initial pressure of $\mathrm{NH}_{3}$ ?

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 26

Which of the following statements is (are) true? For the false statements, correct them.
a. At constant temperature, the lighter the gas molecules, the faster the average velocity of the gas molecules.
b. At constant temperature, the heavier the gas molecules, the larger the average kinetic energy of the gas molecules.
c. A real gas behaves most ideally when the container volume is relatively large and the gas molecules are moving relatively quickly.
d. As temperature increases, the effect of interparticle interactions on gas behavior is increased.
e. At constant $V$ and $T$, as gas molecules are added into a container, the number of collisions per unit area increases resulting in a higher pressure.
f. The kinetic molecular theory predicts that pressure is inversely proportional to temperature at constant volume and mol of gas.

Tom Comey

Numerade Educator

Problem 27

Freon-12 $\left(\mathrm{CF}_{2} \mathrm{Cl}_{2}\right)$ is commonly used as the refrigerant in central home air conditioners. The system is initially charged to a pressure of $4.8$ atm. Express this pressure in each of the following units $(1 \mathrm{~atm}=14.7 \mathrm{psi})$.
a. $\mathrm{mm} \mathrm{Hg}$
b. torr
c. $\mathrm{Pa}$
d. $\mathrm{psi}$

Cathy Geisel

Numerade Educator

Problem 28

A gauge on a compressed gas cylinder reads 2200 psi (pounds per square inch; $1 \mathrm{~atm}=14.7 \mathrm{psi}$ ). Express this pressure in each of the following units.
a. standard atmospheres
b. megapascals (MPa)
c. torr

Cathy Geisel

Numerade Educator

Problem 29

A sealed-tube manometer (as shown below) can be used to measure pressures below atmospheric pressure. The tube above the mercury is evacuated. When there is a vacuum in the flask, the mercury levels in both arms of the U-tube are equal. If a gaseous sample is introduced into the flask, the mercury levels are different. The difference $h$ is a measure of the pressure of the gas inside the flask. If $h$ is equal to $6.5 \mathrm{~cm}$, calculate the pressure in the flask in torr, pascals, and atmospheres.

Cathy Geisel

Numerade Educator

Problem 30

If the sealed-tube manometer in Exercise 29 had a height difference of $20.0$ inches between the mercury levels, what is the pressure in the flask in torr and atmospheres?

Cathy Geisel

Numerade Educator

Problem 31

A diagram for an open-tube manometer is shown below.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 32

a. If the open-tube manometer in Exercise 31 contains a nonvolatile silicone oil (density $=1.30 \mathrm{~g} / \mathrm{cm}^{3}$ ) instead of mercury (density $=13.6 \mathrm{~g} / \mathrm{cm}^{3}$ ), what are the pressures in the flask as shown in parts a and $\mathrm{b}$ in torr, atmospheres, and pascals?
b. What advantage would there be in using a less dense fluid than mercury in a manometer used to measure relatively small differences in pressure?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 33

A particular balloon is designed by its manufacturer to be inflated to a volume of no more than $2.5 \mathrm{~L}$. If the balloon is filled with $2.0 \mathrm{~L}$ of helium at sea level, is released, and rises to an altitude at which the atmospheric pressure is only $500 . \mathrm{mm} \mathrm{Hg}$, will the balloon burst? (Assume temperature is constant.)

Ma Ednelyn Lim

Numerade Educator

Problem 34

A balloon is filled to a volume of $7.00 \times 10^{2} \mathrm{~mL}$ at a temperature of $20.0^{\circ} \mathrm{C}$. The balloon is then cooled at constant pressure to a temperature of $1.00 \times 10^{2} \mathrm{~K}$. What is the final volume of the balloon?

Cathy Geisel

Numerade Educator

Problem 35

An 11.2-L sample of gas is determined to contain $0.50$ mol of $\mathrm{N}_{2}$. At the same temperature and pressure, how many moles of gas would there be in a 20.-L sample?

Shalini Tyagi

Numerade Educator

Problem 36

Consider the following chemical equation.
$$2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)$$
If $25.0 \mathrm{~mL}$ of $\mathrm{NO}_{2}$ gas is completely converted to $\mathrm{N}_{2} \mathrm{O}_{4}$ gas under the same conditions, what volume will the $\mathrm{N}_{2} \mathrm{O}_{4}$ occupy?

Shalini Tyagi

Numerade Educator

Problem 37

Complete the following table for an ideal gas.
$\begin{array}{llccc}
& P(\text { atm }) & V(\mathrm{~L}) & n(\mathrm{~mol}) & T \\
\hline \text { a. } & 5.00 & & 2.00 & 155^{\circ} \mathrm{C} \\
\hline \text { b. } & 0.300 & 2.00 & & 155 \mathrm{~K} \\
\hline \text { c. } & 4.47 & 25.0 & 2.01 & \\
\hline \text { d. } & & 2.25 & 10.5 & 75^{\circ} \mathrm{C}
\end{array}$

Ma Ednelyn Lim

Numerade Educator

Problem 38

Complete the following table for an ideal gas.
$$
\begin{array}{llllr}
& & & & \\
\text { a. } & 7.74 \times 10^{3} \mathrm{~Pa} & 12.2 \mathrm{~mL} & & 25^{\circ} \mathrm{C} \\
\text { b. } & & 43.0 \mathrm{~mL} & 0.421 \mathrm{~mol} & 223 \mathrm{~K} \\
\text { c. } & 455 \text { torr } & & 4.4 \times 10^{-2} \mathrm{~mol} & 331^{\circ} \mathrm{C} \\
\text { d. } & 745 \mathrm{~mm} \mathrm{Hg} & 11.2 \mathrm{~L} & 0.401 \mathrm{~mol} &
\end{array}
$$

Shalini Tyagi

Numerade Educator

Problem 39

Suppose two $200.0$ - $\mathrm{L}$ tanks are to be filled separately with the gases helium and hydrogen. What mass of each gas is needed to produce a pressure of 135 atm in its respective tank at $24^{\circ} \mathrm{C}$ ?

Dr. Satish Ingale

Dr. Satish Ingale

Numerade Educator

Problem 40

A flask that can withstand an internal pressure of 2500 torr, but no more, is filled with a gas at $21.0^{\circ} \mathrm{C}$ and 758 torr and heated. At what temperature will it burst?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 41

A 2.50-L container is filled with $175 \mathrm{~g}$ argon.
a. If the pressure is $10.0 \mathrm{~atm}$, what is the temperature?
b. If the temperature is $225 \mathrm{~K}$, what is the pressure?

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 42

A person accidentally swallows a drop of liquid oxygen, $\mathrm{O}_{2}(l)$, which has a density of $1.149 \mathrm{~g} / \mathrm{mL}$. Assuming the drop has a volume of $0.050 \mathrm{~mL}$, what volume of gas will be produced in the person's stomach at body temperature $\left(37^{\circ} \mathrm{C}\right)$ and a pressure of $1.0 \mathrm{~atm} ?$

Joanna Josey

Numerade Educator

Problem 43

A gas sample containing $1.50 \mathrm{~mol}$ at $25^{\circ} \mathrm{C}$ exerts a pressure of 400. torr. Some gas is added to the same container and the temperature is increased to $50 .{ }^{\circ} \mathrm{C}$. If the pressure increases to 800 . torr, how many moles of gas were added to the container? Assume a constant-volume container.

Tom Comey

Numerade Educator

Problem 44

A bicycle tire is filled with air to a pressure of $100 .$ psi at a temperature of $19^{\circ} \mathrm{C}$. Riding the bike on asphalt on a hot day increases the temperature of the tire to $58^{\circ} \mathrm{C}$. The volume of the tire increases by $4.0 \%$. What is the new pressure in the bicycle tire?

Shalini Tyagi

Numerade Educator

Problem 45

Consider two separate gas containers at the following conditions:
$$
\begin{array}{ll}
\text { Container A } & \text { Container B } \\
\hline \text { Contents: } \mathrm{SO}_{2}(g) & \text { Contents: unknown gas } \\
\text { Pressure }=P_{\mathrm{A}} & \text { Pressure }=P_{\mathrm{B}} \\
\text { Moles of gas }=1.0 \mathrm{~mol} & \text { Moles of gas }=2.0 \mathrm{~mol} \\
\text { Volume }=1.0 \mathrm{~L} & \text { Volume }=2.0 \mathrm{~L} \\
\text { Temperature }=7^{\circ} \mathrm{C} & \text { Temperature }=287^{\circ} \mathrm{C}
\end{array}
$$
How is the pressure in container B related to the pressure in container A?

Ma Ednelyn Lim

Numerade Educator

Problem 46

A container is filled with an ideal gas to a pressure of $40.0$ atm at $0^{\circ} \mathrm{C}$.
a. What will be the pressure in the container if it is heated to $45^{\circ} \mathrm{C} ?$
b. At what temperature would the pressure be $1.50 \times 10^{2}$ atm?
c. At what temperature would the pressure be $25.0 \mathrm{~atm} ?$

Shalini Tyagi

Numerade Educator

Problem 47

An idcal gas is contained in a cylinder with a volume of $5.0 \times$ $10^{2} \mathrm{~mL}$ at a temperature of $30 .{ }^{\circ} \mathrm{C}$ and a pressure of $710 .$ torr. The gas is then compressed to a volume of $25 \mathrm{~mL}$, and the temperature is raised to $820 .{ }^{\circ} \mathrm{C}$. What is the new pressure of the gas?

Shalini Tyagi

Numerade Educator

Problem 48

A compressed gas cylinder contains $1.00 \times 10^{3} \mathrm{~g}$ of argon gas. The pressure inside the cylinder is $2050 .$ psi (pounds per square inch) at a temperature of $18^{\circ} \mathrm{C}$. How much gas remains in the cylinder if the pressure is decreased to 650 . psi at a temperature of $26^{\circ} \mathrm{C}$ ?

Joanna Josey

Numerade Educator

Problem 49

A sealed balloon is filled with $1.00 \mathrm{~L}$ of helium at $23^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm} .$ The balloon rises to a point in the atmosphere where the pressure is 220 . torr and the temperature is $-31^{\circ} \mathrm{C}$. What is the change in volume of the balloon as it ascends from $1.00$ atm to a pressure of 220 . torr?

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 50

A hot-air balloon is filled with air to a volume of $4.00 \times 10^{3} \mathrm{~m}^{3}$
at 745 torr and $21^{\circ} \mathrm{C}$. The air in the balloon is then heated to $62^{\circ} \mathrm{C}$, causing the balloon to expand to a volume of $4.20 \times 10^{3} \mathrm{~m}^{3}$. What is the ratio of the number of moles of air in the heated balloon to the original number of moles of air in the balloon? (Hint: Openings in the balloon allow air to flow in and out. Thus the pressure in the balloon is always the same as that of the atmosphere.)

Joanna Josey

Numerade Educator

Problem 51

Consider the following reaction:
$$4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \rightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)$$
It takes $2.00 \mathrm{~L}$ of pure oxygen gas at STP to react completely with a certain sample of aluminum. What is the mass of aluminum reacted?

Cathy Geisel

Numerade Educator

Problem 52

A student adds $4.00 \mathrm{~g}$ of dry ice (solid $\mathrm{CO}_{2}$ ) to an empty balloon. What will be the volume of the balloon at STP after all the dry ice sublimes (converts to gaseous $\mathrm{CO}_{2}$ )?

Cathy Geisel

Numerade Educator

Problem 53

Air bags are activated when a severe impact causes a steel ball to compress a spring and electrically ignite a detonator cap. This causes sodium azide $\left(\mathrm{NaN}_{3}\right)$ to decompose explosively according to the following reaction:
$$2 \mathrm{NaN}_{3}(s) \longrightarrow 2 \mathrm{Na}(s)+3 \mathrm{~N}_{2}(g)$$
What mass of $\mathrm{NaN}_{3}(s)$ must be reacted to inflate an air bag to $70.0 \mathrm{~L}$ at STP?

William Mills

Numerade Educator

Problem 54

Concentrated hydrogen peroxide solutions are explosively decomposed by traces of transition metal ions (such as Mn or $\mathrm{Fe}$ ):
$$2 \mathrm{H}_{2} \mathrm{O}_{2}(a q) \rightarrow 2 \mathrm{H}_{2} \mathrm{O}(l)+\mathrm{O}_{2}(g)$$
What volume of pure $\mathrm{O}_{2}(g)$, collected at $27^{\circ} \mathrm{C}$ and 746 torr, would be generated by decomposition of $125 \mathrm{~g}$ of a $50.0 \%$ by mass hydrogen peroxide solution? Ignore any water vapor that may be present.

Joanna Josey

Numerade Educator

Problem 55

In 1897 the Swedish explorer Andreé tried to reach the North Pole in a balloon. The balloon was filled with hydrogen gas. The hydrogen gas was prepared from iron splints and diluted sulfuric acid. The reaction is
$$\mathrm{Fe}(s)+\mathrm{H}_{2} \mathrm{SO}_{4}(a q) \longrightarrow \mathrm{FeSO}_{4}(a q)+\mathrm{H}_{2}(g)$$
The volume of the balloon was $4800 \mathrm{~m}^{3}$ and the loss of hydrogen gas during filling was estimated at $20 . \%$. What mass of iron splints and $98 \%$ (by mass) $\mathrm{H}_{2} \mathrm{SO}_{4}$ were needed to ensure the complete filling of the balloon? Assume a temperature of $0^{\circ} \mathrm{C}$, a pressure of $1.0$ atm during filling, and $100 \%$ yield.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 56

Sulfur trioxide, $\mathrm{SO}_{3}$, is produced in enormous quantities each year for use in the synthesis of sulfuric acid.
$$\begin{aligned}
\mathrm{S}(s)+\mathrm{O}_{2}(g) & \rightarrow \mathrm{SO}_{2}(g) \\
2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) & \rightarrow 2 \mathrm{SO}_{3}(g)
\end{aligned}$$
What volume of $\mathrm{O}_{2}(\mathrm{~g})$ at $350 .{ }^{\circ} \mathrm{C}$ and a pressure of $5.25$ atm is needed to completely convert $5.00 \mathrm{~g}$ of sulfur to sulfur trioxide?

Anatole Borisov

Anatole Borisov

Numerade Educator

Problem 57

Consider the reaction between $50.0 \mathrm{~mL}$ of liquid methyl alcohol, $\mathrm{CH}_{3} \mathrm{OH}$ (density $=0.850 \mathrm{~g} / \mathrm{mL}$ ), and $22.8 \mathrm{~L}$ of $\mathrm{O}_{2}$ at $27^{\circ} \mathrm{C}$
and a pressure of $2.00 \mathrm{~atm} .$ The products of the reaction are $\mathrm{CO}_{2}(g)$ and $\mathrm{H}_{2} \mathrm{O}(g) .$ Calculate the number of moles of $\mathrm{H}_{2} \mathrm{O}$
formed if the reaction goes to completion.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 58

Urea $\left(\mathrm{H}_{2} \mathrm{NCONH}_{2}\right)$ is used extensively as a nitrogen source in fertilizers. It is produced commercially from the reaction of ammonia and carbon dioxide:
$$2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \underset{\text { Pressure }}{\stackrel{\text { Heat }}{\text { Pressur }} \mathrm{H}_{2} \mathrm{NCONH}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(g)}$$
Ammonia gas at $223^{\circ} \mathrm{C}$ and 90 . atm flows into a reactor at a rate of $500 . \mathrm{L} / \mathrm{min}$. Carbon dioxide at $223^{\circ} \mathrm{C}$ and $45 \mathrm{~atm}$ flows into the reactor at a rate of $600 . \mathrm{L} / \mathrm{min}$. What mass of urea is produced per minute by this reaction assuming $100 \%$ yield?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 59

Hydrogen cyanide is prepared commercially by the reaction of methane, $\mathrm{CH}_{4}(g)$, ammonia, $\mathrm{NH}_{3}(g)$, and oxygen, $\mathrm{O}_{2}(g)$, at high temperature. The other product is gaseous water.
a. Write a chemical equation for the reaction.
b. What volume of $\mathrm{HCN}(g)$ can be obtained from $20.0 \mathrm{~L} \mathrm{CH}_{4}(g)$, $20.0 \mathrm{~L} \mathrm{NH}_{3}(g)$, and $20.0 \mathrm{~L} \mathrm{O}_{2}(g) ?$ The volumes of all gases are measured at the same temperature and pressure.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 60

Methanol, $\mathrm{CH}_{3} \mathrm{OH}$, can be produced by the following reaction:
$$\mathrm{CO}(g)+2 \mathrm{H}_{2}(g) \longrightarrow \mathrm{CH}_{3} \mathrm{OH}(g)$$
Hydrogen at STP flows into a reactor at a rate of $16.0 \mathrm{~L} / \mathrm{min} .$ Carbon monoxide at STP flows into the reactor at a rate of $25.0 \mathrm{~L} / \mathrm{min}$. If $5.30 \mathrm{~g}$ of methanol is produced per minute, what is the percent yield of the reaction?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 61

An unknown diatomic gas has a density of $3.164 \mathrm{~g} / \mathrm{L}$ at STP. What is the identity of the gas?

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 62

A compound has the empirical formula CHCl. A 256-mL flask, at $373 \mathrm{~K}$ and 750 . torr, contains $0.800 \mathrm{~g}$ of the gaseous compound. Give the molecular formula.

Joanna Josey

Numerade Educator

Problem 63

Uranium hexafluoride is a solid at room temperature, but it boils at $56^{\circ} \mathrm{C}$. Determine the density of uranium hexafluoride at $60 .{ }^{\circ} \mathrm{C}$ and 745 torr.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 64

Given that a sample of air is made up of nitrogen, oxygen, and argon in the mole fractions $78 \% \mathrm{~N}_{2}, 21 \% \mathrm{O}_{2}$, and $1.0 \%$ Ar, what is the density of air at standard temperature and pressure?

Tom Comey

Numerade Educator

Problem 65

A piece of solid carbon dioxide, with a mass of $7.8 \mathrm{~g}$, is placed in a 4.0-L otherwise empty container at $27^{\circ} \mathrm{C}$. What is the pressure in the container after all the carbon dioxide vaporizes? If $7.8 \mathrm{~g}$ solid carbon dioxide were placed in the same container but it already contained air at 740 torr, what would be the partial pressure of carbon dioxide and the total pressure in the container after the carbon dioxide vaporizes?

Dr. Satish Ingale

Dr. Satish Ingale

Numerade Educator

Problem 66

A mixture of $1.00 \mathrm{~g} \mathrm{H}_{2}$ and $1.00 \mathrm{~g}$ He is placed in a $1.00-\mathrm{L}$ container at $27^{\circ} \mathrm{C}$. Calculate the partial pressure of each gas and the total pressure.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 67

Consider the flasks in the following diagram. What are the final partial pressures of $\mathrm{H}_{2}$ and $\mathrm{N}_{2}$ after the stopcock between the two flasks is opened? (Assume the final volume is $3.00 \mathrm{~L}$.) What is the total pressure (in torr)?

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 68

Consider the flask apparatus in Exercise 67, which now contains $2.00 \mathrm{~L}$ of $\mathrm{H}_{2}$ at a pressure of 360 . torr and $1.00 \mathrm{~L}$ of $\mathrm{N}_{2}$ at an unknown pressure. If the total pressure in the flasks is 320 . torr after the stopcock is opened, determine the initial pressure of $\mathrm{N}_{2}$ in the $1.00-\mathrm{L}$ flask.

Shalini Tyagi

Numerade Educator

Problem 69

The partial pressure of $\mathrm{CH}_{4}(g)$ is $0.175 \mathrm{~atm}$ and that of $\mathrm{O}_{2}(g)$ is $0.250$ atm in a mixture of the two gases.
a. What is the mole fraction of each gas in the mixture?
b. If the mixture occupies a volume of $10.5 \mathrm{~L}$ at $65^{\circ} \mathrm{C}$, calculate the total number of moles of gas in the mixture.
c. Calculate the number of grams of each gas in the mixture.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 70

A $1.00-\mathrm{L}$ gas sample at $100 .{ }^{\circ} \mathrm{C}$ and 600 . torr contains $50.0 \%$ helium and $50.0 \%$ xenon by mass. What are the partial pressures of the individual gases?

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 71

Small quantities of hydrogen gas can be prepared in the laboratory by the addition of aqueous hydrochloric acid to metallic zinc.
$$\mathrm{Zn}(s)+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g)$$
Typically, the hydrogen gas is bubbled through water for collection and becomes saturated with water vapor. Suppose 240 . $\mathrm{mL}$ of hydrogen gas is collected at $30 .{ }^{\circ} \mathrm{C}$ and has a total pressure of $1.032$ atm by this process. What is the partial pressure of hydrogen gas in the sample? How many grams of zinc must have reacted to produce this quantity of hydrogen? (The vapor pressure of water is 32 torr at $30^{\circ} \mathrm{C}$.)

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 72

Helium is collected over water at $25^{\circ} \mathrm{C}$ and $1.00 \mathrm{~atm}$ total pressure. What total volume of gas must be collected to obtain $0.586 \mathrm{~g}$ of helium? (At $25^{\circ} \mathrm{C}$ the vapor pressure of water is $23.8$ torr.)

Joanna Josey

Numerade Educator

Problem 73

At elevated temperatures, sodium chlorate decomposes to produce sodium chloride and oxygen gas. A $0.8765-\mathrm{g}$ sample of impure sodium chlorate was heated until the production of oxygen gas ceased. The oxygen gas collected over water occupied $57.2 \mathrm{~mL}$ at a temperature of $22^{\circ} \mathrm{C}$ and a pressure of 734 torr. Calculate the mass percent of $\mathrm{NaClO}_{3}$ in the original sample. (At $22^{\circ} \mathrm{C}$ the vapor pressure of water is $19.8$ torr.)

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 74

Xenon and fluorine will react to form binary compounds when a mixture of these two gases is heated to $400^{\circ} \mathrm{C}$ in a nickel reaction vessel. A 100.0-mL nickel container is filled with xenon and fluorine, giving partial pressures of $1.24 \mathrm{~atm}$ and $10.10 \mathrm{~atm}$, respectively, at a temperature of $25^{\circ} \mathrm{C}$. The reaction vessel is heated to $400{ }^{\circ} \mathrm{C}$ to cause a reaction to occur and then cooled to a temperature at which $\mathrm{F}_{2}$ is a gas and the xenon fluoride compound produced is a nonvolatile solid. The remaining $\mathrm{F}_{2}$ gas is transferred to another $100.0-\mathrm{mL}$ nickel container, where the pressure of $\mathrm{F}_{2}$ at $25^{\circ} \mathrm{C}$ is $7.62$ atm. Assuming all of the xenon has reacted, what is the formula of the product?

Joanna Josey

Numerade Educator

Problem 75

Hydrogen azide, $\mathrm{HN}_{3}$, decomposes on heating by the following unbalanced reaction:
$$\mathrm{HN}_{3}(g) \longrightarrow \mathrm{N}_{2}(g)+\mathrm{H}_{2}(g)$$
If $3.0$ atm of pure $\mathrm{HN}_{3}(g)$ is decomposed initially, what is the final total pressure in the reaction container? What are the partial pressures of nitrogen and hydrogen gas? Assume the volume and temperature of the reaction container are constant.

Anand Jangid

Numerade Educator

Problem 76

Some very effective rocket fuels are composed of lightweight liquids. The fuel composed of dimethylhydrazine $\left[\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N}_{2} \mathrm{H}_{2}\right]$ mixed with dinitrogen tetroxide was used to power the Lunar Lander in its missions to the moon. The two components react according to the following equation:
$\left(\mathrm{CH}_{3}\right)_{2} \mathrm{~N}_{2} \mathrm{H}_{2}(l)+2 \mathrm{~N}_{2} \mathrm{O}_{4}(l) \longrightarrow 3 \mathrm{~N}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)+2 \mathrm{CO}_{2}(g)$
If $150 \mathrm{~g}$ of dimethylhydrazine reacts with excess dinitrogen tetroxide and the product gases are collected at $27^{\circ} \mathrm{C}$ in an evacuated 250 - $\mathrm{L}$ tank, what is the partial pressure of nitrogen gas produced and what is the total pressure in the tank assuming the reaction has $100 \%$ yield?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 77

Calculate the average kinetic energies of $\mathrm{CH}_{4}$ and $\mathrm{N}_{2}$ molecules at $273 \mathrm{~K}$ and $546 \mathrm{~K}$.

Shalini Tyagi

Numerade Educator

Problem 78

A 100.-L flask contains a mixture of methane, $\mathrm{CH}_{4}$, and argon at $25^{\circ} \mathrm{C}$. The mass of argon present is $228 \mathrm{~g}$ and the mole fraction of methane in the mixture is $0.650$. Calculate the total kinetic energy of the gaseous mixture.

Shalini Tyagi

Numerade Educator

Problem 79

Calculate the root mean square velocities of $\mathrm{CH}_{4}$ and $\mathrm{N}_{2}$ molecules at $273 \mathrm{~K}$ and $546 \mathrm{~K}$.

Sima Sarker

Numerade Educator

Problem 80

Consider separate $1.0$ -L samples of $\mathrm{He}(g)$ and $\mathrm{UF}_{6}(g)$, both at $1.00 \mathrm{~atm}$ and containing the same number of moles. What ratio of temperatures for the two samples would produce the same root mean square velocity?

Joanna Josey

Numerade Educator

Problem 81

Consider a 1.0-L container of neon gas at STP. Will the average kinetic energy, average velocity, and frequency of collisions of gas molecules with the walls of the container increase, decrease, or remain the same under each of the following conditions?
a. The temperature is increased to $100^{\circ} \mathrm{C}$.
b. The temperature is decreased to $-50^{\circ} \mathrm{C}$.
c. The volume is decreased to $0.5 \mathrm{~L}$.
d. The number of moles of neon is doubled.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 82

Consider two gases, A and B, each in a 1.0-L container with both gases at the same temperature and pressure. The mass of gas $\mathrm{A}$ in the container is $0.34 \mathrm{~g}$ and the mass of gas $\mathrm{B}$ in the container is $0.48 \mathrm{~g}$.
a. Which gas sample has the most molecules present? Explain.
b. Which gas sample has the largest average kinetic energy? Explain.
c. Which gas sample has the fastest average velocity? Explain.
d. How can the pressure in the two containers be equal to each other since the larger gas $\mathrm{B}$ molecules collide with the container walls more forcefully?

Joanna Josey

Numerade Educator

Problem 83

Consider three identical flasks filled with different gases. Flask A: $\mathrm{CO}$ at 760 torr and $0^{\circ} \mathrm{C}$
Flask B: $\mathrm{N}_{2}$ at 250 torr and $0^{\circ} \mathrm{C}$ Flask C: $\mathrm{H}_{2}$ at 100 torr and $0^{\circ} \mathrm{C}$
a. In which flask will the molecules have the greatest average kinetic energy?
b. In which flask will the molecules have the greatest average velocity?

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 84

Consider separate $1.0$ -L gaseous samples of $\mathrm{H}_{2}, \mathrm{Xe}, \mathrm{Cl}_{2}$, and $\mathrm{O}_{2}$ all at STP.
a. Rank the gases in order of increasing average kinetic energy.
b. Rank the gases in order of increasing average velocity.
c. How can separate $1.0$ -L samples of $\mathrm{O}_{2}$ and $\mathrm{H}_{2}$ each have the same average velocity?

Joanna Josey

Numerade Educator

Problem 85

Freon- 12 is used as a refrigerant in central home air conditioners. The rate of effusion of Freon-12 to Freon-11 (molar mass = $137.4 \mathrm{~g} / \mathrm{mol}$ ) is $1.07: 1 .$ The formula of Freon-12 is one of the following: $\mathrm{CF}_{4}, \mathrm{CF}_{3} \mathrm{Cl}, \mathrm{CF}_{2} \mathrm{Cl}_{2}, \mathrm{CFCl}_{3}$, or $\mathrm{CCl}_{4} .$ Which formula is correct for Freon-12?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 86

The rate of effusion of a particular gas was measured and found to be $24.0 \mathrm{~mL} / \mathrm{min}$. Under the same conditions, the rate of effusion of pure methane $\left(\mathrm{CH}_{4}\right)$ gas is $47.8 \mathrm{~mL} / \mathrm{min}$. What is the molar mass of the unknown gas?

Joanna Josey

Numerade Educator

Problem 87

One way of separating oxygen isotopes is by gaseous diffusion of carbon monoxide. The gaseous diffusion process behaves like an effusion process. Calculate the relative rates of effusion of ${ }^{12} \mathrm{C}^{16} \mathrm{O},{ }^{12} \mathrm{C}^{17} \mathrm{O}$, and ${ }^{12} \mathrm{C}^{18} \mathrm{O} .$ Name some advantages and disadvantages of separating oxygen isotopes by gaseous diffusion of carbon dioxide instead of carbon monoxide.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 88

It took $4.5$ minutes for $1.0 \mathrm{~L}$ helium to effuse through a porous barrier. How long will it take for $1.0 \mathrm{~L} \mathrm{Cl}_{2}$ gas to effuse under identical conditions?

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 89

Calculate the pressure exerted by $0.5000 \mathrm{~mol} \mathrm{~N}_{2}$ in a $1.0000-\mathrm{L}$ container at $25.0^{\circ} \mathrm{C}$
a. using the ideal gas law.
b. using the van der Waals equation.
c. Compare the results.

Nicole Krahulik

Nicole Krahulik

Numerade Educator

Problem 90

Calculate the pressure exerted by $0.5000 \mathrm{~mol} \mathrm{~N}_{2}$ in a $10.000-\mathrm{L}$ container at $25.0^{\circ} \mathrm{C}$
a. using the ideal gas law.
b. using the van der Waals equation.
c. Compare the results.
d. Compare the results with those in Exercise 89 .

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 91

Use the data in Table $5.4$ to calculate the partial pressure of $\mathrm{He}$ in dry air assuming that the total pressure is $1.0$ atm. Assuming a temperature of $25^{\circ} \mathrm{C}$, calculate the number of He atoms per cubic centimeter.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 92

A 1.0-L sample of air is collected at $25^{\circ} \mathrm{C}$ at sea level $(1.00 \mathrm{~atm})$. Estimate the volume this sample of air would have at an altitude of $15 \mathrm{~km}$ (see Fig. 5.30).

Shalini Tyagi

Numerade Educator

Problem 93

Write reactions to show how nitric and sulfuric acids are produced in the atmosphere.

Shalini Tyagi

Numerade Educator

Problem 94

Write reactions to show how the nitric and sulfuric acids in acid rain react with marble and limestone. (Both marble and limestone are primarily calcium carbonate.)

Shalini Tyagi

Numerade Educator

Problem 95

Draw a qualitative graph to show how the first property varies with the second in each of the following (assume $1 \mathrm{~mol}$ of an ideal gas and $T$ in kelvins).
a. $P V$ versus $V$ with constant $T$
b. $P$ versus $T$ with constant $V$
c. $T$ versus $V$ with constant $P$
d. $P$ versus $V$ with constant $T$
e. $P$ versus $1 / V$ with constant $T$
f. $P V / T$ versus $P$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 96

At STP, $1.0 \mathrm{~L} \mathrm{Br}_{2}$ reacts completely with $3.0 \mathrm{~L} \mathrm{~F}_{2}$, producing 2.0 $\mathrm{L}$ of a product. What is the formula of the product? (All substances are gases.)

Joanna Josey

Numerade Educator

Problem 97

A form of Boyle's law is $P V=k$ (at constant $T$ and $n$ ). Table $5.1$ contains actual data from pressure-volume experiments conducted by Robert Boyle. The value of $k$ in most experiments is $14.1 \times 10^{2}$ in $\mathrm{Hg} \cdot \mathrm{in}^{3}$. Express $k$ in units of atm $\cdot$ L. In Sample Exercise $5.3, k$ was determined for $\mathrm{NH}_{3}$ at various pressures and volumes. Give some reasons why the $k$ values differ so dramatically between Sample Exercise $5.3$ and Table $5.1$.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 98

An ideal gas at $7^{\circ} \mathrm{C}$ is in a spherical flexible container having a radius of $1.00 \mathrm{~cm}$. The gas is heated at constant pressure to $88^{\circ} \mathrm{C}$. Determine the radius of the spherical container after the gas is heated. (Volume of a sphere $=4 / 3 \pi r^{3}$.)

Joanna Josey

Numerade Educator

Problem 99

A 2.747-g sample of manganese metal is reacted with excess HCl gas to produce $3.22 \mathrm{~L}$ of $\mathrm{H}_{2}(g)$ at $373 \mathrm{~K}$ and $0.951$ atm and a manganese chloride compound $\left(\mathrm{Mn} \mathrm{Cl}_{x}\right) .$ What is the formula of the manganese chloride compound produced in the reaction?

Shalini Tyagi

Numerade Educator

Problem 100

Equal moles of hydrogen gas and oxygen gas are mixed in a flexible reaction vessel and then sparked to initiate the formation of gaseous water. Assuming that the reaction goes to completion, what is the ratio of the final volume of the gas mixture to the initial volume of the gas mixture if both volumes are measured at the same temperature and pressure?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 101

A 15.0-L tank is filled with $\mathrm{H}_{2}$ to a pressure of $2.00 \times 10^{2}$ atm. How many balloons (each $2.00 \mathrm{~L}$ ) can be inflated to a pressure of $1.00$ atm from the tank? Assume that there is no temperature change and that the tank cannot be emptied below $1.00$ atm pressure.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 102

A spherical glass container of unknown volume contains helium gas at $25^{\circ} \mathrm{C}$ and $1.960 \mathrm{~atm}$. When a portion of the helium is withdrawn and adjusted to $1.00 \mathrm{~atm}$ at $25^{\circ} \mathrm{C}$, it is found to have a volume of $1.75 \mathrm{~cm}^{3}$. The gas remaining in the first container shows a pressure of $1.710 \mathrm{~atm}$. Calculate the volume of the spherical container.

Joanna Josey

Numerade Educator

Problem 103

A 2.00-L sample of $\mathrm{O}_{2}(g)$ was collected over water at a total pressure of 785 torr and $25^{\circ} \mathrm{C}$. When the $\mathrm{O}_{2}(g)$ was dried (water vapor removed), the gas had a volume of $1.94 \mathrm{~L}$ at $25^{\circ} \mathrm{C}$ and 785 torr. Calculate the vapor pressure of water at $25^{\circ} \mathrm{C}$.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 104

A 20.0-L stainless steel container was charged with $2.00 \mathrm{~atm}$ of hydrogen gas and $3.00$ atm of oxygen gas. A spark ignited the mixture, producing water. What is the pressure in the tank at $25^{\circ} \mathrm{C} ?$ at $125^{\circ} \mathrm{C} ?$

Shalini Tyagi

Numerade Educator

Problem 105

Metallic molybdenum can be produced from the mineral molybdenite, $\mathrm{MoS}_{2} .$ The mineral is first oxidized in air to molybdenum trioxide and sulfur dioxide. Molybdenum trioxide is then reduced to metallic molybdenum using hydrogen gas. The balanced equations are
$$\begin{aligned}
\mathrm{MoS}_{2}(s)+\frac{7}{2} \mathrm{O}_{2}(g) \rightarrow \mathrm{MoO}_{3}(s)+2 \mathrm{SO}_{2}(g) \\
\mathrm{MoO}_{3}(s)+3 \mathrm{H}_{2}(g) \rightarrow \mathrm{Mo}(s)+3 \mathrm{H}_{2} \mathrm{O}(l)
\end{aligned}$$
Calculate the volumes of air and hydrogen gas at $17^{\circ} \mathrm{C}$ and $1.00$ atm that are necessary to produce $1.00 \times 10^{3} \mathrm{~kg}$ of pure molybdenum from $\mathrm{MoS}_{2}$. Assume air contains $21 \%$ oxygen by volume and assume $100 \%$ yield for each reaction.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 106

Nitric acid is produced commercially by the Ostwald process. In the first step ammonia is oxidized to nitric oxide:
$$4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$
Assume this reaction is carried out in the apparatus diagramed below.
The stopcock between the two reaction containers is opened, and the reaction proceeds using proper catalysts. Calculate the partial pressure of NO after the reaction is complete. Assume $100 \%$ yield for the reaction, assume the final container volume is $3.00 \mathrm{~L}$, and assume the temperature is constant.

Jennifer Hudspeth

Jennifer Hudspeth

Numerade Educator

Problem 107

In the "Méthode Champenoise," grape juice is fermented in a wine bottle to produce sparkling wine. The reaction is
$$\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q) \longrightarrow 2 \mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(a q)+2 \mathrm{CO}_{2}(g)$$
Fermentation of $750 .$ mL grape juice (density $=1.0 \mathrm{~g} / \mathrm{cm}^{3}$ ) is allowed to take place in a bottle with a total volume of $825 \mathrm{~mL}$ until $12 \%$ by volume is ethanol $\left(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\right)$. Assuming that the $\mathrm{CO}_{2}$ is insoluble in $\mathrm{H}_{2} \mathrm{O}$ (actually, a wrong assumption), what would be the pressure of $\mathrm{CO}_{2}$ inside the wine bottle at $25^{\circ} \mathrm{C}$ ? (The density of ethanol is $0.79 \mathrm{~g} / \mathrm{cm}^{3}$.)

Tracy Tourville

Tracy Tourville

Numerade Educator

Problem 108

One of the chemical controversies of the nineteenth century concerned the element beryllium (Be). Berzelius originally claimed that beryllium was a trivalent element (forming $\mathrm{Be}^{3+}$ ions) and that it gave an oxide with the formula $\mathrm{Be}_{2} \mathrm{O}_{3}$. This resulted in a calculated atomic mass of $13.5$ for beryllium. In formulating his periodic table, Mendeleev proposed that beryllium was divalent (forming $\mathrm{Be}^{2+}$ ions) and that it gave an oxide with the formula $\mathrm{BeO}$. This assumption gives an atomic mass of $9.0 .$ In 1894 , A. Combes (Comptes Rendus 1894 , p. 1221) reacted beryllium with the anion $\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2}^{-}$ and measured the density of the gaseous product. Combes's data for two different experiments are as follows:
$$\begin{array}{lll}
& {\text {I} }& {\text { II }} \\
\hline \text { Mass } & 0.2022 \mathrm{~g} & 0.2224 \mathrm{~g} \\
\text { Volume } & 22.6 \mathrm{~cm}^{3} & 26.0 \mathrm{~cm}^{3} \\
\text { Temperature } & 13^{\circ} \mathrm{C} & 17^{\circ} \mathrm{C} \\
\text { Pressure } & 765.2 \mathrm{~mm} \mathrm{Hg} & 764.6 \mathrm{~mm}
\end{array}$$
If beryllium is a divalent metal, the molecular formula of the product will be $\mathrm{Be}\left(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2}\right)_{2}$; if it is trivalent, the formula will be $\mathrm{Be}\left(\mathrm{C}_{5} \mathrm{H}_{7} \mathrm{O}_{2}\right)_{3}$. Show how Combes's data help to confirm that beryllium is a divalent metal.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 109

The nitrogen content of organic compounds can be determined by the Dumas method. The compound in question is first reacted by passage over hot $\mathrm{CuO}(s)$
$$\text { Compound } \underset{\mathrm{CuO}(s)}{\stackrel{\mathrm{Hot}}{\longrightarrow} \mathrm{N}_{2}(g)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(g)}$$
The product gas is then passed through a concentrated solution of $\mathrm{KOH}$ to remove the $\mathrm{CO}_{2}$. After passage through the $\mathrm{KOH}$ solution, the gas contains $\mathrm{N}_{2}$ and is saturated with water vapor. In a given experiment a $0.253-\mathrm{g}$ sample of a compound produced $31.8 \mathrm{~mL} \mathrm{~N}_{2}$ saturated with water vapor at $25^{\circ} \mathrm{C}$ and 726 torr. What is the mass percent of nitrogen in the compound? (The vapor pressure of water at $25^{\circ} \mathrm{C}$ is $23.8$ torr. $)$

Crystal Wang

Numerade Educator

Problem 110

A compound containing only $\mathrm{C}, \mathrm{H}$, and $\mathrm{N}$ yields the following data.
i. Complete combustion of $35.0 \mathrm{mg}$ of the compound produced $33.5 \mathrm{mg}$ of $\mathrm{CO}_{2}$ and $41.1 \mathrm{mg}$ of $\mathrm{H}_{2} \mathrm{O}$.
ii. A $65.2-\mathrm{mg}$ sample of the compound was analyzed for nitrogen by the Dumas method (see Exercise 109), giving $35.6 \mathrm{~mL}$ of $\mathrm{N}_{2}$ at 740 . torr and $25^{\circ} \mathrm{C}$.
iii. The effusion rate of the compound as a gas was measured and found to be $24.6 \mathrm{~mL} / \mathrm{min}$. The effusion rate of argon gas, under identical conditions, is $26.4 \mathrm{~mL} / \mathrm{min}$. What is the molecular formula of the compound?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 111

An organic compound contains $\mathrm{C}, \mathrm{H}, \mathrm{N}$, and $\mathrm{O}$. Combustion of $0.1023 \mathrm{~g}$ of the compound in excess oxygen yielded $0.2766 \mathrm{~g}$ of $\mathrm{CO}_{2}$ and $0.0991 \mathrm{~g}$ of $\mathrm{H}_{2} \mathrm{O}$. A sample of $0.4831 \mathrm{~g}$ of the compound was analyzed for nitrogen by the Dumas method (see Exercise 109). At STP, $27.6 \mathrm{~mL}$ of dry $\mathrm{N}_{2}$ was obtained. In a third experiment, the density of the compound as a gas was found to be $4.02 \mathrm{~g} / \mathrm{L}$ at $127^{\circ} \mathrm{C}$ and 256 torr. What are the empirical and molecular formulas of the compound?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 112

Consider the following diagram: Container A (with porous walls) is filled with air at STP. It is then inserted into a large enclosed container (B), which is then flushed with $\mathrm{H}_{2}(g)$. What will happen to the pressure inside container A? Explain your answer.

Joanna Josey

Numerade Educator

Problem 113

Without looking at tables of values, which of the following gases would you expect to have the largest value of the van der Waals constant $b: \mathrm{H}_{2}, \mathrm{~N}_{2}, \mathrm{CH}_{4}, \mathrm{C}_{2} \mathrm{H}_{6}$, or $\mathrm{C}_{3} \mathrm{H}_{8} ?$ From the values in Table
$5.3$ for the van der Waals constant $a$ for the gases $\mathrm{H}_{2}, \mathrm{CO}_{2}, \mathrm{~N}_{2}$ and $\mathrm{CH}_{4}$, predict which of these gas molecules show the strongest intermolecular attractions.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 114

An important process for the production of acrylonitrile $\left(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{~N}\right)$ is given by the following reaction:
$2 \mathrm{C}_{3} \mathrm{H}_{6}(g)+2 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{C}_{3} \mathrm{H}_{3} \mathrm{~N}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$
A 150.-L reactor is charged to the following partial pressures at $25^{\circ} \mathrm{C}:$
$$\begin{aligned}
P_{\mathrm{C}, \mathrm{H}_{6}} &=0.500 \mathrm{MPa} \\
P_{\mathrm{NH}_{3}} &=0.800 \mathrm{MPa} \\
P_{\mathrm{O}_{2}} &=1.500 \mathrm{MPa}
\end{aligned}$$
What mass of acrylonitrile can be produced from this mixture $\left(\mathrm{Mpa}=10^{6} \mathrm{~Pa}\right) ?$

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 115

A chemist weighed out $5.14 \mathrm{~g}$ of a mixture containing unknown amounts of $\mathrm{BaO}(s)$ and $\mathrm{CaO}(s)$ and placed the sample in a $1.50-\mathrm{L}$ flask containing $\mathrm{CO}_{2}(g)$ at $30.0^{\circ} \mathrm{C}$ and $750 .$ torr. After the reaction to form $\mathrm{BaCO}_{3}(s)$ and $\mathrm{CaCO}_{3}(s)$ was completed, the pressure of $\mathrm{CO}_{2}(g)$ remaining was $230 .$ torr. Calculate the mass percentages of $\mathrm{CaO}(s)$ and $\mathrm{BaO}(s)$ in the mixture.

Joanna Josey

Numerade Educator

Problem 116

A mixture of chromium and zinc weighing $0.362 \mathrm{~g}$ was reacted with an excess of hydrochloric acid. After all the metals in the mixture reacted, $225 \mathrm{~mL}$ of dry hydrogen gas was collected at $27^{\circ} \mathrm{C}$ and 750 . torr. Determine the mass percent Zn in the metal sample. [Zinc reacts with hydrochloric acid to produce zinc chloride and hydrogen gas; chromium reacts with hydrochloric acid to produce chromium(III) chloride and hydrogen gas.]

Joanna Josey

Numerade Educator

Problem 117

Consider a sample of a hydrocarbon (a compound consisting of only carbon and hydrogen) at $0.959 \mathrm{~atm}$ and $298 \mathrm{~K}$. Upon combusting the entire sample in oxygen, you collect a mixture of gaseous carbon dioxide and water vapor at $1.51 \mathrm{~atm}$ and $375 \mathrm{~K}$. This mixture has a density of $1.391 \mathrm{~g} / \mathrm{L}$ and occupies a volume four times as large as that of the pure hydrocarbon. Determine the molecular formula of the hydrocarbon.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 118

You have an equimolar mixture of the gases $\mathrm{SO}_{2}$ and $\mathrm{O}_{2}$, along with some He, in a container fitted with a piston. The density of this mixture at STP is $1.924 \mathrm{~g} / \mathrm{L}$. Assume ideal behavior and constant temperature and pressure.
a. What is the mole fraction of He in the original mixture?
b. The $\mathrm{SO}_{2}$ and $\mathrm{O}_{2}$ react to completion to form $\mathrm{SO}_{3}$. What is the density of the gas mixture after the reaction is complete?

Joanna Josey

Numerade Educator

Problem 119

Methane $\left(\mathrm{CH}_{4}\right)$ gas flows into a combustion chamber at a rate of 200. L/min at $1.50$ atm and ambient temperature. Air is added to the chamber at $1.00 \mathrm{~atm}$ and the same temperature, and the gases are ignited.
a. To ensure complete combustion of $\mathrm{CH}_{4}$ to $\mathrm{CO}_{2}(\mathrm{~g})$ and $\mathrm{H}_{2} \mathrm{O}(\mathrm{g})$, three times as much oxygen as is necessary is reacted. Assuming air is 21 mole percent $\mathrm{O}_{2}$ and 79 mole percent $\mathrm{N}_{2}$, calculate the flow rate of air necessary to deliver the required amount of oxygen.
b. Under the conditions in part a, combustion of methane was not complete as a mixture of $\mathrm{CO}_{2}(g)$ and $\mathrm{CO}(g)$ was produced. It was determined that $95.0 \%$ of the carbon in the exhaust gas was present in $\mathrm{CO}_{2}$. The remainder was present as carbon in CO. Calculate the composition of the exhaust gas in terms of mole fraction of $\mathrm{CO}, \mathrm{CO}_{2}, \mathrm{O}_{2}, \mathrm{~N}_{2}$, and $\mathrm{H}_{2} \mathrm{O} .$ Assume $\mathrm{CH}_{4}$ is completely reacted and $\mathrm{N}_{2}$ is unreacted.

David Collins

Numerade Educator

Problem 120

A steel cylinder contains $5.00 \mathrm{~mol}$ of graphite (pure carbon) and $5.00 \mathrm{~mol}$ of $\mathrm{O}_{2}$. The mixture is ignited and all the graphite reacts. Combustion produces a mixture of $\mathrm{CO}$ gas and $\mathrm{CO}_{2}$ gas. After the cylinder has cooled to its original temperature, it is found that the pressure of the cylinder has increased by $17.0 \%$. Calculate the mole fractions of $\mathrm{CO}, \mathrm{CO}_{2}$, and $\mathrm{O}_{2}$ in the final gaseous mixture.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 121

The total mass that can be lifted by a balloon is given by the difference between the mass of air displaced by the balloon and the mass of the gas inside the balloon. Consider a hot-air balloon that approximates a sphere $5.00 \mathrm{~m}$ in diameter and contains air heated to $65^{\circ} \mathrm{C}$. The surrounding air temperature is $21^{\circ} \mathrm{C}$. The pressure in the balloon is equal to the atmospheric pressure, which is 745 torr.
a. What total mass can the balloon lift? Assume that the average molar mass of air is $29.0 \mathrm{~g} / \mathrm{mol}$. (Hint: Heated air is less dense than cool air.)
b. If the balloon is filled with enough helium at $21^{\circ} \mathrm{C}$ and 745 torr to achieve the same volume as in part a, what total mass can the balloon lift?
c. What mass could the hot-air balloon in part a lift if it were on the ground in Denver, Colorado, where a typical atmospheric pressure is 630 . torr?

Joanna Josey

Numerade Educator

Problem 122

You have a sealed, flexible balloon filled with argon gas. The atmospheric pressure is $1.00 \mathrm{~atm}$ and the temperature is $25^{\circ} \mathrm{C}$. The air has a mole fraction of nitrogen of $0.790$, the rest being oxygen.
a. Explain why the balloon would float when heated. Make sure to discuss which factors change and which remain constant, and why this matters. Be complete.
b. Above what temperature would you heat the balloon so that it would float?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 123

You have a helium balloon at $1.00 \mathrm{~atm}$ and $25^{\circ} \mathrm{C}$. You want to make a hot-air balloon with the same volume and same lift as the helium balloon. Assume air is $79.0 \%$ nitrogen, $21.0 \%$ oxygen by volume. The "lift" of a balloon is given by the difference between the mass of air displaced by the balloon and the mass of gas inside the balloon.
a. Will the temperature in the hot-air balloon have to be higher or lower than $25^{\circ} \mathrm{C}$ ? Explain.
b. Calculate the temperature of the air required for the hot-air balloon to provide the same lift as the helium balloon at $1.00$ atm and $25^{\circ} \mathrm{C}$. Assume atmospheric conditions are $1.00 \mathrm{~atm}$ and $25^{\circ} \mathrm{C}$.

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 124

We state that the ideal gas law tends to hold best at low pressures and high temperatures. Show how the van der Waals equation simplifies to the ideal gas law under these conditions.

Joanna Josey

Numerade Educator

Problem 125

Atmospheric scientists often use mixing ratios to express the concentrations of trace compounds in air. Mixing ratios are often expressed as ppmv (parts per million volume):
ppmv of $X=\frac{\text { vol. of } X \text { at STP }}{\text { total vol. of air at STP }} \times 10^{6}$
On a recent autumn day, the concentration of carbon monoxide in the air in downtown Denver, Colorado, reached $3.0 \times 10^{2}$ ppmv. The atmospheric pressure at that time was 628 torr, and the temperature was $0^{\circ} \mathrm{C}$.
a. What was the partial pressure of $\mathrm{CO}$ ?
b. What was the concentration of $\mathrm{CO}$ in molecules per cubic centimeter?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 126

Nitrogen gas $\left(\mathrm{N}_{2}\right)$ reacts with hydrogen gas $\left(\mathrm{H}_{2}\right)$ to form $\mathrm{am}-$ monia gas $\left(\mathrm{NH}_{3}\right)$. You have nitrogen and hydrogen gases in a 15.0-L container fitted with a movable piston (the piston allows the container volume to change so as to keep the pressure constant inside the container). Initially the partial pressure of each reactant gas is $1.00 \mathrm{~atm}$. Assume the temperature is constant and that the reaction goes to completion.
a. Calculate the partial pressure of ammonia in the container after the reaction has reached completion.
b. Calculate the volume of the container after the reaction has reached completion.

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 127

In the presence of nitric acid, $\mathrm{UO}^{2+}$ undergoes a redox process. It is converted to $\mathrm{UO}_{2}{ }^{2+}$ and nitric oxide (NO) gas is produced according to the following unbalanced equation:
$$\mathrm{NO}_{3}^{-}(a q)+\mathrm{UO}^{2+}(a q) \longrightarrow \mathrm{NO}(g)+\mathrm{UO}_{2}^{2+}(a q)$$
If $2.55 \times 10^{2} \mathrm{~mL}$ of $\mathrm{NO}(g)$ is isolated at $29^{\circ} \mathrm{C}$ and $1.5 \mathrm{~atm}$, what amount (moles) of $\mathrm{UO}^{2+}$ was used in the reaction?

Tom Comey

Numerade Educator

Problem 128

Silane, $\mathrm{SiH}_{4}$, is the silicon analogue of methane, $\mathrm{CH}_{4}$. It is prepared industrially according to the following equations:
$$\begin{aligned}
\mathrm{Si}(s)+3 \mathrm{HCl}(g) & \longrightarrow \mathrm{HSiCl}_{3}(l)+\mathrm{H}_{2}(g) \\
4 \mathrm{HSiCl}_{3}(l) & \longrightarrow \mathrm{SiH}_{4}(g)+3 \mathrm{SiCl}_{4}(l)
\end{aligned}$$
a. If $156 \mathrm{~mL}$ of $\mathrm{HSiCl}_{3}(d=1.34 \mathrm{~g} / \mathrm{mL})$ is isolated when $15.0 \mathrm{~L}$
of $\mathrm{HCl}$ at $10.0 \mathrm{~atm}$ and $35^{\circ} \mathrm{C}$ is used, what is the percent yield of $\mathrm{HSiCl}_{3} ?$
b. When $156 \mathrm{~mL}$ of $\mathrm{HSiCl}_{3}$ is heated, what volume of $\mathrm{SiH}_{4}$ at $10.0 \mathrm{~atm}$ and $35^{\circ} \mathrm{C}$ will be obtained if the percent yield of the reaction is $93.1 \%$ ?

Susan Hallstrom

Susan Hallstrom

Numerade Educator

Problem 129

Solid thorium(IV) fluoride has a boiling point of $1680^{\circ} \mathrm{C}$. What is the density of a sample of gaseous thorium(IV) fluoride at its boiling point under a pressure of $2.5$ atm in a 1.7-L container? Which gas will effuse faster at $1680^{\circ} \mathrm{C}$, thorium(IV) fluoride or uranium(III) fluoride? How much faster?

A. Elizabeth Hildreth

A. Elizabeth Hildreth

Numerade Educator

Problem 130

Natural gas is a mixture of hydrocarbons, primarily methane $\left(\mathrm{CH}_{4}\right)$ and ethane $\left(\mathrm{C}_{2} \mathrm{H}_{6}\right) .$ A typical mixture might have $\chi_{\text {methane }}=0.915$ and $\chi_{\text {ethane }}=0.085$. What are the partial pressures of the two gases in a $15.00$ -L container of natural gas at $20 .{ }^{\circ} \mathrm{C}$ and $1.44$ atm? Assuming complete combustion of both gases in the natural gas sample, what is the total mass of water formed?

Joanna Josey

Numerade Educator

Problem 131

Use the following information to identify element $\mathrm{A}$ and $\mathrm{com}$ pound $\mathrm{B}$, then answer questions a and $\mathrm{b}$.
An empty glass container has a mass of $658.572 \mathrm{~g} .$ It has a mass of $659.452 \mathrm{~g}$ after it has been filled with nitrogen gas at a pressure of 790 . torr and a temperature of $15^{\circ} \mathrm{C}$. When the container is evacuated and refilled with a certain element (A) at a pressure of 745 torr and a temperature of $26^{\circ} \mathrm{C}$, it has a mass of $660.59 \mathrm{~g}$
Compound B, a gaseous organic compound that consists of $85.6 \%$ carbon and $14.4 \%$ hydrogen by mass, is placed in a stainless steel vessel (10.68 L) with excess oxygen gas. The vessel is placed in a constant-temperature bath at $22^{\circ} \mathrm{C}$. The pressure in the vessel is $11.98$ atm. In the bottom of the vessel is a container that is packed with Ascarite and a desiccant. Ascarite is asbestos impregnated with sodium hydroxide; it quantitatively absorbs carbon dioxide: $$2 \mathrm{NaOH}(s)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{Na}_{2} \mathrm{CO}_{3}(s)+\mathrm{H}_{2} \mathrm{O}(l)$$
The desiccant is anhydrous magnesium perchlorate, which quantitatively absorbs the water produced by the combustion reaction as well as the water produced by the above reaction. Neither the Ascarite nor the desiccant reacts with compound $\mathrm{B}$ or oxygen. The total mass of the container with the Ascarite and desiccant is $765.3 \mathrm{~g}$.
The combustion reaction of compound $\mathrm{B}$ is initiated by a spark. The pressure immediately rises, then begins to decrease, and finally reaches a steady value of $6.02 \mathrm{~atm}$. The stainless steel vessel is carefully opened, and the mass of the container inside the vessel is found to be $846.7 \mathrm{~g}$.
$\mathrm{A}$ and $\mathrm{B}$ react quantitatively in a $1: 1 \mathrm{~mole}$ ratio to form one mole of the single product, gas $\mathrm{C}$.
a. How many grams of $\mathrm{C}$ will be produced if $10.0 \mathrm{~L}$ of $\mathrm{A}$ and $8.60 \mathrm{~L}$ of $\mathrm{B}$ (each at $\mathrm{STP}$ ) are reacted by opening a stopcock connecting the two samples?
b. What will be the total pressure in the system?

Susan Hallstrom

Susan Hallstrom

Numerade Educator