Chapter 8

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.

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.

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

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

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?

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 a 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.

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.

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?

At the same conditions of pressure and temperature, ammonia gas is less dense than air. Why is this true?

For each of the quantities listed below, explain which of the following properties (mass of the molecule, density of the gas sample, temperature of the gas sample, size of the molecule, and number of moles of gas) must be known to calculate the quantity. a. average kinetic energy b. average number of collisions per second with other gas molecules c. average force of each impact with the wall of the container d. root mean square velocity e. average number of collisions with a given area of the container f. distance between collisions

You have two containers each with 1 mole of xenon gas at \(15^{\circ} \mathrm{C} .\) Container \(\mathrm{A}\) has a volume of \(3.0 \mathrm{L},\) and container \(\mathrm{B}\) has a volume of 1.0 L. Explain how the following quantities compare between the two containers. a. the average kinetic energy of the Xe atoms b. the force with which the Xe atoms collide with the container walls c. the root mean square velocity of the Xe atoms d. the collision frequency of the Xe atoms (with other atoms) e. the pressure of the Xe sample

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

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 atm? If the level is different, by what factor? Explain.

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?

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?

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

Consider two different containers, each filled with 2 moles of Ne(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.

In Example \(8-11\) of the text, the molar volume of \(\mathrm{N}_{2}(g)\) at \(\mathrm{STP}\) is given as \(22.42 \mathrm{L} / \mathrm{mol} \mathrm{N}_{2} .\) How is this number calculated? How does the molar volume of \(\mathrm{He}(g)\) at \(\mathrm{STP}\) compare to the molar volume of \(\mathrm{N}_{2}(g)\) at \(\mathrm{STP}\) (assuming ideal gas behavior)? Is the molar volume of \(\mathrm{N}_{2}(g)\) at 1.000 atm and \(25.0^{\circ} \mathrm{C}\) equal to, less than, or greater than 22.42 L/mol? Explain. Is the molar volume of \(\mathrm{N}_{2}(g)\) collected over water at a total pressure of 1.000 atm and \(0.0^{\circ} \mathrm{C}\) equal to, less than, or greater than \(22.42 \mathrm{L} / \mathrm{mol} ?\) Explain.

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

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 \(\mathrm{NH}_{3} ?\)

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 moles of gas.

From the values in Table \(8-3\) 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.

Without looking at a table 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 \(\mathrm{C}_{3} \mathrm{H}_{8} ?\)

Ideal gas particles are assumed to be volumeless and to neither attract nor repel each other. Why are these assumptions crucial to the validity of Dalton's law of partial pressures?

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 atm \(=14.7\) psi). a. \(\mathrm{mm} \mathrm{Hg}\) b. \(torr\) c. \(Pa\) d. \(psi\)

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

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

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?

An \(11.1\) - \(\mathrm{L}\) sample? sample of gas is determined to contain \(0.50 \) \(\mathrm{mole}\) sample?of \(\mathrm{N}_{2} .\) At the same temperature and pressure, how many moles of gas would there be in a \(20 .\) - \(\mathrm{L}\) sample?

Consider the following chemical equation. $$2 \mathrm{NO}_{2}(g) \longrightarrow \mathrm{N}_{2} \mathrm{O}_{4}(g)$$ If \(25.0 \mathrm{mL} \mathrm{NO}_{2}\) 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?

Complete the following table for an ideal gas. $$\begin{array}{|lccc|}\hline P(\mathrm{atm}) & V(\mathrm{L}) & n(\mathrm{mol}) & T \\ \hline 5.00 & & 2.00 & 155^{\circ} \mathrm{C} \\\\\hline0.300 & 2.00 & & 155 \mathrm{K} \\ \hline 4.47 & 25.0 & 2.01 & \\\\\hline & 2.25 & 10.5 & 75^{\circ} \mathrm{C} \\\ \hline\end{array}$$

Complete the following table for an ideal gas. $$\begin{aligned} &-\\\ &\begin{array}{|llll|} \hline {P} & {V} & {n} & {\boldsymbol{T}} \\ \hline 7.74 \times 10^{3} \mathrm{Pa} & 12.2 \mathrm{mL} & & 25^{\circ} \mathrm{C} \\ \hline & 43.0 \mathrm{mL} & 0.421 \mathrm{mol} & 223 \mathrm{K} \\ \hline 455 \text { torr } & & 4.4 \times 10^{-2} \mathrm{mol} & 331^{\circ} \mathrm{C} \\ \hline 745 \mathrm{mm} \mathrm{Hg} & 11.2 \mathrm{L} & 0.401 \mathrm{mol} & \\ \hline \end{array} \end{aligned}$$

Suppose two 200.0 - \(L\) tanks are to be filled separately with the gases helium and hydrogen. What mass of each gas is needed to produce a pressure of 2.70 atm in its respective tank at \(24^{\circ} \mathrm{C} ?\)

The average lung capacity of a human is \(6.0 \mathrm{~L}\). How many moles of air are in your lungs when you are in the following situations? a. At sea level \((T=298 \mathrm{~K}, P=1.00 \mathrm{~atm})\). b. \(10 . \mathrm{m}\) below water \((T=298 \mathrm{~K}, P=1.97 \mathrm{~atm})\). c. At the top of Mount Everest \((T=200 . \mathrm{K}, P=0.296 \mathrm{~atm})\).

A person accidentally swallows a drop of liquid oxygen, \(\mathbf{O}_{2}(l)\) 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 \(1.0 \mathrm{atm}\)?

A gas sample containing \(1.50\) moles 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.

A bicycle tire is filled with air to a pressure of \(75\) 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?

A container is filled with an ideal gas to a pressure of 11.0 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 6.50 atm? c. At what temperature would the pressure be 25.0 atm?

An ideal 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?

A compressed gas cylinder contains \(1.00 \times 10^{3} \mathrm{g}\) 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 \(26^{\circ} \mathrm{C} ?\)

A sealed balloon is filled with \(1.00 \mathrm{L}\) helium at \(23^{\circ} \mathrm{C}\) and 1.00 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 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.)

Consider the following reaction: $$4 \mathrm{Al}(s)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{Al}_{2} \mathrm{O}_{3}(s)$$ 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?

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 \(\mathrm{CO}_{2}\) )?

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 (NaN, ) 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 \(\mathrm{STP} ?\)

Concentrated hydrogen peroxide solutions are explosively decomposed by traces of transition metal ions (such as Mn or Fe): $$2 \mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(i)+\mathrm{O}_{2}(g)$$ What volume of pure \(\mathbf{O}_{2}(g),\) 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.

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.

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

An important process for the production of acrylonitrile \(\left(\mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}\right)\) is given by the following equation: $$2 \mathrm{C}_{3} \mathrm{H}_{6}(g)+2 \mathrm{NH}_{3}(g)+3 \mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{C}_{3} \mathrm{H}_{3} \mathrm{N}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)$$ A \(150 .\)-\(\mathrm{L}\)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 \(\left(\mathrm{MPa}=10^{6} \mathrm{Pa}\right) ?\)

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: $$2 \mathrm{NH}_{3}(g)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{H}_{2} \mathrm{NCONH}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(g)$$ Ammonia gas at \(223^{\circ} \mathrm{C}\) and \(90 .\) atm flows into a reactor at a rate of \(500 .\) L/min. Carbon dioxide at \(223^{\circ} \mathrm{C}\) and \(45\) atm flows into the reactor at a rate of \(600 .\) L/min. What mass of urea is produced per minute by this reaction assuming \(100 \%\) yield?