Chapter 8

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

What are the conditions represented by STP?

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

What is the definition of pressure?

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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