Chapter 5

A ten-gallon methane tank contains \(1.243\) mol of methane \(\left(\mathrm{CH}_{4}\right)\) at \(74^{\circ} \mathrm{F}\). Express the volume of the tank in liters, the amount of methane in the tank in grams, and the temperature of the tank in Kelvin.

A 6.00-ft cylinder has a radius of 26 in. It contains \(189 \mathrm{lb}\) of helium at \(25^{\circ} \mathrm{C}\). Express the volume of the cylinder \(\left(V=\pi r^{2} h\right)\) in liters, the amount of helium in moles, and the temperature in Kelvin.

A cylinder with a movable piston records a volume of \(12.6 \mathrm{~L}\) when \(3.0 \mathrm{~mol}\) of oxygen is added. The gas in the cylinder has a pressure of \(5.83\) atm. The cylinder develops a leak and the volume of the gas is now recorded to be \(12.1 \mathrm{~L}\) at the same pressure. How many moles of oxygen are lost?

A tank is filled with a gas to a pressure of \(977 \mathrm{~mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C}\). When the tank is heated, the pressure increases to \(1.50 \mathrm{~atm}\). To what temperature was the gas heated?

A sample of \(\mathrm{CO}_{2}\) gas at \(22^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) has a volume of \(2.00 \mathrm{~L}\). Determine the ratio of the original volume to the final volume when (a) the pressure and amount of gas remain unchanged and the Celsius temperature is doubled. (b) the pressure and amount of gas remain unchanged and the Kelvin temperature is doubled.

I A sample of air is originally at \(32^{\circ} \mathrm{C}\). If \(P\) and \(n\) are kept constant, to what temperature must the air be cooled to (a) decrease its volume by \(25 \%\) ? (b) decrease its volume to \(25 \%\) of its original volume?

A tire is inflated to a gauge pressure of \(28.0\) psi at \(71^{\circ} \mathrm{F}\). Gauge pressure is the pressure above atmospheric pressure, which is \(14.7\) psi. After several hours of driving, the air in the tire has a temperature of \(115^{\circ} \mathrm{F}\). What is the gauge pressure of the air in the tire? What is the actual pressure of the air in the tire? Assume that the tire volume changes are negligible.

A 38.0-L gas tank at \(35^{\circ} \mathrm{C}\) has nitrogen at a pressure of \(4.65 \mathrm{~atm}\). The contents of the tank are transferred without loss to an evacuated 55.0-L tank in a cold room where the temperature is \(4^{\circ} \mathrm{C}\). What is the pressure in the tank?

A sealed syringe has \(25.0 \mathrm{~mL}\) of air at \(23^{\circ} \mathrm{C}\) and \(745 \mathrm{~mm} \mathrm{Hg}\) pressure. The syringe is transferred to a water bath maintained at \(82^{\circ} \mathrm{C}\). The volume of the gas in the syringe increased by \(8.0 \%\). What is the pressure in the syringe? Did the pressure increase?

A balloon filled with helium has a volume of \(1.28 \times 10^{3} \mathrm{~L}\) at sea level where the pressure is \(0.998\) atm and the temperature is \(31^{\circ} \mathrm{C}\). The balloon is taken to the top of a mountain where the pressure is \(0.753 \mathrm{~atm}\) and the temperature is \(-25^{\circ} \mathrm{C}\). What is the volume of the balloon at the top of the mountain?

A flask has \(1.35\) mol of hydrogen gas at \(25^{\circ} \mathrm{C}\) and a pressure of \(1.05\) atm. Nitrogen gas is added to the flask at the same temperature until the pressure rises to \(1.64\) atm. How many moles of nitrogen gas are added?

A two-liter plastic soft drink bottle can withstand a pressure of 5 atm. Half a cup (approximately \(120 \mathrm{~mL}\) ) of ethyl alcohol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}(d=\) \(0.789 \mathrm{~g} / \mathrm{mL}\) ), is poured into a soft drink bottle at room temperature. The bottle is then heated to \(100^{\circ} \mathrm{C}\) (3 significant figures), changing the liquid alcohol to a gas. Will the soft drink bottle withstand the pressure, or will it explode?

A piece of dry ice \(\left(\mathrm{CO}_{2}(s)\right)\) has a mass of \(22.50 \mathrm{~g}\). It is dropped into an evacuated 2.50-L flask. What is the pressure in the flask at \(-4^{\circ} \mathrm{C} ?\)

A 2.00-L tank, evacuated and empty, has a mass of \(725.6 \mathrm{~g}\). It is filled with butane gas \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\) at \(22^{\circ} \mathrm{C}\) to a pressure of \(1.78 \mathrm{~atm} .\) What is the mass of the tank after it is filled?

Calculate the densities (in grams per liter) of the following gases at \(75^{\circ} \mathrm{F}\) and \(1.33\) bar. (a) argon (b) ammonia (c) acetylene \(\left(\mathrm{C}_{2} \mathrm{H}_{2}\right)\)

In Calculate the densities (in grams per liter) of the following gases at \(97^{\circ} \mathrm{C}\) and \(755 \mathrm{~mm} \mathrm{Hg}\) (a) hydrogen chloride (b) sulfur dioxide (c) butane \(\left(\mathrm{C}_{4} \mathrm{H}_{10}\right)\)

Helium-filled balloons rise in the air because the density of helium is less than the density of air. (a) If air has an average molar mass of \(29.0 \mathrm{~g} / \mathrm{mol}\), what is the density of air at \(25^{\circ} \mathrm{C}\) and \(770 \mathrm{~mm} \mathrm{Hg} ?\) (b) What is the density of helium at the same temperature and pressure? (c) Would a balloon filled with carbon dioxide at the same temperature and pressure rise?

The air is said to be "thinner" in higher altitudes than at sea level. Compare the density of air at sea level where the barometric pressure is \(755 \mathrm{~mm} \mathrm{Hg}\) and the temperature is \(0^{\circ} \mathrm{C}\) with the density of air on top of \(\mathrm{Mt}\). Everest at the same temperature. The barometric pressure at that altitude is \(210 \mathrm{~mm} \mathrm{Hg}\) (3 significant figures). Take the molar mass of air to be \(29.0 \mathrm{~g} / \mathrm{mol}\).

Cyclopropane mixed in the proper ratio with oxygen can be used as an anesthetic. At \(755 \mathrm{~mm} \mathrm{Hg}\) and \(25^{\circ} \mathrm{C}\), it has a density of \(1.71 \mathrm{~g} / \mathrm{L}\). (a) What is the molar mass of cyclopropane? (b) Cyclopropane is made up of \(85.7 \% \mathrm{C}\) and \(14.3 \% \mathrm{H}\). What is the molecular formula of cyclopropane?

Phosgene is a highly toxic gas made up of carbon, oxygen, and chlorine atoms. Its density at \(1.05\) atm and \(25^{\circ} \mathrm{C}\) is \(4.24 \mathrm{~g} / \mathrm{L}\). (a) What is the molar mass of phosgene? (b) Phosgene is made up of \(12.1 \% \mathrm{C}, 16.2 \% \mathrm{O}\), and \(71.7 \% \mathrm{Cl}\). What is the molecular formula of phosgene?

The gas in the discharge cell of a laser contains (in mole percent) \(11 \% \mathrm{CO}_{2}, 5.3 \% \mathrm{~N}_{2}\), and \(84 \% \mathrm{He}\) (a) What is the molar mass of this mixture? (b) Calculate the density of this gas mixture at \(32^{\circ} \mathrm{C}\) and \(758 \mathrm{~mm} \mathrm{Hg}\). (c) What is the ratio of the density of this gas to that of air \((\mathrm{MM}=29.0 \mathrm{~g} / \mathrm{mol})\) at the same conditions?

Exhaled air contains \(74.5 \% \mathrm{~N}_{2}, 15.7 \% \mathrm{O}_{2}, 3.6 \% \mathrm{CO}_{2}\), and \(6.2 \% \mathrm{H}_{2} \mathrm{O}\) (mole percent). (a) Calculate the molar mass of exhaled air. (b) Calculate the density of exhaled air at \(37^{\circ} \mathrm{C}\) and \(757 \mathrm{~mm} \mathrm{Hg}\), and compare the value obtained with that for ordinary air (MM = \(29.0 \mathrm{~g} / \mathrm{mol}\) ).

A 1.58-g sample of \(\mathrm{C}_{2} \mathrm{H}_{3} \mathrm{X}_{3}(g)\) has a volume of \(297 \mathrm{~mL}\) at \(769 \mathrm{~mm} \mathrm{Hg}\) and \(35^{\circ} \mathrm{C}\). Identify the element \(\mathrm{X}\).

A \(2.00-g\) sample of \(S X_{6}(g)\) has a volume of \(329.5 \mathrm{~cm}^{3}\) at \(1.00 \mathrm{~atm}\) and \(20^{\circ} \mathrm{C}\). Identify the element \(\mathrm{X}\). Name the compound.

Nitrogen oxide is a pollutant commonly found in smokestack emissions. One way to remove it is to react it with ammonia. $$ 4 \mathrm{NH}_{3}(g)+6 \mathrm{NO}(g) \longrightarrow 5 \mathrm{~N}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) $$ How many liters of ammonia are required to change \(12.8 \mathrm{~L}\) of nitrogen oxide to nitrogen gas? Assume \(100 \%\) yield and that all gases are measured at the same temperature and pressure.

Dichlorine oxide is used as bactericide to purify water. It is produced by the chlorination of sulfur dioxide gas. $$ \mathrm{SO}_{2}(g)+2 \mathrm{Cl}_{2}(g) \longrightarrow \mathrm{SOCl}_{2}(l)+\mathrm{Cl}_{2} \mathrm{O}(g) $$ How many liters of \(\mathrm{Cl}_{2} \mathrm{O}\) can be produced by mixing \(5.85 \mathrm{~L}\) of \(\mathrm{SO}_{2}\) and \(9.00 \mathrm{~L}\) of \(\mathrm{Cl}_{2}\) ? How many liters of the reactant in excess are present after reaction is complete? Assume \(100 \%\) yield and that all the gases are measured at the same temperature and pressure.

Hydrogen sulfide gas \(\left(\mathrm{H}_{2} \mathrm{~S}\right)\) is responsible for the foul odor of rotten eggs. When it reacts with oxygen, sulfur dioxide gas and steam are produced. (a) Write a balanced equation for the reaction. (b) How many liters of \(\mathrm{H}_{2} \mathrm{~S}\) would be required to react with excess oxygen to produce \(12.0 \mathrm{~L}\) of \(\mathrm{SO}_{2}\) ? The reaction yield is \(88.5 \%\). Assume constant temperature and pressure throughout the reaction.

Dinitrogen oxide, commonly called nitrous oxide, is used as a propellant gas for whipped-cream dispensers. It is prepared by heating ammonium nitrate to \(250^{\circ} \mathrm{C}\). Water vapor is also formed. (a) Write a balanced equation for the decomposition of ammonium nitrate into nitrous oxide and steam. (b) What volume of dinitrogen oxide gas is formed at \(250^{\circ} \mathrm{C}\) and 1,0 atm when \(5.00 \mathrm{~g}\) of \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) is heated? Assume \(100 \%\) yield.

When hydrogen peroxide decomposes, oxygen is produced: $$ 2 \mathrm{H}_{2} \mathrm{O}_{2}(a q) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}+\mathrm{O}_{2}(g) $$ What volume of oxygen gas at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) is produced from the decomposition of \(25.00 \mathrm{~mL}\) of a \(30.0 \%\) (by mass) solution of hydrogen peroxide \((d=1.05 \mathrm{~g} / \mathrm{mL}) ?\)

Nitroglycerine is an explosive used by the mining industry. It detonates according to the following equation: $$ 4 \mathrm{C}_{3} \mathrm{H}_{5} \mathrm{~N}_{3} \mathrm{O}_{9}(l) \longrightarrow 12 \mathrm{CO}_{2}(g)+6 \mathrm{~N}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{O}_{2}(g) $$ What volume is occupied by the gases produced when \(10.00 \mathrm{~g}\) of nitroglycerine explodes? 'The total pressure is \(1.45 \mathrm{~atm}\) at \(523^{\circ} \mathrm{C}\).

Ammonium nitrate can be used as an effective explosive because it decomposes into a large number of gaseous products. At a sufficiently high temperature, ammonium nitrate decomposes into nitrogen, oxygen, and steam. (a) Write a balanced equation for the decomposition of ammonium nitrate. (b) If \(1.00 \mathrm{~kg}\) of ammonium nitrate is sealed into a \(50.0\) - \(\mathrm{L}\) steel drum and heated to \(787^{\circ} \mathrm{C}\), what is the pressure in the drum, assuming \(100 \%\) decomposition?

Some chambers used to grow bacteria that thrive on \(\mathrm{CO}_{2}\) have a gas mixture consisting of \(95.0 \% \mathrm{CO}_{2}\) and \(5.0 \% \mathrm{O}_{2}\) (mole percent). What is the partial pressure of each gas if the total pressure is \(735 \mathrm{~mm} \mathrm{Hg}\) ?

A certain laser uses a gas mixture consisting of \(9.00 \mathrm{~g} \mathrm{HCl}, 2.00 \mathrm{~g} \mathrm{H}_{2}\) and \(165.0 \mathrm{~g}\) of Ne. What pressure is exerted by the mixture in a \(75.0\) -L tank at \(22^{\circ} \mathrm{C}\) ? Which gas has the smallest partial pressure?

The contents of a tank of natural gas at \(1.20 \mathrm{~atm}\) is analyzed. The analysis showed the following mole percents: \(88.6 \% \mathrm{CH}_{4}, 8.9 \% \mathrm{C}_{2} \mathrm{H}_{6}\), and \(2.5 \%\) \(\mathrm{C}_{3} \mathrm{H}_{3}\). What is the partial pressure of each gas in the tank?

A sample of gas collected over water at \(42^{\circ} \mathrm{C}\) occupies a volume of one liter. The wet gas has a pressure of \(0.986\) atm. The gas is dried, and the dry gas occupies \(1.04 \mathrm{~L}\) with a pressure of \(1.00 \mathrm{~atm}\) at \(90^{\circ} \mathrm{C}\). Using this information, calculate the vapor pressure of water at \(42^{\circ} \mathrm{C}\).

A sample of oxygen gas is collected over water at \(25^{\circ} \mathrm{C}\) (vp \(\mathrm{H}_{2} \mathrm{O}(l)=23.8 \mathrm{~mm} \mathrm{Hg}\) ). The wet gas occupies a volume of \(7.28 \mathrm{~L}\) at a total pressure of \(1.25\) bar. If all the water is removed, what volume will the dry oxygen occupy at a pressure of \(1.07 \mathrm{~atm}\) and a temperature of \(37^{\circ} \mathrm{C}\) ?

When acetylene, \(\mathrm{C}_{2} \mathrm{H}_{2}\), is burned in oxygen, carbon dioxide and steam are formed. A sample of acetylene with a volume of \(7.50 \mathrm{~L}\) and a pressure of \(1.00\) atm is burned in excess oxygen at \(225^{\circ} \mathrm{C}\). The products are transferred without loss to a 10.0-L flask at the same temperature. (a) Write a balanced equation for the reaction. (b) What is the total pressure of the products in the \(10.0\) - \(\mathrm{L}\) flask? (c) What is the partial pressure of each of the products in the flask?

Nitrogen can react with steam to form ammonia and nitrogen oxide gases. A 20.0-L sample of nitrogen at \(173^{\circ} \mathrm{C}\) and \(772 \mathrm{~mm} \mathrm{Hg}\) is made to react with an excess of steam. The products are collected at room temperature \(\left(25^{\circ} \mathrm{C}\right)\) into an evacuated flask with a volume of \(15.0 \mathrm{~L}\). (a) Write a balanced equation for the reaction. (b) What is the total pressure of the products in the collecting flask after the reaction is complete? (c) What is the partial pressure of each of the products in the flask?

A sample of oxygen is collected over water at \(22^{\circ} \mathrm{C}\) and \(752 \mathrm{~mm} \mathrm{Hg}\) in a 125-mL flask. The vapor pressure of water at \(22^{\circ} \mathrm{C}\) is \(19.8 \mathrm{~mm} \mathrm{Hg}\). (a) What is the partial pressure of oxygen? (b) How many moles of dry gas are collected? (c) How many moles of wet gas are in the flask? (d) If \(0.0250 \mathrm{~g}\) of \(\mathrm{N}_{2}(\mathrm{~g})\) are added to the flask at the same temperature, what is the partial pressure of nitrogen in the flask? (e) What is the total pressure in the flask after nitrogen is added?

Hydrogen is collected over water at \(25^{\circ} \mathrm{C}\) and \(748 \mathrm{~mm} \mathrm{Hg}\) in a 250-mL (3 significant figures) flask. The vapor pressure of water at \(25^{\circ} \mathrm{C}\) is \(23.8 \mathrm{~mm} \mathrm{Hg}\) (a) What is the partial pressure of hydrogen? (b) How many moles of water are in the flask? (c) How many moles of dry gas are collected? (d) If \(0.0186 \mathrm{~g}\) of \(\mathrm{He}\) are added to the flask at the same temperature, what is the partial pressure of helium in the flask? (e) What is the total pressure in the flask after helium is added?

E Rank the following gases \(\begin{array}{llll}\text { NO } & \text { Ar } & \text { N }_{2} & \text { N }_{2} \mathrm{O}_{5}\end{array}\) in order of (a) increasing speed of effusion through a tiny opening. (b) increasing time of effusion.

Rank the gases \(\mathrm{Xe}, \mathrm{CH}_{4}, \mathrm{~F}_{2}\) and \(\mathrm{CH}_{2} \mathrm{~F}_{2}\) in order of (a) increasing speed of effusion through a tiny opening. (b) increasing time of effusion.

What is the ratio of the rate of effusion of the most abundant gas, nitrogen, to the lightest gas, hydrogen?

A gas effuses \(1.55\) times faster than propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) at the same temperature and pressure. (a) Is the gas heavier or lighter than propane? (b) What is the molar mass of the gas?

It takes \(12.6 \mathrm{~s}\) for \(1.73 \times 10^{-3} \mathrm{~mol}\) of \(\mathrm{CO}\) to effuse through a pinhole. Under the same conditions, how long will it take for the same amount of \(\mathrm{CO}_{2}\) to effuse through the same pinhole?

The normal boiling points of \(\mathrm{CO}\) and \(\mathrm{SO}_{2}\) are \(-192^{\circ} \mathrm{C}\) and \(-10^{\circ} \mathrm{C}\), respectively. (a) At \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{~atm}\), which gas would you expect to have a molar volume closest to the ideal value? (b) If you wanted to reduce the deviation from ideal gas behavior, in what direction would you change the temperature? The pressure?

A sample of methane gas \(\left(\mathrm{CH}_{4}\right)\) is at \(50^{\circ} \mathrm{C}\) and \(20 \mathrm{~atm}\). Would you expect it to behave more or less ideally if (a) the pressure were reduced to 1 atm? (b) the temperature were reduced to \(-50^{\circ} \mathrm{C}\) ?

When air pollution is high, ozone \(\left(\mathrm{O}_{3}\right)\) contents can reach \(0.60 \mathrm{ppm}\) (i.e., \(0.60\) mol ozone per million mol air). How many molecules of ozone are present per liter of polluted air if the barometric pressure is \(755 \mathrm{~mm} \mathrm{Hg}\) and the temperature is \(79^{\circ} \mathrm{F} ?\)

A mixture of \(3.5 \mathrm{~mol}\) of \(\mathrm{Kr}\) and \(3.9 \mathrm{~mol}\) of He occupies a \(10.00-\mathrm{L}\) container at \(300 \mathrm{~K}\). Which gas has the larger (a) average translational energy? (b) partial pressure? (c) mole fraction? (d) effusion rate?

Given that \(1.00\) mol of neon and \(1.00\) mol of hydrogen chloride gas are in separate containers at the same temperature and pressure, calculate each of the following ratios. (a) volume \(\mathrm{Ne} /\) volume \(\mathrm{HCl}\) (b) density Ne/density HCl (c) average translational energy Ne/average translational energy HCl (d) number of Ne atoms/number of HCl molecules