Chapter 5

A 4.00-g sample of FeS containing nonsulfide impurities reacted with \(\mathrm{HCl}\) to give \(896 \mathrm{~mL}\) of \(\mathrm{H}_{2} \mathrm{~S}\) at \(14^{\circ} \mathrm{C}\) and \(782 \mathrm{mmHg} .\) Calculate mass percent purity of the sample.

State Dalton's law of partial pressures and explain what mole fraction is. Does mole fraction have units?

A sample of air contains only nitrogen and oxygen gases whose partial pressures are 0.80 atm and 0.20 atm, respectively. Calculate the total pressure and the mole fractions of the gases.

A mixture of gases contains \(0.31 \mathrm{~mol} \mathrm{CH}_{4}, 0.25 \mathrm{~mol}\) \(\mathrm{C}_{2} \mathrm{H}_{6},\) and \(0.29 \mathrm{~mol} \mathrm{C}_{3} \mathrm{H}_{8} .\) The total pressure is 1.50 atm. Calculate the partial pressures of the gases.

A 2.5 -L flask at \(15^{\circ} \mathrm{C}\) contains a mixture of \(\mathrm{N}_{2}, \mathrm{He}\) and Ne at partial pressures of 0.32 atm for \(\mathrm{N}_{2}\), 0.15 atm for \(\mathrm{He},\) and 0.42 atm for \(\mathrm{Ne} .\) (a) Calculate the total pressure of the mixture. (b) Calculate the volume in liters at STP occupied by He and Ne if the \(\mathrm{N}_{2}\) is removed selectively.

Dry air near sea level has the following composition by volume: \(\mathrm{N}_{2}, 78.08\) percent; \(\mathrm{O}_{2}, 20.94\) percent; Ar, 0.93 percent; \(\mathrm{CO}_{2}, 0.05\) percent. The atmospheric pressure is 1.00 atm. Calculate (a) the partial pressure of each gas in atm and (b) the concentration of each gas in moles per liter at \(0^{\circ} \mathrm{C}\).

A mixture of helium and neon gases is collected over water at \(28.0^{\circ} \mathrm{C}\) and \(745 \mathrm{mmHg} .\) If the partial pressure of helium is \(368 \mathrm{mmHg}\), what is the partial pressure of neon? (Vapor pressure of water at \(28^{\circ} \mathrm{C}=\) \(28.3 \mathrm{mmHg} .\) )

A piece of sodium metal reacts completely with water as follows: $$ 2 \mathrm{Na}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow 2 \mathrm{NaOH}(a q)+\mathrm{H}_{2}(g) $$ The hydrogen gas generated is collected over water at \(25.0^{\circ} \mathrm{C}\). The volume of the gas is \(246 \mathrm{~mL}\) measured at 1.00 atm. Calculate the number of grams of sodium used in the reaction. (Vapor pressure of water at \(25^{\circ} \mathrm{C}=0.0313\) atm. \()\)

A sample of zinc metal reacts completely with an excess of hydrochloric acid: $$ \operatorname{Zn}(s)+2 \mathrm{HCl}(a q) \longrightarrow \mathrm{ZnCl}_{2}(a q)+\mathrm{H}_{2}(g) $$ The hydrogen gas produced is collected over water at \(25.0^{\circ} \mathrm{C}\) using an arrangement similar to that shown in Figure \(5.15 .\) The volume of the gas is \(7.80 \mathrm{~L},\) and the pressure is \(0.980 \mathrm{~atm} .\) Calculate the amount of zinc metal in grams consumed in the reaction. (Vapor pressure of water at \(25^{\circ} \mathrm{C}=23.8 \mathrm{mmHg} .\) )

Helium is mixed with oxygen gas for deep-sea divers. Calculate the percent by volume of oxygen gas in the mixture if the diver has to submerge to a depth where the total pressure is 4.2 atm. The partial pressure of oxygen is maintained at 0.20 atm at this depth.

What are the basic assumptions of the kinetic molecular theory of gases? How does the kinetic molecular theory explain Boyle's law, Charles' law, Avogadro's law, and Dalton's law of partial pressures?

What does the Maxwell speed distribution curve tell us? Does Maxwell's theory work for a sample of 200 molecules? Explain.

Which of the following statements is correct? (a) Heat is produced by the collision of gas molecules against one another. (b) When a gas is heated, the molecules collide with one another more often.

What is the difference between gas diffusion and effusion? State Graham's law and define the terms in Equation (5.17)

Compare the root-mean-square speeds of \(\mathrm{O}_{2}\) and \(\mathrm{UF}_{6}\) at \(65^{\circ} \mathrm{C}\)

The average distance traveled by a molecule between successive collisions is called mean free path. For a given amount of a gas, how does the mean free path of a gas depend on (a) density, (b) temperature at constant volume, (c) pressure at constant temperature, (d) volume at constant temperature, and (e) size of the atoms?

At a certain temperature the speeds of six gaseous molecules in a container are \(2.0 \mathrm{~m} / \mathrm{s}, 2.2 \mathrm{~m} / \mathrm{s}, 2.6 \mathrm{~m} / \mathrm{s}\) \(2.7 \mathrm{~m} / \mathrm{s}, 3.3 \mathrm{~m} / \mathrm{s},\) and \(3.5 \mathrm{~m} / \mathrm{s} .\) Calculate the root- mean-square speed and the average speed of the molecules. These two average values are close to each other, but the root-mean-square value is always the larger of the two. Why?

A gas evolved from the fermentation of glucose is found to effuse through a porous barrier in \(15.0 \mathrm{~min} .\) Under the same conditions of temperature and pressure, it takes an equal volume of \(\mathrm{N}_{2} 12.0 \mathrm{~min}\) to effuse through the same barrier. Calculate the molar mass of the gas and suggest what the gas might be.

Nickel forms a gaseous compound of the formula \(\mathrm{Ni}(\mathrm{CO})_{x} .\) What is the value of \(x\) given the fact that under the same conditions of temperature and pressure, methane \(\left(\mathrm{CH}_{4}\right)\) effuses 3.3 times faster than the compound?

Cite two pieces of evidence to show that gases do not behave ideally under all conditions.

Under what set of conditions would a gas be expected to behave most ideally: (a) high temperature and low pressure, (b) high temperature and high pressure, (c) low temperature and high pressure, or (d) low temperature and low pressure?

(a) A real gas is introduced into a flask of volume \(V\). Is the corrected volume of the gas greater or less than \(V ?\) (b) Ammonia has a larger \(a\) value than neon does (see Table 5.4 ). What can you conclude about the relative strength of the attractive forces between molecules of ammonia and between atoms of neon?

At \(27^{\circ} \mathrm{C}, 10.0\) moles of a gas in a 1.50 -L container exert a pressure of 130 atm. Is this an ideal gas?

Discuss the following phenomena in terms of the gas laws: (a) the pressure increase in an automobile tire on a hot day; (b) the "popping" of a paper bag; (c) the expansion of a weather balloon as it rises in the air; (d) the loud noise heard when a lightbulb shatters.

Under the same conditions of temperature and pressure, which of the following gases would behave most ideally: Ne, \(\mathrm{N}_{2}\), or \(\mathrm{CH}_{4}\) ? Explain.

Nitroglycerin, an explosive compound, decomposes according to the equation \(4 \mathrm{C}_{3} \mathrm{H}_{5}\left(\mathrm{NO}_{3}\right)_{3}(s) \longrightarrow\) $$ 12 \mathrm{CO}_{2}(g)+10 \mathrm{H}_{2} \mathrm{O}(g)+6 \mathrm{~N}_{2}(g)+\mathrm{O}_{2}(g) $$ Calculate the total volume of gases when collected at 1.2 atm and \(25^{\circ} \mathrm{C}\) from \(2.6 \times 10^{2} \mathrm{~g}\) of nitroglycerin. What are the partial pressures of the gases under these conditions?

The empirical formula of a compound is \(\mathrm{CH}\). At \(200^{\circ} \mathrm{C}, 0.145 \mathrm{~g}\) of this compound occupies \(97.2 \mathrm{~mL}\) at a pressure of 0.74 atm. What is the molecular formula of the compound?

The boiling point of liquid nitrogen is \(-196^{\circ} \mathrm{C}\). On the basis of this information alone, do you think nitrogen is an ideal gas?

In the metallurgical process of refining nickel, the metal is first combined with carbon monoxide to form tetracarbonylnickel, which is a gas at \(43^{\circ} \mathrm{C}\) : $$ \mathrm{Ni}(s)+4 \mathrm{CO}(g) \longrightarrow \mathrm{Ni}(\mathrm{CO})_{4}(g) $$ This reaction separates nickel from other solid impurities. (a) Starting with \(86.4 \mathrm{~g}\) of \(\mathrm{Ni}\), calculate the pressure of \(\mathrm{Ni}(\mathrm{CO})_{4}\) in a container of volume \(4.00 \mathrm{~L}\). (Assume the above reaction goes to completion.) (b) At temperatures above \(43^{\circ} \mathrm{C}\), the pressure of the gas is observed to increase much more rapidly than predicted by the ideal gas equation. Explain.

The partial pressure of carbon dioxide varies with seasons. Would you expect the partial pressure in the Northern Hemisphere to be higher in the summer or winter? Explain.

A barometer having a cross-sectional area of \(1.00 \mathrm{~cm}^{2}\) at sea level measures a pressure of \(76.0 \mathrm{~cm}\) of mercury. The pressure exerted by this column of mercury is equal to the pressure exerted by all the air on \(1 \mathrm{~cm}^{2}\) of Earth's surface. Given that the density of mercury is \(13.6 \mathrm{~g} / \mathrm{mL}\) and the average radius of Earth is \(6371 \mathrm{~km},\) calculate the total mass of Earth's atmosphere in kilograms. (Hint: The surface area of a sphere is \(4 \pi r^{2},\) where \(r\) is the radius of the sphere.)

Some commercial drain cleaners contain a mixture of sodium hydroxide and aluminum powder. When the mixture is poured down a clogged drain, the following reaction occurs: $$ \begin{array}{r} 2 \mathrm{NaOH}(a q)+2 \mathrm{Al}(s)+6 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \\ 2 \mathrm{NaAl}(\mathrm{OH})_{4}(a q)+3 \mathrm{H}_{2}(g) \end{array} $$ The heat generated in this reaction helps melt away obstructions such as grease, and the hydrogen gas released stirs up the solids clogging the drain. Calculate the volume of \(\mathrm{H}_{2}\) formed at \(23^{\circ} \mathrm{C}\) and \(1.00 \mathrm{~atm}\) if \(3.12 \mathrm{~g}\) of \(\mathrm{Al}\) are treated with an excess of \(\mathrm{NaOH}\).

The volume of a sample of pure HCl gas was \(189 \mathrm{~mL}\) at \(25^{\circ} \mathrm{C}\) and \(108 \mathrm{mmHg} .\) It was completely dissolved in about \(60 \mathrm{~mL}\) of water and titrated with an \(\mathrm{NaOH}\) solution; \(15.7 \mathrm{~mL}\) of the \(\mathrm{NaOH}\) solution were required to neutralize the \(\mathrm{HCl}\). Calculate the molarity of the \(\mathrm{NaOH}\) solution.

Propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}\right)\) burns in oxygen to produce carbon dioxide gas and water vapor. (a) Write a balanced equation for this reaction. (b) Calculate the number of liters of carbon dioxide measured at STP that could be produced from \(7.45 \mathrm{~g}\) of propane.

Consider this apparatus. When a small amount of water is introduced into the flask by squeezing the bulb of the medicine dropper, water is squirted upward out of the long glass tubing. Explain this observation. (Hint: Hydrogen chloride gas is soluble in water.)

Describe how you would measure, by either chemical or physical means, the partial pressures of a mixture of gases of the following composition: (a) \(\mathrm{CO}_{2}\) and \(\mathrm{H}_{2,}(\mathrm{~b}) \mathrm{He}\) and \(\mathrm{N}_{2}\)

A certain hydrate has the formula \(\mathrm{MgSO}_{4} \cdot x \mathrm{H}_{2} \mathrm{O}\). A quantity of \(54.2 \mathrm{~g}\) of the compound is heated in an oven to drive off the water. If the steam generated exerts a pressure of 24.8 atm in a \(2.00-\mathrm{L}\) container \(\mathrm{at}\) \(120^{\circ} \mathrm{C},\) calculate \(x\)

A mixture of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) and \(\mathrm{MgCO}_{3}\) of mass \(7.63 \mathrm{~g}\) is reacted with an excess of hydrochloric acid. The \(\mathrm{CO}_{2}\) gas generated occupies a volume of \(1.67 \mathrm{~L}\) at 1.24 atm and \(26^{\circ} \mathrm{C}\). From these data, calculate the percent composition by mass of \(\mathrm{Na}_{2} \mathrm{CO}_{3}\) in the mixture.

The following apparatus can be used to measure atomic and molecular speed. Suppose that a beam of metal atoms is directed at a rotating cylinder in a vacuum. A small opening in the cylinder allows the atoms to strike a target area. Because the cylinder is rotating, atoms traveling at different speeds will strike the target at different positions. In time, a layer of the metal will deposit on the target area, and the variation in its thickness is found to correspond to Maxwell's speed distribution. In one experiment it is found that at \(850^{\circ} \mathrm{C}\) some bismuth (Bi) atoms struck the target at a point \(2.80 \mathrm{~cm}\) from the spot directly opposite the slit. The diameter of the cylinder is \(15.0 \mathrm{~cm}\) and it is rotating at 130 revolutions per second. (a) Calculate the speed (m/s) at which the target is moving. (Hint: The circumference of a circle is given by \(2 \pi r,\) where \(r\) is the radius. \()\) (b) Calculate the time (in seconds) it takes for the target to travel \(2.80 \mathrm{~cm} .\) (c) Determine the speed of the Bi atoms. Compare your result in (c) with the \(u_{\mathrm{rms}}\) of \(\mathrm{Bi}\) at \(850^{\circ} \mathrm{C}\). Comment on the difference.

If \(10.00 \mathrm{~g}\) of water are introduced into an evacuated flask of volume \(2.500 \mathrm{~L}\) at \(65^{\circ} \mathrm{C},\) calculate the mass of water vaporized. (Hint: Assume that the volume of the remaining liquid water is negligible; the vapor pressure of water at \(65^{\circ} \mathrm{C}\) is \(187.5 \mathrm{mmHg} .\)

Commercially, compressed oxygen is sold in metal cylinders. If a 120-L cylinder is filled with oxygen to a pressure of 132 atm at \(22^{\circ} \mathrm{C},\) what is the mass (in grams) of \(\mathrm{O}_{2}\) present? How many liters of \(\mathrm{O}_{2}\) gas at 1.00 atm and \(22^{\circ} \mathrm{C}\) could the cylinder produce? (Assume ideal behavior.)

The shells of hard-boiled eggs sometimes crack due to the rapid thermal expansion of the shells at high temperatures. Suggest another reason why the shells may crack.

Ethylene gas \(\left(\mathrm{C}_{2} \mathrm{H}_{4}\right)\) is emitted by fruits and is known to be responsible for their ripening. Based on this information, explain why a bunch of bananas ripens faster in a closed paper bag than in a bowl.

Some ballpoint pens have a small hole in the main body of the pen. What is the purpose of this hole?

The gas laws are vitally important to scuba divers. The pressure exerted by \(33 \mathrm{ft}\) of seawater is equivalent to 1 atm pressure. (a) A diver ascends quickly to the surface of the water from a depth of \(36 \mathrm{ft}\) without exhaling gas from his lungs. By what factor will the volume of his lungs increase by the time he reaches the surface? Assume that the temperature is constant. (b) The partial pressure of oxygen in air is about 0.20 atm. (Air is 20 percent oxygen by volume.) In deep-sea diving, the composition of air the diver breathes must be changed to maintain this partial pressure. What must the oxygen content (in percent by volume) be when the total pressure exerted on the diver is 4.0 atm? (At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles of gases.) (Hint: See the Chemistry in Action essay "Scuba Diving and the Gas Laws" in Section \(5.6 . ?\)

Nitrous oxide \(\left(\mathrm{N}_{2} \mathrm{O}\right)\) can be obtained by the thermal decomposition of ammonium nitrate \(\left(\mathrm{NH}_{4} \mathrm{NO}_{3}\right) .\) (a) Write a balanced equation for the reaction. (b) In a certain experiment, a student obtains \(0.340 \mathrm{~L}\) of the gas at \(718 \mathrm{mmHg}\) and \(24^{\circ} \mathrm{C}\). If the gas weighs \(0.580 \mathrm{~g},\) calculate the value of the gas constant.

Two vessels are labeled A and B. Vessel A contains \(\mathrm{NH}_{3}\) gas at \(70^{\circ} \mathrm{C},\) and vessel \(\mathrm{B}\) contains \(\mathrm{Ne}\) gas at the same temperature. If the average kinetic energy of \(\mathrm{NH}_{3}\) is \(7.1 \times 10^{-21} \mathrm{~J} / \mathrm{molecule},\) calculate the rootmean- square speed of Ne atoms.

The following procedure is a simple though somewhat crude way to measure the molar mass of a gas. A liquid of mass \(0.0184 \mathrm{~g}\) is introduced into a syringe like the one shown here by injection through the rubber tip using a hypodermic needle. The syringe is then transferred to a temperature bath heated to \(45^{\circ} \mathrm{C},\) and the liquid vaporizes. The final volume of the vapor (measured by the outward movement of the plunger) is \(5.58 \mathrm{~mL}\) and the atmospheric pressure is \(760 \mathrm{mmHg}\). Given that the compound's empirical formula is \(\mathrm{CH}_{2}\), determine the molar mass of the compound.

In 1995 a man suffocated as he walked by an abandoned mine in England. At that moment there was a sharp drop in atmospheric pressure due to a change in the weather. Suggest what might have caused the man's death.

Acidic oxides such as carbon dioxide react with basic oxides like calcium oxide (CaO) and barium oxide \((\mathrm{BaO})\) to form salts (metal carbonates). (a) Write equations representing these two reactions. (b) A student placed a mixture of \(\mathrm{BaO}\) and \(\mathrm{CaO}\) of combined mass \(4.88 \mathrm{~g}\) in a 1.46 - \(\mathrm{L}\) flask containing carbon dioxide gas at \(35^{\circ} \mathrm{C}\) and \(746 \mathrm{mmHg}\). After the reactions were complete, she found that the \(\mathrm{CO}_{2}\) pressure had dropped to \(252 \mathrm{mmHg}\). Calculate the percent composition by mass of the mixture. Assume volumes of the solids are negligible.