Chapter 10

A \(1.00 \mathrm{~L}\) container was filled by pumping into it \(1.00 \mathrm{~L}\) of \(\mathrm{N}_{2}\) at \(20.0 \mathrm{~cm} \mathrm{Hg}, 1.00 \mathrm{~L}\) of \(\mathrm{O}_{2}\) at 155 torr, and 1.00 \(L\) of \(H e\) at 0.450 atm. All volumes and pressures were measured at the same temperature. What was the total pressure inside the container after the mixture was made?

A special gas mixture, BAR 97 High without \(\mathrm{NO},\) is used in engine emission testing and contains \(16.3 \mathrm{~atm} \mathrm{CO}_{2}\), 8270 torr \(\mathrm{CO},\) and \(331 \mathrm{~mm} \mathrm{Hg}\) propane with the 108 atm nitrogen. What was the total pressure in the gas cylinder?

What are the mole fraction and the mole percent of oxygen in exhaled air if \(P_{\mathrm{O}_{2}}\) is 116 torr and \(P_{\text {total }}\) is 788 torr?

A mixture of 26,000 torr \(\mathrm{CO}_{2}\) and 104,000 torr \(\mathrm{N}_{2}\) is sold for packaging food. What are the mole fraction and mole percent of \(\mathrm{CO}_{2}\) in this mixture?

A \(0.200 \mathrm{~mol}\) sample of a mixture of \(\mathrm{N}_{2}\) and \(\mathrm{CO}_{2}\) with a total pressure of 845 torr was exposed to an excess of solid \(\mathrm{CaO},\) which reacts with \(\mathrm{CO}_{2}\) according to the equation $$ \mathrm{CaO}(s)+\mathrm{CO}_{2}(g) \longrightarrow \mathrm{CaCO}_{3}(s) $$ After the reaction was complete, the pressure of the gas had dropped to 322 torr. How many moles of \(\mathrm{CO}_{2}\) were in the original mixture? (Assume no change in volume or temperature.)

The methane from the landfills, Problem 10.70 , is saturated with water. What volume of "wet" methane would you have to collect at \(20.0^{\circ} \mathrm{C}\) and 742 torr to be sure that the sample contains \(244 \mathrm{~mL}\) of dry methane (also at 742 torr \() ?\)

Under conditions in which the density of \(\mathrm{CO}_{2}\) is \(1.96 \mathrm{~g} \mathrm{~L}^{-1}\) and that of \(\mathrm{N}_{2}\) is \(1.25 \mathrm{~g} \mathrm{~L}^{-1}\), which gas will effuse more rapidly? What will be the ratio of the rates of effusion of \(\mathrm{N}_{2}\) to \(\mathrm{CO}_{2}\) ?

A mixture of He and Ne needs to be separated. What will be the ratio of the rates of effusion of He and Ne?

Arrange the following gases in order of increasing rate of diffusion at \(25^{\circ} \mathrm{C}: \mathrm{Cl}_{2}, \mathrm{C}_{2} \mathrm{H}_{4}, \mathrm{SO}_{2}\)

For the gases \(\mathrm{CO}, \mathrm{CO}_{2}, \mathrm{NO},\) and \(\mathrm{NO}_{2},\) which gas will effuse the fastest? Which gas the slowest? Which gases will be the most difficult to separate by effusion?

An unknown gas \(X\) effuses 1.65 times faster than \(\mathrm{C}_{3} \mathrm{H}_{8}\). What is the molecular mass of gas \(X ?\)

One of the oldest units for atmospheric pressure is \(\mathrm{lb}\) in. \(^{-2}\) (pounds per square inch, or psi). Calculate the numerical value of the standard atmosphere in these units to three significant figures. Calculate the mass in pounds of a uniform column of water \(33.9 \mathrm{ft}\) high having an area of \(1.00 \mathrm{in} .{ }^{2}\) at its base. (Use the following data: density of mercury \(=13.6 \mathrm{~g} \mathrm{~mL}^{-1} ;\) density of water \(=1.00 \mathrm{~g} \mathrm{~mL}^{-1}\); \(1 \mathrm{~mL}=1 \mathrm{~cm}^{3} ; 1 \mathrm{lb}=454 \mathrm{~g}\) $$ \text { in. }=2.54 \mathrm{~cm} .) $$

Suppose you were planning to move a house by transporting it on a large trailer. The house has an estimated weight of 45.6 tons \((1\) ton \(=2000 \mathrm{lb})\). The trailer is expected to weigh 8.3 tons. Each wheel of the trailer will have tires inflated to a gauge pressure of 85 psi (which is actually 85 psi above atmospheric pressure). If the area of contact between a tire and the pavement can be no larger than \(100.0 \mathrm{in}^{2}(10.0\) in. \(\times 10.0\) in. \(),\) what is the minimum number of wheels the trailer must have? (Remember, tires are mounted in multiples of two on a trailer. Assume that atmospheric pressure is 14.7 psi.)

A bubble of air escaping from a diver's mask rises from a depth of \(100 \mathrm{ft}\) to the surface where the pressure is \(1.00 \mathrm{~atm} .\) Initially, the bubble has a volume of \(10.0 \mathrm{~mL}\). Assuming none of the air dissolves in the water, how many times larger is the bubble just as it reaches the surface? Use your answer to explain why scuba divers constantly exhale as they slowly rise from a deep dive. (The density of seawater is approximately \(1.025 \mathrm{~g} \mathrm{~mL}^{-1}\); the density of mercury is \(13.6 \mathrm{~g} \mathrm{~mL}^{-1}\).)

Early one cool \(\left(60.0^{\circ} \mathrm{F}\right)\) morning you start on a bike ride with the atmospheric pressure at \(14.7 \mathrm{lb}\) in. \(^{-2}\) and the tire gauge pressure at \(50.0 \mathrm{lb}\) in. \(^{-2}\). (Gauge pressure is the amount that the pressure exceeds atmospheric pressure.) By late afternoon, the air had warmed up considerably, and this plus the heat generated by tire friction sent the temperature inside the tire to \(104^{\circ} \mathrm{F}\). What will the tire gauge now read, assuming that the volume of the air in the tire and the atmospheric pressure have not changed?

A sample of a new anti-malarial drug with a mass of \(0.2394 \mathrm{~g}\) was made to undergo a series of reactions that changed all of the nitrogen in the compound into \(\mathrm{N}_{2}\). This gas had a volume of \(18.90 \mathrm{~mL}\) when collected over water at \(23.80^{\circ} \mathrm{C}\) and a pressure of 746.0 torr. At \(23.80^{\circ} \mathrm{C}\), the vapor pressure of water is 22.110 torr. When \(6.478 \mathrm{mg}\) of the compound was burned in pure oxygen, \(17.57 \mathrm{mg}\) of \(\mathrm{CO}_{2}\) and \(4.319 \mathrm{mg}\) of \(\mathrm{H}_{2} \mathrm{O}\) were obtained. What are the percentages of \(\mathrm{C}\) and \(\mathrm{H}\) in this compound? (a) Assuming that any undetermined element is oxygen, write an empirical formula for the compound. (b) The molecular mass of the compound was found to be 324 . What is its molecular formula?

Carbon dioxide can be made in the lab by the reaction of hydrochloric acid with calcium carbonate. How many milliliters of \(\mathrm{dry} \mathrm{CO}_{2}\) at \(20.0^{\circ} \mathrm{C}\) and 745 torr can be prepared from a mixture of \(12.3 \mathrm{~g}\) of \(\mathrm{CaCO}_{3}\) and \(185 \mathrm{~mL}\) of \(0.250 \mathrm{MHCl} ?\)