Chapter 9

1\. An automobile air bag requires about \(62 \mathrm{~L}\) of nitrogen gas in order to inflate. The nitrogen gas is produced by the decomposition of sodium azide, according to the equation shown below $$ 2 \mathrm{NaN}_{3}(s) \rightarrow 2 \mathrm{Na}(s)+3 \mathrm{~N} 2(g) $$ What mass of sodium azide is necessary to produce the required volume of nitrogen at \(25^{\circ} \mathrm{C}\) and 1 atm? 2\. When \(\mathrm{Fe} 2 \mathrm{O}_{3}\) is heated in the presence of carbon, CO 2 gas is produced, according to the equation shown below. A sample of \(96.9\) grams of \(\mathrm{Fe} 2 \mathrm{O}_{3}\) is heated in the presence of excess carbon and the CO2 produced is collected and measured at 1 atm and \(453 \mathrm{~K}\). What volume of \(\mathrm{CO}_{2}\) will be observed? $$ 2 \mathrm{Fe}_{2} \mathrm{O}_{3}(\mathrm{~s})+3 \mathrm{C}(\mathrm{s}) \rightarrow 4 \mathrm{Fe}(\mathrm{s})+3 \mathrm{CO}_{2}(\mathrm{~g}) $$ 3\. The reaction of zinc and hydrochloric acid generates hydrogen gas, according to the equation shown below. An unknown quantity of zinc in a sample is observed to produce \(7.50 \mathrm{~L}\) of hydrogen gas at a temperature of \(404 \mathrm{~K}\) and a pressure of \(1.75 \mathrm{~atm} .\) How many moles of zinc were in the sample? $$ \mathrm{Zn}(\mathrm{s})+2 \mathrm{HCl}(a q) \rightarrow \mathrm{ZnCl} 2(a q)+\mathrm{H} 2(g) $$

The value of the proportionality constant \(R\), can be calculated from the fact that exactly one mole of a gas at exactly 1 atm and at 0 "C \((273 \mathrm{~K})\) has a volume of \(22.414 \mathrm{~L}\). Solution Substituting in the equation: $$ \begin{array}{c} P V=n R T \text { or } R=\frac{P V}{n T} \\ R=\frac{(1 a t m)(22.414 L)}{(1 m o l e)(273 K)}=0.082057 L \text { atm } m o l^{-1} K^{-1} \end{array} $$

1\. A container with a piston contains a sample of gas. Initially, the pressure in the container is exactly 1 atm, but the volume is unknown. The piston is adjusted so that the volume is \(0.155 \mathrm{~L}\) and the pressure is \(956 \mathrm{~mm}\) Hg; what was the initial volume? 2\. The pressure of \(12.5 \mathrm{~L}\) of a gas is \(0.82 \mathrm{~atm}\). If the pressure changes to \(1.32 \mathrm{~atm}\), what will the final volume be? A sample of helium gas has a pressure of \(860.0 \mathrm{~mm}\) Hg. This gas is transferred to a different container having a volume of \(25.0 \mathrm{~L}\); in this new container, the pressure is determined to be \(770.0 \mathrm{~mm}\) Hg. What was the initial volume of the gas?

A sample of oxygen occupies \(17.5 \mathrm{~L}\) at \(0.75 \mathrm{~atm}\) and \(298 \mathrm{~K}\). The temperature is raised to \(303 \mathrm{~K}\) and the pressure is increased to \(0.987\) atm. What is the final volume of the sample?

1\. A sample of methane has a volume of \(17.5 \mathrm{~L}\) at \(100.0^{\circ} \mathrm{C}\) and \(1.72 \mathrm{~atm}\). How many moles of methane are in the sample? 2\. A \(0.0500 \mathrm{~L}\) sample of a gas has a pressure of \(745 \mathrm{~mm} \mathrm{Hg}\) at \(26.4^{\circ} \mathrm{C}\). The temperatureis now raised to \(404.4 \mathrm{~K}\) and the volume is allowed to expand until a final pressure of \(1.06\) atm is reached. What is the final volume of the gas? 3\. When \(128.9\) grams of cyclopropane \(\left(\mathrm{C}_{3} \mathrm{H}_{6}\right)\) are placed into an \(8.00 \mathrm{~L}\) cylinder at \(298 \mathrm{~K}\), the pressure is observed to be \(1.24\) atm. A piston in the cylinder is now adjusted so that the volume is now \(12.00 \mathrm{~L}\) and the pressure is \(0.88 \mathrm{~atm} .\) What is the final temperature of the gas?