Chapter 10

The pressure of a gas is \(440 \mathrm{mm}\) Hg. Express this pressure in units of (a) atmospheres, (b) bars, and (c) kilopascals.

The average barometric pressure at an altitude of \(10 \mathrm{km}\) is \(210 \mathrm{mm}\) Hg. Express this pressure in atmospheres, bars, and kilopascals.

Indicate which represents the higher pressure in each of the following pairs: (a) \(534 \mathrm{mm}\) Hg or 0.754 bar (b) \(534 \mathrm{mm}\) Hg or \(650 \mathrm{kPa}\) (c) 1.34 bar or \(934 \mathrm{kPa}\)

Put the following in order of increasing pressure: \(363 \mathrm{mm} \mathrm{Hg}, 363 \mathrm{kPa}, 0.256 \mathrm{atm},\) and \(0.523 \mathrm{bar}\)

A sample of nitrogen gas has a pressure of \(67.5 \mathrm{mm} \mathrm{Hg}\) in a \(500 .\) -mL flask. What is the pressure of this gas sample when it is transferred to a \(125-\mathrm{mL}\) flask at the same temperature?

\(.\) A sample of \(\mathrm{CO}_{2}\) gas has a pressure of \(56.5 \mathrm{mm}\) Hg in a 125 -mL flask. The sample is transferred to a new flask, where it has a pressure of \(62.3 \mathrm{mm}\) Hg at the same temperature. What is the volume of the new flask?

You have 3.5 L of \(\mathrm{NO}\) at a temperature of \(22.0^{\circ} \mathrm{C}\) What volume would the NO occupy at \(37^{\circ} \mathrm{C} ?\) (Assume the pressure is constant.)

A 5.0 -mL sample of \(\mathrm{CO}_{2}\) gas is enclosed in a gastight syringe (Figure 10.2 ) at \(22^{\circ} \mathrm{C}\). If the syringe is immersed in an ice bath \(\left(0^{\circ} \mathrm{C}\right),\) what is the new gas volume, assuming that the pressure is held constant?

You have 3.6 L of \(\mathrm{H}_{2}\) gas at \(380 \mathrm{mm} \mathrm{Hg}\) and \(25^{\circ} \mathrm{C} .\) What is the pressure of this gas if it is transferred to a 5.0 -L flask at \(0.0^{\circ} \mathrm{C} ?\)

You have a sample of \(\mathrm{CO}_{2}\) in flask \(\mathrm{A}\) with a volume of \(25.0 \mathrm{mL}\). At \(20.5^{\circ} \mathrm{C},\) the pressure of the gas is \(436.5 \mathrm{mm}\) Hg. To find the volume of another flask, B, you move the \(\mathrm{CO}_{2}\) to that flask and find that its pressure is now \(94.3 \mathrm{mm}\) Hg at 24.5 "C. What is the volume of flask B?

You have a sample of gas in a flask with a volume of 250 mL. At \(25.5^{\circ} \mathrm{C},\) the pressure of the gas is \(360 \mathrm{mm} \mathrm{Hg} .\) If you decrease the temperature to \(-5.0^{\circ} \mathrm{C},\) what is the gas pressure at the lower temperature?

A sample of gas occupies \(135 \mathrm{mL}\) at \(22.5^{\circ} \mathrm{C} ;\) the pressure is \(165 \mathrm{mm}\) Hg. What is the pressure of the gas sample when it is placed in a 252 -mL flask at a temperature of \(0.0^{\circ} \mathrm{C} ?\)

One of the cylinders of an automobile engine has a volume of \(400 . \mathrm{cm}^{3} .\) The engine takes in air at a pressure of 1.00 atm and a temperature of \(15^{\circ} \mathrm{C}\) and compresses the air to a volume of \(50.0 \mathrm{cm}^{3}\) at \(77^{\circ} \mathrm{C} .\) What is the final pressure of the gas in the cylinder? (The ratio of before and after volumesin this case, 400: 50 or \(8: 1-\) is called the compression ratio.

A helium-filled balloon of the type used in longdistance flying contains \(420,000 \mathrm{ft}^{3}\left(1.2 \times 10^{7} \mathrm{L}\right)\) of helium. Suppose you fill the balloon with helium on the ground, where the pressure is \(737 \mathrm{mm} \mathrm{Hg}\) and the temperature is \(16.0^{\circ} \mathrm{C}\) When the balloon ascends to a height of 2 miles, where the pressure is only \(600 . \mathrm{mm}\) Hg and the temperature is \(-33^{\circ} \mathrm{C},\) what volume is occupied by the helium gas? Assume the pressure inside the balloon matches the external pressure.

Nitrogen monoxide reacts with oxygen to give nitrogen dioxide. $$ 2 \mathrm{NO}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{NO}_{2}(\mathrm{g}) $$ (a) You wish to react \(\mathrm{NO}\) and \(\mathrm{O}_{2}\) in the correct stoichiometric ratio. The sample of NO has a volume of 150 mL. What volume of \(\mathrm{O}_{2}\) is required (at the same pressure and temperature)? (b) What volume of \(\mathrm{NO}_{2}\) (at the same pressure and temperature) is formed in this reaction?

Ethane burns in air to give \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{CO}_{2}\) $$ 2 \mathrm{C}_{2} \mathrm{H}_{6}(\mathrm{g})+7 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 4 \mathrm{CO}_{2}(\mathrm{g})+6 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$ What volume of \(\mathrm{O}_{2}(\mathrm{L})\) is required for complete reaction with \(5.2 \mathrm{L}\) of \(\mathrm{C}_{2} \mathrm{H}_{6}\) ? What volume of \(\mathrm{H}_{2} \mathrm{O}\) vapor (L) is produced? Assume all gases are measured at the same temperature and pressure.

A \(1.25-\mathrm{g}\) sample of \(\mathrm{CO}_{2}\) is contained in a \(750 .-\mathrm{mL}\) flask at \(22.5^{\circ} \mathrm{C} .\) What is the pressure of the gas?

A balloon holds \(30.0 \mathrm{kg}\) of helium. What is the volume of the balloon if its pressure is 1.20 atm and the temperature is \(22^{\circ} \mathrm{C} ?\)

A flask is first evacuated so that it contains no gas at all. Then, \(2.2 \mathrm{g}\) of \(\mathrm{CO}_{2}\) is introduced into the flask. On warming to \(22^{\circ} \mathrm{C},\) the gas exerts a pressure of \(318 \mathrm{mm}\) Hg. What is the volume of the flask?

A steel cylinder holds \(1.50 \mathrm{g}\) of ethanol, \(\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{OH}\). What is the pressure of the ethanol vapor if the cylinder has a volume of \(251 \mathrm{cm}^{3}\) and the temperature is \(250^{\circ} \mathrm{C} ?\) (Assume all of the ethanol is in the vapor phase at this temperature.)

A balloon for long-distance flying contains \(1.2 \times 10^{7} \mathrm{L}\) of helium. If the helium pressure is \(737 \mathrm{mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C},\) what mass of helium (in grams) does the balloon contain?

What mass of helium, in grams, is required to fill a 5.0 -L balloon to a pressure of 1.1 atm at \(25^{\circ} \mathrm{C} ?\)

Forty miles above Earth's surface, the temperature is \(250 \mathrm{K},\) and the pressure is only \(0.20 \mathrm{mm} \mathrm{Hg} .\) What is the density of air (in grams per liter) at this altitude? (Assume the molar mass of air is \(28.96 \mathrm{g} / \mathrm{mol.}\)

A gaseous organofluorine compound has a density of \(0.355 \mathrm{g} / \mathrm{L}\) at \(17^{\circ} \mathrm{C}\) and \(189 \mathrm{mm} \mathrm{Hg}\) What is the molar mass of the compound?

Chloroform is a common liquid used in the laboratory. It vaporizes readily. If the pressure of chloroform vapor in a flask is \(195 \mathrm{mm}\) Hg at \(25.0^{\circ} \mathrm{C}\) and the density of the vapor is \(1.25 \mathrm{g} / \mathrm{L},\) what is the molar mass of chloroform?

A 1.007 -g sample of an unknown gas exerts a pressure of \(715 \mathrm{mm}\) Hg in a 452 -mL container at \(23^{\circ} \mathrm{C} .\) What is the molar mass of the gas?

A \(0.0130-\mathrm{g}\) sample of a gas with an empirical formula of \(\mathrm{C}_{4} \mathrm{H}_{5}\) is placed in a 165 -mL flask. It has a pressure of \(13.7 \mathrm{mm}\) Hg at \(22.5^{\circ} \mathrm{C}\). What is the molecular formula of the compound?

A new boron hydride, \(\mathrm{B}_{x} \mathrm{H}_{y}\) has been isolated. To find its molar mass, you measure the pressure of the gas in a known volume at a known temperature. The following experimental data are collected: Mass of gas \(=12.5 \mathrm{mg} \quad\) Pressure of gas \(=24.8 \mathrm{mm} \mathrm{Hg}\) Temperature \(=25^{\circ} \mathrm{C} \quad\) Volume of flask \(=125 \mathrm{mL}\) Which formula corresponds to the calculated molar mass? (a) \(\mathrm{B}_{2} \mathrm{H}_{6}\) (b) \(\mathrm{B}_{4} \mathrm{H}_{10}\) (c) \(\mathrm{B}_{5} \mathrm{H}_{9}\) (d) \(\mathrm{B}_{6} \mathrm{H}_{10}\) (e) \(\mathrm{B}_{10} \mathrm{H}_{14}\)

Acetaldehyde is a common liquid compound that vaporizes readily. Determine the molar mass of acetaldehyde from the following data: Sample mass \(=0.107\) g Volume of gas \(=125 \mathrm{mL}\) Temperature \(=0.0^{\circ} \mathrm{C} \quad\) Pressure \(=331 \mathrm{mm} \mathrm{Hg}\)

Iron reacts with hydrochloric acid to produce iron(II) chloride and hydrogen gas: $$ \mathrm{Fe}(\mathrm{s})+2 \mathrm{HCl}(\mathrm{aq}) \rightarrow \mathrm{FeCl}_{2}(\mathrm{aq})+\mathrm{H}_{2}(\mathrm{g}) $$ The \(\mathrm{H}_{2}\) gas from the reaction of \(2.2 \mathrm{g}\) of iron with excess acid is collected in a 10.0 -L flask at \(25^{\circ} \mathrm{C}\) What is the pressure of the \(\mathrm{H}_{2}\) gas in this flask?

Silane, \(\operatorname{SiH}_{4}\), reacts with \(\mathrm{O}_{2}\) to give silicon dioxide and water: $$ \mathrm{SiH}_{4}(\mathrm{g})+2 \mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{SiO}_{2}(\mathrm{s})+2 \mathrm{H}_{2} \mathrm{O}(\ell) $$ A 5.20 -L sample of \(\mathrm{SiH}_{4}\) gas at \(356 \mathrm{mm}\) Hg pressure and \(25^{\circ} \mathrm{C}\) is allowed to react with \(\mathrm{O}_{2}\) gas. What volume of \(\mathrm{O}_{2}\) gas, in liters, is required for complete reaction if the oxygen has a pressure of \(425 \mathrm{mm} \mathrm{Hg}\) at \(25^{\circ} \mathrm{C} ?\)

Sodium azide, the explosive compound in automobile air bags, decomposes according to the following equation: $$ 2 \mathrm{NaN}_{3}(\mathrm{s}) \rightarrow 2 \mathrm{Na}(\mathrm{s})+3 \mathrm{N}_{2}(\mathrm{g}) $$ What mass of sodium azide is required to provide the nitrogen needed to inflate a 75.0 -L bag to a pressure of 1.3 atm at \(25^{\circ} \mathrm{C} ?\)

The hydrocarbon octane \(\left(\mathrm{C}_{8} \mathrm{H}_{18}\right)\) burns to give \(\mathrm{CO}_{2}\) and water vapor: $$ 2 \mathrm{C}_{8} \mathrm{H}_{18}(\mathrm{g})+25 \mathrm{O}_{2}(\mathrm{g}) \rightarrow 16 \mathrm{CO}_{2}(\mathrm{g})+18 \mathrm{H}_{2} \mathrm{O}(\mathrm{g}) $$ If a 0.048 -g sample of octane burns completely in \(\mathrm{O}_{2},\) what will be the pressure of water vapor in a \(4.75-\mathrm{L}\) flask at \(30.0^{\circ} \mathrm{C} ?\) If the \(\mathrm{O}_{2}\) gas needed for complete combustion was contained in a \(4.75-\mathrm{L}\) flask at \(22^{\circ} \mathrm{C},\) what would its pressure be?

Hydrazine reacts with \(\mathrm{O}_{2}\) according to the following equation: $$ \mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g}) \rightarrow \mathrm{N}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\ell) $$ Assume the \(\mathrm{O}_{2}\) needed for the reaction is in a \(450-\mathrm{L}\) tank at \(23^{\circ} \mathrm{C} .\) What must the oxygen pressure be in the tank to have enough oxygen to consume \(1.00 \mathrm{kg}\) of hydrazine completely?

5\. A self-contained underwater breathing apparatus (SCUBA) uses canisters containing potassium superoxide. The superoxide consumes the \(\mathrm{CO}_{2}\) exhaled by a person and replaces it with oxygen. $$ 4 \mathrm{KO}_{2}(\mathrm{s})+2 \mathrm{CO}_{2}(\mathrm{g}) \rightarrow 2 \mathrm{K}_{2} \mathrm{CO}_{3}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g}) $$ What mass of \(\mathrm{KO}_{2}\), in grams, is required to react with \(8.90 \mathrm{L}\) of \(\mathrm{CO}_{2}\) at \(22.0^{\circ} \mathrm{C}\) and \(767 \mathrm{mm} \mathrm{Hg} ?\)

What is the total pressure in atmospheres of a gas mixture that contains \(1.0 \mathrm{g}\) of \(\mathrm{H}_{2}\) and \(8.0 \mathrm{g}\) of \(\mathrm{Ar}\) in a \(3.0-\mathrm{L}\) container at \(27^{\circ} \mathrm{C}\) ? What are the partial pressures of the two gases?

A cylinder of compressed gas is labeled "Composition (mole \%): \(4.5 \% \mathrm{H}_{2} \mathrm{S}, 3.0 \% \mathrm{CO}_{2},\) balance \(\mathrm{N}_{2} .\) The pressure gauge attached to the cylinder reads 46 atm. Calculate the partial pressure of each gas, in atmospheres, in the cylinder.

A halothane-oxygen mixture \(\left(\mathrm{C}_{2} \mathrm{HBrClF}_{3}+\mathrm{O}_{2}\right)\) can be used as an anesthetic. A tank containing such a mixture has the following partial pressures: \(P\) (halothane) \(=170 \mathrm{mm} \mathrm{Hg}\) and \(P\left(\mathrm{O}_{2}\right)=570 \mathrm{mm} \mathrm{Hg}\) (a) What is the ratio of the number of moles of halothane to the number of moles of \(\mathrm{O}_{2} ?\) (b) If the tank contains \(160 \mathrm{g}\) of \(\mathrm{O}_{2}\), what mass of \(\mathrm{C}_{2} \mathrm{HBrClF}_{3}\) is present?

A collapsed balloon is filled with He to a volume of \(12.5 \mathrm{L}\) at a pressure of 1.00 atm. Oxygen, \(\mathrm{O}_{2}\) is then added so that the final volume of the balloon is 26 L with a total pressure of 1.00 atm. The temperature, which remains constant throughout, is \(21.5^{\circ} \mathrm{C}\) (a) What mass of He does the balloon contain? (b) What is the final partial pressure of He in the balloon? (c) What is the partial pressure of \(\mathrm{O}_{2}\) in the balloon? (d) What is the mole fraction of each gas?

You have two flasks of equal volume. Flask A contains \(\mathrm{H}_{2}\) at \(0^{\circ} \mathrm{C}\) and 1 atm pressure. Flask \(\mathrm{B}\) contains \(\mathrm{CO}_{2}\) gas at \(25^{\circ} \mathrm{C}\) and 2 atm pressure. Compare these two gases with respect to each of the following: (a) average kinetic energy per molecule (b) root mean square speed (c) number of molecules (d) mass of gas

Equal masses of gaseous \(\mathrm{N}_{2}\) and \(\mathrm{Ar}\) are placed in separate flasks of equal volume at the same temperature. Tell whether each of the following statements is true or false. Briefly explain your answer in each case. (a) There are more molecules of \(\mathrm{N}_{2}\) present than atoms of Ar. (b) The pressure is greater in the Ar flask. (c) The Ar atoms have a greater rms speed than the \(\mathrm{N}_{2}\) molecules. (d) The \(\mathrm{N}_{2}\) molecules collide more frequently with the walls of the flask than do the Ar atoms.

Calculate the rms speed for CO molecules at \(25^{\circ} \mathrm{C} .\) What is the ratio of this speed to that of \(\mathrm{Ar}\) atoms at the same temperature?

Place the following gases in order of increasing rms speed at \(25^{\circ} \mathrm{C}: \mathrm{Ar}, \mathrm{CH}_{4}, \mathrm{N}_{2}, \mathrm{CH}_{2} \mathrm{F}_{2}\)

In each pair of gases below, tell which will effuse faster: (a) \(\mathrm{CO}_{2}\) or \(\mathrm{F}_{2}\) (b) \(\mathrm{O}_{2}\) or \(\mathrm{N}_{2}\) (c) \(\mathrm{C}_{2} \mathrm{H}_{4}\) or \(\mathrm{C}_{2} \mathrm{H}_{6}\) (d) two chlorofluorocarbons: \(\operatorname{CFCl}_{3}\) or \(\mathrm{C}_{2} \mathrm{Cl}_{2} \mathrm{F}_{4}\)

Argon gas is 10 times denser than helium gas at the same temperature and pressure. Which gas is predicted to effuse faster? How much faster?

A gas whose molar mass you wish to know effuses through an opening at a rate one third as fast as that of helium gas. What is the molar mass of the unknown gas?

A A sample of uranium fluoride is found to effuse at the rate of \(17.7 \mathrm{mg} / \mathrm{h}\). Under comparable conditions, gaseous \(\mathrm{I}_{2}\) effuses at the rate of \(15.0 \mathrm{mg} / \mathrm{h} .\) What is the molar mass of the uranium fluoride? (Hint: Rates must be converted to units of moles per time.

Under which set of conditions will \(\mathrm{CO}_{2}\) deviate most from ideal gas behavior? (a) \(1 \mathrm{atm}, 0^{\circ} \mathrm{C}\) (b) 0.1 atm, \(100^{\circ} \mathrm{C}\) (c) \(10 \mathrm{atm}, 0^{\circ} \mathrm{C}\) (d) \(1 \mathrm{atm}, 100^{\circ} \mathrm{C}\)

Under which set of conditions will \(\mathrm{Cl}_{2}\) deviate least from ideal gas behavior? (a) \(1 \mathrm{atm}, 0^{\circ} \mathrm{C}\) (b) 0.1 atm, \(100^{\circ} \mathrm{C}\) (c) \(10 \mathrm{atm}, 0^{\circ} \mathrm{C}\) (d) \(1 \mathrm{atm}, 100^{\circ} \mathrm{C}\)

In the text, it is stated that the pressure of 4.00 mol of \(\mathrm{Cl}_{2}\) in a \(4.00-\mathrm{L}\) tank at \(100.0^{\circ} \mathrm{C}\) should be 26.0 atm if calculated using the van der Waals equation. Verify this result, and compare it with the pressure predicted by the ideal gas law.