Chapter 6

Convert each pressure to an equivalent pressure (a) 736 mmHg; (b) 0.776 bar; in atmospheres. (c) 892 Torr; (d) 225 kPa.

Calculate the height of a column of liquid glycerol \(\overline{\left(d=1.26 \mathrm{g} / \mathrm{cm}^{3}\right), \text { in meters, required to exert the }}\) same pressure as \(3.02 \mathrm{m}\) of \(\mathrm{CCl}_{4}(\mathrm{l})\left(d=1.59 \mathrm{g} / \mathrm{cm}^{3}\right)\)

What is the pressure (in \(\mathrm{mmHg}\) ) of the gas inside the apparatus below if \(P_{\text {bar. }}=740 \mathrm{mm} \mathrm{Hg}, h_{1}=30 \mathrm{mm}\) and \(h_{2}=50 \mathrm{mm} ?\)

At times, a pressure is stated in units of mass per unit area rather than force per unit area. Express \(P=1 \mathrm{atm}\) in the unit \(\mathrm{kg} / \mathrm{cm}^{2}\) [Hint: How is a mass in kilograms related to a force?]

A sample of \(\mathrm{O}_{2}(\mathrm{g})\) has a volume of \(26.7 \mathrm{L}\) at 762 Torr. What is the new volume if, with the temperature and amount of gas held constant, the pressure is (a) lowered to 385 Torr; (b) increased to 3.68 atm?

An 886 mL sample of \(\mathrm{Ne}(\mathrm{g})\) is at \(752 \mathrm{mmHg}\) and \(26^{\circ} \mathrm{C}\). What will be the new volume if, with the pressure and amount of gas held constant, the temperature is (a) increased to \(98^{\circ} \mathrm{C} ;\) (b) lowered to \(-20^{\circ} \mathrm{C} ?\)

If 3.0 L of oxygen gas at \(177^{\circ} \mathrm{C}\) is cooled at constant pressure until the volume becomes \(1.50 \mathrm{L}\), then what is the final temperature?

We want to change the volume of a fixed amount of gas from \(725 \mathrm{mL}\) to 2.25 L while holding the temperature constant. To what value must we change the pressure if the initial pressure is \(105 \mathrm{kPa} ?\)

A 35.8 L cylinder of \(\mathrm{Ar}(\mathrm{g})\) is connected to an evacuated 1875 L tank. If the temperature is held constant and the final pressure is \(721 \mathrm{mmHg}\), what must have been the original gas pressure in the cylinder, in atmospheres?

A weather balloon filled with He gas has a volume of \(2.00 \times 10^{3} \mathrm{m}^{3}\) at ground level, where the atmospheric pressure is 1.000 atm and the temperature \(27^{\circ}\) C. After the balloon rises high above Earth to a point where the atmospheric pressure is 0.340 atm, its volume increases to \(5.00 \times 10^{3} \mathrm{m}^{3} .\) What is the temperature of the atmosphere at this altitude?

What is the mass of argon gas in a \(75.0 \mathrm{mL}\) volume at STP?

You purchase a bag of potato chips at an ocean beach to take on a picnic in the mountains. At the picnic, you notice that the bag has become inflated, almost to the point of bursting. Use your knowledge of gas behavior to explain this phenomenon.

A sample of gas has a volume of \(4.25 \mathrm{L}\) at \(25.6^{\circ} \mathrm{C}\) and \(748 \mathrm{mmHg} .\) What will be the volume of this gas at \(26.8^{\circ} \mathrm{C}\) and \(742 \mathrm{mmHg} ?\)

A 10.0 g sample of a gas has a volume of \(5.25 \mathrm{L}\) at \(25^{\circ} \mathrm{C}\) and \(762 \mathrm{mm} \mathrm{Hg} .\) If \(2.5 \mathrm{g}\) of the same gas is added to this constant 5.25 L volume and the temperature raised to \(62^{\circ} \mathrm{C},\) what is the new gas pressure?

A constant-volume vessel contains \(12.5 \mathrm{g}\) of a gas at 21 ^ C. If the pressure of the gas is to remain constant as the temperature is raised to \(210^{\circ} \mathrm{C}\), how many grams of gas must be released?

A 34.0 L cylinder contains \(305 \mathrm{g} \mathrm{O}_{2}(\mathrm{g})\) at \(22^{\circ} \mathrm{C} .\) How many grams of \(\mathrm{O}_{2}(\mathrm{g})\) must be released to reduce the pressure in the cylinder to 1.15 atm if the temperature remains constant?

What is the volume, in milliliters, occupied by \(89.2 \mathrm{g} \mathrm{CO}_{2}(\mathrm{g})\) at \(37^{\circ} \mathrm{C}\) and \(737 \mathrm{mmHg} ?\)

A 12.8 L cylinder contains \(35.8 \mathrm{g} \mathrm{O}_{2}\) at \(46^{\circ} \mathrm{C}\). What is the pressure of this gas, in atmospheres?

\(\mathrm{Kr}(\mathrm{g})\) in a 18.5 L cylinder exerts a pressure of \(11.2 \mathrm{atm}\) at \(28.2^{\circ} \mathrm{C} .\) How many grams of gas are present?

A 72.8 L constant-volume cylinder containing \(7.41 \mathrm{g}\) He is heated until the pressure reaches 3.50 atm. What is the final temperature in degrees Celsius?

What is the pressure, in pascals, exerted by \(1242 \mathrm{g}\) CO(g) when confined at \(-25^{\circ} \mathrm{C}\) to a cylindrical tank \(25.0 \mathrm{cm}\) in diameter and \(1.75 \mathrm{m}\) high?

What is the molar volume of an ideal gas at (a) \(25^{\circ} \mathrm{C}\) and 1.00 atm; \((b) 100^{\circ} \mathrm{C}\) and 748 Torr?

At what temperature is the molar volume of an ideal gas equal to \(22.4 \mathrm{L},\) if the pressure of the gas is \(2.5 \mathrm{atm} ?\)

A 0.418 g sample of gas has a volume of \(115 \mathrm{mL}\) at \(66.3^{\circ} \mathrm{C}\) and \(743 \mathrm{mm} \mathrm{Hg} .\) What is the molar mass of this gas?

What is the molar mass of a gas found to have a density of \(0.841 \mathrm{g} / \mathrm{L}\) at \(415 \mathrm{K}\) and 725 Torr?

What is the molecular formula of a gaseous fluoride of sulfur containing \(70.4 \%\) F and having a density of approximately \(4.5 \mathrm{g} / \mathrm{L}\) at \(20^{\circ} \mathrm{C}\) and \(1 \mathrm{atm} ?\)

A 2.650 g sample of a gaseous compound occupies \(428 \mathrm{mL}\) at \(24.3^{\circ} \mathrm{C}\) and \(742 \mathrm{mmHg} .\) The compound consists of \(15.5 \%\) C \(, 23.0 \%\) Cl, and \(61.5 \%\) F, by mass. What is its molecular formula?

A gaseous hydrocarbon weighing \(0.231 \mathrm{g}\) occupies a volume of \(102 \mathrm{mL}\) at \(23^{\circ} \mathrm{C}\) and \(749 \mathrm{mmHg} .\) What is the molar mass of this compound? What conclusion can you draw about its molecular formula?

A 132.10 mL glass vessel weighs 56.1035 g when evacuated and \(56.2445 \mathrm{g}\) when filled with the gaseous hydrocarbon acetylene at \(749.3 \mathrm{mmHg}\) and \(20.02^{\circ} \mathrm{C}\) What is the molar mass of acetylene? What conclusion can you draw about its molecular formula?

A particular application calls for \(\mathrm{N}_{2}(\mathrm{g})\) with a density of \(1.80 \mathrm{g} / \mathrm{L}\) at \(32^{\circ} \mathrm{C} .\) What must be the pressure of the \(\mathrm{N}_{2}(\mathrm{g})\) in millimeters of mercury? What is the molar volume under these conditions?

Monochloroethylene is used to make polyvinylchloride (PVC). It has a density of \(2.56 \mathrm{g} / \mathrm{L}\) at \(22.8^{\circ} \mathrm{C}\) and 756 mmHg. What is the molar mass of monochloroethylene? What is the molar volume under these conditions?

In order for a gas-filled balloon to rise in air, the density of the gas in the balloon must be less than that of air. (a) Consider air to have a molar mass of \(28.96 \mathrm{g} / \mathrm{mol}\) determine the density of air at \(25^{\circ} \mathrm{C}\) and \(1 \mathrm{atm},\) in g/L. (b) Show by calculation that a balloon filled with carbon dioxide at \(25^{\circ} \mathrm{C}\) and 1 atm could not be expected to rise in air at \(25^{\circ} \mathrm{C}\)

The density of phosphorus vapor is \(2.64 \mathrm{g} / \mathrm{L}\) at \(310^{\circ} \mathrm{C}\) and \(775 \mathrm{mm}\) Hg. What is the molecular formula of the phosphorus under these conditions?

A particular gaseous hydrocarbon that is \(82.7 \%\) C and \(17.3 \%\) H by mass has a density of \(2.33 \mathrm{g} / \mathrm{L}\) at \(23^{\circ} \mathrm{C}\) and \(746 \mathrm{mm} \mathrm{Hg} .\) What is the molecular formula of this hydrocarbon?

How many liters of \(\mathrm{H}_{2}(\mathrm{g})\) at STP are produced per gram of \(\mathrm{Al}(\mathrm{s})\) consumed in the following reaction? \(2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \longrightarrow 2 \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{g})\)

A particular coal sample contains \(3.28 \%\) S by mass. When the coal is burned, the sulfur is converted to \(\mathrm{SO}_{2}(\mathrm{g}) .\) What volume of \(\mathrm{SO}_{2}(\mathrm{g}),\) measured at \(23^{\circ} \mathrm{C}\) and \(738 \mathrm{mm} \mathrm{Hg},\) is produced by burning \(1.2 \times 10^{6} \mathrm{kg}\) of this coal?

A 3.57 g sample of a \(\mathrm{KCl}-\mathrm{KClO}_{3}\) mixture is decomposed by heating and produces \(119 \mathrm{mL} \mathrm{O}_{2}(\mathrm{g})\) measured at \(22.4^{\circ} \mathrm{C}\) and \(738 \mathrm{mm} \mathrm{Hg}\). What is the mass percent of \(\mathrm{KClO}_{3}\) in the mixture? $$2 \mathrm{KClO}_{3}(\mathrm{s}) \longrightarrow 2 \mathrm{KCl}(\mathrm{s})+3 \mathrm{O}_{2}(\mathrm{g})$$

Hydrogen peroxide, \(\mathrm{H}_{2} \mathrm{O}_{2},\) is used to disinfect contact lenses. How many milliliters of \(\mathrm{O}_{2}(\mathrm{g})\) at \(22^{\circ} \mathrm{C}\) and \(752 \mathrm{mmHg}\) can be liberated from \(10.0 \mathrm{mL}\) of an aqueous solution containing \(3.00 \% \mathrm{H}_{2} \mathrm{O}_{2}\) by mass? The density of the aqueous solution of \(\mathrm{H}_{2} \mathrm{O}_{2}\) is \(1.01 \mathrm{g} / \mathrm{mL}\) $$2 \mathrm{H}_{2} \mathrm{O}_{2}(\mathrm{aq}) \longrightarrow 2 \mathrm{H}_{2} \mathrm{O}(1)+\mathrm{O}_{2}(\mathrm{g})$$

Calculate the volume of \(\mathrm{H}_{2}(\mathrm{g}),\) measured at \(26^{\circ} \mathrm{C}\) and 751 Torr, required to react with \(28.5 \mathrm{LCO}(\mathrm{g})\) measured at \(0^{\circ} \mathrm{C}\) and 760 Torr, in this reaction. $$3 \mathrm{CO}(\mathrm{g})+7 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(1)$$

The Haber process is the principal method for fixing nitrogen (converting \(\mathrm{N}_{2}\) to nitrogen compounds). $$\mathrm{N}_{2}(\mathrm{g})+3 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow 2 \mathrm{NH}_{3}(\mathrm{g})$$ Assume that the reactant gases are completely converted to \(\mathrm{NH}_{3}(\mathrm{g})\) and that the gases behave ideally. (a) What volume of \(\mathrm{NH}_{3}(\mathrm{g})\) can be produced from 152 \(\mathrm{L} \mathrm{N}_{2}(\mathrm{g})\) and \(313 \mathrm{L}\) of \(\mathrm{H}_{2}(\mathrm{g})\) if the gases are measured at \(315^{\circ} \mathrm{C}\) and 5.25 atm? (b) What volume of \(\mathrm{NH}_{3}(\mathrm{g}),\) measured at \(25^{\circ} \mathrm{C}\) and\(727 \mathrm{mmHg},\) can be produced from \(152 \mathrm{L} \mathrm{N}_{2}(\mathrm{g})\) and \(313 \mathrm{L} \mathrm{H}_{2}(\mathrm{g}),\) measured at \(315^{\circ} \mathrm{C}\) and \(5.25 \mathrm{atm} ?\)

What is the volume, in liters, occupied by a mixture of 15.2 \(\mathrm{g} \mathrm{Ne}(\mathrm{g})\) and \(34.8 \mathrm{g} \mathrm{Ar}(\mathrm{g})\) at 7.15 atm pressure and \(26.7^{\circ} \mathrm{C} ?\)

A 2.35 L container of \(\mathrm{H}_{2}(\mathrm{g})\) at \(762 \mathrm{mmHg}\) and \(24^{\circ} \mathrm{C}\) is connected to a 3.17 L container of \(\mathrm{He}(\mathrm{g})\) at \(728 \mathrm{mmHg}\) and \(24^{\circ} \mathrm{C}\). After mixing, what is the total gas pressure, in millimeters of mercury, with the temperature remaining at \(24^{\circ} \mathrm{C} ?\)

Which actions would you take to establish a pressure of 2.00 atm in a 2.24 L cylinder containing \(1.60 \mathrm{g} \mathrm{O}_{2}(\mathrm{g})\) at \(0^{\circ} \mathrm{C} ?\) (a) add \(1.60 \mathrm{g} \mathrm{O}_{2} ;\) (b) release \(0.80 \mathrm{g} \mathrm{O}_{2} ;\) (c) add \(2.00 \mathrm{g} \mathrm{He} ;\) (d) add \(0.60 \mathrm{g}\) He.

A 2.00 L container is filled with \(\operatorname{Ar}(g)\) at 752 mm Hg and \(35^{\circ} \mathrm{C} .\) A \(0.728 \mathrm{g}\) sample of \(\mathrm{C}_{6} \mathrm{H}_{6}\) vapor is then added. (a) What is the total pressure in the container? (b) What is the partial pressure of \(\mathrm{Ar}\) and of \(\mathrm{C}_{6} \mathrm{H}_{6} ?\)

A 4.0 L sample of \(\mathrm{O}_{2}\) gas has a pressure of 1.0 atm. A 2.0 L sample of \(\mathrm{N}_{2}\) gas has a pressure of 2.0 atm. If these two samples are mixed and then compressed in a 2.0 L vessel, what is the final pressure of the mixture? Assume that the temperature remains unchanged.

A 1.65 g sample of \(\mathrm{Al}\) reacts with excess \(\mathrm{HCl}\), and the liberated \(\mathrm{H}_{2}\) is collected over water at \(25^{\circ} \mathrm{C}\) at a barometric pressure of \(744 \mathrm{mmHg} .\) What volume of gaseous mixture, in liters, is collected? $$2 \mathrm{Al}(\mathrm{s})+6 \mathrm{HCl}(\mathrm{aq}) \longrightarrow 2 \mathrm{AlCl}_{3}(\mathrm{aq})+3 \mathrm{H}_{2}(\mathrm{g})$$

An \(89.3 \mathrm{mL}\) sample of wet \(\mathrm{O}_{2}(\mathrm{g})\) is collected over water at \(21.3^{\circ} \mathrm{C}\) at a barometric pressure of \(756 \mathrm{mmHg}\) (vapor pressure of water at \(21.3^{\circ} \mathrm{C}=19 \mathrm{mmHg}\) ). (a) What is the partial pressure of \(\mathrm{O}_{2}(\mathrm{g})\) in the sample collected, in millimeters of mercury? (b) What is the volume percent \(\mathrm{O}_{2}\) in the gas collected? (c) How many grams of \(\mathrm{O}_{2}\) are present in the sample?

A sample of \(\mathrm{O}_{2}(\mathrm{g})\) is collected over water at \(24^{\circ} \mathrm{C}\) The volume of gas is 1.16 L. In a subsequent experiment, it is determined that the mass of \(\mathrm{O}_{2}\) present is 1.46 g. What must have been the barometric pressure at the time the gas was collected? (Vapor pressure of water \(=22.4 \text { Torr. })\)

A 1.072 g sample of \(\mathrm{He}(\mathrm{g})\) is found to occupy a volume of 8.446 L when collected over hexane at \(25.0^{\circ} \mathrm{C}\) and \(738.6 \mathrm{mmHg}\) barometric pressure. Use these data to determine the vapor pressure of hexane at \(25^{\circ} \mathrm{C}\).

At elevated temperatures, solid sodium chlorate \(\left(\mathrm{NaClO}_{3}\right)\) decomposes to produce sodium chloride, \(\mathrm{NaCl},\) and \(\mathrm{O}_{2}\) gas. A \(0.8765 \mathrm{g}\) sample of impure sodium chlorate was heated until the production of oxygen ceased. The oxygen gas was collected over water and occupied a volume of \(57.2 \mathrm{mL}\) at \(23.0^{\circ} \mathrm{C}\) and 734 Torr. Calculate the mass percentage of \(\mathrm{NaClO}_{3}\) in the original sample. Assume that none of the impurities produce oxygen on heating. The vapor pressure of water is 21.07 Torr at \(23^{\circ} \mathrm{C}\).