Chapter 10

Birds and sailplanes take advantage of thermals (rising columns of warm air) to gain altitude with less effort than usual. Why does warm air rise?

How does the density of a gas sample change when (a) its pressure is increased and (b) its temperature is decreased?

Four empty balloons, each with a mass of \(10.0 \mathrm{g},\) are inflated to a volume of \(20.0 \mathrm{L}\). The first balloon contains He, the second Ne, the third \(\mathrm{CO}_{2},\) and the fourth CO. If the density of air at \(25^{\circ} \mathrm{C}\) and 1.00 atm is \(1.17 \mathrm{g} / \mathrm{L},\) how many of the balloons float in it?

A 30.0 mL flask contains 0.078 g of a volatile oxide of sulfur. The pressure in the flask is \(750 \mathrm{mmHg}\), and the temperature is \(22^{\circ} \mathrm{C}\) a. What is the density of the gas? b. Is the gas \(\mathrm{SO}_{2}\) or \(\mathrm{SO}_{3} ?\)

A 100.0 mL flask contains 0.193 g of a volatile oxide of nitrogen. The pressure in the flask is \(760 \mathrm{mmHg}\) at \(17^{\circ} \mathrm{C}\) a. Calculate the density of the gas. b. Is the gas \(\mathrm{NO}, \mathrm{NO}_{2},\) or \(\mathrm{N}_{2} \mathrm{O}_{5} ?\)

The density of an unknown gas is \(1.107 \mathrm{g} / \mathrm{L}\) at \(300 \mathrm{K}\) and \(740 \mathrm{mmHg}\) a. What is the molar mass of the gas? b. Could this gas be \(\mathrm{CO}\) or \(\mathrm{CO}_{2} ?\)

A gas containing chlorine and oxygen has a density of \(2.875 \mathrm{g} / \mathrm{L}\) at \(756 \mathrm{mmHg}\) and \(11^{\circ} \mathrm{C}\) a. Calculate the molar mass of the gas. b. What is the most likely molecular formula of the gas?

Acid precipitation dripping on limestone produces carbon dioxide by the following reaction: \(\mathrm{CaCO}_{3}(s)+2 \mathrm{H}^{+}(a q) \rightarrow \mathrm{Ca}^{2+}(a q)+\mathrm{CO}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(\ell)\) Suppose that \(8.6 \mathrm{mL}\) of \(\mathrm{CO}_{2}\) were produced at \(15^{\circ} \mathrm{C}\) and \(760 \mathrm{mmHg}\) a. How many moles of \(\mathrm{CO}_{2}\) were produced? b. How many milligrams of \(\mathrm{CaCO}_{3}\) were consumed?

Oxygen is generated by the thermal decomposition of potassium chlorate: $$2 \mathrm{KClO}_{3}(s) \rightarrow 2 \mathrm{KCl}(s)+3 \mathrm{O}_{2}(g)$$ How many grams of \(\mathrm{KClO}_{3}\) are needed to generate \(200.0 \mathrm{L}\) of oxygen at 0.85 atm and \(273 \mathrm{K} ?\)

Nitrogen gas is a product of the thermal decomposition of ammonium dichromate, (NH_), Cr,O_: $$\left(\mathrm{NH}_{4}\right)_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}(s) \rightarrow \mathrm{N}_{2}(g)+\mathrm{Cr}_{2} \mathrm{O}_{3}(s)+4 \mathrm{H}_{2} \mathrm{O}(g)$$ How many liters of \(\mathrm{N}_{2}\) are produced during the decomposition of 100.0 grams of ammonium dichromate \((M=252.07 \mathrm{g} / \mathrm{mol})\) at \(22^{\circ} \mathrm{C}\) and a pressure of 757 torr?

Healthy Air for Submariners The CO, that builds up in the air of a submerged submarine can be removed by reacting it with an aqueous solution of 2 -aminoethanol: \(\mathrm{CO}_{2}(g)+2 \mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{2}(a q) \rightarrow\) $$\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{NH}_{3}^{+}(a q)+\mathrm{HOCH}_{2} \mathrm{CH}_{2} \mathrm{NHCO}_{2}^{-}(a q)$$ If a sailor exhales \(125 \mathrm{mL}\) of \(\mathrm{CO}_{2}\) per minute at \(23^{\circ} \mathrm{C}\) and1.02 atm, what volume of \(4.0 \mathrm{M}\) 2-aminocthanol is needed per sailor in a 24 -hour period?

Miners' Lamps Before the development of reliable batterics, miners' lamps burned acetylene produced by the reaction of calcium carbide with water: $$\mathrm{CaC}_{2}(s)+\mathrm{H}_{2} \mathrm{O}(\ell) \rightarrow \mathrm{C}_{2} \mathrm{H}_{2}(g)+\mathrm{CaO}(s)$$ Suppose a lamp uses \(4.8 \mathrm{L}\) of acetylene per hour at 1.02 atm pressure and \(25^{\circ} \mathrm{C}\) a. How many moles of \(\mathrm{C}_{2} \mathrm{H}_{2}\) are used per hour? b. How many grams of calcium carbide are consumed for a four-hour shift?

What is meant by the partial pressure of a gas?

Can a barometer be used to measure just the partial pressure of oxygen in the atmosphere? Why or why not?

A gas mixture contains \(7.0 \mathrm{g} \mathrm{N}_{2}, 2.0 \mathrm{g} \mathrm{H}_{2},\) and \(16.0 \mathrm{g} \mathrm{CH}_{4}\) What is the mole fraction of \(\mathrm{H}_{2}\) in the mixture?

A sample of oxygen is collected over water at \(25^{\circ} \mathrm{C}\) and 1.00 atm. If the total sample volume is 0.480 \(\mathrm{L}\), how many moles of \(\mathrm{O}_{2}\) are collected?

The following reactions are carried out in sealed containers. Will the total pressure after each reaction is complete be greater than, less than, or equal to the total pressure before the reaction? Assume all reactants and products are gases at the same temperature. a. \(\mathrm{N}_{2} \mathrm{O}_{5}(g)+\mathrm{NO}_{2}(g) \rightarrow 3 \mathrm{NO}(g)+2 \mathrm{O}_{2}(g)\) b. \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{SO}_{3}(g)\) c. \(\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \rightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\)

In each of the following gas-phase reactions, determine whether the total pressure at the end of the reaction (carried out in a sealed, rigid vessel) will be greater than, less than, or equal to the total pressure at the beginning. Assume all reactants and products are gases at the same temperature. a. \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g)\) b. \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\) c. \(2 \mathrm{NO}(g)+\mathrm{O}_{2}(g) \rightarrow 2 \mathrm{NO}_{2}(g)\)

Scuba Diving A scuba diver is at a depth of \(50 \mathrm{m}\), where the pressure is 5.0 atm. What should be the mole fraction of \(\mathrm{O}_{2}\) in the gas mixture the diver breathes to achieve the same \(P_{\mathrm{O}_{2}}\) as at sea level?

A highly efficient hot-water heater fueled by natural gas can heat water at the rate of 33,500 BTU/hour ( 1 BTU or British thermal unit \(=1.055 \mathrm{kJ}) .\) During exactly one hour of operation, what volume of natural gas would be consumed at STP? Assume natural gas is mostly methane \(\left(\mathrm{CH}_{4}\right),\) which has a fuel value of \(55.5 \mathrm{kJ} / \mathrm{g}\).

The hot-water heater described in question 10.107 can be modified to burn propane \(\left(\mathrm{C}_{3} \mathrm{H}_{8}, \text { fuel value }=50.4 \mathrm{kJ} / \mathrm{g}\right)\) instead of natural gas. What volume of propane gas would be consumed at STP by the water heater during exactly one hour of operation?

Ammonia is produced industrially from the reaction of hydrogen with nitrogen under pressure in a sealed reactor. What is the percent decrease in total pressure of a sealed reaction vessel during the reaction between \(\mathrm{H}_{2}\) at a partial pressure of 2.4 atm and \(\mathrm{N}_{2}\) at a partial pressure of 3.6 atm if half of the \(\mathrm{H}_{2}\) is consumed? No other gases are present initially in the reactor.

Why do real gases behave non-ideally at very low temperatures and very high pressures?

Under what conditions is the pressure exerted by a real gas less than that predicted for an ideal gas?

Why do the values of the van red Walls constant \(b\) of the noble gas elements increase with atomic number?

Why does the value of the constant \(a\) in the van der Weals equation generally increase with the molar mass of the gas?

Explain why the van der Weals constant \(a\) is greater for \(\mathrm{Ar}\) than it is for He.

Which noble gas is expected to deviate the most from ideal behavior in a graph of PV/RT versus \(P ?\)

At high pressures, real gases do not behave ideally. a. Use the van der Waals equation and data in the text to calculate the pressure exerted by \(50.0 \mathrm{g}\) of \(\mathrm{H}_{2}\) at \(20^{\circ} \mathrm{C}\) in a \(1.00 \mathrm{L}\) container. b. Repeat the calculation assuming that the gas behaves like an ideal gas.

Planetary Atmospheres Saturn's largest moon, Titan, has a surface atmospheric pressure of 1220 torr. The atmosphere consists of \(82 \% \mathrm{N}_{2}, 12 \% \mathrm{Ar},\) and \(6 \% \mathrm{CH}_{4} \mathrm{by}\) volume. Calculate the partial pressure of each gas in Titan's atmosphere. Chilly temperatures aside, could life as we know it exist on Titan?

Blood Pressure A typical blood pressure in a resting adult is "120 over 80," meaning 120 \(\mathrm{mmHg}\) with each beat of the heart and 80 mm Hg of pressure between heartbeats. Express these pressures in the following units: (a) torr; (b) atm; (c) bar; (d) kPa.

The pressure in an aerosol can is 1.2 atm at \(27^{\circ} \mathrm{C}\). The can will withstand a pressure of 3.0 atm. Will it burst if heated in a campfire to \(450^{\circ} \mathrm{C} ?\)

Uranus has a total atmospheric pressure of \(130 \mathrm{kPa}\) and consists of the following gases: \(83 \% \mathrm{H}_{2}, 15 \% \mathrm{He},\) and \(2 \%\) \(\mathrm{CH}_{4}\) by volume. Calculate the partial pressure of each gas in Uranus's atmosphere.

Derive an equation that expresses the ratio of the densities \(\left(d_{1} \text { and } d_{2}\right)\) of a gas under two different combinations of temperature and pressure: \(\left(T_{1}, P_{1}\right)\) and \(\left(T_{2}, P_{2}\right)\).

Denitrification in the Environment In some aquatic ecosystems, nitrate \(\left(\mathrm{NO}_{3}^{-}\right)\) is converted to nitrite \(\left(\mathrm{NO}_{2}^{-}\right),\) which then decomposes to nitrogen and water. As an example of this second reaction, consider the decomposition of ammonium nitrite: $$\mathrm{NH}_{4} \mathrm{NO}_{2}(a q) \rightarrow \mathrm{N}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(\ell) $$ What is the change in pressure in a sealed 10.0 L. vessel due to the formation of \(\mathrm{N}_{2}\) gas when the ammonium nitrite in \(1.00 \mathrm{L}\) of \(1.0 \mathrm{M} \mathrm{NH}_{4} \mathrm{NO}_{2}\) decomposes at \(25^{\circ} \mathrm{C} ?\)

Using Wetlands to Treat Agricultural Waste Wetlands can play a significant role in removing fertilizer residues from rain runoff and groundwater. One way they do this is through denitrification, which converts nitrate ions to nitrogen gas: \(2 \mathrm{NO}_{3}^{-}(a q)+5 \mathrm{CO}(g)+2 \mathrm{H}^{+}(a q) \right-arrow \mathrm{N}_{2}(g)+\mathrm{H}_{2} \mathrm{O}(\ell)+5 \mathrm{CO}_{2}(g)\) Suppose \(200.0 \mathrm{g}\) of \(\mathrm{NO}_{3}^{-}\) flows into a swamp each day. a. What volume of \(\mathrm{N}_{2}\) would be produced at \(17^{\circ} \mathrm{C}\) and 1.00 atm if the denitrification process were complete? b. What volume of \(\mathrm{CO}_{2}\) would be produced? c. Suppose the gas mixture produced by the decomposition reaction is trapped in a container at \(17^{\circ} \mathrm{C} ;\) what is the density of the mixture, assuming \(P_{\text {total }}\) \(=1.00\) atm?

Decay Products of Uranium Minerals Radon and helium are both by-products of the radioactive decay of uranium minerals. A fresh sample of carnotite, \(\mathrm{K}_{2}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{VO}_{4}\right)_{2}\) \(\cdot 3 \mathrm{H}_{2} \mathrm{O},\) is put on display in a museum. Calculate the relative rates of diffusion of helium and radon under fixed conditions of pressure and temperature. Which gas diffuses more rapidly through the display case?

The reaction between potassium super-oxide and carbon dioxide is used to produce \(0.200 \mathrm{L}\) of \(\mathrm{O}_{2},\) which is collected over water at \(25.0^{\circ} \mathrm{C} .\) The atmospheric pressure is 750.0 torr. The vapor pressure of water at \(25.0^{\circ} \mathrm{C}\) is 24.0 torr. How many moles of \(\mathrm{O}_{2}\) have becn collected? $$4 \mathrm{KO}_{2}(s)+2 \mathrm{CO}_{2}(g) \rightarrow 2 \mathrm{K}_{2} \mathrm{CO}_{3}(s)+3 \mathrm{O}_{2}(g)$$

On October \(26,2014,\) Alan Eustace set a record for the highest parachute jump when he dropped from a balloon at an altitude of \(41,419 \mathrm{m},\) where the atmospheric pressure is only \(5.6 \mathrm{mmH} \mathrm{g}\) a. What is the density of air at this height? b. Is the mean free path of a gas molecule longer or shorter at this altitude than at sea level?