Chapter 6

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?

Which will increase the density of a gas: doubling its temperature or doubling its pressure?

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 \(0.00117 \mathrm{g} / \mathrm{mL}\) which of the balloons float in this air?

A 150.0 mL flask contains \(0.391 \mathrm{g}\) of a volatile oxide of sulfur. The pressure in the flask is \(750 \mathrm{mm} \mathrm{Hg}\), and the temperature is \(22^{\circ} \mathrm{C} .\) 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 \(17^{\circ} \mathrm{C} .\) Is the gas \(\mathrm{NO}, \mathrm{NO}_{2},\) or \(\mathrm{N}_{2} \mathrm{O}_{5} ?\)

A 0.375 g sample of benzene vapor has a volume of \(149 \mathrm{mL}\) measured at \(95.0^{\circ} \mathrm{C}\) and 740.0 torr. Calculate the molar mass of benzene.

Calculate the density of toluene vapor (molar mass \(92 \mathrm{g} /\) mol) at 1.00 atm pressure and \(227.0^{\circ} \mathrm{C}\).

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?

Which gas sample has the largest volume at \(25^{\circ} \mathrm{C}\) and 1 atm pressure? \((\mathrm{a}) 0.500\) mol of \(\mathrm{dry} \mathrm{H}_{2} ;\) (b) 0.500 mol of dry \(\mathrm{N}_{2} ;\) (c) 0.500 mol of wet \(\mathrm{H}_{2}\left(\mathrm{H}_{2} \text { collected over water }\right)\)

A mixture of gases has a partial pressure of \(\mathrm{N}_{2}=0.5\) atm and a partial pressure of \(\mathrm{O}_{2}=1.0 \mathrm{atm} .\) Which molecules experience more collisions: the molecules of nitrogen or the molecules of oxygen?

Why does the partial pressure of water increase as temperature increases?

What pressure is exerted by a gas mixture containing \(2.00 \mathrm{g}\) of \(\mathrm{H}_{2}\) and \(7.00 \mathrm{g}\) of \(\mathrm{N}_{2}\) at \(273^{\circ} \mathrm{C}\) in a \(10.0 \mathrm{L}\) container? What is the contribution of \(\mathrm{N}_{2}\) to the total pressure?

A gas mixture contains \(7.0 \mathrm{g}\) of \(\mathrm{N}_{2}, 2.0 \mathrm{g}\) of \(\mathrm{H}_{2},\) and \(16.0 \mathrm{g}\) of \(\mathrm{CH}_{4}\). What is the mole fraction of \(\mathrm{H}_{2}\) in the mixture? Calculate the pressure of the gas mixture and the partial pressure of each constituent gas if the mixture is in a \(1.00 \mathrm{L}\) vessel at \(0^{\circ} \mathrm{C}\).

On November \(9,1961,\) the Bell \(\mathrm{X}-15\) test aircraft exceeded Mach \(6,\) or six times the speed of sound. A few weeks later it reached an elevation above 300,000 feet, effectively putting it in space. The combustion of ammonia and oxygen provided the fuel for the X-15. a. Write a balanced chemical equation for the combustion of ammonia given that nitrogen ends up as nitrogen dioxide. b. What ratio of partial pressures of ammonia and oxygen is needed for this reaction?

Before settling on hydrogen as the fuel of choice for space vehicles, several other fuels were explored, including hydrazine, \(\mathrm{N}_{2} \mathrm{H}_{4},\) and pentaboranc, \(\mathrm{B}_{5} \mathrm{H}_{11} .\) Both are gases under conditions in space. a. Write balanced chemical equations for the combustion of hydrazine and pentaborane given that the products in addition to water are \(\mathrm{NO}_{2}(g)\) and \(\mathrm{B}_{2} \mathrm{O}_{3}(s),\) respectively. b. What ratios of partial pressures of hydrazine to oxygen and pentaborane to oxygen are needed for these reactions?

A sample of oxygen was collected over water at \(25^{\circ} \mathrm{C}\) and \(1.00 \mathrm{atm}\) a. If the total sample volume was \(0.480 \mathrm{L},\) how many moles of \(\mathrm{O}_{2}\) were collected? \- b. If the same volume of oxygen is collected over ethanol instead of water, does it contain the same number of moles of \(\mathrm{O}_{2} ?\)

Water and ethanol were removed from the \(\mathrm{O}_{2}\) samples in Problem 6.107 a. What is the volume of the dry \(\mathrm{O}_{2}\) gas sample at \(25^{\circ} \mathrm{C}\) and 1.00 atm? b. What is the volume of the dry \(\mathrm{O}_{2}\) gas sample at \(25^{\circ} \mathrm{C}\) and 1.00 atm if \(P_{\text {ethanol }}=50 \mathrm{mmHg}\) at \(25^{\circ} \mathrm{C} ?\)

The following reactions were 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. \(\mathrm{C}_{3} \mathrm{H}_{8}(g)+5 \mathrm{O}_{2}(g) \rightarrow 3 \mathrm{CO}_{2}(g)+4 \mathrm{H}_{2} \mathrm{O}(g)\) d. \(4 \mathrm{NH}_{3}(g)+5 \mathrm{O}_{2}(g) \rightarrow 4 \mathrm{NO}(g)+6 \mathrm{H}_{2} \mathrm{O}(g)\)

The following reactions were carried out in a cylinder with a piston. If the external pressure is constant, in which reactions will the volume of the cylinder increase? Assume all reactants and products are gases at the same temperature. a. \(\mathrm{CH}_{4}(g)+\mathrm{NH}_{3}(g) \rightarrow \mathrm{HCN}(g)+3 \mathrm{H}_{2}(g)\) b. \(\mathrm{H}_{2} \mathrm{S}(g)+2 \mathrm{O}_{2}(g) \rightarrow \mathrm{H}_{2} \mathrm{O}(g)+\mathrm{SO}_{3}(g)\) c. \(\mathrm{H}_{2}(g)+\mathrm{Cl}_{2}(g) \rightarrow 2 \mathrm{HCl}(g)\) d. \(2 \mathrm{NO}_{2}(g) \rightarrow 2 \mathrm{NO}(g)+\mathrm{O}_{2}(g)\)

Climbers use pure oxygen near the summits of 8000 -m peaks, where \(P_{\mathrm{atm}}=0.35\) atm (Figure \(P 6.111\) ). How much more \(\mathrm{O}_{2}\) is there in a lung full of pure \(\mathrm{O}_{2}\) at this elevation than in a lung full of air at sea level? (IMAGE CANNOT COPY)

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 produce the same partial pressure of oxygen as the gas mixture at sea level?

Ozone reacts completely with NO, producing \(\mathrm{NO}_{2}\) and \(\mathrm{O}_{2}\). A \(10.0 \mathrm{L}\) vessel is filled with 0.280 mol of \(\mathrm{NO}\) and 0.280 mol of \(\mathrm{O}_{3}\) at \(350 \mathrm{K}\). Find the partial pressure of each product and the total pressure in the flask at the end of the reaction.

Ammonia is produced industrially from the reaction of hydrogen with nitrogen under pressure in a sealed reactor. What is the percent decrease in pressure of a sealed reaction vessel during the reaction between \(3.60 \times 10^{3} \mathrm{mol}\) of \(\mathrm{H}_{2}\) and \(1.20 \times 10^{3} \mathrm{mol}\) of \(\mathrm{N}_{2}\) if half of the \(\mathrm{N}_{2}\) is consumed?

What is meant by the root-mean-square speed of gas molecules?

Why don't all molecules in a sample of air move at exactly the same speed?

How does the root-mean-square speed of the molecules in a gas vary with (a) molar mass and (b) temperature?

Does pressure affect the root-mean-square speed of the molecules in a gas? Explain your answer.

How can Graham's law of effusion be used to determine the molar mass of an unknown gas?

Is the ratio of the rates of effusion of two gases the same as the ratio of their root-mean-square speeds?

What is the difference between diffusion and effusion?

If gas X diffuses faster in air than gas \(Y\), is gas X also likely to effuse faster than gas \(\mathrm{Y} ?\)

Rank the gases \(\mathrm{SO}_{2}, \mathrm{CO}_{2},\) and \(\mathrm{NO}_{2}\) in order of increasing root-mean-square speed at \(0^{\circ} \mathrm{C}\).

In a mixture of \(\mathrm{CH}_{4}, \mathrm{NH}_{3},\) and \(\mathrm{N}_{2},\) which gas molecules are, on average, moving fastest?

At \(286 \mathrm{K},\) three gases, \(\mathrm{A}, \mathrm{B},\) and \(\mathrm{C},\) have root-mean-square speeds of \(360 \mathrm{m} / \mathrm{s}, 441 \mathrm{m} / \mathrm{s},\) and \(472 \mathrm{m} / \mathrm{s},\) respectively. Which gas is \(\mathrm{O}_{2} ?\)

Determine the root-mean-square speed of \(\mathrm{CO}_{2}\) molecules that have an average kinetic energy of \(4.2 \times 10^{-21} \mathrm{J}\) per molecule.

The root-mean-square speed of He gas at \(300 \mathrm{K}\) is \(1.370 \times 10^{3} \mathrm{m} / \mathrm{s} .\) Sketch a graph of \(u_{\mathrm{rms}, \mathrm{He}}\) versus \(T\) for \(T=300,450,600,750,\) and \(900 \mathrm{K} .\) Is the graph linear?

The root-mean-square speed of \(\mathrm{N}_{2}\) gas at \(300 \mathrm{K}\) is \(516.8 \mathrm{m} / \mathrm{s}\) Why doesn't doubling the temperature also double \(u_{\mathrm{rms}, \mathrm{N}_{2}} ?\)

What is the ratio of the root-mean-square speed of \(\mathrm{D}_{2}\) to that of \(\mathrm{H}_{2}\) at constant temperature?

Enriching Uranium The two isotopes of uranium, \(^{238} \mathrm{U}\) and \(^{235} \mathrm{U},\) can be separated by diffusion of the corresponding UF \(_{6}\) gases. What is the ratio of the root-mean-square speed of \(^{238} \mathrm{UF}_{6}\) to that of \(^{235} \mathrm{UF}_{6}\) at constant temperature?

A student measured the relative rate of effusion of carbon dioxide and propane, \(\mathrm{C}_{3} \mathrm{H}_{8},\) and found that they effuse at exactly the same rate. Did the student make a mistake?

The density of Ne at \(760 \mathrm{mmHg}\) is exactly half its density at 2.00 atm at constant temperature. Is the root-meansquare speed of Ne at 2.00 atm half, twice, or the same as \(u_{\mathrm{rms}, \mathrm{Ne}}\) at \(760 \mathrm{mmH} \mathrm{g} ?\)

An unknown pure gas X effuses at half the rate of effusion of \(\mathrm{O}_{2}\) at the same temperature and pressure. What is the molar mass of gas X?

Radon and helium are both by-products of the radioactive decay of uranium minerals. A fresh sample of carnotite, \(\mathrm{K}_{2}\left(\mathrm{UO}_{2}\right)_{2}\left(\mathrm{VO}_{4}\right)_{2}\) \(3 \mathrm{H}_{2} \mathrm{O},\) 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?

During photosynthesis, green plants preferentially use \(^{12} \mathrm{CO}_{2}\) over \(^{13} \mathrm{CO}_{2}\) in making sugars, and food scientists can frequently determine the source of sugars used in foods on the basis of the ratio of \(^{12} \mathrm{C}\) to \(^{13} \mathrm{C}\) in a sample. a. Calculate the relative rates of diffusion of \(^{13} \mathrm{CO}_{2}\) and \(^{12} \mathrm{CO}_{2}\) b. Specify which gas diffuses faster.

At a fixed temperature, how much faster does NO effuse than \(\mathrm{NO}_{2} ?\)

One balloon was filled with \(\mathrm{H}_{2},\) another with He. The person responsible for filling them neglected to label them. After 24 h the volumes of both balloons had decreased but by different amounts. Which balloon contained hydrogen?

Rearrange the van der Waals equation to solve for \(P .\) Why is the pressure exerted by a real gas lower than the pressure for an ideal gas at the same temperature and volume?

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