Chapter 6

When solid \(\mathrm{KClO}_{3}\) is heated strongly, it decomposes to form solid potassium chloride, \(\mathrm{KCl}\), and \(\mathrm{O}_{2}\) gas. \(\mathrm{A}\) \(0.415 \mathrm{g}\) sample of impure \(\mathrm{KClO}_{3}\) is heated strongly and the \(\mathrm{O}_{2}\) gas produced by the decomposition is collected over water. When the wet \(\mathrm{O}_{2}\) gas is cooled back to \(26^{\circ} \mathrm{C}\), the total volume is \(229 \mathrm{mL}\) and the total pressure is 323 Torr. What is the mass percentage of \(\mathrm{KClO}_{3}\) in the original sample? Assume that none of the impurities produce oxygen on heating. The vapor pressure of water is 25.22 Torr at \(26^{\circ} \mathrm{C}\).

Calculate \(u_{\mathrm{rms}},\) in meters per second, for \(\mathrm{Cl}_{2}(\mathrm{g})\) molecules at \(30^{\circ} \mathrm{C}\)

The \(u_{\mathrm{rms}}\) of \(\mathrm{H}_{2}\) molecules at \(273 \mathrm{K}\) is \(1.84 \times 10^{3} \mathrm{m} / \mathrm{s}\) At what temperature is \(u_{\mathrm{rms}}\) for \(\mathrm{H}_{2}\) twice this value?

Determine \(u_{\mathrm{m}}, \bar{u},\) and \(u_{\mathrm{rms}}\) for a group of ten automobiles clocked by radar at speeds of 38,44,45,48,50 \(55,55,57,58,\) and \(60 \mathrm{mi} / \mathrm{h},\) respectively.

Calculate the average kinetic energy, \(\bar{e}_{k},\) for \(\mathrm{O}_{2}(\mathrm{g})\) at \(298 \mathrm{K}\) and \(1.00 \mathrm{atm}\)

Calculate the total kinetic energy, in joules, of \(155 \mathrm{g} \mathrm{N}_{2}(\mathrm{g})\) at \(25^{\circ} \mathrm{C}\) and 1.00 atm. \([\text {Hint}:\) First calculate the average kinetic energy, \(\bar{e}_{k}\).

A sample of \(\mathrm{N}_{2}(\mathrm{g})\) effuses through a tiny hole in \(38 \mathrm{s}\) What must be the molar mass of a gas that requires \(64 \mathrm{s}\) to effuse under identical conditions?

What are the ratios of the diffusion rates for the pairs of gases (a) \(\mathrm{N}_{2}\) and \(\mathrm{O}_{2} ;\) (b) \(\mathrm{H}_{2} \mathrm{O}\) and \(\mathrm{D}_{2} \mathrm{O}\) \(\left(\mathrm{D}=\text { deuterium, i.e., }_{1}^{2} \mathrm{H}\right) ;\) (c) \(^{14} \mathrm{CO}_{2}\) and \(^{12} \mathrm{CO}_{2}\) (d) \(^{235} \mathrm{UF}_{6}\) and \(^{238} \mathrm{UF}_{6} ?\)

Explain why it is necessary to include the density of \(\mathrm{Hg}(1)\) and the value of the acceleration due to gravity, \(g,\) in a precise definition of a millimeter of mercury (page 194 ).

A compound is \(85.6 \%\) carbon by mass. The rest is hydrogen. When \(10.0 \mathrm{g}\) of the compound is evaporated at \(50.0^{\circ} \mathrm{C},\) the vapor occupies \(6.30 \mathrm{L}\) at \(1.00 \mathrm{atm}\) pressure. What is the molecular formula of the compound?

A 0.7178 g sample of a hydrocarbon occupies a volume of \(390.7 \mathrm{mL}\) at \(65.0^{\circ} \mathrm{C}\) and \(99.2 \mathrm{kPa}\). When the sample is burned in excess oxygen, \(2.4267 \mathrm{g} \mathrm{CO}_{2}\) and \(0.4967 \mathrm{g} \mathrm{H}_{2} \mathrm{O}\) are obtained. What is the molecular formula of the hydrocarbon? Write a plausible structural formula for the molecule.

A 3.05 g sample of \(\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{s})\) is introduced into an evacuated 2.18 L flask and then heated to \(250^{\circ} \mathrm{C}\).What is the total gas pressure, in atmospheres, in the flask at \(250^{\circ} \mathrm{C}\) when the \(\mathrm{NH}_{4} \mathrm{NO}_{3}\) has completely decomposed? $$\mathrm{NH}_{4} \mathrm{NO}_{3}(\mathrm{s}) \longrightarrow \mathrm{N}_{2} \mathrm{O}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$

Ammonium nitrite, \(\mathrm{NH}_{4} \mathrm{NO}_{2}\), decomposes according to the chemical equation below. $$\mathrm{NH}_{4} \mathrm{NO}_{2}(\mathrm{s}) \longrightarrow \mathrm{N}_{2}(\mathrm{g})+2 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$ What is the total volume of products obtained when \(128 \mathrm{g} \mathrm{NH}_{4} \mathrm{NO}_{2}\) decomposes at \(819^{\circ} \mathrm{C}\) and \(101 \mathrm{kPa} ?\)

A mixture of \(1.00 \mathrm{g} \mathrm{H}_{2}\) and \(8.60 \mathrm{g} \mathrm{O}_{2}\) is introduced into a 1.500 L flask at \(25^{\circ} \mathrm{C}\). When the mixture is ignited, an explosive reaction occurs in which water is the only product. What is the total gas pressure when the flask is returned to \(25^{\circ} \mathrm{C} ?\) (The vapor pressure of water at \(25^{\circ} \mathrm{C}\) is \(23.8 \mathrm{mmHg}\).)

In the reaction of \(\mathrm{CO}_{2}(\mathrm{g})\) and solid sodium peroxide \(\left(\mathrm{Na}_{2} \mathrm{O}_{2}\right),\) solid sodium carbonate \(\left(\mathrm{Na}_{2} \mathrm{CO}_{3}\right)\) and oxy- gen gas are formed. This reaction is used in submarines and space vehicles to remove expired \(\mathrm{CO}_{2}(\mathrm{g})\) and to generate some of the \(\mathrm{O}_{2}(\mathrm{g})\) required for breathing. Assume that the volume of gases exchanged in the lungs equals \(4.0 \mathrm{L} / \mathrm{min},\) the \(\mathrm{CO}_{2}\) content of expired air is \(3.8 \% \mathrm{CO}_{2}\) by volume, and the gases are at \(25^{\circ} \mathrm{C}\) and \(735 \mathrm{mmHg}\). If the \(\mathrm{CO}_{2}(\mathrm{g})\) and \(\mathrm{O}_{2}(\mathrm{g})\) in the above reaction are measured at the same temperature and pressure, (a) how many milliliters of \(\mathrm{O}_{2}(\mathrm{g})\) are produced per minute and \((\mathrm{b})\) at what rate is the \(\mathrm{Na}_{2} \mathrm{O}_{2}(\mathrm{s})\) consumed, in grams per hour?

What is the partial pressure of \(\mathrm{Cl}_{2}(\mathrm{g}),\) in millimeters of mercury, at \(0.00^{\circ} \mathrm{C}\) and 1.00 atm in a gaseous mixture that consists of \(46.5 \% \mathrm{N}_{2}, 12.7 \% \mathrm{Ne},\) and \(40.8 \%\) \(\mathrm{Cl}_{2},\) by mass?

A gaseous mixture of He and \(\mathrm{O}_{2}\) has a density of \(0.518 \mathrm{g} / \mathrm{L}\) at \(25^{\circ} \mathrm{C}\) and \(721 \mathrm{mm} \mathrm{Hg} .\) What is the mass percent He in the mixture?

When working with a mixture of gases, it is sometimes convenient to use an apparent molar mass (a weightedaverage molar mass). Think in terms of replacing the mixture with a hypothetical single gas. What is the apparent molar mass of air, given that air is \(78.08 \% \mathrm{N}_{2}\) \(20.95 \% \mathrm{O}_{2,0.93 \%} \mathrm{Ar}_{\left(\text {and } 0.036 \% \mathrm{CO}_{2},\text { by volume? } \right.}\)

Gas cylinder A has a volume of 48.2 L and contains \(\mathrm{N}_{2}(\mathrm{g})\) at 8.35 atm at \(25^{\circ} \mathrm{C} .\) Gas cylinder \(\mathrm{B},\) of unknown volume, contains \(\mathrm{He}(\mathrm{g})\) at 9.50 atm and \(25^{\circ} \mathrm{C} .\) When the two cylinders are connected and the gases mixed, the pressure in each cylinder becomes 8.71 atm. What is the volume of cylinder \(\mathrm{B} ?\)

The heat required to sustain animals while they hibernate comes from the biochemical combustion of fatty acids, such as arachidonic acid, \(\mathrm{C}_{20} \mathrm{H}_{32} \mathrm{O}_{2}\) What volume of air, measured at \(298 \mathrm{K}\) and \(1.00 \mathrm{atm}\) is required to burn \(2.00 \mathrm{kg} \mathrm{C}_{20} \mathrm{H}_{32} \mathrm{O}_{2} ?\) Air is approximately \(78.1 \% \mathrm{N}_{2}\) and \(20.9 \% \mathrm{O}_{2},\) by volume. Other gases make up the remaining \(1.0 \%\)

A mixture of \(\mathrm{H}_{2}(\mathrm{g})\) and \(\mathrm{O}_{2}(\mathrm{g})\) is prepared by electrolyzing \(1.32 \mathrm{g}\) water, and the mixture of gases is collected over water at \(30^{\circ} \mathrm{C}\) and \(748 \mathrm{mmHg} .\) The volume of "wet" gas obtained is 2.90 L. What must be the vapor pressure of water at \(30^{\circ} \mathrm{C} ?\) $$2 \mathrm{H}_{2} \mathrm{O}(1) \stackrel{\text { electrolysis }}{\longrightarrow} 2 \mathrm{H}_{2}(\mathrm{g})+\mathrm{O}_{2}(\mathrm{g})$$

Aluminum (Al) and iron (Fe) each react with hydrochloric acid solution (HCl) to produce a chloride salt and hydrogen gas, \(\mathrm{H}_{2}(\mathrm{g}) .\) A \(0.1924 \mathrm{g}\) sample of a mixture of \(\mathrm{Al}\) and \(\mathrm{Fe}\) is treated with excess \(\mathrm{HCl}\) solution. A volume of \(159 \mathrm{mL}\) of \(\mathrm{H}_{2}\) gas is collected over water at \(19.0^{\circ} \mathrm{C}\) and 841 Torr. What is the percent (by mass) of Fe in the mixture? The vapor pressure of water at \(19.0^{\circ} \mathrm{C}\) is 16.5 Torr.

A 0.168 L sample of \(\mathrm{O}_{2}(\mathrm{g})\) is collected over water at \(26^{\circ} \mathrm{C}\) and a barometric pressure of \(737 \mathrm{mm} \mathrm{Hg}\). In the gas that is collected, what is the percent water vapor (a) by volume; (b) by number of molecules; (c) by mass? (Vapor pressure of water at \(26^{\circ} \mathrm{C}=25.2 \mathrm{mmHg}\).)

Chlorine dioxide, \(\mathrm{ClO}_{2}\), is sometimes used as a chlorinating agent for water treatment. It can be prepared from the reaction below: \(\mathrm{Cl}_{2}(\mathrm{g})+4 \mathrm{NaClO}(\mathrm{aq}) \longrightarrow 4 \mathrm{NaCl}(\mathrm{aq})+2 \mathrm{ClO}_{2}(\mathrm{g})\) In an experiment, \(1.0 \mathrm{L} \mathrm{Cl}_{2}(\mathrm{g}),\) measured at \(10.0^{\circ} \mathrm{C}\) and 4.66 atm, is dissolved in 0.750 L of 2.00 M \(\mathrm{NaClO}(\mathrm{aq}) .\) If \(25.9 \mathrm{g}\) of pure \(\mathrm{ClO}_{2}\) is obtained, then what is the percent vield for this experiment?

The amount of ozone, \(\mathrm{O}_{3}\), in a mixture of gases can be determined by passing the mixture through a solution of excess potassium iodide, KI. Ozone reacts with the iodide ion as follows: $$\begin{aligned} \mathrm{O}_{3}(\mathrm{g})+3 \mathrm{I}^{-}(\mathrm{aq})+\mathrm{H}_{2} \mathrm{O}(1) & \longrightarrow \\ \mathrm{O}_{2}(\mathrm{g})+\mathrm{I}_{3}^{-}(\mathrm{aq}) &+2 \mathrm{OH}^{-}(\mathrm{aq}) \end{aligned}$$ The amount of \(I_{3}^{-}\) produced is determined by titrating with thiosulfate ion, \(\mathrm{S}_{2} \mathrm{O}_{3}^{2-}:\) $$\mathrm{I}_{3}^{-}(\mathrm{aq})+2 \mathrm{S}_{2} \mathrm{O}_{3}^{2-}(\mathrm{aq}) \longrightarrow 3 \mathrm{I}^{-}(\mathrm{aq})+\mathrm{S}_{4} \mathrm{O}_{6}^{2-}(\mathrm{aq})$$ A mixture of gases occupies a volume of \(53.2 \mathrm{L}\) at \(18^{\circ} \mathrm{C}\) and \(0.993 \mathrm{atm} .\) The mixture is passed slowly through a solution containing an excess of KI to ensure that all the ozone reacts. The resulting solution requires \(26.2 \mathrm{mL}\) of \(0.1359 \mathrm{M} \mathrm{Na}_{2} \mathrm{S}_{2} \mathrm{O}_{3}\) to titrate to the end point. Calculate the mole fraction of ozone in the original mixture.

A nitrogen molecule ( \(\mathrm{N}_{2}\) ) having the average kinetic energy at \(300 \mathrm{K}\) is released from Earth's surface to travel upward. If the molecule could move upward without colliding with other molecules, then how high would it go before coming to rest? Give your answer in kilometers. [Hint: When the molecule comes to rest, the potential energy of the molecule will be \(m g h\) where \(m\) is the molecular mass in kilograms, \(g=9.81 \mathrm{m} \mathrm{s}^{-2}\) is the acceleration due to gravity, and \(h\) is the height, in meters, above Earth's surface.]

If the van der Waals equation is solved for volume, a cubic equation is obtained. (a) Derive the equation below by rearranging equation (6.26). \(V^{3}-n\left(\frac{R T+b P}{P}\right) V^{2}+\left(\frac{n^{2} a}{P}\right) V-\frac{n^{3} a b}{P}=0\) (b) What is the volume, in liters, occupied by \(185 \mathrm{g}\) \(\mathrm{CO}_{2}(\mathrm{g})\) at a pressure of \(125 \mathrm{atm}\) and \(286 \mathrm{K} ?\) For \(\mathrm{CO}_{2}(\mathrm{g})\) \(a=3.61 \mathrm{L}^{2} \mathrm{atm} \mathrm{mol}^{-2}\) and \(b=0.0429 \mathrm{Lmol}^{-1}\) [Hint: Use the ideal gas equation to obtain an estimate of the volume. Then refine your estimate, either by trial and error, or using the method of successive approximations. See Appendix A, pages A5-A6, for a description of the method of successive approximations.

According to the CRC Handbook of Chemistry and Physics (83rd ed.), the molar volume of \(\mathrm{O}_{2}(\mathrm{g})\) is \(0.2168 \mathrm{Lmol}^{-1}\) at \(280 \mathrm{K}\) and \(10 \mathrm{MPa}\). (Note: \(1 \mathrm{MPa}=\) \(\left.1 \times 10^{6} \mathrm{Pa} .\right)\)(a) Use the van der Waals equation to calculate the pressure of one mole of \(\mathrm{O}_{2}(\mathrm{g})\) at \(280 \mathrm{K}\) if the volume is 0.2168 L. What is the \% error in the calculated pressure? The van der Waals constants are \(a=1.382 \mathrm{L}^{2}\) bar \(\mathrm{mol}^{-2}\) and \(b=0.0319 \mathrm{L} \mathrm{mol}^{-1}\) (b) Use the ideal gas equation to calculate the volume of one mole of \(\mathrm{O}_{2}(\mathrm{g})\) at \(280 \mathrm{K}\) and \(10 \mathrm{MPa}\). What is the \% error in the calculated volume?

A \(0.156 \mathrm{g}\) sample of a magnesium-aluminum alloy dissolves completely in an excess of \(\mathrm{HCl}(\mathrm{aq}) .\) The liberated \(\mathrm{H}_{2}(\mathrm{g})\) is collected over water at \(5^{\circ} \mathrm{C}\) when the barometric pressure is 752 Torr. After the gas is collected, the water and gas gradually warm to the prevailing room temperature of \(23^{\circ} \mathrm{C} .\) The pressure of the collected gas is again equalized against the barometric pressure of 752 Torr, and its volume is found to be \(202 \mathrm{mL}\). What is the percent composition of the magnesium-aluminum alloy? (Vapor pressure of water: \(6.54 \mathrm{mmHg}\) at \(5^{\circ} \mathrm{C}\) and \(21.07 \mathrm{mmHg}\) at \(\left.23^{\circ} \mathrm{C}\right)\)

In research that required the careful measurement of gas densities, John Rayleigh, a physicist, found that the density of \(\mathrm{O}_{2}(\mathrm{g})\) had the same value whether the gas was obtained from air or derived from one of its compounds. The situation with \(\mathrm{N}_{2}(\mathrm{g})\) was different, however. The density of \(\mathrm{N}_{2}(\mathrm{g})\) had the same value when the \(\mathrm{N}_{2}(\mathrm{g})\) was derived from any of various compounds, but a different value if the \(\mathrm{N}_{2}(\mathrm{g})\) was extracted from air. In \(1894,\) Rayleigh enlisted the aid of William Ramsay, a chemist, to solve this apparent mystery; in the course of their work they discovered the noble gases. (a) Why do you suppose that the \(\mathrm{N}_{2}(\mathrm{g})\) extracted from liquid air did not have the same density as \(\mathrm{N}_{2}(\mathrm{g})\) obtained from its compounds? (b) Which gas do you suppose had the greater density: \(\mathrm{N}_{2}(\mathrm{g})\) extracted from air or \(\mathrm{N}_{2}(\mathrm{g})\) prepared from nitrogen compounds? Explain. (c) The way in which Ramsay proved that nitrogen gas extracted from air was itself a mixture of gases involved allowing this nitrogen to react with magnesium metal to form magnesium nitride. Explain the significance of this experiment. (d) Calculate the percent difference in the densities at \(0.00^{\circ} \mathrm{C}\) and 1.00 atm of Rayleigh's \(\mathrm{N}_{2}(\mathrm{g})\) extracted from air and \(\mathrm{N}_{2}(\mathrm{g})\) derived from nitrogen compounds. [The volume percentages of the major components of air are \(78.084 \% \mathrm{N}_{2}, 20.946 \% \mathrm{O}_{2}, 0.934 \% \mathrm{Ar},\) and \(0.0379 \% \mathrm{CO}_{2} .\)

The equation \(d / P=M / R T,\) which can be derived from equation \((6.14),\) suggests that the ratio of the density \((d)\) to pressure (P) of a gas at constant temperature should be a constant. The gas density data at the end of this question were obtained for \(\mathrm{O}_{2}(\mathrm{g})\) at various pressures at \(273.15 \mathrm{K}\) (a) Calculate values of \(d / P,\) and with a graph or by other means determine the ideal value of the term \(d / P\) for \(\mathrm{O}_{2}(\mathrm{g})\) at \(273.15 \mathrm{K}\) [Hint: The ideal value is that associated with a perfect (ideal) gas.] (b) Use the value of \(d / P\) from part (a) to calculate a precise value for the atomic mass of oxygen, and compare this value with that listed on the inside front cover. $$\begin{array}{lllll} P, \mathrm{mmHg}: & 760.00 & 570.00 & 380.00 & 190.00 \\ d, \mathrm{g} / \mathrm{L}: & 1.428962 & 1.071485 & 0.714154 & 0.356985 \end{array}$$

A sounding balloon is a rubber bag filled with \(\mathrm{H}_{2}(\mathrm{g})\) and carrying a set of instruments (the payload). Because this combination of bag, gas, and payload has a smaller mass than a corresponding volume of air, the balloon rises. As the balloon rises, it expands. From the table below, estimate the maximum height to which a spherical balloon can rise given the mass of balloon, \(1200 \mathrm{g} ;\) payload, \(1700 \mathrm{g}\) : quantity of \(\mathrm{H}_{2}(\mathrm{g})\) in balloon, \(120 \mathrm{ft}^{3}\) at \(0.00^{\circ} \mathrm{C}\) and \(1.00 \mathrm{atm}\); diameter of balloon at maximum height, 25 ft. Air pressure and temperature as functions of altitude are: $$\begin{array}{ccl} \hline \text { Altitude, km } & \text { Pressure, mb } & \text { Temperature, } \mathrm{K} \\ \hline 0 & 1.0 \times 10^{3} & 288 \\ 5 & 5.4 \times 10^{2} & 256 \\ 10 & 2.7 \times 10^{2} & 223 \\ 20 & 5.5 \times 10^{1} & 217 \\ 30 & 1.2 \times 10^{1} & 230 \\ 40 & 2.9 \times 10^{0} & 250 \\ 50 & 8.1 \times 10^{-1} & 250 \\ 60 & 2.3 \times 10^{-1} & 256 \\ \hline \end{array}$$

In your own words, define or explain each term or symbol. (a) atm; (b) STP; (c) \(R ;\) (d) partial pressure; (e) \(u_{\mathrm{rms}}\).

Briefly describe each concept or process: (a) absolute zero of temperature; (b) collection of a gas over water; (c) effusion of a gas; (d) law of combining volumes.

Explain the important distinctions between (a) barometer and manometer; (b) Celsius and Kelvin temperature; (c) ideal gas equation and general gas equation; (d) ideal gas and real gas.

For a fixed amount of gas at a fixed pressure, changing the temperature from \(100.0^{\circ} \mathrm{C}\) to \(200 \mathrm{K}\) causes the gas volume to (a) double; (b) increase, but not to twice its original value; (c) decrease; (d) stay the same.

Which of the following choices represents the molar volume of an ideal gas at \(25^{\circ} \mathrm{C}\) and 1.5 atm? (a) \((298 \times 1.5 / 273) \times 22.4 \mathrm{L} ;\) (b) \(22.4 \mathrm{L}\) (c) \((273 \times 1.5 / 298) \times 22.4 \mathrm{L}\) (d) \([298 /(273 \times 1.5)] \times 22.4 \mathrm{L}\) (e) \([273 /(298 \times 1.5)] \times 22.4 \mathrm{L}\)

The gas with the greatest density at STP is (a) \(\mathrm{N}_{2} \mathrm{O}\) (b) \(\mathrm{Kr} ;\) (c) \(\mathrm{SO}_{3} ;\) (d) \(\mathrm{Cl}_{2}\).

If the Kelvin temperature of a sample of ideal gas doubles (e.g., from 200 K to 400 K), what happens to the root-mean-square speed, \(u_{\mathrm{rms}}\) ? (a) \(u_{\mathrm{rms}}\) increases by a factor of \(\sqrt{2} ;\) (b) \(u_{\mathrm{rms}}\) increases by a factor of \(2 ;(\mathrm{c}) u_{\mathrm{rms}}\) decreases by a factor of 2 (d) \(u_{\mathrm{rms}}\) increases by a factor of \(4 ;\) (e) \(u_{\mathrm{rms}}\) decreases by a factor of 4.

Consider the statements (a) to (e) below. Assume that \(\mathrm{H}_{2}(\mathrm{g})\) and \(\mathrm{O}_{2}(\mathrm{g})\) behave ideally. State whether each of the following statements is true or false. For each false statement, explain how you would change it to make it a true statement. (a) Under the same conditions of temperature and pressure, the average kinetic energy of \(\mathrm{O}_{2}\) molecules is less than that of \(\mathrm{H}_{2}\) molecules. (b) Under the same conditions of temperature and pressure, \(\mathrm{H}_{2}\) molecules move faster, on average, than \(\mathrm{O}_{2}\) molecules. (c) The volume of \(1.00 \mathrm{mol}\) of \(\mathrm{H}_{2}(\mathrm{g})\) at \(25.0^{\circ} \mathrm{C}\) 1.00 atm is \(22.4 \mathrm{L}\) (d) The volume of \(2.0 \mathrm{g} \mathrm{H}_{2}(\mathrm{g})\) is equal to the volume of \(32.0 \mathrm{g} \mathrm{O}_{2}(\mathrm{g}),\) at the same temperature and pressure. (e) In a mixture of \(\mathrm{H}_{2}\) and \(\mathrm{O}_{2}\) gases, with partial pressures \(P_{\mathrm{H}_{2}}\) and \(P_{\mathrm{O}_{2}^{\prime}}\) respectively, the total pressure is the larger of \(P_{\mathrm{H}_{2}}\) and \(P_{\mathrm{O}_{2}}\).

A sample of \(\mathrm{O}_{2}(\mathrm{g})\) is collected over water at \(23^{\circ} \mathrm{C}\) and a barometric pressure of 751 Torr. The vapor pressure of water at \(23^{\circ} \mathrm{C}\) is \(21 \mathrm{mmHg}\). The partial pressure of \(\mathrm{O}_{2}(\mathrm{g})\) in the sample collected is (a) \(21 \mathrm{mmHg}_{i}\) (b) 751 Torr; \((\mathrm{c}) 0.96 \mathrm{atm} ;\) (d) \(1.02 \mathrm{atm}\).

At \(0^{\circ} \mathrm{C}\) and 0.500 atm, 4.48 L of gaseous \(\mathrm{NH}_{3}\) (a) contains \(6.02 \times 10^{22}\) molecules; (b) has a mass of \(17.0 \mathrm{g} ;(\mathrm{c})\) contains \(0.200 \mathrm{mol} \mathrm{NH}_{3} ;\) (d) has a mass of \(3.40 \mathrm{g}\).

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 \(1.60 \mathrm{g} \mathrm{O}_{2} ;(\mathrm{b})\) add \(0.60 \mathrm{g} \mathrm{He}(\mathrm{g}) ;(\mathrm{c})\) add \(2.00 \mathrm{g} \mathrm{He}(\mathrm{g})\) (d) release \(0.80 \mathrm{g} \mathrm{O}_{2}(\mathrm{g})\)

Carbon monoxide, \(\mathrm{CO}\), and hydrogen react according to the equation below. $$3 \mathrm{CO}(\mathrm{g})+7 \mathrm{H}_{2}(\mathrm{g}) \longrightarrow \mathrm{C}_{3} \mathrm{H}_{8}(\mathrm{g})+3 \mathrm{H}_{2} \mathrm{O}(\mathrm{g})$$ What volume of which reactant gas remains if \(12.0 \mathrm{LCO}(\mathrm{g})\) and \(25.0 \mathrm{L} \mathrm{H}_{2}(\mathrm{g})\) are allowed to react? Assume that the volumes of both gases are measured at the same temperature and pressure.

Under which conditions is \(\mathrm{Cl}_{2}\) most likely to behave like an ideal gas? Explain. (a) \(100^{\circ} \mathrm{C}\) and \(10.0 \mathrm{atm}\) (b) \(0^{\circ} \mathrm{C}\) and 0.50 atm; \((\mathrm{c}) 200^{\circ} \mathrm{C}\) and \(0.50 \mathrm{atm}\) (d) \(400^{\circ} \mathrm{C}\) and \(10.0 \mathrm{atm}\).

Explain why the height of the mercury column in a barometer is independent of the diameter of the barometer tube.

A gaseous hydrocarbon that is \(82.7 \%\) C and \(17.3 \%\) H by mass has a density of \(2.35 \mathrm{g} / \mathrm{L}\) at \(25^{\circ} \mathrm{C}\) and 752 Torr. What is the molecular formula of this hydrocarbon?

Appendix E describes a useful study aid known as concept mapping. Using the method presented in Appendix \(\mathrm{E}\), construct a concept map illustrating the different concepts to show the relationships among all the gas laws described in this chapter.