Chapter 10

Mars has an average atmospheric pressure of 709 pa. Would it be easier or harder to drink from a straw on Mars than on Earth? Explain.

Consider the sample of gas depicted here. What would the drawing look like if the volume and temperature remained constant while you removed enough of the gas to decrease the pressure by a factor of \(2 ?\) [Section 10.3\(]\) (a) It would contain the same number of molecules. (b) It would contain half as many molecules. (c) It would contain twice as many molecules. (d) There is insufficient data to say.

Imagine that the reaction \(2 \mathrm{CO}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{CO}_{2}(g)\) occurs in a container that has a piston that moves to maintain a constant pressure when the reaction occurs at constant temperature. Which of the following statements describes how the volume of the container changes due to the reaction: (a) the volume increases by \(50 \%,(\mathbf{b})\) the volume increases by \(33 \%\), (c) the volume remains constant, (d) the volume decreases by \(33 \%,(\mathbf{e})\) the volume decreases by \(50 \% .\)

Suppose you have a fixed amount of an ideal gas at a constant volume. If the pressure of the gas is doubled while the volume is held constant, what happens to its temperature?

Which of the following statements is false? (a) Gases are far less dense than liquids. (b) Gases are far more compressible than liquids. (c) Because liquid water and liquid carbon tetrachloride do not mix, neither do their vapors. (d) The volume occupied by a gas is determined by the volume of its container.

(a) Are you more likely to see the density of a gas reported in \(\mathrm{g} / \mathrm{mL}, \mathrm{g} / \mathrm{L},\) or \(\mathrm{kg} / \mathrm{cm}^{3} ?(\mathbf{b})\) Which units are appropriate for expressing atmospheric pressures, \(\mathrm{N}, \mathrm{Pa}, \mathrm{atm}, \mathrm{kg} / \mathrm{m}^{2} ?\) (c) Which is most likely to be a gas at room temperature and ordinary atmospheric pressure, \(\mathrm{F}_{2}, \mathrm{Br}_{2}, \mathrm{~K}_{2} \mathrm{O}\)

A person weighing \(75 \mathrm{~kg}\) is standing on a threelegged stool. The stool momentarily tilts so that the entire weight is on one foot. If the contact area of each foot is \(5.0 \mathrm{~cm}^{2},\) calculate the pressure exerted on the underlying surface in (a) bars, \((\mathbf{b})\) atmospheres, and (c) pounds per square inch.

A set of bookshelves rests on a hard floor surface on four legs, each having a cross-sectional dimension of \(4.0 \times 5.0 \mathrm{~cm}\) in contact with the floor. The total mass of the shelves plus the books stacked on them is \(200 \mathrm{~kg}\). Calculate the pressure in atmospheres exerted by the shelf footings on the surface.

(a) How high in meters must a column of ethanol be to exert a pressure equal to that of a \(100-\mathrm{mm}\) column of mercury? The density of ethanol is \(0.79 \mathrm{~g} / \mathrm{mL}\), whereas that of mercury is \(13.6 \mathrm{~g} / \mathrm{mL}\). (b) What pressure, in atmospheres, is exerted on the body of a diver if she is \(10 \mathrm{~m}\) below the surface of the water when the atmospheric pressure is \(100 \mathrm{kPa}\) ? Assume that the density of the water is \(1.00=1.00 \times 10^{3} \mathrm{~kg} / \mathrm{m}^{3}\). The gravitational constant is \(9.81 \mathrm{~m} / \mathrm{s}^{2}\), and \(1 \mathrm{~Pa}=1 \mathrm{~kg} / \mathrm{ms}^{2}\).

The highest barometric pressure ever recorded was 823.7 torr at Agata in Siberia, Russia on December 31,1968 . Convert this pressure to \((\mathbf{a})\) atm, (b) \(\mathrm{mm} \mathrm{Hg}\) (c) pascals, (d) bars, (e) psi.

Perform the following conversions: (a) 0.912 atm to torr, (b) 0.685 bar to kilopascals, (c) \(655 \mathrm{~mm}\) Hg to atmospheres, (d) \(1.323 \times 10^{5}\) Pa to atmospheres, (e) 2.50 atm to psi.

In the United States, barometric pressures are generally reported in inches of mercury (in. Hg). On a beautiful summer day in Chicago, the barometric pressure is 30.45 in. Hg. (a) Convert this pressure to torr. (b) Convert this pressure to atm.

Hurricane Wilma of 2005 is the most intense hurricane on record in the Atlantic basin, with a low-pressure reading of 882 mbar (millibars). Convert this reading into (a) atmospheres, \((\mathbf{b})\) torr, and \((\mathbf{c})\) inches of \(\mathrm{Hg}\).

An open-end manometer containing mercury is connected to a container of gas, as depicted in Sample Exercise 10.2 . What is the pressure of the enclosed gas in torr in each of the following situations? (a) The mercury in the arm attached to the gas is \(15.4 \mathrm{~mm}\) higher than in the one open to the atmosphere; atmospheric pressure is \(0.985 \mathrm{~atm}\). (b) The mercury in the arm attached to the gas is \(12.3 \mathrm{~mm}\) lower than in the one open to the atmosphere; atmospheric pressure is \(0.99 \mathrm{~atm}\)

You have a gas at \(25^{\circ} \mathrm{C}\) confined to a cylinder with a movable piston. Which of the following actions would double the gas pressure? (a) Lifting up on the piston to double the volume while keeping the temperature constant; (b) Heating the gas so that its temperature rises from \(25^{\circ} \mathrm{C}\) to \(50^{\circ} \mathrm{C}\), while keeping the volume constant; (c) Pushing down on the piston to halve the volume while keeping the temperature constant.

A fixed quantity of gas at \(25^{\circ} \mathrm{C}\) exhibits a pressure of \(99 \mathrm{kPa}\) and occupies a volume of \(4.00 \mathrm{~L}\). (a) Calculate the volume the gas will occupy if the pressure is increased to \(202.6 \mathrm{kPa}\) whilethe temperature is held constant. (b) Calculate the volume the gas will occupy if the temperature is increased to \(100^{\circ} \mathrm{C}\) while the pressure is held constant.

(a) Amonton's law expresses the relationship between pressure and temperature. Use Charles's law and Boyle's law to derive the proportionality relationship between \(P\) and \(T .(\mathbf{b})\) If a car tire is filled to a pressure of 220.6 kPa measured at \(24^{\circ} \mathrm{C}\), what will be the tire pressure if the tires heat up to \(49^{\circ} \mathrm{C}\) during driving?

In the contact process, sulfur dioxide and oxygen gas react to form sulfur trioxide as follows: $$ 2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{SO}_{3}(g) $$ At a certain temperature and pressure, \(50 \mathrm{~L}\) of \(\mathrm{SO}_{2}\) reacts with \(25 \mathrm{~L}\) of \(\mathrm{O}_{2}\). If all the \(\mathrm{SO}_{2}\) and \(\mathrm{O}_{2}\) are consumed, what volume of \(\mathrm{SO}_{3}\), at the same temperature and pressure, will be produced?

To derive the ideal-gas equation, we assume that the volume of a gas's atoms/molecules can be neglected. Given that the atomic radius of argon \(0.097 \mathrm{nm},\) and knowing that a sphere has a volume of \(4 \pi r^{3} / 3,\) calculate the fraction of space that Ar atoms occupy in a sample of argon at STP.

Suppose you are given two 2 -L flasks and told that one contains a gas of molar mass 28 , the other a gas of molar mass 56 , both at the same temperature and pressure. The mass of gas in the flask \(A\) is \(1.0 \mathrm{~g}\) and the mass of gas in the flask \(\mathrm{B}\) is \(2.0 \mathrm{~g}\). Which flask contains the gas of molar mass \(28,\) and which contains the gas of molar mass \(56 ?\)

Suppose you are given two flasks at the same temperature, one of volume \(2 \mathrm{~L}\) and the other of volume \(3 \mathrm{~L}\). The 2 -L flask contains \(4.8 \mathrm{~g}\) of gas, and the gas pressure is \(x \mathrm{kPa}\). The 3 -L flask contains \(0.36 \mathrm{~g}\) of gas, and the gas pressure is \(0.1 x\). Do the two gases have the same molar mass? If not, which contains the gas of higher molar mass?

Calculate each of the following quantities for an ideal gas: (a) the volume of the gas, in liters, if \(1.50 \mathrm{~mol}\) has a pressure of \(126.7 \mathrm{kPa}\) at a temperature of \(-6^{\circ} \mathrm{C} ;(\mathbf{b})\) the absolute temperature of the gas at which \(3.33 \times 10^{-3}\) mol occupies \(478 \mathrm{~mL}\) at \(99.99 \mathrm{kPa} ;(\mathbf{c})\) the pressure, in pascals, if \(0.00245 \mathrm{~mol}\) occupies \(413 \mathrm{~mL}\) at \(138^{\circ} \mathrm{C} ;\) (d) the quantity of gas, in moles, if \(126.5 \mathrm{~L}\) at \(54^{\circ} \mathrm{C}\) has a pressure of \(11.25 \mathrm{kPa} .\)

The Goodyear blimps, which frequently fly over sporting events, hold approximately \(4955 \mathrm{~m}^{3}\) of helium. If the gas is at \(23^{\circ} \mathrm{C}\) and \(101.33 \mathrm{kPa}\), what mass of helium is in a blimp?

A neon sign is made of glass tubing whose inside diameter is \(3.0 \mathrm{~cm}\) and length is \(10.0 \mathrm{~m}\). If the sign contains neon at a pressure of \(265 \mathrm{~Pa}\) at \(30^{\circ} \mathrm{C}\), how many grams of neon are in the sign?

(a) Calculate the number of molecules in a deep breath of air whose volume is \(2.25 \mathrm{~L}\) at body temperature, \(37^{\circ} \mathrm{C},\) and a pressure of \(97.99 \mathrm{kPa} .(\mathbf{b})\) The adult blue whale has a lung capacity of \(5.0 \times 10^{3} \mathrm{~L}\). Calculate the mass of air (assume an average molar mass of \(28.98 \mathrm{~g} / \mathrm{mol}\) ) contained in an adult blue whale's lungs at \(0.0^{\circ} \mathrm{C}\) and \(101.33 \mathrm{kPa}\), assuming the air behaves ideally.

(a) If the pressure exerted by ozone, \(\mathrm{O}_{3}\), in the stratosphere is \(304 \mathrm{~Pa}\) and the temperature is \(250 \mathrm{~K}\), how many ozone molecules are in a liter? (b) Carbon dioxide makes up approximately \(0.04 \%\) of Earth's atmosphere. If you collect a \(2.0-\mathrm{L}\) sample from the atmosphere at sea level ( \(101.33 \mathrm{kPa}\) ) on a warm day \(\left(27^{\circ} \mathrm{C}\right),\) how many \(\mathrm{CO}_{2}\) molecules are in your sample?

A scuba diver's tank contains \(2.50 \mathrm{~kg}\) of \(\mathrm{O}_{2}\) compressed into a volume of 11.0 L. (a) Calculate the gas pressure inside the tank at \(10^{\circ} \mathrm{C}\). (b) What volume would this oxygen occupy at \(25^{\circ} \mathrm{C}\) and \(101.33 \mathrm{kPa} ?\)

A 50.0 g sample of solid \(\mathrm{CO}_{2}\) (dry ice) is added at \(-100^{\circ} \mathrm{C}\) to an evacuated (all of the gas removed) container with a volume of \(5.0 \mathrm{~L}\). If the container is sealed and then allowed to warm to room temperature \(\left(25^{\circ} \mathrm{C}\right)\) so that the entire solid \(\mathrm{CO}_{2}\) is converted to a gas, what is the pressure inside the container?

A \(334-\mathrm{mL}\) cylinder for use in chemistry lectures contains \(5.225 \mathrm{~g}\) of helium at \(23^{\circ} \mathrm{C}\). How many grams of helium must be released to reduce the pressure to 7.60 MPa assuming ideal gas behavior?

Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of \(\mathrm{Cl}_{2}\) gas is \(8.70 \mathrm{~L}\) at \(119.3 \mathrm{kPa}\) and \(24^{\circ} \mathrm{C}\). (a) How many grams of \(\mathrm{Cl}_{2}\) are in the sample? (b) What volume will the \(\mathrm{Cl}_{2}\) occupy at STP? (c) At what temperature will the volume be \(15.00 \mathrm{~L}\) if the pressure is \(116.8 \mathrm{kPa}\) (d) At what pressure will the volume equal \(5.00 \mathrm{~L}\) if the temperature is \(58^{\circ} \mathrm{C} ?\)

Chlorine is widely used to purify municipal water supplies and to treat swimming pool waters. Suppose that the volume of a particular sample of \(\mathrm{Cl}_{2}\) gas is \(8.70 \mathrm{~L}\) at \(119.3 \mathrm{kPa}\) and \(24^{\circ} \mathrm{C}\). (a) How many grams of \(\mathrm{Cl}_{2}\) are in the sample? (b) What volume will the \(\mathrm{Cl}_{2}\) occupy at STP? (c) At what temperature will the volume be \(15.00 \mathrm{~L}\) if the pressure is \(116.8 \mathrm{kPa}\) (d) At what pressure will the volume equal \(5.00 \mathrm{~L}\) if the temperature is \(58^{\circ} \mathrm{C} ?\)

In an experiment reported in the scientific literature, male cockroaches were made to run at different speeds on a miniature treadmill while their oxygen consumption was measured. In 30 minutes the average cockroach (running at \(0.08 \mathrm{~km} / \mathrm{h})\) consumed \(1.0 \mathrm{~mL}\) of \(\mathrm{O}_{2}\) at \(101.33 \mathrm{kPa}\) pressure and \(20^{\circ} \mathrm{C}\) per gram of insect mass. (a) How many moles of \(\mathrm{O}_{2}\) would be consumed in 1 day by a 6.3 -g cockroach moving at this speed? (b) This same cockroach is caught by a child and placed in a 2.0-L fruit jar with a tight lid. Assuming the same level of continuous activity as in the research, how much of the available \(\mathrm{O}_{2}\) will the cockroach consume in 1 day? (Air is \(21 \mathrm{~mol} \% \mathrm{O}_{2}\).)

The physical fitness of athletes is measured by \({ }^{4} V_{\mathrm{O}_{2}}\) max," which is the maximum volume of oxygen consumed by an individual during incremental exercise (for example, on a treadmill). An average male has a \(V_{\mathrm{O}_{2}}\) max of \(45 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{kg}\) body mass/min, but a world-class male athlete can have a \(V_{\mathrm{O}_{2}}\) max reading of \(88.0 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{kg}\) body mass \(/ \mathrm{min}\). (a) Calculate the volume of oxygen, in \(\mathrm{mL}\), consumed in \(1 \mathrm{hr}\) by an average man who weighs \(85 \mathrm{~kg}\) and has a \(V_{\mathrm{O}_{2}}\) max reading of \(47.5 \mathrm{~mL}\) \(\mathrm{O}_{2} / \mathrm{kg}\) body mass \(/ \mathrm{min} .(\mathbf{b})\) If this man lost \(10 \mathrm{~kg}\), exercised, and increased his \(V_{\mathrm{O}_{2}} \max\) to \(65.0 \mathrm{~mL} \mathrm{O}_{2} / \mathrm{kg}\) body mass \(/ \mathrm{min}\) how many \(\mathrm{mL}\) of oxygen would he consume in \(1 \mathrm{hr}\) ?

Rank the following gases from least dense to most dense at \(101.33 \mathrm{kPa}\) and \(298 \mathrm{~K}: \mathrm{O}_{2}, \mathrm{Ar}, \mathrm{NH}_{3}, \mathrm{HCl}\)

Rank the following gases and vapors from least dense to most dense at \(101.33 \mathrm{kPa}\) and \(298 \mathrm{~K}:\) water vapor \(\left(\mathrm{H}_{2} \mathrm{O}(g)\right),\) nitrogen \(\left(\mathrm{N}_{2}\right),\) hydrogen sulfide \(\left(\mathrm{H}_{2} \mathrm{~S}\right)\)

Which of the following statements best explains why a closed balloon filled with helium gas rises in air? (a) Helium is a monatomic gas, whereas nearly all the molecules that make up air, such as nitrogen and oxygen, are diatomic. (b) The average speed of helium atoms is greater than the average speed of air molecules, and the greater speed of collisions with the balloon walls propels the balloon upward. (c) Because the helium atoms are of lower mass than the average air molecule, the helium gas is less dense than air. The mass of the balloon is thus less than the mass of the air displaced by its volume. (d) Because helium has a lower molar mass than the average air molecule, the helium atoms are in faster motion. This means that the temperature of the helium is greater than the air temperature. Hot gases tend to rise.

Which of the following statements best explains why nitrogen gas at STP is less dense than Xe gas at STP? (a) Because Xe is a noble gas, there is less tendency for the Xe atoms to repel one another, so they pack more densely in the gaseous state. (b) Xe atoms have a higher mass than \(\mathrm{N}_{2}\) molecules. Because both gases at STP have the same number of molecules per unit volume, the Xe gas must be denser. (c) The Xe atoms are larger than \(\mathrm{N}_{2}\) molecules and thus take up a larger fraction of the space occupied by the gas. (d) Because the Xe atoms are much more massive than the \(\mathrm{N}_{2}\) molecules, they move more slowly and thus exert less upward force on the gas container and make the gas appear denser.

(a) Calculate the density of dinitrogen tetroxide gas \(\left(\mathrm{N}_{2} \mathrm{O}_{4}\right)\) at \(111.5 \mathrm{kPa}\) and \(0{ }^{\circ} \mathrm{C}\). (b) Calculate the molar mass of a gas if \(2.70 \mathrm{~g}\) occupies \(0.97 \mathrm{~L}\) at \(134.7 \mathrm{~Pa}\) and \(100^{\circ} \mathrm{C}\).

(a) Calculate the density of sulfur hexafluoride gas at 94.26 \(\mathrm{kPa}\) and \(21^{\circ} \mathrm{C}\). (b) Calculate the molar mass of a vapor that has a density of \(7.135 \mathrm{~g} / \mathrm{L}\) at \(12{ }^{\circ} \mathrm{C}\) and \(99.06 \mathrm{kPa}\).

In the Dumas-bulb technique for determining the molar mass of an unknown liquid, you vaporize the sample of a liquid that boils below \(100^{\circ} \mathrm{C}\) in a boiling-water bath and determine the mass of vapor required to fill the bulb. From the following data, calculate the molar mass of the unknown liquid: mass of unknown vapor, \(1.012 \mathrm{~g} ;\) volume of bulb, \(354 \mathrm{~cm}^{3}\); pressure, \(98.93 \mathrm{kPa} ;\) temperature, \(99^{\circ} \mathrm{C}\).

The molar mass of a volatile substance was determined by the Dumas-bulb method described in Exercise 10.53 . The unknown vapor had a mass of \(2.55 \mathrm{~g} ;\) the volume of the bulb was \(500 \mathrm{~mL}\), pressure \(101.33 \mathrm{kPa}\), and temperature \(37^{\circ} \mathrm{C} .\) Calculate the molar mass of the unknown vapor.

Magnesium can be used as a "getter" in evacuated enclosures to react with the last traces of oxygen. (The magnesium is usually heated by passing an electric current through a wire or ribbon of the metal.) If an enclosure of \(5.67 \mathrm{~L}\) has a partial pressure of \(\mathrm{O}_{2}\) of \(7.066 \mathrm{mPa}\) at \(30^{\circ} \mathrm{C},\) what mass of magnesium will react according to the following equation? $$ 2 \mathrm{Mg}(s)+\mathrm{O}_{2}(g) \longrightarrow 2 \mathrm{MgO}(s) $$

Calcium hydride, \(\mathrm{CaH}_{2}\), reacts with water to form hydrogen gas: $$ \mathrm{CaH}_{2}(s)+2 \mathrm{H}_{2} \mathrm{O}(l) \longrightarrow \mathrm{Ca}(\mathrm{OH})_{2}(a q)+2 \mathrm{H}_{2}(g) $$ This reaction is sometimes used to inflate life rafts, weather balloons, and the like, when a simple, compact means of generating \(\mathrm{H}_{2}\) is desired. How many grams of \(\mathrm{CaH}_{2}\) are needed to generate \(145 \mathrm{~L}\) of \(\mathrm{H}_{2}\) gas if the pressure of \(\mathrm{H}_{2}\) is \(110 \mathrm{kPa}\) at \(21^{\circ} \mathrm{C} ?\)

The metabolic oxidation of glucose, \(\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6},\) in our bodies produces \(\mathrm{CO}_{2},\) which is expelled from our lungs as a gas: $$ \mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}(a q)+6 \mathrm{O}_{2}(g) \longrightarrow 6 \mathrm{CO}_{2}(g)+6 \mathrm{H}_{2} \mathrm{O}(l) $$ (a) Calculate the volume of dry \(\mathrm{CO}_{2}\) produced at normal body temperature, \(37^{\circ} \mathrm{C},\) and \(101.33 \mathrm{kPa}\) when \(10.0 \mathrm{~g}\) of glucose is consumed in this reaction. (b) Calculate the volume of oxygen you would need, at \(100 \mathrm{kPa}\) and \(298 \mathrm{~K},\) to completely oxidize \(15.0 \mathrm{~g}\) of glucose.

Consider a mixture of two gases, \(A\) and \(B\), confined in a closed vessel. A quantity of a third gas, \(\mathrm{C}\), is added to the same vessel at the same temperature. How does the addition of gas \(C\) affect the following: (a) the partial pressure of gas \(\mathrm{A},(\mathbf{b})\) the total pressure in the vessel, (c) the mole fraction of gas B?

A mixture containing \(0.50 \mathrm{~mol} \mathrm{H}_{2}(g), 1.00 \mathrm{~mol} \mathrm{O}_{2}(g)\), and 3.50 \(\mathrm{mol} \mathrm{N}_{2}(g)\) is confined in a 25.0-L vessel at \(25^{\circ} \mathrm{C}\). (a) Calculate the total pressure of the mixture. (b) Calculate the partial pressure of each of the gases in the mixture.

A deep-sea diver uses a gas cylinder with a volume of \(10.0 \mathrm{~L}\) and a content of \(51.2 \mathrm{~g}\) of \(\mathrm{O}_{2}\) and \(32.6 \mathrm{~g}\) of He. Calculate the partial pressure of each gas and the total pressure if the temperature of the gas is \(19^{\circ} \mathrm{C}\).

The atmospheric concentration of \(\mathrm{CO}_{2}\) gas is presently 407 ppm (parts per million, by volume; that is, 407 L of every \(10^{6} \mathrm{~L}\) of the atmosphere are \(\mathrm{CO}_{2}\) ). What is the mole fraction of \(\mathrm{CO}_{2}\) in the atmosphere?

A plasma-screen TV contains thousands of tiny cells tilled with a mixture of Xe, Ne, and He gases that emits light of specific wavelengths when a voltage is applied. A particular plasma cell, \(0.900 \mathrm{~mm} \times 0.300 \mathrm{~mm} \times 10.0 \mathrm{~mm}\), contains \(4 \%\) Xe in a 1:1 Ne:He mixture at a total pressure of \(66.66 \mathrm{kPa}\). Calculate the number of Xe, Ne, and He atoms in the cell and state the assumptions you need to make in your calculation.

A piece of dry ice (solid carbon dioxide) with a mass of \(20.0 \mathrm{~g}\) is placed in a 25.0-L vessel that already contains air at \(50.66 \mathrm{kPa}\) and \(25^{\circ} \mathrm{C}\). After the carbon dioxide has totally sublimed, what is the partial pressure of the resultant \(\mathrm{CO}_{2}\) gas, and the total pressure in the container at \(25^{\circ} \mathrm{C} ?\)