CHAPTER 6:

GASES

The following information is often presented on the first page of exams covering this chapter under the heading: “potentially useful information.”

(P + n^{2}a/V^{2})(V - nb) = nRT R = 0.0826 L-atm/mol-K

N = 6.022 x 10^{23} particles per mole STP = 0°C and 1 atm

1 atm = 760 mmHg = 760 torr = 101.325 kPa

Ideal Gases

6-1. Which of the following elements or compounds is most likely to be a gas at room temperature?

(a) a metal such as sodium (Na).

(b) an alloy of two metals such as bronze, which is a mixture of copper (Cu) and tin (Sn).

(c) a salt such as MgO.

(d) a nonmetal such as chlorine (Cl_{2}).

(e) none of these elements or compounds will be a gas at room temperature.

Answer: (d)

6-2. Which graph isn’t a straight line for an ideal gas?

(a) V versus T (n and P constant)

(b) T versus P (n and V constant)

(c) P versus 1/V (n and T constant)

(d) n versus 1/T (P and V constant)

(e) n versus 1/P (V and T constant)

Answer: (e)

6-4. If equal weights of O_{2} and N_{2} are placed in identical containers at the same
temperature, which of the following statements is true? (N = 14.0; O = 16.0 amu)

(a) Both flasks contain the same number of molecules.

(b) The pressure in the flask that contains N_{2} will be greater than the pressure in
the flask that contains O_{2}.

(c) There will be more molecules in the flask that contains O_{2} than the flask that
contains N_{2}.

(d) This question can't be answered unless we know the weights of O_{2} and N_{2} in
the flasks.

(e) None of the above are correct.

Answer: (b)

6-5. Two identical flasks are at the same temperature. One is filled with 2 grams of hydrogen, the other with 28 grams of nitrogen gas. Which property would be different for the two samples?

(a) pressure (b) average kinetic energy (c) density

(d) the number of molecules in each container (e) the weight of the container

Answer: (c)

6-6. Why does a hot air balloon rise when the air in the balloon is heated?

(a) The average kinetic energy of the air molecules increases, and the collisions between these molecules and the walls of the balloon make it rise.

(b) The pressure of the gas inside the balloon increases, pushing up on the balloon.

(c) The gas expands, forcing some of the gas to escape from the bottom of the balloon, and the decrease in the density of the gas lifts the balloon.

(d) The balloon expands, causing it to rise.

(e) The hot air rises inside the balloon, which produces enough force to lift the balloon.

Answer: (c)

6-7. Which would always lead to an increase in the average kinetic energy of a gas?

(a) Increasing the volume by decreasing the pressure.

(b) Increasing the pressure by decreasing the volume.

(c) Increasing the pressure by increasing the number of molecules of gas.

(d) Increasing the volume by increasing the temperature of the gas.

(e) All of the above are equally effective ways of increasing the average kinetic energy of a gas.

Answer: (d)

6-8. Which isn’t a basic assumption of the kinetic theory?

(a) Gases consist of a large number of tiny particles in constant random motion.

(b) The distance between gas particles is large compared with their diameters, and therefore most of the volume of a gas is empty space.

(c) Gas particles move in a straight line until they collide with another gas particle or the walls of the container.

(d) The average kinetic energy of the particles in a gas is proportional to the temperature of the gas and that factor alone.

(e) All of the above are basic assumptions of the kinetic theory.

Answer: (e)

6-9. Which isn’t one of the postulates of the kinetic molecular theory?

(a) At a constant temperature, all of the particles have the same speed.

(b) Gas particles are in constant motion.

(c) Gas particles move in a straight line between collisions.

(d) The volume of the particles is negligibly small compared to the volume of the container.

(e) There are no forces of attraction between gas particles.

Answer: (a)

6-10. Which isn’t a postulate of the kinetic molecular theory?

(a) The mass of a molecule is negligibly small.

(b) The volume of a molecule is a negligibly small fraction of the volume of the container.

(c) The number of molecules in a gas is very large.

(d) The molecules are in a state of constant, random motion.

(e) The attractive forces between molecules is negligibly small.

Answer: (a)

6-11. Describe how the kinetic molecular theory can be used to explain the relationship between two of the following pairs of quantities.

(a) P and T (b) P and V (c) P and n (d) V and T (e) V and n

Density

6-12. Uranium reacts with fluorine to produce a compound that is a gas at 57°C. The density of this gas is 13.0 g/L at 57°C and 1 atm pressure. What is the molecular formula of this compound? (AW, F = 19.0, U = 238 amu)

(a) UF_{2} (b) UF_{3} ( c) UF_{4} (d) UF_{5} (e) UF_{6}

Answer: (e)

6-13. Which of the following gases would have the largest density at 25°C and 1.00 atm pressure?

(a) methane, CH_{4} (b) acetylene, C_{2}H_{2} (c) ethylene, C_{2}H_{4}

(d) ethane, C_{2}H_{6} (e) propane, C_{3}H_{8}

Answer: (e)

6-14. Which of the following gases has a density of 1.72 g/L at 10°C and 1 atm pressure? (AW: H = 1.01; He = 4.00; C = 12.01; Ne = 20.18; P = 30.97; Ar = 39.95)

(a) He (b) Ne (c) Ar (d) CH_{4} (e) P_{4}

Answer: (c)

6-15. What is the density of NO(g) at 25°C and 783 mmHg? (AW: N = 14.01: 0 = 16.00 amu)

(a) 1.26 g/L (b) 2.68 g/L ( c) 3.12 g/L (d) 3.76 g/L (e) 22.4 g/L

Answer: (a)

6-16. Which of the gases in Group VIllA of the periodic table has a density of 3.7407 g/L at 0°C and 1 atm?

(a) He (b) Ne (c) Ar (d) Kr (e) Xe

Answer: (d)

6-17. Calculate the molecular formula of diazomethane if this compound is 28.6% C, 4.8% H and 66.6% N by weight and the density of this gas is 1.72 g/L at 25°C and 1 atm.

Answer: CH_{2}N_{2}

Gas-Phase Reactions

6-18. Methane (CH_{4}) combines with oxygen (O_{2}) to produce carbon dioxide (CO_{2}) and
water (H_{2}O). When 3.0 L of methane is burned in 5.0 L of oxygen, how many L of CO_{2}
are formed, assuming that the volumes of all gases are measured at 400°C and 4.00
atm pressure? (AW, H =-37-1.01, C = 12.0, 0 = 16.0 amu)

(a) 2.5 L (b) 3.0 L (c) 5.0 L (d) 8.0 L (e) none of these

Answer: (a)

6-19. The first step of the Ostwald process for making nitric acid involves a reaction between ammonia and oxygen to form nitrogen oxide and water.

4 NH_{3}(g) + 5 O_{2}(g) ➝ 4 NO(g) + 6 H_{2}O(g)

How many liters of O_{2} gas at 650°C and 1.00 atm pressure are needed to react with 48
L of NH_{3} at the same temperature and pressure?

(a) 32 L (b) 38 L (c) 48 L (d) 60 L (e) 72 L

Answer: (d)

6-20. Cyclopropane is an anaesthetic that is 85.63% carbon and 14.37% hydrogen by weight. Calculate its molecular formula if 0.45 liters of cyclopropane react with excess oxygen at 120°C and 0.72 atm to form 1.35 liters of carbon dioxide and 1.35 liters of water vapor.

Answer: C_{3}H_{6}

6-21. Cyclopropane, a gas containing only carbon and hydrogen, is an anesthetic. If
0.45 L of cyclopropane at 120°C and 0.72 atm reacts with excess O_{2} to give 1.35 L of
CO_{2}(g) and 1.35 L of H_{2}O(g) at the same temperature and pressure, what is the percent
by weight of carbon in cyclopropane?

(a) 33.3% (b) 41.8% (c) 45.0% (d) 85.7% (e) 90.0%

Answer: (d)

6-22. Nitrogen gas reacts with hydrogen gas to produce gaseous ammonia. How many liters of product at STP can be formed if 6 L of hydrogen gas at STP reacts with a stoichiometric amount of nitrogen gas?

(a) 1 L (b) 2 L (c) 3 L (d) 4 L (e) 6 L

Answer: (d)

6-23. What is the empirical formula of the product of the following reaction

__ N_{2}O_{3}(g) + __ O_{3}(g) ➝

if 3.00 L of N_{2}O_{3} react with 1.00 L of O_{3} to give 6.00 L of the product, all gases
measured at STP?

(a) NO (b) NO_{2} (c) NO_{3} (d) N_{2}O_{5} (e) none of the above

Answer: (b)

6-24. 15 L of acetylene (C_{2}H_{4}) were burned in 15 L of O_{2}. If acetylene burns in oxygen
to form CO_{2} and H_{2}O,

2 C_{2}H_{2}(g) + 3 O_{2}(g) ➝ 4 CO_{2}(g) + 2 H_{2}O(g)

what would be the total volume of the products after the reaction mixture cools back to room temperature?

(a) 18 L (b) 25 L (c) 30 L (d) 40 L (e) 45 L

Answer: (a)

6-25. What volume of NH_{3}(g) at STP is required to prepare 49.8 g of (NH_{4})_{2}SO_{4} by the
reaction of ammonia with sulfuric acid? (AW: H = 1.01, N = 14.0, O = 16.0, S = 32.1
amu)

(a) 0.377 L (b) 6.41 L (c) 8.4 L (d) 12.84 L (e) 16.9 L

Answer: (e)

6-26. N_{2}H_{4} decomposes at a fixed temperature in a closed container to form N_{2}(g) and
H_{2}(g). If the reaction goes to completion, the final pressure will be:

(a) The same as the initial pressure.

(b) Twice the initial pressure.

(c) Three times the initial pressure.

(d) One-half the initial pressure.

(e) One-third the initial pressure.

Answer: (c)

Ideal Gas Calculations: One Moment in Time

6-27. Which sample would have the largest volume at 25°C and 750 mmHg?

(a) 100 g CH_{4} (b) 100 g CO_{2} (c) 100 g NO (d) 100 g SO_{2}

(e) all of these samples would have the same volume at 25°C and 750 mmHg

Answer: (a)

6-28. What is the volume of 1.00 mole of an ideal gas at 25°C and 1.00 atm pressure?

(a) 0.0409 L (b) 2.05 L (c) 22.4 L (d) 24.5 L (e) none of the above

Answer: (d)

A small gas cylinder of helium used in chemistry lecture demonstrations has a volume of 275 mL at a pressure of 1823 kPa at 24.7°C. Use this information to answer questions 29-31.

6-29. The volume of helium measured at 772 torr and 24.7°C needed to fill the cylinder
is: (a) 45.9 mL (b) 303 mL (c) 4870 mL (d) 4.95 x 10^{4} mL (e) 4.86 x 10^{5} mL

Answer: (c)

6-30. At what temperature would the helium gas in the cylinder exhibit a pressure of 25.0 atm?

(a) 4.96°C (b) 34.3°C (c) 58.8°C (d) 140°C (e) 307°C

Answer: (d)

6-31. The number of grams of helium in the cylinder is:

(a) 0.202 g (b) 0.810 g (c) 1.24 g (d) 4.96 g (e) none of these

Answer: (b)

6-32. Polypropylene is a plastic formed by polymerizing propylene, which has the
empirical formula CH_{2}. If a sample of propylene with a mass of 21.0 grams occupies a
volume of 11.2 L at STP (0°C and 1 atm), what is the molecular formula of this gas?

(a) CH_{2} (b) C_{2}H_{4} (c) C_{3}H_{6} (d) C_{4}H_{8} (e) none of these

Answer: (c)

6-33. A 2.91 gram sample of a gaseous compound that contains only boron and hydrogen has a volume of 1.22 L at 25°C and 1.09 atm. What is the formula of this compound? (AW: H = 1.01, B = 10.8 amu)

(a) B_{2}H_{6} (b) B_{4}H_{10} (c) B_{5}H_{9} (d) B_{6}H_{10} (e) B_{6}H_{12}

Answer: (b)

6-34. For which of the following compounds would a 1.00 gram sample occupy a
volume of 390 cm^{3} at 25°C and 0.993 atm?

(a) B_{2}H_{6} (b) B_{4}H_{10} (c) B_{5}H_{9} (d) B_{5}H_{11} (e) B_{6}H_{10}

Answer: (c)

6-35. Equal volumes of oxygen and an unknown gas weigh 3.00 grams and 7.50 grams, respectively. Which of the following is the unknown gas?

(a) CO_{2} (b) NO (c) NO_{2} (d) SO_{2} (e) SO_{3}

Answer: (e)

6-36. What is the identity of an unknown metal if 1.00 gram of this metal reacts with excess acid according to the equation

M(s) + 2 H^{+}(aq) ➝ M^{2+}(aq) + H_{2}(g)

to produce 374 mL of H_{2} gas at 25°C and one atm pressure?

(a) Mg, 24.3 g/mol (b) Ca, 40.1 g/mol (c) Mn, 54.9 g/mol

(d) Zn, 65.3 g/mol (e) Sr, 87.6 g/mol

Answer: (d)

6-37. Calculate the weight of a flask if the flask filled with oxygen weighs 125.000 grams while the flask filled with argon weighs 125.384 grams.

Answer: 123.452

6-39. Ether was one of the first anesthetics discovered. Assume that several mL of ether are placed in a bulb with a volume of 293 mL, and the bulb is immersed in water at 36°C until the last drop of liquid disappears, leaving the bulb filled with ether vapor. The bulb is then removed from the water bath, and the weight of ether that condenses in the bulb is measured. If 0.841 grams of ether collect in this experiment at a pressure of 746 mmHg, what is the molecular weight of ether?

Answer: 74.15 g/mol

6-40. How many cm^{3} of liquid SO_{2} (d = 1.46 g/cm^{3}) can be obtained by compressing
1.00 liter of the gas collected at 25°C and 1 atm?

Answer: 1.79 cm^{3}

6-41. Calculate the volume of hydrogen bromide that can be prepared by reacting 10.0 grams of phosphorus tribromide with excess water at 21°C and 753 mmHg.

PBr_{3}(l) + 3 H_{2}O(l) ➝ 3 HBr(g) + H_{3}PO_{3}(aq)

Answer: 2.65 L

6-42. Calculate the volume of oxygen at 0°C and 1 atm pressure that can be produced
by decomposing 100 mL of hydrogen peroxide if this solution is 27.6% H_{2}O_{2} by weight
and the density is 1.09 g/cm^{3}.

2 H_{2}O_{2}(l) ➝ 2 H_{2}O(l) + O_{2}(g)

Answer: 9.91 L

6-43. Calculate the volume of H_{2}S gas collected at 25°C and 1 atm needed to
precipitate all of the Cu^{2+} from a 250 mL of a 0.10 *M* Cu^{2+} solution.

Cu^{2+}(aq) + H_{2}S(g) ➝ CuS(s) + 2 H^{+}(aq)

Answer: 0.611 L

Ideal Gas Calculations: Now and Later

6-44. 0.500 mol of Ar gas occupies a volume of 4.07 L at 25°C and 3.00 atm pressure. What volume will the gas occupy at STP (0°C and 1.00 atm pressure)?

(a) 1.24 L (b) 1.48 L (c) 4.07 L (d) 11.2 L (e) 13.3 L

Answer: (d)

6-45. A cylindrical container with a movable piston initially holds 1.5 moles of gas at a pressure of 4.0 atmospheres and a volume of 2.5 liters. If the piston is moved to create a volume of 5.0 liters while simultaneously withdrawing 0.75 moles of gas, what is the final pressure?

(a) 0.50 atm (b) 1.0 atm (c) 2.0 atm (d) 4.0 atm (e) 8.0 atm

Answer: (b)

6-46. What is the final temperature if a sample of ammonia gas, initially at a pressure of 3.00 atmospheres, a temperature of 500 K, and a volume of 275 L is changed to a volume of 200 L and a pressure of 2.50 atm?

(a) 303 K (b) 436 K (c) 573 K (d) 825 K (e) none of the above

Answer: (a)

6-47. At 25°C and one atmosphere pressure, 4/5ths of the pressure of the atmosphere
is due to N_{2} and 1/5th is due to O_{2}. What fraction of the pressure at 10 atms and 100°C
would be due to N_{2}?

Answer: 4/5ths

Partial Pressure

6-48. A sealed container holds 150 g of ammonia, 150 g of carbon dioxide, and 150 g of nitrogen gases. What is the mole fraction of the carbon dioxide? (AW, H = 1.01, C = 12.0, N = 14.0, 0 = 16.0 amu)

(a) 0. 00758 (b) 0. 0227 (c) 0.194 (d) 0. 333 (e) 3.41

Answer: (c)

6-49. What is the total pressure when 0.400 g of H_{2}, 2.00 g of N_{2}, and 10.5 g of CO_{2} are
injected into a 10.0 liter flask at 273 K? (AW, H = 1.01, C = 12.0, N = 14.0, 0 = 16.0
amu) (a) 0.571 atm (b) 0.877 atm (c) 1.14 atm (d) 1.75 atm

(e) it is impossible to determine the answer from the data given

Answer: (c)

6-50. Calculate the total pressure in a 10.0 liter flask at 27°C of a sample of gas that contains 6.0 grams of hydrogen, 15.2 grams of nitrogen, and 16.8 grams of helium.

Answer: 19.1 atm

6-51. Calculate the volume of the flask that would contain 0.40 moles of oxygen, 0.60 moles of nitrogen, and 1.50 moles of hydrogen at 25°C and a total pressure of 1.80 atm. Calculate the partial pressure of each gas.

Answer: 34.0 L

6-52. 0.300 L of H_{2} gas was collected over water at 27°C on a day when the
atmospheric pressure was 745 torr. What would be the volume of H_{2} gas at 760 torr
after the water vapor was removed? (P_{H2O} = 27 torr at 27°C)

(a) 0.283 L (b) 0.294 L (c) 0.300 L (d) 0.306 L (e) 0. 318 L

Answer: (a)

6-53. Oxygen is bubbled through water before it is given to a patient in a hospital. What
volume of pure oxygen gas at 21°C and 750 torr pressure would a patient receive if the
patient breathed 0.250 L of O_{2} bubbled through water at this temperature and
pressure? (P_{H2O} ^{=} 19 torr at 21°C)

(a) 0.00633 L (b) 0.244 L (c) 0.250 L (d) 0.256L (e) none of the above

Answer: (b)

6-54. A metal reacts with acid to form hydrogen gas as shown by the following equation.

M(s) + 2 H^{+}(aq) ➝ M^{2+}(aq) + H_{2}(g)

What is the atomic weight of this metal if 3.49 grams of the metal generates enough hydrogen collected over water to fill a bottle with a volume of 2.20 L at 25°C and 1.00 atmosphere pressure under conditions where the vapor pressure of the solution is 23.8 torr?

(a) 19.4 g/mol (b) 37.6 g/mol (c) 38.8 g/mol

(d) 40.0 g/mol (e) none of the above

Answer: (d)

Graham's Law

6-56. If the average speed of O_{2} molecules at STP is 4.3 x 10^{2} meters per second, what
is the average speed of H_{2} molecules at the same temperature and pressure? (AW: H =
1.01; 0 = 16.0)

(a) 1.1 x 10^{2} (b) 2.2 x 10^{2} (c) 8.6 x 10^{2} (d) 1.7 x 10^{3} (e) none of the above

Answer: (d)

6-57. The root-mean-square speed of CH_{4} molecules at 25°C is about 0.56 km/s. What
is the root-mean-square speed of a H_{2} molecule at 25°C?

(a) 0.070 km/s (b) 0.20 km/s (c) 1.1 km/s (d) 1.6 km/s (e) 4.5 km/s

Answer: (d)

6-58. Bromine vapor at a given temperature is roughly 5 times denser than oxygen gas.
Calculate the relative rates at which Br_{2}(g) and O_{2}(g) diffuse.

Answer: O_{2} should diffuse roughly 2.2 times faster

6-59. N_{2}O and NO are often known by the trivial names: nitrous oxide and nitric oxide.
Associate the correct formula with the appropriate trivial name if nitric oxide diffuses
through a pinhole 1.21 times as fast as nitrous oxide.

Answer: nitrous oxide = N_{2}O, nitric oxide = NO

6-60. Which of the following gases would diffuse fastest at room temperature?

(a) NH_{3} (b) CO (c) H_{2}S (d) F_{2} (e) CO_{2}

Answer: (a)

6-61. Nitrogen and oxygen are allowed to effuse through a porous barrier at 295 K. If nitrogen effuses at a rate of 0.0355 moles per minute, what is the rate of effusion of oxygen?

(a) 0.0311 mol/min (b) 0.0332 mol/min (c) 0.0380 mol/min

(d) 0.0405 mol/min (e) 31.1 mol/min

Answer: (b)

6-62. Assume that a container is filled with a mixture of SO_{3} and Ne. The molecular
weight of SO_{3} is 80 g/mol and the atomic weight of Ne is 20 g/mol. The average velocity
of an SO_{3} molecule is:

(a) one-fourth that of a Ne atom.

(b) one-half that of a Ne atom.

(c) the same as a Ne atom.

(d) two times that of a Ne atom.

(e) 4 times that of a Ne atom.

Answer: (b)

6-63. A lecture room contains 50 rows of seats — numbered 1 through 50 from front to
back. Ammonia is released from the front of the room at the same instant that hydrogen
chloride gas is released from the back. Assuming Graham's law of diffusion, over which
row of students will a white cloud of ammonium chloride form? (MW: NH_{3} = 17.0; HCl =
36.5, NH_{4}Cl = 53.5 g/mol) (a) 10 (b) 20 (c) 30 (d) 40 (e) 50

Answer: (c)

6-64. A lecture hall has 45 rows of seats — numbered 1 through 50 from front to back.
If laughing gas, N_{2}O, is released from the front of the room at the same time hydrogen
cyanide, HCN, is released from the back of the room, in roughly which row (counting
from the front) will students first begin to die laughing? (MW: HCN = 27.0; N_{2}O = 44.0
g/mol) (a) 10 (b) 20 (c) 25 (d) 30 (e) 40

Answer: (b)

6-65. The average velocity of a gas molecule is given by the equation

u = (3/2 RT/MW)^{1/2}

where R is 8.314 J/mol-K. A helium atom challenges a UF_{6} molecule to a race. To give
a fair handicap, the helium agrees to travel at 4.2 K while the UF_{6} travels at 329 K. Who
wins the race?

Answer: He (barely)

6-66. ^{235}U and ^{238}U are separated on the basis of the relative rates of diffusion of ^{235}UF_{6}
and ^{238}UF_{6}. Calculate the relative rates of diffusion of these two compounds.

Answer: 1.0043:1, ^{235}UF_{6} being slightly faster

6-67. The atomic weight of radon was first estimated by measuring its rate of diffusion compared with mercury vapor. If Hg gas diffuses 1.052 times as fast as Rn, what is the atomic weight of Rn?

Answer: 222 g/mol

van der Waals Equation

6-68. 2.11 moles of C_{3}H_{8} are allowed to burn in the presence of excess O_{2} to form CO_{2}
and H_{2}O.

C_{3}H_{8}(g) + 5 O_{2}(g) ➝ 3 CO_{2}(g) + 4 H_{2}O(g)

The carbon dioxide is isolated from all other gases and stored in a 1.25 L container at 0°C. What is the pressure in this container if the gas obeys the ideal gas equation?

(a) 18 atm (b) 38 atm (c) 113 atm (d) 1,130 atm (e) none of the above

Answer: (c)

6-69. According to the van der Waals equation, what is the actual pressure in the
container described in the previous question? [For CO_{2}, *a* = 3.592 L^{2}-atm/mol^{2},* b* =
0.04267 L/mol]

(a) 52.6 atm (b) 92.1 atm (c) 114 atm (d) 145 atm (e) none of the above

Answer: (a)

6-70. The ideal gas equation predicts that a plot of the pressure times the volume of a
gas versus the pressure of this gas should be a horizontal straight line. When these
quantities are graphed for CO_{2}, however, we find that PV dips far below the theoretical
straight line at first. This can be explained as follows.

(a) the force of attraction between the CO_{2} molecules makes the product of the
pressure times the volume of this gas smaller than predicted from the
ideal gas equation.

(b) the volume of the CO_{2} molecules makes the product of the pressure times
the volume of this gas smaller than predicted from the ideal gas equation.

(c) the force of attraction between the CO_{2} molecules makes the product of the
pressure times the volume of this gas larger than predicted from the ideal
gas equation.

(d) the volume of the CO_{2} molecules makes the product of the pressure times
the volume of this gas larger than predicted from the ideal gas equation.

(e) there is no way to explain the difference between a real gas and the predictions of the ideal gas equation.

Answer: (a)