Suggested problems Chapter 5
5.23
Using the concepts developed in this chapter, explain the following observations.
b) You are not supposed to dispose of aerosol cans in fire.
c) The lid of a water bottle pops off when the bottle sits in the sun.
d) A balloon pops when you squeeze it.
Answer: a) At constant volume, the pressure of a gas is directly proportional to temperature (P ∝ T). b) The
vapor pressure of the H2O increases with increasing temperature. d) At constant temperature, the pressure of a
gas is inversely proportional to the volume (P ∝ 1/V).
5.27
Consider the following setup, which shows identical containers connected by a tube with a valve that is
presently closed. The container on the left has 1.0 mol of H2 gas; the container on the right has 1.0 mol of O2.
Closed valve
H2
O2
Note: Acceptable answers to some of these questions might be “both” or “neither one”.
a) Which container has the greater density of gas?
b) Which container has molecules that are moving at a faster average molecular speed?
c) Which container has more molecules?
d) If the valve is opened, will the pressure in each of the containers change? If it does, how will it change
(increase, decrease or no change)?
e) 2.0 mol of Ar is added to the system with the valve open. What fraction of the total pressure will be due to
the H2?
Answer: a) O2, b) H2, c) both, d) there will be no pressure change, e) 1/4
5.31
A gas in a closed-tube manometer has a measured pressure of 0.047 atm. Calculate the pressure in mmHg.
Answer: 36 mmHg
5.33
Suppose you had a 3.15-L sample of neon gas at 21°C and a pressure of 0.951 atm. What would be the volume
of this gas if the pressure were increased to 1.292 atm while the temperature remained constant?
Answer: 2.32 L
5.35
You have a cylinder of argon gas at 19.8 atm pressure at 19°C. The volume of argon in the cylinder is 50.0 L.
What would be the volume of the gas if you allowed it to expend to the pressure of the surrounding air (0.974
atm)? Assume the temperature remains constant.
Answer: 1.02 x 103 L
5.37
A McLeod gauge measures low gas pressures by compressing a known volume of the gas at constant
temperature. If 315 cm3 of gas is compressed to a volume of 0.0457 cm3 under a pressure of 2.51 kPa, what was
the original pressure?
Answer: 3.64 x 10-4 kPa
5.39
A sample of nitrogen gas at 18°C and 760 mmHg has a volume of 3.92 mL. What is the volume at 0°C and 1 atm f
pressure?
Answer: 3.68 L
5.43
A vessel containing 39.5 cm3 of helium gas at 25°C and 106 kPa was inverted and placed in cold ethanol. As the
gas contracted, ethanol was forced into the vessel to maintain the same pressure of helium. If this required 7.7
cm3 of ethanol, what was the final temperature of the helium?
Answer: 240 K
5.45
A bacterial culture isolated from sewage produced 35.5 mL of methane, CH 4, at 31°C and 753 mmHg. What is
the volume of this methane at standard temperature and pressure (0°C, 760 mmHg)?
Answer: 31.6 mL
5.47
In the presence of a platinum catalyst, ammonia, NH3, burns in oxygen, O2, to give nitric oxide, NO, and water
vapor. How many volumes of nitric oxide are obtained from one volume of ammonia, assuming each gas is at
the same temperature and pressure?
Answer: 1 volume
5.49
Starting from the ideal gas law, prove that the volume of a mole of gas is inversely proportional to the pressure
at constant temperature (Boyle’s Law).
Answer: PV = nRT; V = nRT/P; if temperature and moles remain constant, V = constant x 1/P
5.51
A cylinder of oxygen gas contains 91.3 g O2. If the volume of the cylinder is 8.58 L, what is the pressure of the O 2
if the gas temperature is 21°C?
Answer: 8.02 atm
5.55
The maximum safe pressure that a certain 4.00-L vessel can hold is 3.50 atm. If the vessel contains 0.410 mol of
gas, what is the maximum temperature (in degrees Celsius) to which this vessel can be subjected?
Answer: 143°C
5.57
What is the density of ammonia gas, NH3, at 31°C and 751 mmHg? Obtain the density in grams per liter.
Answer: 0.675 g/L
5.61
A chemist vaporized a liquid compound and determined its density. If the density of the vapor at 90°C and 753
mmHg is 1.585 g/L, what is the molecular weight of the compound?
Answer: 47.7 g/mol
5.63
A 2.56-g sample of a colorless liquid was vaporized in a 250-mL flask at 121°C and 786 mmHg. What is the
molecular weight of this substance?
Answer: 3.20 x 102 g/mol
5.65
Ammonium chloride, NH4Cl, is a white solid. When heated to 325°C, it gives a vapor that is a mixture of
ammonia and hydrogen chloride.
NH4Cl(s) → NH3(g) + HCl(g)
Suppose someone contends that the vapor consists of NH4Cl molecules rather than a mixture of NH3 and HCl.
Could you decide between these alternative views on the basis of gas-density measurements? Explain.
Answer: Gas density depends on molecular weight or average molecular weight of a mixture. Thus, the density
of a gas NH4Cl would be greater than that of a mixture of NH3 and HCl, since NH3 and HCl have lower molecular
weights.
5.67
Calcium carbide reacts with water to produce acetylene gas, C2H2.
CaC2(s) + H2O(l) → Ca(OH)2(aq) + C2H2(g)
Calculate the volume (in liters) of acetylene produced at 26°C and 684 mmHg from 0.050 mol CaC2 and excess
H2O.
Answer: 1.4 L
5.69
Lithium hydroxide, LiOH, is used in spacecraft to recondition the air absorbing the carbon dioxide exhaled by
astronauts. The reaction is
2LiOH + CO2(g) → Li2CO3(s) + H2O(l)
What volume of carbon dioxide gas at 21°C and 781 mmHg could be absorbed by 327 g of lithium hydroxide?
Answer: 160. L
5.73
Ammonium sulfate is used as a nitrogen and sulfur fertilizer. It is produced by reacting ammonia with sulfuric
acid. Write the balanced equation for the reaction of gaseous ammonia with sulfuric acid solution. What volume
(in liters) of ammonia at 15°C and 1.15 atm is required to produce 150.0 g of ammonium sulfate?
Answer: 2NH3(l) + H2SO4(aq) → (NH4)2SO4(aq); 46.7 L
5.75
Calculate the total pressure (in atm) of a mixture of 0.0200 mol of helium, He, and 0.0100 mol of hydrogen, H 2,
in a 2.50-L flask at 10°C. Assume ideal gas behavior.
Answer: 0.279 atm
5.77
A 200.0-mL flask contains 1.03 mg O2 and 0.56 mg He at 15°C. Calculate the partial pressures of oxygen and of
helium in the flask. What is the total pressure?
Answer: P(O2) = 3.80 x 10-3 atm; P(He) = 0.017 atm; P(total) = 0.020 atm
5.79
The gas from a certain volcano had the following composition in mole percent (that is, mole fraction x 100):
65.0% CO2, 25.0% H2, 5.4% HCl, 2.8% HF, 1.7% SO2, and 0.1% H2S. What would be the partial pressure of these
gases if the total pressure of volcanic gas were 760 mmHg?
Answer: P(CO2) = 494 mmHg; P(H2) =190. mmHg; P(HCl) = 41 mmHg; P(HF) = 21 mmHg; P(SO 2) = 13 mmHg;
P(H2S) = 0.8 mmHg